Let ry denote the sample correlation between y; and x,i = 1,..., n, and r2 denote the coefficient of determination in the simple linear regression of y; on a constant and x. Show that rzy = (sign of b,\Vr², where b, is the slope of the estimated regression equation ŷ = bo + b,x. %3D

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
6th Edition
ISBN:9781337111348
Author:Bruce Crauder, Benny Evans, Alan Noell
Publisher:Bruce Crauder, Benny Evans, Alan Noell
Chapter5: A Survey Of Other Common Functions
Section5.6: Higher-degree Polynomials And Rational Functions
Problem 1TU: The following fictitious table shows kryptonite price, in dollar per gram, t years after 2006. t=...
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Let
denote the sample correlation between y; and x,i = 1,..., n, and r? denote the coefficient of
Yi
determination in the simple linear regression of y; on a constant and x;. Show that
Tyy = (sign of b)/Vr?, where b, is the slope of the estimated regression equationŷ = bo + bịx.
Transcribed Image Text:Problem 4 Let denote the sample correlation between y; and x,i = 1,..., n, and r? denote the coefficient of Yi determination in the simple linear regression of y; on a constant and x;. Show that Tyy = (sign of b)/Vr?, where b, is the slope of the estimated regression equationŷ = bo + bịx.
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