Tamil Nadu Board of Secondary EducationHSC Commerce Class 11

# Obtain the two regression lines from the following data N = 20, ∑X = 80, ∑Y = 40, ∑X2 = 1680, ∑Y2 = 320 and ∑XY = 480. - Business Mathematics and Statistics

Sum

Obtain the two regression lines from the following data N = 20, ∑X = 80, ∑Y = 40, ∑X2 = 1680, ∑Y2 = 320 and ∑XY = 480.

#### Solution

N = 20, ∑X = 80, ∑Y = 40, ∑X2 = 1680, ∑Y2 = 320 and ∑XY = 480

bar"X" = (sum"X")/"N" = 80/20 = 4

bar"Y" - (sum"Y")/"N" = 40/20 = 2

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

= (20(480) - (80)(40))/(20(1680) - (80)^2)

= (9600 - 3200)/(33600 - 6400)

= 6400/27200

= 0.235

= 0.24

Regression line of Y on X

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

Y − 2 = 0.24 (X − 4)

Y = 0.24X − 0.96 + 2

Y = 0.24X + 1.04

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

= (20(480) - (80)(40))/(20(320) - (40)^2)

= (9600 - 3200)/(6400 - 1600)

= 6400/4800

= 1.33

Regression line of X on Y

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

X – 4 = 1.33 (Y – 2)

X = 1.33Y – 2.66 + 4

X = 1.33Y + 1.34

Concept: Regression Analysis
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Chapter 9: Correlation and Regression Analysis - Exercise 9.2 [Page 226]