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# Non contributing variable in multiple linear regression

A non-contributing predictor variable whose P value is more than .50 is added to an existing multiple linear regression model. It will increase R2 value. I want to know if the same variable is removed from the regression model what will happen?

R2 value going down or no change in R2 value or will it affect mean square error.

Take an example we remove non significant variables in backward elimination method in SAS.. does this reduce r2 value if we remove non significant predictor variable?

Sameer

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‎12-23-2016 01:56 AM
Posts: 2,655

## Re: Non contributing variable in multiple linear regression

As @ballardw said, it is data dependent.  Suppose it is highly correlated with a linear combination of two or three other variables, but is not a good predictior in and of itself.  Removing it could alleviate multicollinearity, which would result in an increase in R^2.  If the nonsignificant variables are completely independent from all other predictor variables, then per the calculation of R^2, it should decrease.  But in real data, you DON'T KNOW whether this is the case or not.

Blanket statements rarely apply without examining the data.

Steve Denham

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Posts: 10,880

## Re: Non contributing variable in multiple linear regression

Yes, no or maybe. Insufficient information. Very data and procedure dependent.

Contributor
Posts: 56

## Re: Non contributing variable in multiple linear regression

In simple  wanted to know can removing non significant vaiables reduce R2 or keep it unchanged in regression?

Solution
‎12-23-2016 01:56 AM
Posts: 2,655

## Re: Non contributing variable in multiple linear regression

As @ballardw said, it is data dependent.  Suppose it is highly correlated with a linear combination of two or three other variables, but is not a good predictior in and of itself.  Removing it could alleviate multicollinearity, which would result in an increase in R^2.  If the nonsignificant variables are completely independent from all other predictor variables, then per the calculation of R^2, it should decrease.  But in real data, you DON'T KNOW whether this is the case or not.

Blanket statements rarely apply without examining the data.

Steve Denham

Occasional Contributor
Posts: 6

## Re: Non contributing variable in multiple linear regression

In MLR we see the R2 value increases by the increase in the predictor variables , but are we not interested in Adj R2 in case of multiple regression ?. More over few text speaks about the control variables which can have effect on the coefficients.
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