. R and r are defined bySSRE(-)(-9)SryR?r =SST'VSrr Syy(1) Show R2 = p2.

Answered: R and r are defined by E(r, – 5)(y – T)…

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter6: Linear Transformations

Section6.CR: Review Exercises

Problem 41CR: For T:P4R5, and rank (T)=3, find nullity (T).

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Related questions

Question

. 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

$r = \frac{S_{x y}}{\sqrt{S_{x x} S_{y y}}} r^{2} = \frac{S S R}{S_{y y}}$

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

$S S R = \sum_{i = 1}^{n} {({\hat{y}}_{i} - \bar{y})}^{2} = r e g r e s s i o n s u m o f s q u a r e s S S T = \sum_{i = 1}^{n} {(y_{i} - \bar{y})}^{2} = t o t a l s u m o f s q u a r e s$