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R and r are defined by E(r, – 5)(y – T) Sry VS., Syy SSR R2 r = SST' (1) Show R? = r².

R and r are defined by E(r, – 5)(y – T) Sry VS., Syy SSR R2 r = SST' (1) Show R? = r².

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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Question
. R and r are defined by SSR E(-)(-9) Sry R? r = SST' VSrr Syy (1) Show R2 = p2.
Transcribed Image Text:. R and r are defined by SSR E(-)(-9) Sry R? r = SST' VSrr Syy (1) Show R2 = p2.
Expert Solution
Step 1

If y = a+bx is the linear equation 

Correlation attempts to measure the strength of the relationship between the two variables by means of a single number referred as Correlation Coefficient

The measure of linear association between the two variables X and Y is estimated by the sample correlation coefficient r 

r = SxySxxSyyr2 = SSRSyy

then r2 is usually referred to as the sample coefficient of determination

SSR = ∑i=1ny^i -y¯2 = regression sum of squaresSST = ∑i=1nyi-y¯2 = total sum of squares

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