![Page 1: Finding Relationships Among Variablesthen Crosstabs.... Put Technology in either the row variable or column variable, and put Bush Winner in the other. Click the Statistics button,](https://reader035.vdocuments.us/reader035/viewer/2022062602/5e9d79850ab64c7184663520/html5/thumbnails/1.jpg)
Chi-Squared Test for IndependenceCorrelationRegression
Finding Relationships Among Variables
MGMT 662: Integrative Research Project
August 14, 2008.
MGMT 662: Integrative Research Project Finding Relationships Among Variables
![Page 2: Finding Relationships Among Variablesthen Crosstabs.... Put Technology in either the row variable or column variable, and put Bush Winner in the other. Click the Statistics button,](https://reader035.vdocuments.us/reader035/viewer/2022062602/5e9d79850ab64c7184663520/html5/thumbnails/2.jpg)
Chi-Squared Test for IndependenceCorrelationRegression
Goals of this section 2/ 23
Learn how detect linear relationships between variables.
Learn how to detect relationships between ordinal andcategorical variables.
Learn how to estimation the relationship between manyvariables.
MGMT 662: Integrative Research Project Finding Relationships Among Variables
![Page 3: Finding Relationships Among Variablesthen Crosstabs.... Put Technology in either the row variable or column variable, and put Bush Winner in the other. Click the Statistics button,](https://reader035.vdocuments.us/reader035/viewer/2022062602/5e9d79850ab64c7184663520/html5/thumbnails/3.jpg)
Chi-Squared Test for IndependenceCorrelationRegression
Contingency TableHypothesis TestExample
Chi-Squared Test for Independence 3/ 23
Used to determine if two categorical variables are related.
Example: mortality rates on the Titanic:
Data in the table are always frequencies that fall intoindividual categories.
Could use this table to test if two variables are independent.
MGMT 662: Integrative Research Project Finding Relationships Among Variables
![Page 4: Finding Relationships Among Variablesthen Crosstabs.... Put Technology in either the row variable or column variable, and put Bush Winner in the other. Click the Statistics button,](https://reader035.vdocuments.us/reader035/viewer/2022062602/5e9d79850ab64c7184663520/html5/thumbnails/4.jpg)
Chi-Squared Test for IndependenceCorrelationRegression
Contingency TableHypothesis TestExample
Chi-Squared Test for Independence 3/ 23
Used to determine if two categorical variables are related.
Example: mortality rates on the Titanic:
Data in the table are always frequencies that fall intoindividual categories.
Could use this table to test if two variables are independent.
MGMT 662: Integrative Research Project Finding Relationships Among Variables
![Page 5: Finding Relationships Among Variablesthen Crosstabs.... Put Technology in either the row variable or column variable, and put Bush Winner in the other. Click the Statistics button,](https://reader035.vdocuments.us/reader035/viewer/2022062602/5e9d79850ab64c7184663520/html5/thumbnails/5.jpg)
Chi-Squared Test for IndependenceCorrelationRegression
Contingency TableHypothesis TestExample
Chi-Squared Test for Independence 3/ 23
Used to determine if two categorical variables are related.
Example: mortality rates on the Titanic:
Data in the table are always frequencies that fall intoindividual categories.
Could use this table to test if two variables are independent.
MGMT 662: Integrative Research Project Finding Relationships Among Variables
![Page 6: Finding Relationships Among Variablesthen Crosstabs.... Put Technology in either the row variable or column variable, and put Bush Winner in the other. Click the Statistics button,](https://reader035.vdocuments.us/reader035/viewer/2022062602/5e9d79850ab64c7184663520/html5/thumbnails/6.jpg)
Chi-Squared Test for IndependenceCorrelationRegression
Contingency TableHypothesis TestExample
Chi-Squared Test for Independence 3/ 23
Used to determine if two categorical variables are related.
Example: mortality rates on the Titanic:
Data in the table are always frequencies that fall intoindividual categories.
Could use this table to test if two variables are independent.
MGMT 662: Integrative Research Project Finding Relationships Among Variables
![Page 7: Finding Relationships Among Variablesthen Crosstabs.... Put Technology in either the row variable or column variable, and put Bush Winner in the other. Click the Statistics button,](https://reader035.vdocuments.us/reader035/viewer/2022062602/5e9d79850ab64c7184663520/html5/thumbnails/7.jpg)
Chi-Squared Test for IndependenceCorrelationRegression
Contingency TableHypothesis TestExample
Test of independence 4/ 23
Null hypothesis: there is no association between the rowvariable and the column variable.
Alternative hypothesis: The two variables are dependent.
Test statistic:
χ2 =∑ (O − E )2
E
O: observed frequency in a cell from the contingency table.
E : expected frequency assuming the row and column variableare independent.
E =(row total)(column total)
grand total
Chi-squared distribution: a distribution skewed to the rightwhose support is always positive.
MGMT 662: Integrative Research Project Finding Relationships Among Variables
![Page 8: Finding Relationships Among Variablesthen Crosstabs.... Put Technology in either the row variable or column variable, and put Bush Winner in the other. Click the Statistics button,](https://reader035.vdocuments.us/reader035/viewer/2022062602/5e9d79850ab64c7184663520/html5/thumbnails/8.jpg)
Chi-Squared Test for IndependenceCorrelationRegression
Contingency TableHypothesis TestExample
Test of independence 4/ 23
Null hypothesis: there is no association between the rowvariable and the column variable.
Alternative hypothesis: The two variables are dependent.
Test statistic:
χ2 =∑ (O − E )2
E
O: observed frequency in a cell from the contingency table.
E : expected frequency assuming the row and column variableare independent.
E =(row total)(column total)
grand total
Chi-squared distribution: a distribution skewed to the rightwhose support is always positive.
MGMT 662: Integrative Research Project Finding Relationships Among Variables
![Page 9: Finding Relationships Among Variablesthen Crosstabs.... Put Technology in either the row variable or column variable, and put Bush Winner in the other. Click the Statistics button,](https://reader035.vdocuments.us/reader035/viewer/2022062602/5e9d79850ab64c7184663520/html5/thumbnails/9.jpg)
Chi-Squared Test for IndependenceCorrelationRegression
Contingency TableHypothesis TestExample
Test of independence 4/ 23
Null hypothesis: there is no association between the rowvariable and the column variable.
Alternative hypothesis: The two variables are dependent.
Test statistic:
χ2 =∑ (O − E )2
E
O: observed frequency in a cell from the contingency table.
E : expected frequency assuming the row and column variableare independent.
E =(row total)(column total)
grand total
Chi-squared distribution: a distribution skewed to the rightwhose support is always positive.
MGMT 662: Integrative Research Project Finding Relationships Among Variables
![Page 10: Finding Relationships Among Variablesthen Crosstabs.... Put Technology in either the row variable or column variable, and put Bush Winner in the other. Click the Statistics button,](https://reader035.vdocuments.us/reader035/viewer/2022062602/5e9d79850ab64c7184663520/html5/thumbnails/10.jpg)
Chi-Squared Test for IndependenceCorrelationRegression
Contingency TableHypothesis TestExample
Test of independence 4/ 23
Null hypothesis: there is no association between the rowvariable and the column variable.
Alternative hypothesis: The two variables are dependent.
Test statistic:
χ2 =∑ (O − E )2
E
O: observed frequency in a cell from the contingency table.
E : expected frequency assuming the row and column variableare independent.
E =(row total)(column total)
grand total
Chi-squared distribution: a distribution skewed to the rightwhose support is always positive.
MGMT 662: Integrative Research Project Finding Relationships Among Variables
![Page 11: Finding Relationships Among Variablesthen Crosstabs.... Put Technology in either the row variable or column variable, and put Bush Winner in the other. Click the Statistics button,](https://reader035.vdocuments.us/reader035/viewer/2022062602/5e9d79850ab64c7184663520/html5/thumbnails/11.jpg)
Chi-Squared Test for IndependenceCorrelationRegression
Contingency TableHypothesis TestExample
Test of independence 4/ 23
Null hypothesis: there is no association between the rowvariable and the column variable.
Alternative hypothesis: The two variables are dependent.
Test statistic:
χ2 =∑ (O − E )2
E
O: observed frequency in a cell from the contingency table.
E : expected frequency assuming the row and column variableare independent.
E =(row total)(column total)
grand total
Chi-squared distribution: a distribution skewed to the rightwhose support is always positive.
MGMT 662: Integrative Research Project Finding Relationships Among Variables
![Page 12: Finding Relationships Among Variablesthen Crosstabs.... Put Technology in either the row variable or column variable, and put Bush Winner in the other. Click the Statistics button,](https://reader035.vdocuments.us/reader035/viewer/2022062602/5e9d79850ab64c7184663520/html5/thumbnails/12.jpg)
Chi-Squared Test for IndependenceCorrelationRegression
Contingency TableHypothesis TestExample
Test of independence 4/ 23
Null hypothesis: there is no association between the rowvariable and the column variable.
Alternative hypothesis: The two variables are dependent.
Test statistic:
χ2 =∑ (O − E )2
E
O: observed frequency in a cell from the contingency table.
E : expected frequency assuming the row and column variableare independent.
E =(row total)(column total)
grand total
Chi-squared distribution: a distribution skewed to the rightwhose support is always positive.
MGMT 662: Integrative Research Project Finding Relationships Among Variables
![Page 13: Finding Relationships Among Variablesthen Crosstabs.... Put Technology in either the row variable or column variable, and put Bush Winner in the other. Click the Statistics button,](https://reader035.vdocuments.us/reader035/viewer/2022062602/5e9d79850ab64c7184663520/html5/thumbnails/13.jpg)
Chi-Squared Test for IndependenceCorrelationRegression
Contingency TableHypothesis TestExample
Test of independence 4/ 23
Null hypothesis: there is no association between the rowvariable and the column variable.
Alternative hypothesis: The two variables are dependent.
Test statistic:
χ2 =∑ (O − E )2
E
O: observed frequency in a cell from the contingency table.
E : expected frequency assuming the row and column variableare independent.
E =(row total)(column total)
grand total
Chi-squared distribution: a distribution skewed to the rightwhose support is always positive.
MGMT 662: Integrative Research Project Finding Relationships Among Variables
![Page 14: Finding Relationships Among Variablesthen Crosstabs.... Put Technology in either the row variable or column variable, and put Bush Winner in the other. Click the Statistics button,](https://reader035.vdocuments.us/reader035/viewer/2022062602/5e9d79850ab64c7184663520/html5/thumbnails/14.jpg)
Chi-Squared Test for IndependenceCorrelationRegression
Contingency TableHypothesis TestExample
Test of independence 4/ 23
Null hypothesis: there is no association between the rowvariable and the column variable.
Alternative hypothesis: The two variables are dependent.
Test statistic:
χ2 =∑ (O − E )2
E
O: observed frequency in a cell from the contingency table.
E : expected frequency assuming the row and column variableare independent.
E =(row total)(column total)
grand total
Chi-squared distribution: a distribution skewed to the rightwhose support is always positive.
MGMT 662: Integrative Research Project Finding Relationships Among Variables
![Page 15: Finding Relationships Among Variablesthen Crosstabs.... Put Technology in either the row variable or column variable, and put Bush Winner in the other. Click the Statistics button,](https://reader035.vdocuments.us/reader035/viewer/2022062602/5e9d79850ab64c7184663520/html5/thumbnails/15.jpg)
Chi-Squared Test for IndependenceCorrelationRegression
Contingency TableHypothesis TestExample
Example: 2000 Florida Presidential Election 5/ 23
Data on all but two counties in Florida on the votingtechnology used and whether Bush had more votes than Gorein the given county.Open floridaelection.xls in SPSS.Click on Analyze menu, select Descriptive Statisticsthen Crosstabs....Put Technology in either the row variable or column variable,and put Bush Winner in the other.Click the Statistics button, select the Chi-square checkbox, and click Continue.Click the Cells button, select the Expected check box, andclick Continue.Click OK. The results show the observed and expectedcontingency tables as well as the results to the Chi-squaredtest (but you want to use 1-tailed significance).
