# X y xy x2 y2 6 9 54 36 81 2 11 22 4 121 10 5 50 100 25 4 8 32 16 64 8 7 □ 64 49 Total = 30 Total = 40 Total = □ Total = □ Total = □ bxy = □□ byx = □□ ∴ Regression equation of x on y is □ ∴ Regressi - Mathematics and Statistics

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Chart
 x y xy x2 y2 6 9 54 36 81 2 11 22 4 121 10 5 50 100 25 4 8 32 16 64 8 7 square 64 49 Total = 30 Total = 40 Total = square Total = 220 Total = square

bxy = square/square

byx = square/square

∴ Regression equation of x on y is square

∴ Regression equation of y on x is square

#### Solution

 x y xy x2 y2 6 9 54 36 81 2 11 22 4 121 10 5 50 100 25 4 8 32 16 64 8 7 56 64 49 Total = 30 Total = 40 Total = 214 Total = 220 Total = 340

From the table, we have

n = 5, ∑x = 30, ∑y = 40, ∑xy = 214, ∑x2 = 220, ∑y2 = 340

barx = (sumx_"i")/"n" = 30/5 = 6

bary = (sumy_"i")/"n" = 40/5 = 8

bxy = (sumxy - "n" bar(x) bar(y))/(sumy^2 - "n" bary^2)

= (214 - 5 xx 6 xx 8)/(340 - 5(8)^2

= (214 - 240)/(340 - 320)

= (-26)/20

bxy = (-13)/10

byx = (sumxy - "n" bar(x) bar(y))/(sumx^2 - "n" barx^2)

= (214 - 5 xx 6 xx 8)/(220 - 5(6)^2

= (214 - 240)/(220 - 180)

= (-26)/40

byx = (-13)/20

∴ Regression equation of x on y is x = – 1.3y + 16.4

∴ Regression equation of y on x is y = – 0.65x + 11.9

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