1. Linear Regression

2. Index of Fit

3. Coefficient of Determination
Correlation between X and Y is given by
Estimate

4. Coefficient of Determination
Correlation between X and Y is given by
Estimate
Estimate

5. Coefficient of Determination
Then, a natural estimate for the correlation r is given by
R is called the coefficient of determination and is an estimate of the correlation between the input x and the response y.

6. Sum of Squares

7. Sum of Squares

8. Residual Analysis

9. Analysis of Residuals

10. Note that if we sum the square of the residuals, we get SSR.

11. Standardized Residuals
But, we do not know s,

12. Standardized Residuals
Our best estimate of s is given by
These are called the standardized residuals

14. Standardized Residuals

15. Residuals

16. Standardized Residuals