MGMT 662: Integrative Research Project Finding Relationships Among Variables
![Page 16: Finding Relationships Among Variablesthen Crosstabs.... Put Technology in either the row variable or column variable, and put Bush Winner in the other. Click the Statistics button,](https://reader035.vdocuments.us/reader035/viewer/2022062602/5e9d79850ab64c7184663520/html5/thumbnails/16.jpg)
Chi-Squared Test for IndependenceCorrelationRegression
Contingency TableHypothesis TestExample
Example: 2000 Florida Presidential Election 5/ 23
Data on all but two counties in Florida on the votingtechnology used and whether Bush had more votes than Gorein the given county.Open floridaelection.xls in SPSS.Click on Analyze menu, select Descriptive Statisticsthen Crosstabs....Put Technology in either the row variable or column variable,and put Bush Winner in the other.Click the Statistics button, select the Chi-square checkbox, and click Continue.Click the Cells button, select the Expected check box, andclick Continue.Click OK. The results show the observed and expectedcontingency tables as well as the results to the Chi-squaredtest (but you want to use 1-tailed significance).
MGMT 662: Integrative Research Project Finding Relationships Among Variables
![Page 17: Finding Relationships Among Variablesthen Crosstabs.... Put Technology in either the row variable or column variable, and put Bush Winner in the other. Click the Statistics button,](https://reader035.vdocuments.us/reader035/viewer/2022062602/5e9d79850ab64c7184663520/html5/thumbnails/17.jpg)
Chi-Squared Test for IndependenceCorrelationRegression
Contingency TableHypothesis TestExample
Example: 2000 Florida Presidential Election 5/ 23
Data on all but two counties in Florida on the votingtechnology used and whether Bush had more votes than Gorein the given county.Open floridaelection.xls in SPSS.Click on Analyze menu, select Descriptive Statisticsthen Crosstabs....Put Technology in either the row variable or column variable,and put Bush Winner in the other.Click the Statistics button, select the Chi-square checkbox, and click Continue.Click the Cells button, select the Expected check box, andclick Continue.Click OK. The results show the observed and expectedcontingency tables as well as the results to the Chi-squaredtest (but you want to use 1-tailed significance).
MGMT 662: Integrative Research Project Finding Relationships Among Variables
![Page 18: Finding Relationships Among Variablesthen Crosstabs.... Put Technology in either the row variable or column variable, and put Bush Winner in the other. Click the Statistics button,](https://reader035.vdocuments.us/reader035/viewer/2022062602/5e9d79850ab64c7184663520/html5/thumbnails/18.jpg)
Chi-Squared Test for IndependenceCorrelationRegression
Contingency TableHypothesis TestExample
Example: 2000 Florida Presidential Election 5/ 23
Data on all but two counties in Florida on the votingtechnology used and whether Bush had more votes than Gorein the given county.Open floridaelection.xls in SPSS.Click on Analyze menu, select Descriptive Statisticsthen Crosstabs....Put Technology in either the row variable or column variable,and put Bush Winner in the other.Click the Statistics button, select the Chi-square checkbox, and click Continue.Click the Cells button, select the Expected check box, andclick Continue.Click OK. The results show the observed and expectedcontingency tables as well as the results to the Chi-squaredtest (but you want to use 1-tailed significance).
MGMT 662: Integrative Research Project Finding Relationships Among Variables
![Page 19: Finding Relationships Among Variablesthen Crosstabs.... Put Technology in either the row variable or column variable, and put Bush Winner in the other. Click the Statistics button,](https://reader035.vdocuments.us/reader035/viewer/2022062602/5e9d79850ab64c7184663520/html5/thumbnails/19.jpg)
Chi-Squared Test for IndependenceCorrelationRegression
Contingency TableHypothesis TestExample
Example: 2000 Florida Presidential Election 5/ 23
Data on all but two counties in Florida on the votingtechnology used and whether Bush had more votes than Gorein the given county.Open floridaelection.xls in SPSS.Click on Analyze menu, select Descriptive Statisticsthen Crosstabs....Put Technology in either the row variable or column variable,and put Bush Winner in the other.Click the Statistics button, select the Chi-square checkbox, and click Continue.Click the Cells button, select the Expected check box, andclick Continue.Click OK. The results show the observed and expectedcontingency tables as well as the results to the Chi-squaredtest (but you want to use 1-tailed significance).
MGMT 662: Integrative Research Project Finding Relationships Among Variables
![Page 20: Finding Relationships Among Variablesthen Crosstabs.... Put Technology in either the row variable or column variable, and put Bush Winner in the other. Click the Statistics button,](https://reader035.vdocuments.us/reader035/viewer/2022062602/5e9d79850ab64c7184663520/html5/thumbnails/20.jpg)
Chi-Squared Test for IndependenceCorrelationRegression
Contingency TableHypothesis TestExample
Example: 2000 Florida Presidential Election 5/ 23
Data on all but two counties in Florida on the votingtechnology used and whether Bush had more votes than Gorein the given county.Open floridaelection.xls in SPSS.Click on Analyze menu, select Descriptive Statisticsthen Crosstabs....Put Technology in either the row variable or column variable,and put Bush Winner in the other.Click the Statistics button, select the Chi-square checkbox, and click Continue.Click the Cells button, select the Expected check box, andclick Continue.Click OK. The results show the observed and expectedcontingency tables as well as the results to the Chi-squaredtest (but you want to use 1-tailed significance).
MGMT 662: Integrative Research Project Finding Relationships Among Variables
![Page 21: Finding Relationships Among Variablesthen Crosstabs.... Put Technology in either the row variable or column variable, and put Bush Winner in the other. Click the Statistics button,](https://reader035.vdocuments.us/reader035/viewer/2022062602/5e9d79850ab64c7184663520/html5/thumbnails/21.jpg)
Chi-Squared Test for IndependenceCorrelationRegression
Contingency TableHypothesis TestExample
Example: 2000 Florida Presidential Election 5/ 23
Data on all but two counties in Florida on the votingtechnology used and whether Bush had more votes than Gorein the given county.Open floridaelection.xls in SPSS.Click on Analyze menu, select Descriptive Statisticsthen Crosstabs....Put Technology in either the row variable or column variable,and put Bush Winner in the other.Click the Statistics button, select the Chi-square checkbox, and click Continue.Click the Cells button, select the Expected check box, andclick Continue.Click OK. The results show the observed and expectedcontingency tables as well as the results to the Chi-squaredtest (but you want to use 1-tailed significance).
MGMT 662: Integrative Research Project Finding Relationships Among Variables
![Page 22: Finding Relationships Among Variablesthen Crosstabs.... Put Technology in either the row variable or column variable, and put Bush Winner in the other. Click the Statistics button,](https://reader035.vdocuments.us/reader035/viewer/2022062602/5e9d79850ab64c7184663520/html5/thumbnails/22.jpg)
Chi-Squared Test for IndependenceCorrelationRegression
Correlation coefficientExample
Correlation 6/ 23
A correlation exists between two variables when one of themis related to the other in some way.
The linear correlation coefficient is a measure of thestrength of the linear relationship between two variables.
Population: ρ =σxy
σxσy
Sample: r =sxysx sy
MGMT 662: Integrative Research Project Finding Relationships Among Variables
![Page 23: Finding Relationships Among Variablesthen Crosstabs.... Put Technology in either the row variable or column variable, and put Bush Winner in the other. Click the Statistics button,](https://reader035.vdocuments.us/reader035/viewer/2022062602/5e9d79850ab64c7184663520/html5/thumbnails/23.jpg)
Chi-Squared Test for IndependenceCorrelationRegression
Correlation coefficientExample
Correlation 6/ 23
A correlation exists between two variables when one of themis related to the other in some way.
The linear correlation coefficient is a measure of thestrength of the linear relationship between two variables.
Population: ρ =σxy
σxσy
Sample: r =sxysx sy
MGMT 662: Integrative Research Project Finding Relationships Among Variables
![Page 24: Finding Relationships Among Variablesthen Crosstabs.... Put Technology in either the row variable or column variable, and put Bush Winner in the other. Click the Statistics button,](https://reader035.vdocuments.us/reader035/viewer/2022062602/5e9d79850ab64c7184663520/html5/thumbnails/24.jpg)
Chi-Squared Test for IndependenceCorrelationRegression
Correlation coefficientExample
Correlation 6/ 23
A correlation exists between two variables when one of themis related to the other in some way.
The linear correlation coefficient is a measure of thestrength of the linear relationship between two variables.
Population: ρ =σxy
σxσy
Sample: r =sxysx sy
MGMT 662: Integrative Research Project Finding Relationships Among Variables
![Page 25: Finding Relationships Among Variablesthen Crosstabs.... Put Technology in either the row variable or column variable, and put Bush Winner in the other. Click the Statistics button,](https://reader035.vdocuments.us/reader035/viewer/2022062602/5e9d79850ab64c7184663520/html5/thumbnails/25.jpg)
Chi-Squared Test for IndependenceCorrelationRegression
Correlation coefficientExample
Correlation 6/ 23
A correlation exists between two variables when one of themis related to the other in some way.
The linear correlation coefficient is a measure of thestrength of the linear relationship between two variables.
Population: ρ =σxy
σxσy
Sample: r =sxysx sy
MGMT 662: Integrative Research Project Finding Relationships Among Variables
![Page 26: Finding Relationships Among Variablesthen Crosstabs.... Put Technology in either the row variable or column variable, and put Bush Winner in the other. Click the Statistics button,](https://reader035.vdocuments.us/reader035/viewer/2022062602/5e9d79850ab64c7184663520/html5/thumbnails/26.jpg)
Chi-Squared Test for IndependenceCorrelationRegression
Correlation coefficientExample
Positive linear correlation 7/ 23
Positive correlation: two variables move in the same direction.
Stronger the correlation: closer the correlation coefficient is to1.
Perfect positive correlation: ρ = 1
MGMT 662: Integrative Research Project Finding Relationships Among Variables
![Page 27: Finding Relationships Among Variablesthen Crosstabs.... Put Technology in either the row variable or column variable, and put Bush Winner in the other. Click the Statistics button,](https://reader035.vdocuments.us/reader035/viewer/2022062602/5e9d79850ab64c7184663520/html5/thumbnails/27.jpg)
Chi-Squared Test for IndependenceCorrelationRegression
Correlation coefficientExample
Positive linear correlation 7/ 23
Positive correlation: two variables move in the same direction.
Stronger the correlation: closer the correlation coefficient is to1.
Perfect positive correlation: ρ = 1
MGMT 662: Integrative Research Project Finding Relationships Among Variables
![Page 28: Finding Relationships Among Variablesthen Crosstabs.... Put Technology in either the row variable or column variable, and put Bush Winner in the other. Click the Statistics button,](https://reader035.vdocuments.us/reader035/viewer/2022062602/5e9d79850ab64c7184663520/html5/thumbnails/28.jpg)
Chi-Squared Test for IndependenceCorrelationRegression
Correlation coefficientExample
Positive linear correlation 7/ 23
Positive correlation: two variables move in the same direction.
Stronger the correlation: closer the correlation coefficient is to1.
