Tamil Nadu Board of Secondary EducationHSC Commerce Class 11th

# Find the equation of the regression line of Y on X, if the observations (Xi, Yi) are the following (1, 4) (2, 8) (3, 2) (4, 12) (5, 10) (6, 14) (7, 16) (8, 6) (9, 18). - Business Mathematics and Statistics

Sum

Find the equation of the regression line of Y on X, if the observations (Xi, Yi) are the following (1, 4) (2, 8) (3, 2) (4, 12) (5, 10) (6, 14) (7, 16) (8, 6) (9, 18).

#### Solution

 X Y X2 Y2 XY 1 4 1 16 4 2 8 4 64 14 3 2 9 4 6 4 12 16 144 48 5 10 25 100 50 6 14 36 196 84 7 16 49 256 112 8 6 64 36 48 9 18 81 324 162 45 90 285 1140 530

N = 9, ΣX = 45, ΣY = 90, ΣX2 = 285, ΣY2 = 1140, ΣXY = 530, bar"X" = (sum"X")/"N" = 45/9 = 5, bar"Y" = (sum"Y")/"N" = 90/9 = 10

byx = ("N"sum"XY" - (sum"X")(sum"Y"))/("N"sum"X"^2 - (sum"X")^2)

= (9(530) - (45)(90))/(9(285) - (45)^2)

= (4770 - 4050)/(2565 - 2025)

= 720/540

= 1.33

Regression line of Y on X:

"Y" - bar"Y" = "b"_"yx"("X" - bar"X")

Y – 10 = 1.33 (X – 5)

Y = 1.33X – 6.65 + 10

Y = 1.33X + 3.35

Concept: Regression Analysis
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