Theory:

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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*

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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)

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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)

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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.