Perfect positive correlation: ρ = 1
MGMT 662: Integrative Research Project Finding Relationships Among Variables
![Page 29: Finding Relationships Among Variablesthen Crosstabs.... Put Technology in either the row variable or column variable, and put Bush Winner in the other. Click the Statistics button,](https://reader035.vdocuments.us/reader035/viewer/2022062602/5e9d79850ab64c7184663520/html5/thumbnails/29.jpg)
Chi-Squared Test for IndependenceCorrelationRegression
Correlation coefficientExample
Negative linear correlation 8/ 23
Negative correlation: two variables move in oppositedirections.Stronger the correlation: closer the correlation coefficient is to-1.Perfect negative correlation: ρ = −1
MGMT 662: Integrative Research Project Finding Relationships Among Variables
![Page 30: Finding Relationships Among Variablesthen Crosstabs.... Put Technology in either the row variable or column variable, and put Bush Winner in the other. Click the Statistics button,](https://reader035.vdocuments.us/reader035/viewer/2022062602/5e9d79850ab64c7184663520/html5/thumbnails/30.jpg)
Chi-Squared Test for IndependenceCorrelationRegression
Correlation coefficientExample
Negative linear correlation 8/ 23
Negative correlation: two variables move in oppositedirections.Stronger the correlation: closer the correlation coefficient is to-1.Perfect negative correlation: ρ = −1
MGMT 662: Integrative Research Project Finding Relationships Among Variables
![Page 31: Finding Relationships Among Variablesthen Crosstabs.... Put Technology in either the row variable or column variable, and put Bush Winner in the other. Click the Statistics button,](https://reader035.vdocuments.us/reader035/viewer/2022062602/5e9d79850ab64c7184663520/html5/thumbnails/31.jpg)
Chi-Squared Test for IndependenceCorrelationRegression
Correlation coefficientExample
Negative linear correlation 8/ 23
Negative correlation: two variables move in oppositedirections.Stronger the correlation: closer the correlation coefficient is to-1.Perfect negative correlation: ρ = −1
MGMT 662: Integrative Research Project Finding Relationships Among Variables
![Page 32: Finding Relationships Among Variablesthen Crosstabs.... Put Technology in either the row variable or column variable, and put Bush Winner in the other. Click the Statistics button,](https://reader035.vdocuments.us/reader035/viewer/2022062602/5e9d79850ab64c7184663520/html5/thumbnails/32.jpg)
Chi-Squared Test for IndependenceCorrelationRegression
Correlation coefficientExample
No linear correlation 9/ 23
Panel (g): no relationship at all.
Panel (h): strong relationship, but not a linear relationship.
Cannot use regular correlation to detect this.
MGMT 662: Integrative Research Project Finding Relationships Among Variables
![Page 33: Finding Relationships Among Variablesthen Crosstabs.... Put Technology in either the row variable or column variable, and put Bush Winner in the other. Click the Statistics button,](https://reader035.vdocuments.us/reader035/viewer/2022062602/5e9d79850ab64c7184663520/html5/thumbnails/33.jpg)
Chi-Squared Test for IndependenceCorrelationRegression
Correlation coefficientExample
No linear correlation 9/ 23
Panel (g): no relationship at all.
Panel (h): strong relationship, but not a linear relationship.
Cannot use regular correlation to detect this.
MGMT 662: Integrative Research Project Finding Relationships Among Variables
![Page 34: Finding Relationships Among Variablesthen Crosstabs.... Put Technology in either the row variable or column variable, and put Bush Winner in the other. Click the Statistics button,](https://reader035.vdocuments.us/reader035/viewer/2022062602/5e9d79850ab64c7184663520/html5/thumbnails/34.jpg)
Chi-Squared Test for IndependenceCorrelationRegression
Correlation coefficientExample
Example: Public Expenditure 10/ 23
Data from 1960! about public expenditures per capita, andvariables that may influence it:
Economic Ability IndexPercentage of people living in metropolitan areas.Percentage growth rate of population from 1950-1960.Percentage of population between the ages of 5-19.Percentage of population over the age of 65.Dummy variable: Western state (1) or not (0).
Is there a statistically significant linear correlation between thepercentage of the population who is young and the publicexpenditure per capita?Is there a statistically significant linear correlation between thepublic expenditure per capita and whether or not the state isa western state?Is there another way to test for this relationship that you havealready learned? (Hint: yes)
MGMT 662: Integrative Research Project Finding Relationships Among Variables
![Page 35: Finding Relationships Among Variablesthen Crosstabs.... Put Technology in either the row variable or column variable, and put Bush Winner in the other. Click the Statistics button,](https://reader035.vdocuments.us/reader035/viewer/2022062602/5e9d79850ab64c7184663520/html5/thumbnails/35.jpg)
Chi-Squared Test for IndependenceCorrelationRegression
Correlation coefficientExample
Example: Public Expenditure 10/ 23
Data from 1960! about public expenditures per capita, andvariables that may influence it:
Economic Ability IndexPercentage of people living in metropolitan areas.Percentage growth rate of population from 1950-1960.Percentage of population between the ages of 5-19.Percentage of population over the age of 65.Dummy variable: Western state (1) or not (0).
Is there a statistically significant linear correlation between thepercentage of the population who is young and the publicexpenditure per capita?Is there a statistically significant linear correlation between thepublic expenditure per capita and whether or not the state isa western state?Is there another way to test for this relationship that you havealready learned? (Hint: yes)
MGMT 662: Integrative Research Project Finding Relationships Among Variables
![Page 36: Finding Relationships Among Variablesthen Crosstabs.... Put Technology in either the row variable or column variable, and put Bush Winner in the other. Click the Statistics button,](https://reader035.vdocuments.us/reader035/viewer/2022062602/5e9d79850ab64c7184663520/html5/thumbnails/36.jpg)
Chi-Squared Test for IndependenceCorrelationRegression
Correlation coefficientExample
Example: Public Expenditure 10/ 23
Data from 1960! about public expenditures per capita, andvariables that may influence it:
Economic Ability IndexPercentage of people living in metropolitan areas.Percentage growth rate of population from 1950-1960.Percentage of population between the ages of 5-19.Percentage of population over the age of 65.Dummy variable: Western state (1) or not (0).
Is there a statistically significant linear correlation between thepercentage of the population who is young and the publicexpenditure per capita?Is there a statistically significant linear correlation between thepublic expenditure per capita and whether or not the state isa western state?Is there another way to test for this relationship that you havealready learned? (Hint: yes)
MGMT 662: Integrative Research Project Finding Relationships Among Variables
![Page 37: Finding Relationships Among Variablesthen Crosstabs.... Put Technology in either the row variable or column variable, and put Bush Winner in the other. Click the Statistics button,](https://reader035.vdocuments.us/reader035/viewer/2022062602/5e9d79850ab64c7184663520/html5/thumbnails/37.jpg)
Chi-Squared Test for IndependenceCorrelationRegression
Correlation coefficientExample
Example: Public Expenditure 10/ 23
Data from 1960! about public expenditures per capita, andvariables that may influence it:
Economic Ability IndexPercentage of people living in metropolitan areas.Percentage growth rate of population from 1950-1960.Percentage of population between the ages of 5-19.Percentage of population over the age of 65.Dummy variable: Western state (1) or not (0).
Is there a statistically significant linear correlation between thepercentage of the population who is young and the publicexpenditure per capita?Is there a statistically significant linear correlation between thepublic expenditure per capita and whether or not the state isa western state?Is there another way to test for this relationship that you havealready learned? (Hint: yes)
MGMT 662: Integrative Research Project Finding Relationships Among Variables
![Page 38: Finding Relationships Among Variablesthen Crosstabs.... Put Technology in either the row variable or column variable, and put Bush Winner in the other. Click the Statistics button,](https://reader035.vdocuments.us/reader035/viewer/2022062602/5e9d79850ab64c7184663520/html5/thumbnails/38.jpg)
Chi-Squared Test for IndependenceCorrelationRegression
Correlation coefficientExample
Example: Public Expenditure 10/ 23
Data from 1960! about public expenditures per capita, andvariables that may influence it:
Economic Ability IndexPercentage of people living in metropolitan areas.Percentage growth rate of population from 1950-1960.Percentage of population between the ages of 5-19.Percentage of population over the age of 65.Dummy variable: Western state (1) or not (0).
Is there a statistically significant linear correlation between thepercentage of the population who is young and the publicexpenditure per capita?Is there a statistically significant linear correlation between thepublic expenditure per capita and whether or not the state isa western state?Is there another way to test for this relationship that you havealready learned? (Hint: yes)
MGMT 662: Integrative Research Project Finding Relationships Among Variables
![Page 39: Finding Relationships Among Variablesthen Crosstabs.... Put Technology in either the row variable or column variable, and put Bush Winner in the other. Click the Statistics button,](https://reader035.vdocuments.us/reader035/viewer/2022062602/5e9d79850ab64c7184663520/html5/thumbnails/39.jpg)
Chi-Squared Test for IndependenceCorrelationRegression
Correlation coefficientExample
Using SPSS 11/ 23
Open publicexp.xls in SPSS.
Go to Analyze menu, select Correlate, select Bivariate.
Throw the two variables you want to estimate the correlationwith into the Variables text box.
Make sure Pearson Correlation Coefficient is selected.
Click on Options if you want to also computer standarddeviations, variances, and covariances.
Click OK!
Presented with a redundant table of correlation coefficientsand p-values.
MGMT 662: Integrative Research Project Finding Relationships Among Variables
![Page 40: Finding Relationships Among Variablesthen Crosstabs.... Put Technology in either the row variable or column variable, and put Bush Winner in the other. Click the Statistics button,](https://reader035.vdocuments.us/reader035/viewer/2022062602/5e9d79850ab64c7184663520/html5/thumbnails/40.jpg)
Chi-Squared Test for IndependenceCorrelationRegression
Correlation coefficientExample
Using SPSS 11/ 23
Open publicexp.xls in SPSS.
Go to Analyze menu, select Correlate, select Bivariate.
Throw the two variables you want to estimate the correlationwith into the Variables text box.
Make sure Pearson Correlation Coefficient is selected.
Click on Options if you want to also computer standarddeviations, variances, and covariances.
Click OK!
Presented with a redundant table of correlation coefficientsand p-values.
MGMT 662: Integrative Research Project Finding Relationships Among Variables
![Page 41: Finding Relationships Among Variablesthen Crosstabs.... Put Technology in either the row variable or column variable, and put Bush Winner in the other. Click the Statistics button,](https://reader035.vdocuments.us/reader035/viewer/2022062602/5e9d79850ab64c7184663520/html5/thumbnails/41.jpg)
Chi-Squared Test for IndependenceCorrelationRegression
Correlation coefficientExample
Using SPSS 11/ 23
Open publicexp.xls in SPSS.
Go to Analyze menu, select Correlate, select Bivariate.
Throw the two variables you want to estimate the correlationwith into the Variables text box.
Make sure Pearson Correlation Coefficient is selected.
Click on Options if you want to also computer standarddeviations, variances, and covariances.
Click OK!
Presented with a redundant table of correlation coefficientsand p-values.
MGMT 662: Integrative Research Project Finding Relationships Among Variables
![Page 42: Finding Relationships Among Variablesthen Crosstabs.... Put Technology in either the row variable or column variable, and put Bush Winner in the other. Click the Statistics button,](https://reader035.vdocuments.us/reader035/viewer/2022062602/5e9d79850ab64c7184663520/html5/thumbnails/42.jpg)
Chi-Squared Test for IndependenceCorrelationRegression
Correlation coefficientExample
Using SPSS 11/ 23
Open publicexp.xls in SPSS.
Go to Analyze menu, select Correlate, select Bivariate.
Throw the two variables you want to estimate the correlationwith into the Variables text box.
Make sure Pearson Correlation Coefficient is selected.
Click on Options if you want to also computer standarddeviations, variances, and covariances.
Click OK!
Presented with a redundant table of correlation coefficientsand p-values.
MGMT 662: Integrative Research Project Finding Relationships Among Variables
![Page 43: Finding Relationships Among Variablesthen Crosstabs.... Put Technology in either the row variable or column variable, and put Bush Winner in the other. Click the Statistics button,](https://reader035.vdocuments.us/reader035/viewer/2022062602/5e9d79850ab64c7184663520/html5/thumbnails/43.jpg)
Chi-Squared Test for IndependenceCorrelationRegression
Correlation coefficientExample
Using SPSS 11/ 23
Open publicexp.xls in SPSS.
Go to Analyze menu, select Correlate, select Bivariate.
Throw the two variables you want to estimate the correlationwith into the Variables text box.
Make sure Pearson Correlation Coefficient is selected.
Click on Options if you want to also computer standarddeviations, variances, and covariances.
Click OK!
