# For 50 students of a class, the regression equation of marks in statistics (X) on the marks in accountancy (Y) is 3y − 5x + 180 = 0. - Mathematics and Statistics

Sum

For 50 students of a class, the regression equation of marks in statistics (X) on the marks in accountancy (Y) is 3y − 5x + 180 = 0.  The variance of marks in statistics is (9/16)^"th" of the variance of marks in accountancy. Find the correlation coefficient between marks in two subjects.

#### Solution

Given, n = 50, X = marks in Statistics,

Y = marks in Accountancy,

Regression equation of X on Y is

3y – 5x + 180 = 0,

bar y = 44,  sigma_X^2 = 9/16 sigma_Y^2

Now, 3y – 5x + 180 = 0 is the regression equation of X on Y.

∴ The equation becomes 5X = 3Y + 180

i.e., X = 3/5 Y + 180/5

Comparing it with X = bXY Y + a', we get

b_(XY) = 3/5, a = 180/5 = 36

a = barx - b_(XY)  bary

∴ 36 = bar x - 3/5 xx 44

∴ 36 = bar x – 26.4

∴ bar x = 36 + 26.4 = 62.4

Also, sigma_X^2 = 9/16 sigma_Y^2

∴ sigma_X^2/sigma_Y^2 = 9/16

∴ sigma_X/sigma_Y = 3/4

b_(XY) = r xx sigma_X/sigma_Y

∴ 3/5 = r xx 3/4

∴ 3/5 xx 4/3 = r

∴ r = 4/5 = 0.8

∴ Mean marks in statistics (barx) are 62.4 and correlation coefficient (r) between marks in the two subjects is 0.8.

Concept: Properties of Regression Coefficients
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Chapter 3: Linear Regression - Exercise 3.3 [Page 50]
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