Coefficient of Determination, Pearson Product Moment Coefficient

1. Linear Regression, Scatter Diagram, Coefficient of
Determination, Pearson Product Moment Correlation
Coefficient

2. Linear Regression

3. Linear Regression
Why is it called LEAST SQUARES METHOD?

4. Linear Regression
Excel Demonstration to
find regression equation

5. Coefficient of Determination
How good is the “FIT” between the actual data and the
regression equation?
The Coefficient of Determination shows a numerical
measure about how good is the “fit” between actual
observations (x,y) and the points generated by the
regression equation
baxy ˆ

6. Coefficient of Determination
y = 0.5x + 1.3
R² = 0.1096
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y = 0.7177x + 0.9677
R² = 0.9394
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y = 0.7177x + 0.9677
R² = 0.9394
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7. Coefficient of Determination
The symbol for the coefficient of determination is
 1,0)range( 22
 rr

8. Coefficient of Determination
y = 0.5x + 1.3
R² = 0.1096
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109.02
r
y = 0.7177x + 0.9677
R² = 0.9394
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939.02
r

9. Coefficient of Determination

10. Coefficient of Determination
y = 0.7177x + 0.9677
R² = 0.9394
0
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0 1 2 3 4 5 6 7
AxisTitle
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11. Coefficient of Determination
y = 0.7177x + 0.9677
R² = 0.9394
0
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2
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5
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0 1 2 3 4 5 6 7
AxisTitle
Axis Title

12. Coefficient of Determination
y = 0.7177x + 0.9677
R² = 0.9394
0
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0 1 2 3 4 5 6 7
AxisTitle
Axis Title

13. Coefficient of Determination

14. Correlation Analysis
How strong is the “relationship” between the variables x
and y?
Coefficient Analysis shows the strength of relationship
between x and y.

15. Coefficient Analysis

16. Correlation Coefficient

17. Correlation Coefficient
Interpretation
10  r

18. Correlation Coefficient
Interpretation
01  r

19. Correlation Coefficient
Interpretation
0r

20. Correlation Coefficient

21. Correlation Coefficient

22. Correlation Coefficient

23. Correlation Coefficient

24. Final Remarks
The correlation coefficient r does not necessarily
indicate causation.
It does not demonstrate a cause-and-effect connection
between variables.
It is a measure that demonstrates how frequently two
variables x and y are observed to occur together.