Presented with a redundant table of correlation coefficientsand p-values.
MGMT 662: Integrative Research Project Finding Relationships Among Variables
![Page 44: Finding Relationships Among Variablesthen Crosstabs.... Put Technology in either the row variable or column variable, and put Bush Winner in the other. Click the Statistics button,](https://reader035.vdocuments.us/reader035/viewer/2022062602/5e9d79850ab64c7184663520/html5/thumbnails/44.jpg)
Chi-Squared Test for IndependenceCorrelationRegression
Correlation coefficientExample
Using SPSS 11/ 23
Open publicexp.xls in SPSS.
Go to Analyze menu, select Correlate, select Bivariate.
Throw the two variables you want to estimate the correlationwith into the Variables text box.
Make sure Pearson Correlation Coefficient is selected.
Click on Options if you want to also computer standarddeviations, variances, and covariances.
Click OK!
Presented with a redundant table of correlation coefficientsand p-values.
MGMT 662: Integrative Research Project Finding Relationships Among Variables
![Page 45: Finding Relationships Among Variablesthen Crosstabs.... Put Technology in either the row variable or column variable, and put Bush Winner in the other. Click the Statistics button,](https://reader035.vdocuments.us/reader035/viewer/2022062602/5e9d79850ab64c7184663520/html5/thumbnails/45.jpg)
Chi-Squared Test for IndependenceCorrelationRegression
Correlation coefficientExample
Using SPSS 11/ 23
Open publicexp.xls in SPSS.
Go to Analyze menu, select Correlate, select Bivariate.
Throw the two variables you want to estimate the correlationwith into the Variables text box.
Make sure Pearson Correlation Coefficient is selected.
Click on Options if you want to also computer standarddeviations, variances, and covariances.
Click OK!
Presented with a redundant table of correlation coefficientsand p-values.
MGMT 662: Integrative Research Project Finding Relationships Among Variables
![Page 46: Finding Relationships Among Variablesthen Crosstabs.... Put Technology in either the row variable or column variable, and put Bush Winner in the other. Click the Statistics button,](https://reader035.vdocuments.us/reader035/viewer/2022062602/5e9d79850ab64c7184663520/html5/thumbnails/46.jpg)
Chi-Squared Test for IndependenceCorrelationRegression
Regression lineInterpreting the slopeVariance Decomposition
Regression 12/ 23
Regression line: equation of the line that describes the linearrelationship between variable x and variable y .
Need to assume that one variable causes another.
x : independent or explanatory variable.y : dependent variable.Variable x can influence the value for variable y , but not viceversa.
Example: Suppose one want to estimate how much smokingaffects lung capacity.
xi : quantity of cigarettes smoked per day by individual i(independent).yi : lung capacity of individual i (dependent).
MGMT 662: Integrative Research Project Finding Relationships Among Variables
![Page 47: Finding Relationships Among Variablesthen Crosstabs.... Put Technology in either the row variable or column variable, and put Bush Winner in the other. Click the Statistics button,](https://reader035.vdocuments.us/reader035/viewer/2022062602/5e9d79850ab64c7184663520/html5/thumbnails/47.jpg)
Chi-Squared Test for IndependenceCorrelationRegression
Regression lineInterpreting the slopeVariance Decomposition
Regression 12/ 23
Regression line: equation of the line that describes the linearrelationship between variable x and variable y .
Need to assume that one variable causes another.
x : independent or explanatory variable.y : dependent variable.Variable x can influence the value for variable y , but not viceversa.
Example: Suppose one want to estimate how much smokingaffects lung capacity.
xi : quantity of cigarettes smoked per day by individual i(independent).yi : lung capacity of individual i (dependent).
MGMT 662: Integrative Research Project Finding Relationships Among Variables
![Page 48: Finding Relationships Among Variablesthen Crosstabs.... Put Technology in either the row variable or column variable, and put Bush Winner in the other. Click the Statistics button,](https://reader035.vdocuments.us/reader035/viewer/2022062602/5e9d79850ab64c7184663520/html5/thumbnails/48.jpg)
Chi-Squared Test for IndependenceCorrelationRegression
Regression lineInterpreting the slopeVariance Decomposition
Regression 12/ 23
Regression line: equation of the line that describes the linearrelationship between variable x and variable y .
Need to assume that one variable causes another.
x : independent or explanatory variable.y : dependent variable.Variable x can influence the value for variable y , but not viceversa.
Example: Suppose one want to estimate how much smokingaffects lung capacity.
xi : quantity of cigarettes smoked per day by individual i(independent).yi : lung capacity of individual i (dependent).
MGMT 662: Integrative Research Project Finding Relationships Among Variables
![Page 49: Finding Relationships Among Variablesthen Crosstabs.... Put Technology in either the row variable or column variable, and put Bush Winner in the other. Click the Statistics button,](https://reader035.vdocuments.us/reader035/viewer/2022062602/5e9d79850ab64c7184663520/html5/thumbnails/49.jpg)
Chi-Squared Test for IndependenceCorrelationRegression
Regression lineInterpreting the slopeVariance Decomposition
Regression 12/ 23
Regression line: equation of the line that describes the linearrelationship between variable x and variable y .
Need to assume that one variable causes another.
x : independent or explanatory variable.y : dependent variable.Variable x can influence the value for variable y , but not viceversa.
Example: Suppose one want to estimate how much smokingaffects lung capacity.
xi : quantity of cigarettes smoked per day by individual i(independent).yi : lung capacity of individual i (dependent).
MGMT 662: Integrative Research Project Finding Relationships Among Variables
![Page 50: Finding Relationships Among Variablesthen Crosstabs.... Put Technology in either the row variable or column variable, and put Bush Winner in the other. Click the Statistics button,](https://reader035.vdocuments.us/reader035/viewer/2022062602/5e9d79850ab64c7184663520/html5/thumbnails/50.jpg)
Chi-Squared Test for IndependenceCorrelationRegression
Regression lineInterpreting the slopeVariance Decomposition
Regression 12/ 23
Regression line: equation of the line that describes the linearrelationship between variable x and variable y .
Need to assume that one variable causes another.
x : independent or explanatory variable.y : dependent variable.Variable x can influence the value for variable y , but not viceversa.
Example: Suppose one want to estimate how much smokingaffects lung capacity.
xi : quantity of cigarettes smoked per day by individual i(independent).yi : lung capacity of individual i (dependent).
MGMT 662: Integrative Research Project Finding Relationships Among Variables
![Page 51: Finding Relationships Among Variablesthen Crosstabs.... Put Technology in either the row variable or column variable, and put Bush Winner in the other. Click the Statistics button,](https://reader035.vdocuments.us/reader035/viewer/2022062602/5e9d79850ab64c7184663520/html5/thumbnails/51.jpg)
Chi-Squared Test for IndependenceCorrelationRegression
Regression lineInterpreting the slopeVariance Decomposition
Regression 12/ 23
Regression line: equation of the line that describes the linearrelationship between variable x and variable y .
Need to assume that one variable causes another.
x : independent or explanatory variable.y : dependent variable.Variable x can influence the value for variable y , but not viceversa.
Example: Suppose one want to estimate how much smokingaffects lung capacity.
xi : quantity of cigarettes smoked per day by individual i(independent).yi : lung capacity of individual i (dependent).
MGMT 662: Integrative Research Project Finding Relationships Among Variables
![Page 52: Finding Relationships Among Variablesthen Crosstabs.... Put Technology in either the row variable or column variable, and put Bush Winner in the other. Click the Statistics button,](https://reader035.vdocuments.us/reader035/viewer/2022062602/5e9d79850ab64c7184663520/html5/thumbnails/52.jpg)
Chi-Squared Test for IndependenceCorrelationRegression
Regression lineInterpreting the slopeVariance Decomposition
Regression 12/ 23
Regression line: equation of the line that describes the linearrelationship between variable x and variable y .
Need to assume that one variable causes another.
x : independent or explanatory variable.y : dependent variable.Variable x can influence the value for variable y , but not viceversa.
Example: Suppose one want to estimate how much smokingaffects lung capacity.
xi : quantity of cigarettes smoked per day by individual i(independent).yi : lung capacity of individual i (dependent).
MGMT 662: Integrative Research Project Finding Relationships Among Variables
![Page 53: Finding Relationships Among Variablesthen Crosstabs.... Put Technology in either the row variable or column variable, and put Bush Winner in the other. Click the Statistics button,](https://reader035.vdocuments.us/reader035/viewer/2022062602/5e9d79850ab64c7184663520/html5/thumbnails/53.jpg)
Chi-Squared Test for IndependenceCorrelationRegression
Regression lineInterpreting the slopeVariance Decomposition
Regression 12/ 23
Regression line: equation of the line that describes the linearrelationship between variable x and variable y .
Need to assume that one variable causes another.
x : independent or explanatory variable.y : dependent variable.Variable x can influence the value for variable y , but not viceversa.
Example: Suppose one want to estimate how much smokingaffects lung capacity.
xi : quantity of cigarettes smoked per day by individual i(independent).yi : lung capacity of individual i (dependent).
MGMT 662: Integrative Research Project Finding Relationships Among Variables
![Page 54: Finding Relationships Among Variablesthen Crosstabs.... Put Technology in either the row variable or column variable, and put Bush Winner in the other. Click the Statistics button,](https://reader035.vdocuments.us/reader035/viewer/2022062602/5e9d79850ab64c7184663520/html5/thumbnails/54.jpg)
Chi-Squared Test for IndependenceCorrelationRegression
Regression lineInterpreting the slopeVariance Decomposition
Regression line 13/ 23
Population regression line:
yi = β0 + β1xi + εi
The actual coefficients β0 and β1 describing the relationshipbetween x and y are unknown.
Use sample data to come up with an estimate of theregression line:
yi = b0 + b1xi + ei
Since x and y are not perfectly correlated, still need to havean error term.
MGMT 662: Integrative Research Project Finding Relationships Among Variables
![Page 55: Finding Relationships Among Variablesthen Crosstabs.... Put Technology in either the row variable or column variable, and put Bush Winner in the other. Click the Statistics button,](https://reader035.vdocuments.us/reader035/viewer/2022062602/5e9d79850ab64c7184663520/html5/thumbnails/55.jpg)
Chi-Squared Test for IndependenceCorrelationRegression
Regression lineInterpreting the slopeVariance Decomposition
Regression line 13/ 23
Population regression line:
yi = β0 + β1xi + εi
The actual coefficients β0 and β1 describing the relationshipbetween x and y are unknown.
Use sample data to come up with an estimate of theregression line:
yi = b0 + b1xi + ei
Since x and y are not perfectly correlated, still need to havean error term.
MGMT 662: Integrative Research Project Finding Relationships Among Variables
![Page 56: Finding Relationships Among Variablesthen Crosstabs.... Put Technology in either the row variable or column variable, and put Bush Winner in the other. Click the Statistics button,](https://reader035.vdocuments.us/reader035/viewer/2022062602/5e9d79850ab64c7184663520/html5/thumbnails/56.jpg)
Chi-Squared Test for IndependenceCorrelationRegression
Regression lineInterpreting the slopeVariance Decomposition
Regression line 13/ 23
Population regression line:
yi = β0 + β1xi + εi
The actual coefficients β0 and β1 describing the relationshipbetween x and y are unknown.
Use sample data to come up with an estimate of theregression line:
yi = b0 + b1xi + ei
Since x and y are not perfectly correlated, still need to havean error term.
MGMT 662: Integrative Research Project Finding Relationships Among Variables
![Page 57: Finding Relationships Among Variablesthen Crosstabs.... Put Technology in either the row variable or column variable, and put Bush Winner in the other. Click the Statistics button,](https://reader035.vdocuments.us/reader035/viewer/2022062602/5e9d79850ab64c7184663520/html5/thumbnails/57.jpg)
Chi-Squared Test for IndependenceCorrelationRegression
Regression lineInterpreting the slopeVariance Decomposition
Regression line 13/ 23
Population regression line:
yi = β0 + β1xi + εi
The actual coefficients β0 and β1 describing the relationshipbetween x and y are unknown.
