simple linear regression and correlation by asst. prof. dr. min aung
TRANSCRIPT
![Page 1: Simple Linear Regression and Correlation by Asst. Prof. Dr. Min Aung](https://reader031.vdocuments.us/reader031/viewer/2022020110/5518c5ea550346881f8b5811/html5/thumbnails/1.jpg)
Simple Linear Regression andCorrelation
by
Asst. Prof. Dr. Min Aung
![Page 2: Simple Linear Regression and Correlation by Asst. Prof. Dr. Min Aung](https://reader031.vdocuments.us/reader031/viewer/2022020110/5518c5ea550346881f8b5811/html5/thumbnails/2.jpg)
When SLR?
• Study a relationship between two variables
• Paired-Samples or matched data
• Interval or ratio level measurement
![Page 3: Simple Linear Regression and Correlation by Asst. Prof. Dr. Min Aung](https://reader031.vdocuments.us/reader031/viewer/2022020110/5518c5ea550346881f8b5811/html5/thumbnails/3.jpg)
Independent and dependent variables
• You want to guess or estimate or compute the
values of the dependent variable.
• In estimating, you will use the values of the
independent variable.
![Page 4: Simple Linear Regression and Correlation by Asst. Prof. Dr. Min Aung](https://reader031.vdocuments.us/reader031/viewer/2022020110/5518c5ea550346881f8b5811/html5/thumbnails/4.jpg)
Predictor and Predicted variables
• Predictor = independent variable.
• Predicted variable = dependent variable.
![Page 5: Simple Linear Regression and Correlation by Asst. Prof. Dr. Min Aung](https://reader031.vdocuments.us/reader031/viewer/2022020110/5518c5ea550346881f8b5811/html5/thumbnails/5.jpg)
Scatter Diagram
• X-axis = independent variable.
• Y-axis = dependent variable.
• Each pair of data A point (x, y)
X
Y
2
3 (2, 3)
![Page 6: Simple Linear Regression and Correlation by Asst. Prof. Dr. Min Aung](https://reader031.vdocuments.us/reader031/viewer/2022020110/5518c5ea550346881f8b5811/html5/thumbnails/6.jpg)
X
Purpose of Drawing Scatter Diagram
• Is there a linear relationship between the two variables X and Y?
• Linear relationship = Scatter points (roughly at least) form the shape of a straight line.
Y
X
Y
Linear relationship No linear relationship
![Page 7: Simple Linear Regression and Correlation by Asst. Prof. Dr. Min Aung](https://reader031.vdocuments.us/reader031/viewer/2022020110/5518c5ea550346881f8b5811/html5/thumbnails/7.jpg)
Measuring Strength of Linear Relationship
• Pearson’s coefficient of correlation r
• Formula (2) (Not used in exam. Just for knowledge)
• Calculator Work For Casio 350MS
Switch the calculator on.
1. Set calculator in LR (Linear Regression) mode:
Press Mode.
Press 3 for Reg (Regression).
Press 1 for Linear.
• Check n. (Checking whether there are old data):
Press Shift 1, next 3, and then =.
![Page 8: Simple Linear Regression and Correlation by Asst. Prof. Dr. Min Aung](https://reader031.vdocuments.us/reader031/viewer/2022020110/5518c5ea550346881f8b5811/html5/thumbnails/8.jpg)
Calculator Work for r
3. Enter Data in Pairs:
x-value , y-value M+
x-value , y-value M+
x-value , y-value M+
4. Check n again: see
step 2 above.
5. Press shift 2, then move by arrow to the right, press
3 for r, and then press =.
Now you see the value of r.
![Page 9: Simple Linear Regression and Correlation by Asst. Prof. Dr. Min Aung](https://reader031.vdocuments.us/reader031/viewer/2022020110/5518c5ea550346881f8b5811/html5/thumbnails/9.jpg)
Interpretation of r (Direct linear relationship)
1. If r is 1 or – 1, then all scatter points are on a straight line.
2. If r is 1, all points are on a straight line with a positive slope.
3. If r is -1, all points are on a straight line with a negative slope.
4. If a straight line has a positive slope, it rises up to the right.
5. If a straight line has a
positive slope, if x
increases, then y increases
for the points (x, y) on it.(small x, small y)
(large x, large y)
6. In this situation, we say that the two variables X and Y are
directly or positively correlated.
![Page 10: Simple Linear Regression and Correlation by Asst. Prof. Dr. Min Aung](https://reader031.vdocuments.us/reader031/viewer/2022020110/5518c5ea550346881f8b5811/html5/thumbnails/10.jpg)
Interpretation of r (Inverse linear relationship)
1. If r is -1, all points are on a straight line with a negative slope.
2. If a straight line has a
negative slope, if x
increases, then y decreases
for the points (x, y) on it.
(small x, large y)
(large x, small y)
6. In this situation, we say that the two variables X and Y are
inversely or negatively correlated.
![Page 11: Simple Linear Regression and Correlation by Asst. Prof. Dr. Min Aung](https://reader031.vdocuments.us/reader031/viewer/2022020110/5518c5ea550346881f8b5811/html5/thumbnails/11.jpg)
Interpretation of r (strength)
1. If r is not exactly 1 or – 1, but it is .9 or - .9, then the points
are around a straight line. They are close to a straight-line
shape.
2. If r is .8 or - .8, then the points are close to a straight-line
shape, but not so well as in case of .9 or -.9.
3. Thus, the closer r is to 1 or – 1, the closer are the points to a
straight-line shape.
