dse 2012 question 11

[football fan]

wont a high r value make the regression line steeper since beta = r * sigma y/ sigma x
please help.

[Dreyfus]

When p(X,Y) is very high...and if we regress Y on X then the predicted Y will be very close to actual Y That means the error terms will explain relatively lower Y values....also correlation implies linear relationship so that when this regression is fitted on a line most of the observation will lie along (x,y)

[Akshay Jain]

the value of correlation coefficient r is dependent on the covariace of x and y and the S.D. of x and the S.D. of y.....so if we differentiate beta coefficient (y on x) w.r.t. r then we will get S.D. of y/S.D. of x but a small change in r will be due to changes in the cov of x and y and S.D. of a and y. This implies that the derivative of Beta (y on x) w.r.t r that is S.D. of y/S.D. of x is not a constant. So we cannot say about whether the reg line will b steeper of flatter w.r.t. 1 unit increase in r.
Also steepness and flatness of reg line is dependent on the initial value of r
if value of r initially is < 0 then a unit increase in r will make the reg line flatter and if value of r initially is >0 then a unit increase in r will make the reg line steeper....so no definite conclusion can be made.

[football fan]

thank you akshay :)