# OLS: Residuals pattern shows a linear relation with respect to the dependent variable

• Nov 18th 2011, 11:42 AM
GordonComstock
OLS: Residuals pattern shows a linear relation with respect to the dependent variable
Hi. I'm attending a statistics course and there's a thing I can't understand. Using a dataset from Verbeek's book, I've found the regression linear model linking wage (as the dependent variable) and years of experience (the independent one) with Gretl. Then, our teacher told us to make the graphic analysis of residuals with respect to both variables (wage and experience). This is the residuals' plot:

http://img100.imageshack.us/img100/7414/bwages.png

The professor told us that this is a bad thing. But I don't understand why. It should be normal that higher wages show higher residuals. Could anyone help me? Thank you in advance!
• Nov 19th 2011, 03:54 PM
SpringFan25
Re: OLS: Residuals pattern shows a linear relation with respect to the dependent vari
What exactly did your professor say that you are disagreeing with?
• Nov 19th 2011, 08:05 PM
CaptainBlack
Re: OLS: Residuals pattern shows a linear relation with respect to the dependent vari
Quote:

Originally Posted by GordonComstock
Hi. I'm attending a statistics course and there's a thing I can't understand. Using a dataset from Verbeek's book, I've found the regression linear model linking wage (as the dependent variable) and years of experience (the independent one) with Gretl. Then, our teacher told us to make the graphic analysis of residuals with respect to both variables (wage and experience). This is the residuals' plot:

http://img100.imageshack.us/img100/7414/bwages.png

The professor told us that this is a bad thing. But I don't understand why. It should be normal that higher wages show higher residuals. Could anyone help me? Thank you in advance!

If the assumptions underlying linear regression hold the residuals will be an uncorrelated random scatter about 0 with constant spread. A systematic deviation from this indicates some violation of the assumptions.

Here you have a linear residual plot, which shows rather than a deviation from the assumptions a failure of the regression process to get the correct regression line. To see this do a linear regression on the residuals and add (or subtract I forget which) the residual regression line from the original, now you will have a better linear fit.

But then again if you do a y on x regression this is not the same as an x on y regression and if you calculate the wrong residual for the regression that you have done you will not get a random scatter in the residual plot. You will get ...

CB