4. Thus, the closer r is to 0, the farther are the points from a
straight-line shape.
5. In r-values, 0.9 are stronger than 0.8, and 0.8 are
weaker than 0.9.
![Page 12: Simple Linear Regression and Correlation by Asst. Prof. Dr. Min Aung](https://reader031.vdocuments.us/reader031/viewer/2022020110/5518c5ea550346881f8b5811/html5/thumbnails/12.jpg)
Interpretation of r (strength)
Values of r
0
No linear relationship
0.5
Weak linear relationship
- 0.5
Weak linear relationship
1
Strong
Perfect
-1
Strong
Perfect
![Page 13: Simple Linear Regression and Correlation by Asst. Prof. Dr. Min Aung](https://reader031.vdocuments.us/reader031/viewer/2022020110/5518c5ea550346881f8b5811/html5/thumbnails/13.jpg)
Testing Linear Relationship
1. Pearson invented a formula to measure the strength and
direction of a linear relationship between two variables.
2. The number given by his formula is called correlation
coefficient. We call it Pearson’s coefficient of
correlation.
3. We write r for this value in a sample, and we write for
this value in a population.
4. Testing whether the correlation is significant is scientific
guessing whether there should be a correlation, in the
population, between the two variables under
consideration.
![Page 14: Simple Linear Regression and Correlation by Asst. Prof. Dr. Min Aung](https://reader031.vdocuments.us/reader031/viewer/2022020110/5518c5ea550346881f8b5811/html5/thumbnails/14.jpg)
Null and Alternate Hypothesis
1. Test correlation: H0: = 0 and Ha: 0
2. Test direct correlation: H0: 0 and Ha: > 0
3. Test inverse correlation: H0: 0 and Ha: < 0
4. Test positive correlation: H0: 0 and Ha: > 0
5. Test inverse correlation: H0: 0 and Ha: < 0
![Page 15: Simple Linear Regression and Correlation by Asst. Prof. Dr. Min Aung](https://reader031.vdocuments.us/reader031/viewer/2022020110/5518c5ea550346881f8b5811/html5/thumbnails/15.jpg)
Three types of test
1. H0: = 0 and Ha: 0 Two-tailed test
2. H0: 0 and Ha: < 0 Left-tailed test
3. H0: 0 and Ha: > 0 Right-tailed test
![Page 16: Simple Linear Regression and Correlation by Asst. Prof. Dr. Min Aung](https://reader031.vdocuments.us/reader031/viewer/2022020110/5518c5ea550346881f8b5811/html5/thumbnails/16.jpg)
Critical value
1. Read t table.
2. Degrees of freedom (Df) = n - 2
3. n = number of pairs of data
4. Right-tailed test Positive sign
5. Left-tailed test Negative sign
6. Two-tailed test Both positive and negative sign
![Page 17: Simple Linear Regression and Correlation by Asst. Prof. Dr. Min Aung](https://reader031.vdocuments.us/reader031/viewer/2022020110/5518c5ea550346881f8b5811/html5/thumbnails/17.jpg)
Test Statistic
1. Test statistic = Strength of evidence supporting alternate hypothesis Ha
2. Original test statistic to test is r.
3. Convert r to t by Formula (10).
4. Learn to compute t by your calculator correctly.
![Page 18: Simple Linear Regression and Correlation by Asst. Prof. Dr. Min Aung](https://reader031.vdocuments.us/reader031/viewer/2022020110/5518c5ea550346881f8b5811/html5/thumbnails/18.jpg)
Rejection region 1
• For a two tailed-test, the rejection region is on the right of
positive critical value and on the left of negative critical value.
Real number line for t values
0 Positive Critical ValueNegative Critical Value
Total area = Level of significance = Probability = α
Rejection regionRejection region
T curve
![Page 19: Simple Linear Regression and Correlation by Asst. Prof. Dr. Min Aung](https://reader031.vdocuments.us/reader031/viewer/2022020110/5518c5ea550346881f8b5811/html5/thumbnails/19.jpg)
Rejection region 2
• For a left-tailed test, the rejection region is on the left of
(negative) critical value.
Real number line for t values
0(Negative) Critical Value
α = Area = Level of significance = Probability
Rejection region
t curve
![Page 20: Simple Linear Regression and Correlation by Asst. Prof. Dr. Min Aung](https://reader031.vdocuments.us/reader031/viewer/2022020110/5518c5ea550346881f8b5811/html5/thumbnails/20.jpg)
Rejection region 3
• For a right-tailed test, the rejection region is on the right of the
(positive) critical value.
Real number line for t values
0 (Positive) Critical Value
Area = Level of significance = Probability = α
Rejection region
t curve
![Page 21: Simple Linear Regression and Correlation by Asst. Prof. Dr. Min Aung](https://reader031.vdocuments.us/reader031/viewer/2022020110/5518c5ea550346881f8b5811/html5/thumbnails/21.jpg)
Decision Rule
• If the test statistic (TS) is in the rejection region, then reject H0.
• Reject H0 = “H0 is false, and hence Ha is true.”
• Fail to reject H0 = “H0 is true, and hence Ha is false.”
![Page 22: Simple Linear Regression and Correlation by Asst. Prof. Dr. Min Aung](https://reader031.vdocuments.us/reader031/viewer/2022020110/5518c5ea550346881f8b5811/html5/thumbnails/22.jpg)
Conclusion
• Conclusion = Decision
• Decision is the last step of statistical procedure.
• Conclusion is the report to the one who asked the original question.