Question

There are 50 students in a class. The regression equation of marks in Economics (X) on marks in Management (F) is 3Y-5X +180=0. The mean marks in Management is 44 and the variance of marks in Economics is 9/16 th of the variance of marks in Management. Find the mean marks in Economics and the coefficient of correlation between marks in the two subjects.

Answer 1

The means of the 2 variables always satisfies the regression equation.

Therefore for F = 44, the mean marks in economics (X) is computed as:

Therefore the mean marks in economics is 62.4

The coefficient of correlation between marks in two subjects is computed here as:

Now as we are given that:

Y = (5/3)X - 180/3
Y = (5/3)X - 60

Cov(Y, X) = Cov((5/3)X - 60, X) = (5/3)Cov(X, X) = (5/3)Var(X)

Also we are given that: Var(X) = (9/16)Var(F)

Therefore Var(F) = (16/9)Var(X)

Putting all the values in the correlation formula, we get:

Therefore 15/16 is the required correlation coefficient value here.