Use sample data to come up with an estimate of theregression line:
yi = b0 + b1xi + ei
Since x and y are not perfectly correlated, still need to havean error term.
MGMT 662: Integrative Research Project Finding Relationships Among Variables
![Page 58: Finding Relationships Among Variablesthen Crosstabs.... Put Technology in either the row variable or column variable, and put Bush Winner in the other. Click the Statistics button,](https://reader035.vdocuments.us/reader035/viewer/2022062602/5e9d79850ab64c7184663520/html5/thumbnails/58.jpg)
Chi-Squared Test for IndependenceCorrelationRegression
Regression lineInterpreting the slopeVariance Decomposition
Regression line 13/ 23
Population regression line:
yi = β0 + β1xi + εi
The actual coefficients β0 and β1 describing the relationshipbetween x and y are unknown.
Use sample data to come up with an estimate of theregression line:
yi = b0 + b1xi + ei
Since x and y are not perfectly correlated, still need to havean error term.
MGMT 662: Integrative Research Project Finding Relationships Among Variables
![Page 59: Finding Relationships Among Variablesthen Crosstabs.... Put Technology in either the row variable or column variable, and put Bush Winner in the other. Click the Statistics button,](https://reader035.vdocuments.us/reader035/viewer/2022062602/5e9d79850ab64c7184663520/html5/thumbnails/59.jpg)
Chi-Squared Test for IndependenceCorrelationRegression
Regression lineInterpreting the slopeVariance Decomposition
Regression line 13/ 23
Population regression line:
yi = β0 + β1xi + εi
The actual coefficients β0 and β1 describing the relationshipbetween x and y are unknown.
Use sample data to come up with an estimate of theregression line:
yi = b0 + b1xi + ei
Since x and y are not perfectly correlated, still need to havean error term.
MGMT 662: Integrative Research Project Finding Relationships Among Variables
![Page 60: Finding Relationships Among Variablesthen Crosstabs.... Put Technology in either the row variable or column variable, and put Bush Winner in the other. Click the Statistics button,](https://reader035.vdocuments.us/reader035/viewer/2022062602/5e9d79850ab64c7184663520/html5/thumbnails/60.jpg)
Chi-Squared Test for IndependenceCorrelationRegression
Regression lineInterpreting the slopeVariance Decomposition
Predicted values and residuals 14/ 23
Given a value for xi , can come up with a predicted value foryi .
yi = b0 + b1xi
This is not likely be the actual value for yi .
Residual is the difference between the actual value of yi andthe predicted value, y .
ei = yi − y = yi − b0 − b1xi
MGMT 662: Integrative Research Project Finding Relationships Among Variables
![Page 61: Finding Relationships Among Variablesthen Crosstabs.... Put Technology in either the row variable or column variable, and put Bush Winner in the other. Click the Statistics button,](https://reader035.vdocuments.us/reader035/viewer/2022062602/5e9d79850ab64c7184663520/html5/thumbnails/61.jpg)
Chi-Squared Test for IndependenceCorrelationRegression
Regression lineInterpreting the slopeVariance Decomposition
Predicted values and residuals 14/ 23
Given a value for xi , can come up with a predicted value foryi .
yi = b0 + b1xi
This is not likely be the actual value for yi .
Residual is the difference between the actual value of yi andthe predicted value, y .
ei = yi − y = yi − b0 − b1xi
MGMT 662: Integrative Research Project Finding Relationships Among Variables
![Page 62: Finding Relationships Among Variablesthen Crosstabs.... Put Technology in either the row variable or column variable, and put Bush Winner in the other. Click the Statistics button,](https://reader035.vdocuments.us/reader035/viewer/2022062602/5e9d79850ab64c7184663520/html5/thumbnails/62.jpg)
Chi-Squared Test for IndependenceCorrelationRegression
Regression lineInterpreting the slopeVariance Decomposition
Predicted values and residuals 14/ 23
Given a value for xi , can come up with a predicted value foryi .
yi = b0 + b1xi
This is not likely be the actual value for yi .
Residual is the difference between the actual value of yi andthe predicted value, y .
ei = yi − y = yi − b0 − b1xi
MGMT 662: Integrative Research Project Finding Relationships Among Variables
![Page 63: Finding Relationships Among Variablesthen Crosstabs.... Put Technology in either the row variable or column variable, and put Bush Winner in the other. Click the Statistics button,](https://reader035.vdocuments.us/reader035/viewer/2022062602/5e9d79850ab64c7184663520/html5/thumbnails/63.jpg)
Chi-Squared Test for IndependenceCorrelationRegression
Regression lineInterpreting the slopeVariance Decomposition
Predicted values and residuals 14/ 23
Given a value for xi , can come up with a predicted value foryi .
yi = b0 + b1xi
This is not likely be the actual value for yi .
Residual is the difference between the actual value of yi andthe predicted value, y .
ei = yi − y = yi − b0 − b1xi
MGMT 662: Integrative Research Project Finding Relationships Among Variables
![Page 64: Finding Relationships Among Variablesthen Crosstabs.... Put Technology in either the row variable or column variable, and put Bush Winner in the other. Click the Statistics button,](https://reader035.vdocuments.us/reader035/viewer/2022062602/5e9d79850ab64c7184663520/html5/thumbnails/64.jpg)
Chi-Squared Test for IndependenceCorrelationRegression
Regression lineInterpreting the slopeVariance Decomposition
Predicted values and residuals 14/ 23
Given a value for xi , can come up with a predicted value foryi .
yi = b0 + b1xi
This is not likely be the actual value for yi .
Residual is the difference between the actual value of yi andthe predicted value, y .
ei = yi − y = yi − b0 − b1xi
MGMT 662: Integrative Research Project Finding Relationships Among Variables
![Page 65: Finding Relationships Among Variablesthen Crosstabs.... Put Technology in either the row variable or column variable, and put Bush Winner in the other. Click the Statistics button,](https://reader035.vdocuments.us/reader035/viewer/2022062602/5e9d79850ab64c7184663520/html5/thumbnails/65.jpg)
Chi-Squared Test for IndependenceCorrelationRegression
Regression lineInterpreting the slopeVariance Decomposition
Least Squares Estimate 15/ 23
How should we obtain the “best fitting line”.
Ordinary least squares (OLS) method.
Choose sample estimates for the regression coefficients thatminimizes:
n∑i=0
(yi − yi )2
MGMT 662: Integrative Research Project Finding Relationships Among Variables
![Page 66: Finding Relationships Among Variablesthen Crosstabs.... Put Technology in either the row variable or column variable, and put Bush Winner in the other. Click the Statistics button,](https://reader035.vdocuments.us/reader035/viewer/2022062602/5e9d79850ab64c7184663520/html5/thumbnails/66.jpg)
Chi-Squared Test for IndependenceCorrelationRegression
Regression lineInterpreting the slopeVariance Decomposition
Least Squares Estimate 15/ 23
How should we obtain the “best fitting line”.
Ordinary least squares (OLS) method.
Choose sample estimates for the regression coefficients thatminimizes:
n∑i=0
(yi − yi )2
MGMT 662: Integrative Research Project Finding Relationships Among Variables
![Page 67: Finding Relationships Among Variablesthen Crosstabs.... Put Technology in either the row variable or column variable, and put Bush Winner in the other. Click the Statistics button,](https://reader035.vdocuments.us/reader035/viewer/2022062602/5e9d79850ab64c7184663520/html5/thumbnails/67.jpg)
Chi-Squared Test for IndependenceCorrelationRegression
Regression lineInterpreting the slopeVariance Decomposition
Least Squares Estimate 15/ 23
How should we obtain the “best fitting line”.
Ordinary least squares (OLS) method.
Choose sample estimates for the regression coefficients thatminimizes:
n∑i=0
(yi − yi )2
MGMT 662: Integrative Research Project Finding Relationships Among Variables
![Page 68: Finding Relationships Among Variablesthen Crosstabs.... Put Technology in either the row variable or column variable, and put Bush Winner in the other. Click the Statistics button,](https://reader035.vdocuments.us/reader035/viewer/2022062602/5e9d79850ab64c7184663520/html5/thumbnails/68.jpg)
Chi-Squared Test for IndependenceCorrelationRegression
Regression lineInterpreting the slopeVariance Decomposition
Least Squares Estimate 15/ 23
How should we obtain the “best fitting line”.
Ordinary least squares (OLS) method.
Choose sample estimates for the regression coefficients thatminimizes:
n∑i=0
(yi − yi )2
MGMT 662: Integrative Research Project Finding Relationships Among Variables
![Page 69: Finding Relationships Among Variablesthen Crosstabs.... Put Technology in either the row variable or column variable, and put Bush Winner in the other. Click the Statistics button,](https://reader035.vdocuments.us/reader035/viewer/2022062602/5e9d79850ab64c7184663520/html5/thumbnails/69.jpg)
Chi-Squared Test for IndependenceCorrelationRegression
Regression lineInterpreting the slopeVariance Decomposition
Interpreting the slope 16/ 23
Interpreting the slope, β1: amount the y is predicted toincrease when increasing x by one unit.
When β1 < 0 there is a negative linear relationship. That isincreasing x causes y to decrease.
When β1 > 0 there is a positive linear relationship. That isincreasing x causes y to increase.
When β1 = 0 there is no linear relationship between x and y .
MGMT 662: Integrative Research Project Finding Relationships Among Variables
![Page 70: Finding Relationships Among Variablesthen Crosstabs.... Put Technology in either the row variable or column variable, and put Bush Winner in the other. Click the Statistics button,](https://reader035.vdocuments.us/reader035/viewer/2022062602/5e9d79850ab64c7184663520/html5/thumbnails/70.jpg)
Chi-Squared Test for IndependenceCorrelationRegression
Regression lineInterpreting the slopeVariance Decomposition
Interpreting the slope 16/ 23
Interpreting the slope, β1: amount the y is predicted toincrease when increasing x by one unit.
When β1 < 0 there is a negative linear relationship. That isincreasing x causes y to decrease.
When β1 > 0 there is a positive linear relationship. That isincreasing x causes y to increase.
When β1 = 0 there is no linear relationship between x and y .
MGMT 662: Integrative Research Project Finding Relationships Among Variables
![Page 71: Finding Relationships Among Variablesthen Crosstabs.... Put Technology in either the row variable or column variable, and put Bush Winner in the other. Click the Statistics button,](https://reader035.vdocuments.us/reader035/viewer/2022062602/5e9d79850ab64c7184663520/html5/thumbnails/71.jpg)
Chi-Squared Test for IndependenceCorrelationRegression
Regression lineInterpreting the slopeVariance Decomposition
Interpreting the slope 16/ 23
Interpreting the slope, β1: amount the y is predicted toincrease when increasing x by one unit.
When β1 < 0 there is a negative linear relationship. That isincreasing x causes y to decrease.
When β1 > 0 there is a positive linear relationship. That isincreasing x causes y to increase.
When β1 = 0 there is no linear relationship between x and y .
MGMT 662: Integrative Research Project Finding Relationships Among Variables
![Page 72: Finding Relationships Among Variablesthen Crosstabs.... Put Technology in either the row variable or column variable, and put Bush Winner in the other. Click the Statistics button,](https://reader035.vdocuments.us/reader035/viewer/2022062602/5e9d79850ab64c7184663520/html5/thumbnails/72.jpg)
Chi-Squared Test for IndependenceCorrelationRegression
Regression lineInterpreting the slopeVariance Decomposition
Interpreting the slope 16/ 23
Interpreting the slope, β1: amount the y is predicted toincrease when increasing x by one unit.
When β1 < 0 there is a negative linear relationship. That isincreasing x causes y to decrease.
When β1 > 0 there is a positive linear relationship. That isincreasing x causes y to increase.
When β1 = 0 there is no linear relationship between x and y .
