Regression

[Arka Bose]

In a multivariate, is is desirable to have some correlation between the regressors? I mean, if there are uncorrelated factors, there might be higher R squared but some regressors may not be important to our analysis?

 

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• When it comes to correlation among regressors, the most desirable situation is when the regressors are not correlated at all. But this does not say anything about the level of R^2.
• Collinearity impacts a regression through standard errors, meaning that statistical significance of regressors will be impacted. This again does not imply anything for R^2. In the case of perfect multicollinearity, you will see a very high R^2 but statistically insignificant coefficients because standard errors are inflated.
• You can add totally irrelevant variables to a regression and you will still get a very high R^2. Having a high R^2 neither mean that you picked the appropriate regressors, nor that your regressors are statistically significant.

Hope this helps.

 

[Arka Bose]

thank you, i do agree with all ur points, i was just thinking whether it was at least wee bit desirable or not.

 

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It becomes less desirable indeed. But it is not a big problem as long as multicollinearity is not severe.