Tamil Nadu Board of Secondary EducationHSC Commerce Class 11

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

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

APPEARS IN

Tamil Nadu Board Samacheer Kalvi Class 11th Business Mathematics and Statistics Answers Guide
Chapter 9 Correlation and Regression Analysis
Exercise 9.2 | Q 1 | Page 226

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