Adjusted correlation coefficient

ankuragrawal.nit
Finance Junkie
Posts: 64
Joined: Sun Apr 01, 2012 10:52 am

Adjusted correlation coefficient

Postby ankuragrawal.nit » Wed Jan 11, 2012 4:58 am

We know that adj R^2 is dependent on k i.e. the no of independent variables by its formula ( any trick to easily remember this formula ? :P)
That said , If I have a situation where I have 5 independent variables and another situation for the same model where I remove two independent variables i.e. k=3 for second case
Now I know that k=5 shd bttr capture the model instead of k=3 (I have a feeling this might not be true always, but why? I mean more independent variables to explain the variation shd be bttr right?)
I have a computed value of adj R^2 for case 1 less than that of case 2
So I go for case 2 i.e. less independent variables simply on the basis of adj R^2 calculation.

Are we contradicting our initial view that adj R^2 is dependent on k?
I mean are we trying to say that adj R^2 gives us a better hint to a multiple linear regression model irrespective of how many independent variables tht model has?

ankuragrawal.nit
Finance Junkie
Posts: 64
Joined: Sun Apr 01, 2012 10:52 am

Re: Adjusted correlation coefficient

Postby ankuragrawal.nit » Fri Jan 13, 2012 1:32 am

Yes , in my example the adj R^2 for 5 variable model was less than that for 3 variable model,
So does that mean it was worth adding the two more variables?
But the answer to the question is the 3 variable model is preferable because of higher adj R^2 values. I saw this question in Schweser's notes as an example. Should I upload it?
Your statement is confusing sir in that You are saying at one point of time that adj R^2 reflects if adding variables was worthy enough so If my adj R^2 is lower for a 20 variable than 5 variable then it wsnt worth adding those extra 15 variables.
Also you are saying that "if the adjusted R-square for 5 independent variables is greater than that for 3 variables, it is clearly not worth adding the extra 2 variables"

This is confusing me. Kindly clarify the same.

The exact question is---

"An analyst runs a regression of mnthly stock returns on 5 independent varbls ovr 60 mnths. The TSS =460
sum of sqrd errors= 170
Calculate R^2 and adj R^2."

R^2= 63%
adj R^2= 59%
second part---
"suppose the analyst now adds 4 more i ndpendent varbls to the regression and R^2 increases to 65%. Identify which model would be preferred and why?"

adj R^2= 58%
R^2= 65%
ans: The analyst would prefer frst model because adj R^2 is higher and the model has 5 independent variables opposed to 9.

plz explain as to where am I lacking in interpretation.



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