regression analysis
DESCRIPTION
multiple regression analysisTRANSCRIPT
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REGRESSION ANALYSIS
-P H SHAMEER
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• An introduction to regression model
• Performing it on SPSS
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INTRODUCTION
• What is regression model?An explanatory methodForecast expressed as a function of a
certain no. of variables that influences its outcome
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2 types of variables
1. DEPENDENT
-which we want to forecast
2. INDEPENDENT
-or predictor variables
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• Eg:
• Predict how much an individual enjoys his/her job
• Dependent variable: job satisfaction
• Independent variables:
salary, academic qualification, age, sex,
no. of years, socio-economic status….
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assumptions
1. LINEAR RELATIONSHIP exists
2. HOMOSCEDASTICITY exists
3. Residuals are INDEPENDENT of one another
4. MULTICOLLINEARITY doesn’t exist
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Analysis for Linearity
Not Linear Linear
x x
Y
x
Y
x
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Residual Analysis for Homoscedasticity
Non-constant variance Constant variance
x x
Y
x x
Y
resi
dua
ls
resi
dua
ls
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SCATTER PLOTS• -helps to visualize, graphically the
relationship between pairs of variables
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Regression Equation
where
a is y intercept
&
b1, b2,..bi are regression coefficients
1 1 2 2' i iy a b x b x b x
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How a & b can be calculated?
• Method of least squares
this method determines the values in such a way that the sum of squared deviations (errors) is minimized
and hence the name least squares
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b=(∑x*y/n) ─ (x * y)
( ∑x2 / n) ─ (x)2
a = y- bx where y = ∑y/n
x= ∑x/n
n is the no. of observations
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forecasting
• Once the relationship is determined , it can be used to make any no. of forecasts simply by inserting the values of X’s
• y = a+b1x1+b2x2+…+bixi
• Caution: the basic relationship should be assessed periodically
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terminology
b - standard regression coefficient: Measure of how strongly each predictor
variable influences the dependent variableE.g.: if b=2.5
change of one standard deviation in the predictor will change 2.5 standard deviations in the forecasting variable
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terminology
RMeasure of correlation between observed
& predicted value of the dependent variable
R -1 t0 1R= n*∑xi*yi-∑xi*∑yi
√(n∑xi2- (∑xi)2) √(n∑yi
2- (∑yi)2)
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Scatter Plots of Data with Various Correlation Coefficients
Y
X
Y
X
Y
X
Y
X
Y
X
r = -1 r = -.6 r = 0
r = +.3r = +1
Y
Xr = 0
Slide from: Statistics for Managers Using Microsoft® Excel 4th Edition, 2004 Prentice-Hall
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terminology…..
R2
variation in Y accounted for by the set of predictors
Measure of how good a forecasting of dep. variable by knowing the independent variables.
When applied to reality, R2 over estimate the success
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terminology…Adjusted R2
The adjustment takes into account the size of the sample and number of predictors
Gives most useful measure of success of our model ( goodness of fit)
R2 range:0 to 1.If R2=0.75, success will be 75%
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Is each X contributing to the prediction of Y?
• Test if each regression coefficient is significantly different than zero given the variables standard error.
– T-test for each regression coefficient
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Performing regression in spss
Eg:importance of several psycholinguistic variables on spelling performance
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variables
Independent:
standardized spelling score(spellsc), chronological age(age), reading age(readage), standardized reading score(standsc)
Dependent variable:
percentage correct spelling(spelperc)
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Performing regression in spss
• SPPS=Statistical Packages in Social Sciences
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Enter the data
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Cont..
>Analyze>regression> lineardialogue box appears
now enter dependent and independent variables
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Selection methods:on relative contribution of independent
variables
1. simultaneous/ enter method
2. Hierarchical method
3. Statistical methods
a. Forward
b. Backward
c. Stepwise
d. Remove
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Now click the statistics button
Now click ‘continue’> then ‘ok’
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Output:
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Cont…
• Here reading age is not a significant predictor
result:
percentage correct spelling=
-232+.406*chronological age
+.394*standardized reading score
+.786*standardized spelling score
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references
Forecasting methods for management
by Spyros Makridas & Steven C Wheelwright
SPSS for psychologists
by Nicola Brace, Richard Kemp & Rosemary Snelger
Research Methods for M.Com
by L.R Potti
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THANKYOU…