MGMT 662: Integrative Research Project Finding Relationships Among Variables
![Page 73: Finding Relationships Among Variablesthen Crosstabs.... Put Technology in either the row variable or column variable, and put Bush Winner in the other. Click the Statistics button,](https://reader035.vdocuments.us/reader035/viewer/2022062602/5e9d79850ab64c7184663520/html5/thumbnails/73.jpg)
Chi-Squared Test for IndependenceCorrelationRegression
Regression lineInterpreting the slopeVariance Decomposition
Example: Public Expenditure 17/ 23
Data from 1960 about public expenditures per capita, andvariables that may influence it.
In SPSS, choose Analyze menu and select Regression andLinear.
Select EX (Expenditure per capita) as your dependentvariable. This is the variable your are interested in explaining.
Select your independent (aka explanatory) variables. Theseare the variables that you think can explain the dependentvariable. I suggest you select these:
ECAB: Economic AbilityMET: MetropolitanGROW: Growth rate of populationWEST: Western state = 1.
MGMT 662: Integrative Research Project Finding Relationships Among Variables
![Page 74: Finding Relationships Among Variablesthen Crosstabs.... Put Technology in either the row variable or column variable, and put Bush Winner in the other. Click the Statistics button,](https://reader035.vdocuments.us/reader035/viewer/2022062602/5e9d79850ab64c7184663520/html5/thumbnails/74.jpg)
Chi-Squared Test for IndependenceCorrelationRegression
Regression lineInterpreting the slopeVariance Decomposition
Example: Public Expenditure 17/ 23
Data from 1960 about public expenditures per capita, andvariables that may influence it.
In SPSS, choose Analyze menu and select Regression andLinear.
Select EX (Expenditure per capita) as your dependentvariable. This is the variable your are interested in explaining.
Select your independent (aka explanatory) variables. Theseare the variables that you think can explain the dependentvariable. I suggest you select these:
ECAB: Economic AbilityMET: MetropolitanGROW: Growth rate of populationWEST: Western state = 1.
MGMT 662: Integrative Research Project Finding Relationships Among Variables
![Page 75: Finding Relationships Among Variablesthen Crosstabs.... Put Technology in either the row variable or column variable, and put Bush Winner in the other. Click the Statistics button,](https://reader035.vdocuments.us/reader035/viewer/2022062602/5e9d79850ab64c7184663520/html5/thumbnails/75.jpg)
Chi-Squared Test for IndependenceCorrelationRegression
Regression lineInterpreting the slopeVariance Decomposition
Example: Public Expenditure 17/ 23
Data from 1960 about public expenditures per capita, andvariables that may influence it.
In SPSS, choose Analyze menu and select Regression andLinear.
Select EX (Expenditure per capita) as your dependentvariable. This is the variable your are interested in explaining.
Select your independent (aka explanatory) variables. Theseare the variables that you think can explain the dependentvariable. I suggest you select these:
ECAB: Economic AbilityMET: MetropolitanGROW: Growth rate of populationWEST: Western state = 1.
MGMT 662: Integrative Research Project Finding Relationships Among Variables
![Page 76: Finding Relationships Among Variablesthen Crosstabs.... Put Technology in either the row variable or column variable, and put Bush Winner in the other. Click the Statistics button,](https://reader035.vdocuments.us/reader035/viewer/2022062602/5e9d79850ab64c7184663520/html5/thumbnails/76.jpg)
Chi-Squared Test for IndependenceCorrelationRegression
Regression lineInterpreting the slopeVariance Decomposition
Example: Public Expenditure 17/ 23
Data from 1960 about public expenditures per capita, andvariables that may influence it.
In SPSS, choose Analyze menu and select Regression andLinear.
Select EX (Expenditure per capita) as your dependentvariable. This is the variable your are interested in explaining.
Select your independent (aka explanatory) variables. Theseare the variables that you think can explain the dependentvariable. I suggest you select these:
ECAB: Economic AbilityMET: MetropolitanGROW: Growth rate of populationWEST: Western state = 1.
MGMT 662: Integrative Research Project Finding Relationships Among Variables
![Page 77: Finding Relationships Among Variablesthen Crosstabs.... Put Technology in either the row variable or column variable, and put Bush Winner in the other. Click the Statistics button,](https://reader035.vdocuments.us/reader035/viewer/2022062602/5e9d79850ab64c7184663520/html5/thumbnails/77.jpg)
Chi-Squared Test for IndependenceCorrelationRegression
Regression lineInterpreting the slopeVariance Decomposition
Example: Public Expenditure 17/ 23
Data from 1960 about public expenditures per capita, andvariables that may influence it.
In SPSS, choose Analyze menu and select Regression andLinear.
Select EX (Expenditure per capita) as your dependentvariable. This is the variable your are interested in explaining.
Select your independent (aka explanatory) variables. Theseare the variables that you think can explain the dependentvariable. I suggest you select these:
ECAB: Economic AbilityMET: MetropolitanGROW: Growth rate of populationWEST: Western state = 1.
MGMT 662: Integrative Research Project Finding Relationships Among Variables
![Page 78: Finding Relationships Among Variablesthen Crosstabs.... Put Technology in either the row variable or column variable, and put Bush Winner in the other. Click the Statistics button,](https://reader035.vdocuments.us/reader035/viewer/2022062602/5e9d79850ab64c7184663520/html5/thumbnails/78.jpg)
Chi-Squared Test for IndependenceCorrelationRegression
Regression lineInterpreting the slopeVariance Decomposition
Example: Public Expenditure 18/ 23
If the percentage of the population living in metropolitanareas in expected to increase by 1%, what change should weexpect in public expenditure?
Is this change statistically significantly different from zero?
Accounting for economic ability, metropolitan population, andpopulation growth, how much more to Western states spendon public expenditure per capita?
MGMT 662: Integrative Research Project Finding Relationships Among Variables
![Page 79: Finding Relationships Among Variablesthen Crosstabs.... Put Technology in either the row variable or column variable, and put Bush Winner in the other. Click the Statistics button,](https://reader035.vdocuments.us/reader035/viewer/2022062602/5e9d79850ab64c7184663520/html5/thumbnails/79.jpg)
Chi-Squared Test for IndependenceCorrelationRegression
Regression lineInterpreting the slopeVariance Decomposition
Example: Public Expenditure 18/ 23
If the percentage of the population living in metropolitanareas in expected to increase by 1%, what change should weexpect in public expenditure?
Is this change statistically significantly different from zero?
Accounting for economic ability, metropolitan population, andpopulation growth, how much more to Western states spendon public expenditure per capita?
MGMT 662: Integrative Research Project Finding Relationships Among Variables
![Page 80: Finding Relationships Among Variablesthen Crosstabs.... Put Technology in either the row variable or column variable, and put Bush Winner in the other. Click the Statistics button,](https://reader035.vdocuments.us/reader035/viewer/2022062602/5e9d79850ab64c7184663520/html5/thumbnails/80.jpg)
Chi-Squared Test for IndependenceCorrelationRegression
Regression lineInterpreting the slopeVariance Decomposition
Example: Public Expenditure 18/ 23
If the percentage of the population living in metropolitanareas in expected to increase by 1%, what change should weexpect in public expenditure?
Is this change statistically significantly different from zero?
Accounting for economic ability, metropolitan population, andpopulation growth, how much more to Western states spendon public expenditure per capita?
MGMT 662: Integrative Research Project Finding Relationships Among Variables
![Page 81: Finding Relationships Among Variablesthen Crosstabs.... Put Technology in either the row variable or column variable, and put Bush Winner in the other. Click the Statistics button,](https://reader035.vdocuments.us/reader035/viewer/2022062602/5e9d79850ab64c7184663520/html5/thumbnails/81.jpg)
Chi-Squared Test for IndependenceCorrelationRegression
Regression lineInterpreting the slopeVariance Decomposition
Sum of Squares Measures of Variation 19/ 23
Sum of Squares Regression (SSR): measure of the amountof variability in the dependent (Y) variable that is explainedby the independent variables (X’s).
SSR =n∑
i=1
(yi − y)2
Sum of Squares Error (SSE): measure of the unexplainedvariability in the dependent variable.
SSE =n∑
i=1
(yi − yi )2
Sum of Squares Total (SST): measure of the totalvariability in the dependent variable. Does the formula belowlook familiar?
SST =n∑
i=1
(yi − y)2
SST = SSR + SSE.
MGMT 662: Integrative Research Project Finding Relationships Among Variables
![Page 82: Finding Relationships Among Variablesthen Crosstabs.... Put Technology in either the row variable or column variable, and put Bush Winner in the other. Click the Statistics button,](https://reader035.vdocuments.us/reader035/viewer/2022062602/5e9d79850ab64c7184663520/html5/thumbnails/82.jpg)
Chi-Squared Test for IndependenceCorrelationRegression
Regression lineInterpreting the slopeVariance Decomposition
Sum of Squares Measures of Variation 19/ 23
Sum of Squares Regression (SSR): measure of the amountof variability in the dependent (Y) variable that is explainedby the independent variables (X’s).
SSR =n∑
i=1
(yi − y)2
Sum of Squares Error (SSE): measure of the unexplainedvariability in the dependent variable.
SSE =n∑
i=1
(yi − yi )2
Sum of Squares Total (SST): measure of the totalvariability in the dependent variable. Does the formula belowlook familiar?
SST =n∑
i=1
(yi − y)2
SST = SSR + SSE.
MGMT 662: Integrative Research Project Finding Relationships Among Variables
![Page 83: Finding Relationships Among Variablesthen Crosstabs.... Put Technology in either the row variable or column variable, and put Bush Winner in the other. Click the Statistics button,](https://reader035.vdocuments.us/reader035/viewer/2022062602/5e9d79850ab64c7184663520/html5/thumbnails/83.jpg)
Chi-Squared Test for IndependenceCorrelationRegression
Regression lineInterpreting the slopeVariance Decomposition
Sum of Squares Measures of Variation 19/ 23
Sum of Squares Regression (SSR): measure of the amountof variability in the dependent (Y) variable that is explainedby the independent variables (X’s).
SSR =n∑
i=1
(yi − y)2
Sum of Squares Error (SSE): measure of the unexplainedvariability in the dependent variable.
SSE =n∑
i=1
(yi − yi )2
Sum of Squares Total (SST): measure of the totalvariability in the dependent variable. Does the formula belowlook familiar?
SST =n∑
i=1
(yi − y)2
SST = SSR + SSE.
MGMT 662: Integrative Research Project Finding Relationships Among Variables
![Page 84: Finding Relationships Among Variablesthen Crosstabs.... Put Technology in either the row variable or column variable, and put Bush Winner in the other. Click the Statistics button,](https://reader035.vdocuments.us/reader035/viewer/2022062602/5e9d79850ab64c7184663520/html5/thumbnails/84.jpg)
Chi-Squared Test for IndependenceCorrelationRegression
Regression lineInterpreting the slopeVariance Decomposition
Sum of Squares Measures of Variation 19/ 23
Sum of Squares Regression (SSR): measure of the amountof variability in the dependent (Y) variable that is explainedby the independent variables (X’s).
SSR =n∑
i=1
(yi − y)2
Sum of Squares Error (SSE): measure of the unexplainedvariability in the dependent variable.
SSE =n∑
i=1
(yi − yi )2
Sum of Squares Total (SST): measure of the totalvariability in the dependent variable. Does the formula belowlook familiar?
SST =n∑
i=1
(yi − y)2
SST = SSR + SSE.
MGMT 662: Integrative Research Project Finding Relationships Among Variables
![Page 85: Finding Relationships Among Variablesthen Crosstabs.... Put Technology in either the row variable or column variable, and put Bush Winner in the other. Click the Statistics button,](https://reader035.vdocuments.us/reader035/viewer/2022062602/5e9d79850ab64c7184663520/html5/thumbnails/85.jpg)
Chi-Squared Test for IndependenceCorrelationRegression
Regression lineInterpreting the slopeVariance Decomposition
Sum of Squares Measures of Variation 19/ 23
Sum of Squares Regression (SSR): measure of the amountof variability in the dependent (Y) variable that is explainedby the independent variables (X’s).
