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The residual of ŷ; is defined by e, = y, – ĝ.. (1) Prove Σ -0 and Σiι u ΣΗ. (2) Prove E1 T;ei = 0 and E, ýie, = 0

The residual of ŷ; is defined by e, = y, – ĝ.. (1) Prove Σ -0 and Σiι u ΣΗ. (2) Prove E1 T;ei = 0 and E, ýie, = 0

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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The residual of ŷ; is defined by e, = y – Ý.- (1) Prove iei = 0 and 1 =E1 9 (2) Prove E C;ei = 0 and E, 9,e, = 0
Transcribed Image Text:The residual of ŷ; is defined by e, = y – Ý.- (1) Prove iei = 0 and 1 =E1 9 (2) Prove E C;ei = 0 and E, 9,e, = 0
Expert Solution
Step 1

(1) In problem 1 we have to prove that :

a) The sum of residuals in regression model that contain an intercept term is always zero. 

b) Sum of observed value is equal to the sum of predicted value. 

(2) And in problem 2 we have to prove :

a) The sum of residual weighted by the corresponding value of the regressor is always equal to zero.

b) The sum of residual weighted by the corresponding fitted value is always equal to zero.

 

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