Tamil Nadu Board of Secondary EducationHSC Commerce Class 11th

# From the data given below: Marks in Economics: 25 28 35 32 31 36 29 38 34 32 Marks in Statistics: 43 46 49 41 36 32 31 30 33 39 Find The two regression equations, - Business Mathematics and Statistics

Sum

From the data given below:

 Marks in Economics: 25 28 35 32 31 36 29 38 34 32 Marks in Statistics: 43 46 49 41 36 32 31 30 33 39

Find

1. The two regression equations,
2. The coefficient of correlation between marks in Economics and Statistics,
3. The mostly likely marks in Statistics when the marks in Economics is 30.

#### Solution

 Marks in Economics (X) Marks in Statistics (Y) x = "X" - bar"X" y = "Y" - bar"Y" x2 y2 xy 25 43 − 7 5 49 25 − 35 28 46 − 4 8 16 64 − 32 35 49 3 11 9 121 33 32 41 0 3 0 9 0 31 36 − 1 − 2 1 4 2 36 32 4 − 6 16 36 − 24 29 31 − 3 − 7 9 49 21 38 30 6 − 8 36 64 − 48 34 33 2 − 5 4 25 − 10 32 39 0 1 0 1 0 320 380 0 0 140 398 − 93

N = 10, ∑X = 320, ∑Y = 280, ∑x2 = 140, ∑y2 = 398, ∑xy = − 93, bar"X" = 320/100 = 32, bar"Y" = 380/100 = 38

(a) Regression equation of X on Y.

bxy = "r"(sigma_"x")/(sigma_"y") = (sum"xy")/(sum"y"^2) = (-93)/398 = − 0.234

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

X − 32 = − 0.234(Y − 38)

X = − 0.234Y + 8.892 + 32

X = − 0.234Y + 40.892

Regression equation of Y on X.

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

byx = "r"(sigma_"x")/(sigma_"y") = (sum"xy")/(sum"y"^2) = (-93)/140 = − 0.664

Y − 38 = − 0.664(X − 32)

Y = − 0.664X + 21.248 + 38

Y = − 0.664X + 59.248

(b) Coefficient of correlation (r) = ±sqrt("b"_"xy" xx "b"_"yx")

= sqrt((-0.234)(-0.664))

= − 0.394

(c) When X = 30, Y = ?

Y = − 0.664(30) + 59.248

= − 19.92 + 59.248

= 39.328

Concept: Regression Analysis
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