Theory:

====

Covariance * Cov(X, Y) = σ_X * σ_Y * Corr(X, Y)* = E [(X - X_bar) (Y - Y_bar) ]

Slope of the Linear regression line: *beta β = Covariance (X, Y) / variance(X)*

β = σ_X * σ_Y * Corr(X, Y) / σ_X² = *Corr(X, Y) * σ_Y / σ_X*

* α = alpha = Y_bar - β * X_bar* = Y intercept of the line.

equation of linear regression: * Y = β * X + α*

================

The given problem:

Here X is the variable denoting the marks in subject A and Y is the variable denoting marks in subject B.

Given data: X_bar = 36 , Y_bar = 85, σ_X = 11 , σ_Y = 8

and Corr(X, Y) = +0.66 or -0.66

So β = 0.66 * 8 / 11 = 0.48

α = alpha = 85 - 0.48 * 36 = 67.72

=> Equation: Y = 0.48 X + 67.72 , OR, B = 0.48 A + 67.72 ---- (1)

========================

I am not sure of the following. I am taking X as variable for the marks in subject B and Y as the variable for the marks in subject A. But correlation coefficient remains the same as: Corr(X,Y) = Corr(Y, X).

β = 0.66 * 11 / 8 = 0.9075

α = 36 - 0.9075 * 85 = - 41.1375

=> equation is: Y = 0.9075 X - 41.1375.

writing in terms of A and B, A = 0.9075 B - 41.1375. --- (2)

============================

marks obtained in subject B = 75.

As per (1), 75 = 0.48 A + 67.72

A = 7.28 /0.48 = 15.17 marks

as per (2) , A = 0.9075 * 75 - 41.1375 = 26.925 marks

I am not really too sure. Please verify.