SSR =n∑
i=1
(yi − y)2
Sum of Squares Error (SSE): measure of the unexplainedvariability in the dependent variable.
SSE =n∑
i=1
(yi − yi )2
Sum of Squares Total (SST): measure of the totalvariability in the dependent variable. Does the formula belowlook familiar?
SST =n∑
i=1
(yi − y)2
SST = SSR + SSE.
MGMT 662: Integrative Research Project Finding Relationships Among Variables
![Page 86: Finding Relationships Among Variablesthen Crosstabs.... Put Technology in either the row variable or column variable, and put Bush Winner in the other. Click the Statistics button,](https://reader035.vdocuments.us/reader035/viewer/2022062602/5e9d79850ab64c7184663520/html5/thumbnails/86.jpg)
Chi-Squared Test for IndependenceCorrelationRegression
Regression lineInterpreting the slopeVariance Decomposition
Sum of Squares Measures of Variation 19/ 23
Sum of Squares Regression (SSR): measure of the amountof variability in the dependent (Y) variable that is explainedby the independent variables (X’s).
SSR =n∑
i=1
(yi − y)2
Sum of Squares Error (SSE): measure of the unexplainedvariability in the dependent variable.
SSE =n∑
i=1
(yi − yi )2
Sum of Squares Total (SST): measure of the totalvariability in the dependent variable. Does the formula belowlook familiar?
SST =n∑
i=1
(yi − y)2
SST = SSR + SSE.
MGMT 662: Integrative Research Project Finding Relationships Among Variables
![Page 87: Finding Relationships Among Variablesthen Crosstabs.... Put Technology in either the row variable or column variable, and put Bush Winner in the other. Click the Statistics button,](https://reader035.vdocuments.us/reader035/viewer/2022062602/5e9d79850ab64c7184663520/html5/thumbnails/87.jpg)
Chi-Squared Test for IndependenceCorrelationRegression
Regression lineInterpreting the slopeVariance Decomposition
Sum of Squares Measures of Variation 19/ 23
Sum of Squares Regression (SSR): measure of the amountof variability in the dependent (Y) variable that is explainedby the independent variables (X’s).
SSR =n∑
i=1
(yi − y)2
Sum of Squares Error (SSE): measure of the unexplainedvariability in the dependent variable.
SSE =n∑
i=1
(yi − yi )2
Sum of Squares Total (SST): measure of the totalvariability in the dependent variable. Does the formula belowlook familiar?
SST =n∑
i=1
(yi − y)2
SST = SSR + SSE.
MGMT 662: Integrative Research Project Finding Relationships Among Variables
![Page 88: Finding Relationships Among Variablesthen Crosstabs.... Put Technology in either the row variable or column variable, and put Bush Winner in the other. Click the Statistics button,](https://reader035.vdocuments.us/reader035/viewer/2022062602/5e9d79850ab64c7184663520/html5/thumbnails/88.jpg)
Chi-Squared Test for IndependenceCorrelationRegression
Regression lineInterpreting the slopeVariance Decomposition
Coefficient of determination 20/ 23
The coefficient of determination is the percentage ofvariability in y that is explained by x .
R2 =SSR
SST
R2 will always be between 0 and 1. The closer R2 is to 1, thebetter x is able to explain y .The more variables you add to the regression, the higher R2
will be.The Adjusted R2 penalizes additional variables.
R2adj = 1− n − 1
n − k − 1
(1− R2
)When the adjusted R2 increases when adding a variable, thenthe additional variable really did help explain the dependentvariable.When the adjusted R2 decreases when adding a variable, thenthe additional variable does not help explain the dependentvariable.
MGMT 662: Integrative Research Project Finding Relationships Among Variables
![Page 89: Finding Relationships Among Variablesthen Crosstabs.... Put Technology in either the row variable or column variable, and put Bush Winner in the other. Click the Statistics button,](https://reader035.vdocuments.us/reader035/viewer/2022062602/5e9d79850ab64c7184663520/html5/thumbnails/89.jpg)
Chi-Squared Test for IndependenceCorrelationRegression
Regression lineInterpreting the slopeVariance Decomposition
Coefficient of determination 20/ 23
The coefficient of determination is the percentage ofvariability in y that is explained by x .
R2 =SSR
SST
R2 will always be between 0 and 1. The closer R2 is to 1, thebetter x is able to explain y .The more variables you add to the regression, the higher R2
will be.The Adjusted R2 penalizes additional variables.
R2adj = 1− n − 1
n − k − 1
(1− R2
)When the adjusted R2 increases when adding a variable, thenthe additional variable really did help explain the dependentvariable.When the adjusted R2 decreases when adding a variable, thenthe additional variable does not help explain the dependentvariable.
MGMT 662: Integrative Research Project Finding Relationships Among Variables
![Page 90: Finding Relationships Among Variablesthen Crosstabs.... Put Technology in either the row variable or column variable, and put Bush Winner in the other. Click the Statistics button,](https://reader035.vdocuments.us/reader035/viewer/2022062602/5e9d79850ab64c7184663520/html5/thumbnails/90.jpg)
Chi-Squared Test for IndependenceCorrelationRegression
Regression lineInterpreting the slopeVariance Decomposition
Coefficient of determination 20/ 23
The coefficient of determination is the percentage ofvariability in y that is explained by x .
R2 =SSR
SST
R2 will always be between 0 and 1. The closer R2 is to 1, thebetter x is able to explain y .The more variables you add to the regression, the higher R2
will be.The Adjusted R2 penalizes additional variables.
R2adj = 1− n − 1
n − k − 1
(1− R2
)When the adjusted R2 increases when adding a variable, thenthe additional variable really did help explain the dependentvariable.When the adjusted R2 decreases when adding a variable, thenthe additional variable does not help explain the dependentvariable.
MGMT 662: Integrative Research Project Finding Relationships Among Variables
![Page 91: Finding Relationships Among Variablesthen Crosstabs.... Put Technology in either the row variable or column variable, and put Bush Winner in the other. Click the Statistics button,](https://reader035.vdocuments.us/reader035/viewer/2022062602/5e9d79850ab64c7184663520/html5/thumbnails/91.jpg)
Chi-Squared Test for IndependenceCorrelationRegression
Regression lineInterpreting the slopeVariance Decomposition
Coefficient of determination 20/ 23
The coefficient of determination is the percentage ofvariability in y that is explained by x .
R2 =SSR
SST
R2 will always be between 0 and 1. The closer R2 is to 1, thebetter x is able to explain y .The more variables you add to the regression, the higher R2
will be.The Adjusted R2 penalizes additional variables.
R2adj = 1− n − 1
n − k − 1
(1− R2
)When the adjusted R2 increases when adding a variable, thenthe additional variable really did help explain the dependentvariable.When the adjusted R2 decreases when adding a variable, thenthe additional variable does not help explain the dependentvariable.
MGMT 662: Integrative Research Project Finding Relationships Among Variables
![Page 92: Finding Relationships Among Variablesthen Crosstabs.... Put Technology in either the row variable or column variable, and put Bush Winner in the other. Click the Statistics button,](https://reader035.vdocuments.us/reader035/viewer/2022062602/5e9d79850ab64c7184663520/html5/thumbnails/92.jpg)
Chi-Squared Test for IndependenceCorrelationRegression
Regression lineInterpreting the slopeVariance Decomposition
Coefficient of determination 20/ 23
The coefficient of determination is the percentage ofvariability in y that is explained by x .
R2 =SSR
SST
R2 will always be between 0 and 1. The closer R2 is to 1, thebetter x is able to explain y .The more variables you add to the regression, the higher R2
will be.The Adjusted R2 penalizes additional variables.
R2adj = 1− n − 1
n − k − 1
(1− R2
)When the adjusted R2 increases when adding a variable, thenthe additional variable really did help explain the dependentvariable.When the adjusted R2 decreases when adding a variable, thenthe additional variable does not help explain the dependentvariable.
MGMT 662: Integrative Research Project Finding Relationships Among Variables
![Page 93: Finding Relationships Among Variablesthen Crosstabs.... Put Technology in either the row variable or column variable, and put Bush Winner in the other. Click the Statistics button,](https://reader035.vdocuments.us/reader035/viewer/2022062602/5e9d79850ab64c7184663520/html5/thumbnails/93.jpg)
Chi-Squared Test for IndependenceCorrelationRegression
Regression lineInterpreting the slopeVariance Decomposition
Coefficient of determination 20/ 23
The coefficient of determination is the percentage ofvariability in y that is explained by x .
R2 =SSR
SST
R2 will always be between 0 and 1. The closer R2 is to 1, thebetter x is able to explain y .The more variables you add to the regression, the higher R2
will be.The Adjusted R2 penalizes additional variables.
R2adj = 1− n − 1
n − k − 1
(1− R2
)When the adjusted R2 increases when adding a variable, thenthe additional variable really did help explain the dependentvariable.When the adjusted R2 decreases when adding a variable, thenthe additional variable does not help explain the dependentvariable.
MGMT 662: Integrative Research Project Finding Relationships Among Variables
![Page 94: Finding Relationships Among Variablesthen Crosstabs.... Put Technology in either the row variable or column variable, and put Bush Winner in the other. Click the Statistics button,](https://reader035.vdocuments.us/reader035/viewer/2022062602/5e9d79850ab64c7184663520/html5/thumbnails/94.jpg)
Chi-Squared Test for IndependenceCorrelationRegression
Regression lineInterpreting the slopeVariance Decomposition
Coefficient of determination 20/ 23
The coefficient of determination is the percentage ofvariability in y that is explained by x .
R2 =SSR
SST
R2 will always be between 0 and 1. The closer R2 is to 1, thebetter x is able to explain y .The more variables you add to the regression, the higher R2
will be.The Adjusted R2 penalizes additional variables.
R2adj = 1− n − 1
n − k − 1
(1− R2
)When the adjusted R2 increases when adding a variable, thenthe additional variable really did help explain the dependentvariable.When the adjusted R2 decreases when adding a variable, thenthe additional variable does not help explain the dependentvariable.
MGMT 662: Integrative Research Project Finding Relationships Among Variables
![Page 95: Finding Relationships Among Variablesthen Crosstabs.... Put Technology in either the row variable or column variable, and put Bush Winner in the other. Click the Statistics button,](https://reader035.vdocuments.us/reader035/viewer/2022062602/5e9d79850ab64c7184663520/html5/thumbnails/95.jpg)
Chi-Squared Test for IndependenceCorrelationRegression
Regression lineInterpreting the slopeVariance Decomposition
Coefficient of determination 20/ 23
The coefficient of determination is the percentage ofvariability in y that is explained by x .
R2 =SSR
SST
R2 will always be between 0 and 1. The closer R2 is to 1, thebetter x is able to explain y .The more variables you add to the regression, the higher R2
will be.The Adjusted R2 penalizes additional variables.
R2adj = 1− n − 1
n − k − 1
(1− R2
)When the adjusted R2 increases when adding a variable, thenthe additional variable really did help explain the dependentvariable.When the adjusted R2 decreases when adding a variable, thenthe additional variable does not help explain the dependentvariable.
MGMT 662: Integrative Research Project Finding Relationships Among Variables
![Page 96: Finding Relationships Among Variablesthen Crosstabs.... Put Technology in either the row variable or column variable, and put Bush Winner in the other. Click the Statistics button,](https://reader035.vdocuments.us/reader035/viewer/2022062602/5e9d79850ab64c7184663520/html5/thumbnails/96.jpg)
Chi-Squared Test for IndependenceCorrelationRegression
Regression lineInterpreting the slopeVariance Decomposition
F-test for Regression Fit 21/ 23
F-test for Regression Fit: Tests if the regression line explainsthe data.
Very, very, very similar to ANOVA F-test.
H0 : β1 = beta2 = ... = βk = 0.
H1 : At least one of the variables has explanatory power (i.e.at least one coefficient is not equal to zero).
F =SSR/(k − 1)
SSE/(n − k)
Where k is the number of explanatory variables.
