1. Multiple Regression

2. Multiple Regression
and

3. Multiple Regression
Taking repeated partial derivatives and setting to 0, we get

4. Partial Derivatives

5. Solving k+1 normal equations

6. Solving k+1 normal equations

7. Solving k+1 normal equations

8. We can solve, but easier in matrix form

9. We can solve, but easier in matrix form

10. We can solve, but easier in matrix form

11. Consider SLR
Dropping subscript 1 since there is only one x variable

12. SLR (continued)

13. SLR (continued)

14. SLR (continued)

15. SLR (continued)

16. SLR (continued)

17. SLR (continued)

18. We can solve, but easier in matrix form

19. We can solve, but easier in matrix form

20. We can solve, but easier in matrix form

21. We can solve, but easier in matrix form
Measures the amount of reduction in the sum of squares of the residuals when using the model
As opposed to the model
R2 is the coefficient of multiple determination Is called the multiple correlation coefficient between Y and the input values.