Given y = 2x -3 →(1) y = 5x +7 →(2) Since both the lines of regression passes through t he mean value s vector x and y the point vector (x,y) must satisfy the two given regression lines
Subtracting the equations (3) and (4), we have
Therefore mean values are
Let us suppose that equation (1) is the line of regression of y on x and equation (2) is the equation of the line of regression of x on y, we have
Since both the regression co- efficients are positive r must be positive
Correlation co- efficient r = 0.63.
Substituting y =1 in (2) We have 5x = 1- 7 = -6
x = -6/5.