MGMT 662: Integrative Research Project Finding Relationships Among Variables
![Page 97: Finding Relationships Among Variablesthen Crosstabs.... Put Technology in either the row variable or column variable, and put Bush Winner in the other. Click the Statistics button,](https://reader035.vdocuments.us/reader035/viewer/2022062602/5e9d79850ab64c7184663520/html5/thumbnails/97.jpg)
Chi-Squared Test for IndependenceCorrelationRegression
Regression lineInterpreting the slopeVariance Decomposition
F-test for Regression Fit 21/ 23
F-test for Regression Fit: Tests if the regression line explainsthe data.
Very, very, very similar to ANOVA F-test.
H0 : β1 = beta2 = ... = βk = 0.
H1 : At least one of the variables has explanatory power (i.e.at least one coefficient is not equal to zero).
F =SSR/(k − 1)
SSE/(n − k)
Where k is the number of explanatory variables.
MGMT 662: Integrative Research Project Finding Relationships Among Variables
![Page 98: Finding Relationships Among Variablesthen Crosstabs.... Put Technology in either the row variable or column variable, and put Bush Winner in the other. Click the Statistics button,](https://reader035.vdocuments.us/reader035/viewer/2022062602/5e9d79850ab64c7184663520/html5/thumbnails/98.jpg)
Chi-Squared Test for IndependenceCorrelationRegression
Regression lineInterpreting the slopeVariance Decomposition
F-test for Regression Fit 21/ 23
F-test for Regression Fit: Tests if the regression line explainsthe data.
Very, very, very similar to ANOVA F-test.
H0 : β1 = beta2 = ... = βk = 0.
H1 : At least one of the variables has explanatory power (i.e.at least one coefficient is not equal to zero).
F =SSR/(k − 1)
SSE/(n − k)
Where k is the number of explanatory variables.
MGMT 662: Integrative Research Project Finding Relationships Among Variables
![Page 99: Finding Relationships Among Variablesthen Crosstabs.... Put Technology in either the row variable or column variable, and put Bush Winner in the other. Click the Statistics button,](https://reader035.vdocuments.us/reader035/viewer/2022062602/5e9d79850ab64c7184663520/html5/thumbnails/99.jpg)
Chi-Squared Test for IndependenceCorrelationRegression
Regression lineInterpreting the slopeVariance Decomposition
F-test for Regression Fit 21/ 23
F-test for Regression Fit: Tests if the regression line explainsthe data.
Very, very, very similar to ANOVA F-test.
H0 : β1 = beta2 = ... = βk = 0.
H1 : At least one of the variables has explanatory power (i.e.at least one coefficient is not equal to zero).
F =SSR/(k − 1)
SSE/(n − k)
Where k is the number of explanatory variables.
MGMT 662: Integrative Research Project Finding Relationships Among Variables
![Page 100: Finding Relationships Among Variablesthen Crosstabs.... Put Technology in either the row variable or column variable, and put Bush Winner in the other. Click the Statistics button,](https://reader035.vdocuments.us/reader035/viewer/2022062602/5e9d79850ab64c7184663520/html5/thumbnails/100.jpg)
Chi-Squared Test for IndependenceCorrelationRegression
Regression lineInterpreting the slopeVariance Decomposition
F-test for Regression Fit 21/ 23
F-test for Regression Fit: Tests if the regression line explainsthe data.
Very, very, very similar to ANOVA F-test.
H0 : β1 = beta2 = ... = βk = 0.
H1 : At least one of the variables has explanatory power (i.e.at least one coefficient is not equal to zero).
F =SSR/(k − 1)
SSE/(n − k)
Where k is the number of explanatory variables.
MGMT 662: Integrative Research Project Finding Relationships Among Variables
![Page 101: Finding Relationships Among Variablesthen Crosstabs.... Put Technology in either the row variable or column variable, and put Bush Winner in the other. Click the Statistics button,](https://reader035.vdocuments.us/reader035/viewer/2022062602/5e9d79850ab64c7184663520/html5/thumbnails/101.jpg)
Chi-Squared Test for IndependenceCorrelationRegression
Regression lineInterpreting the slopeVariance Decomposition
F-test for Regression Fit 21/ 23
F-test for Regression Fit: Tests if the regression line explainsthe data.
Very, very, very similar to ANOVA F-test.
H0 : β1 = beta2 = ... = βk = 0.
H1 : At least one of the variables has explanatory power (i.e.at least one coefficient is not equal to zero).
F =SSR/(k − 1)
SSE/(n − k)
Where k is the number of explanatory variables.
MGMT 662: Integrative Research Project Finding Relationships Among Variables
![Page 102: Finding Relationships Among Variablesthen Crosstabs.... Put Technology in either the row variable or column variable, and put Bush Winner in the other. Click the Statistics button,](https://reader035.vdocuments.us/reader035/viewer/2022062602/5e9d79850ab64c7184663520/html5/thumbnails/102.jpg)
Chi-Squared Test for IndependenceCorrelationRegression
Regression lineInterpreting the slopeVariance Decomposition
Example: Public Expenditure 22/ 23
In the previous example, how much of the variability in publicexpenditure is explained by the following four variables:
ECAB: Economic AbilityMET: MetropolitanGROW: Growth rate of populationWEST: Western state = 1.
Is the combination of these variables significant in explainingpublic expenditure?
Re-run the regression, this time also including:
YOUNG: Percentage of population that is young.OLD: Percentage of population that is old.
MGMT 662: Integrative Research Project Finding Relationships Among Variables
![Page 103: Finding Relationships Among Variablesthen Crosstabs.... Put Technology in either the row variable or column variable, and put Bush Winner in the other. Click the Statistics button,](https://reader035.vdocuments.us/reader035/viewer/2022062602/5e9d79850ab64c7184663520/html5/thumbnails/103.jpg)
Chi-Squared Test for IndependenceCorrelationRegression
Regression lineInterpreting the slopeVariance Decomposition
Example: Public Expenditure 22/ 23
In the previous example, how much of the variability in publicexpenditure is explained by the following four variables:
ECAB: Economic AbilityMET: MetropolitanGROW: Growth rate of populationWEST: Western state = 1.
Is the combination of these variables significant in explainingpublic expenditure?
Re-run the regression, this time also including:
YOUNG: Percentage of population that is young.OLD: Percentage of population that is old.
MGMT 662: Integrative Research Project Finding Relationships Among Variables
![Page 104: Finding Relationships Among Variablesthen Crosstabs.... Put Technology in either the row variable or column variable, and put Bush Winner in the other. Click the Statistics button,](https://reader035.vdocuments.us/reader035/viewer/2022062602/5e9d79850ab64c7184663520/html5/thumbnails/104.jpg)
Chi-Squared Test for IndependenceCorrelationRegression
Regression lineInterpreting the slopeVariance Decomposition
Example: Public Expenditure 22/ 23
In the previous example, how much of the variability in publicexpenditure is explained by the following four variables:
ECAB: Economic AbilityMET: MetropolitanGROW: Growth rate of populationWEST: Western state = 1.
Is the combination of these variables significant in explainingpublic expenditure?
Re-run the regression, this time also including:
YOUNG: Percentage of population that is young.OLD: Percentage of population that is old.
MGMT 662: Integrative Research Project Finding Relationships Among Variables
![Page 105: Finding Relationships Among Variablesthen Crosstabs.... Put Technology in either the row variable or column variable, and put Bush Winner in the other. Click the Statistics button,](https://reader035.vdocuments.us/reader035/viewer/2022062602/5e9d79850ab64c7184663520/html5/thumbnails/105.jpg)
Chi-Squared Test for IndependenceCorrelationRegression
Regression lineInterpreting the slopeVariance Decomposition
Example: Public Expenditure 22/ 23
In the previous example, how much of the variability in publicexpenditure is explained by the following four variables:
ECAB: Economic AbilityMET: MetropolitanGROW: Growth rate of populationWEST: Western state = 1.
Is the combination of these variables significant in explainingpublic expenditure?
Re-run the regression, this time also including:
YOUNG: Percentage of population that is young.OLD: Percentage of population that is old.
MGMT 662: Integrative Research Project Finding Relationships Among Variables
![Page 106: Finding Relationships Among Variablesthen Crosstabs.... Put Technology in either the row variable or column variable, and put Bush Winner in the other. Click the Statistics button,](https://reader035.vdocuments.us/reader035/viewer/2022062602/5e9d79850ab64c7184663520/html5/thumbnails/106.jpg)
Chi-Squared Test for IndependenceCorrelationRegression
Regression lineInterpreting the slopeVariance Decomposition
Example: Public Expenditure 22/ 23
In the previous example, how much of the variability in publicexpenditure is explained by the following four variables:
ECAB: Economic AbilityMET: MetropolitanGROW: Growth rate of populationWEST: Western state = 1.
Is the combination of these variables significant in explainingpublic expenditure?
Re-run the regression, this time also including:
YOUNG: Percentage of population that is young.OLD: Percentage of population that is old.
MGMT 662: Integrative Research Project Finding Relationships Among Variables
![Page 107: Finding Relationships Among Variablesthen Crosstabs.... Put Technology in either the row variable or column variable, and put Bush Winner in the other. Click the Statistics button,](https://reader035.vdocuments.us/reader035/viewer/2022062602/5e9d79850ab64c7184663520/html5/thumbnails/107.jpg)
Chi-Squared Test for IndependenceCorrelationRegression
Regression lineInterpreting the slopeVariance Decomposition
Example: Public Expenditure 22/ 23
In the previous example, how much of the variability in publicexpenditure is explained by the following four variables:
ECAB: Economic AbilityMET: MetropolitanGROW: Growth rate of populationWEST: Western state = 1.
Is the combination of these variables significant in explainingpublic expenditure?
Re-run the regression, this time also including:
YOUNG: Percentage of population that is young.OLD: Percentage of population that is old.
MGMT 662: Integrative Research Project Finding Relationships Among Variables
![Page 108: Finding Relationships Among Variablesthen Crosstabs.... Put Technology in either the row variable or column variable, and put Bush Winner in the other. Click the Statistics button,](https://reader035.vdocuments.us/reader035/viewer/2022062602/5e9d79850ab64c7184663520/html5/thumbnails/108.jpg)
Chi-Squared Test for IndependenceCorrelationRegression
Regression lineInterpreting the slopeVariance Decomposition
Example: Public Expenditure 23/ 23
What happened to the coefficient of determination?
What happened to the adjusted coefficient of determination?What is your interpretation?
What happened to the estimated effect of the other variables:metropolitan area? Western state?
MGMT 662: Integrative Research Project Finding Relationships Among Variables
![Page 109: Finding Relationships Among Variablesthen Crosstabs.... Put Technology in either the row variable or column variable, and put Bush Winner in the other. Click the Statistics button,](https://reader035.vdocuments.us/reader035/viewer/2022062602/5e9d79850ab64c7184663520/html5/thumbnails/109.jpg)
Chi-Squared Test for IndependenceCorrelationRegression
Regression lineInterpreting the slopeVariance Decomposition
Example: Public Expenditure 23/ 23
What happened to the coefficient of determination?
What happened to the adjusted coefficient of determination?What is your interpretation?
What happened to the estimated effect of the other variables:metropolitan area? Western state?
MGMT 662: Integrative Research Project Finding Relationships Among Variables
![Page 110: Finding Relationships Among Variablesthen Crosstabs.... Put Technology in either the row variable or column variable, and put Bush Winner in the other. Click the Statistics button,](https://reader035.vdocuments.us/reader035/viewer/2022062602/5e9d79850ab64c7184663520/html5/thumbnails/110.jpg)
Chi-Squared Test for IndependenceCorrelationRegression
Regression lineInterpreting the slopeVariance Decomposition
Example: Public Expenditure 23/ 23
What happened to the coefficient of determination?
What happened to the adjusted coefficient of determination?What is your interpretation?
What happened to the estimated effect of the other variables:metropolitan area? Western state?
MGMT 662: Integrative Research Project Finding Relationships Among Variables