# X y x-x¯ y-y¯ (x-x¯)(y-y¯) (x-x¯)2 (y-y¯)2 1 5 – 2 – 4 8 4 16 2 7 – 1 – 2 □ 1 4 3 9 0 0 0 0 0 4 11 1 2 2 4 4 5 13 2 4 8 1 16 Total = 15 Total = 45 Total = 0 Total = 0 Total = □ Total = 10 Total = 40 - Mathematics and Statistics

Chart
 x y x - barx y - bary (x - barx)(y - bary) (x - barx)^2 (y - bary)^2 1 5 – 2 – 4 8 4 16 2 7 – 1 – 2 square 1 4 3 9 0 0 0 0 0 4 11 1 2 2 4 4 5 13 2 4 8 1 16 Total = 15 Total = 45 Total = 0 Total = 0 Total = square Total = 10 Total = 40

Mean of x = barx = square

Mean of y = bary = square

bxy = square/square

byx = square/square

Regression equation of x on y is (x - barx) = "b"_(xy)  (y - bary)

∴ Regression equation x on y is square

Regression equation of y on x is (y - bary) = "b"_(yx)  (x - barx)

∴ Regression equation of y on x is square

#### Solution

 x y x - barx y - bary (x - barx)(y - bary) (x - barx)^2 (y - bary)^2 1 5 – 2 – 4 8 4 16 2 7 – 1 – 2 2 1 4 3 9 0 0 0 0 0 4 11 1 2 2 4 4 5 13 2 4 8 1 16 Total = 15 Total = 45 Total = 0 Total = 0 Total = 20 Total = 10 Total = 40

Mean of x = barx = (sumx)/"n" = 3

Mean of y = bar = (sumy)/"n" = 9

bxy = (sum(x - barx)(y - bary))/(sum(y - bary)^2) = 20/40 = 1/2

byx =  (sum(x - barx)(y - bary))/(sum(x - barx)^2) = 20/10 = 2

Regression equation of x on y is (x - barx) = "b"_(xy)  (y - bary)

i.e., ("X" - 3) = 1/2 ("Y" - 9)

∴ Regression equation x on y is 2X – Y + 3 = 0

Regression equation of y on x is (y - bary) = "b"_(yx)  (x - barx)

i.e., (Y – 9) = 2(X – 3)

∴ Regression equation of y on x is 2X – Y + 3 = 0

Concept: Properties of Regression Coefficients
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Chapter 2.3: Linear Regression - Q.5
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