Multiple regression

[hei.so]

Heteroskedasticity does not affect the consistency of the estimators of regression parameters.
Heteroskedasticity does not affect estimates of the regression coefficients.
Serial correlation does not affect the consistency of the estimators of regression parameters.
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What do these statements mean? How come they do not affect the parameters?

 

[varunvajpayee]

Both Heteroskedasticity and Serial correlation are related to residual error. Estimated value(b1,b2) are not impact by these problems.
where as multicollinearity depicts correlation among indepdent varaibles so when you calculate regression cofficient(b1,b2) from regression equation they will biased.

 

[varunvajpayee]

Heteroskedasticity and Serial correlation will result in type 1 error (small error term) where as multicollinearity will result in type 2 error (large error term).

 

[tickersu]

varunvajpayee wrote:
Both Heteroskedasticity and Serial correlation are related to residual error. Estimated value(b1,b2) are not impact by these problems. This is assuming that the regression equation doesn’t contain a lagged value of the dependent variable to predict the DV.
Edit: for serial correlation, I mean.
where as multicollinearity depicts correlation among indepdent varaibles so when you calculate regression cofficient(b1,b2) from regression equation they will biased. This is incorrect. Multicollinearity does not affect the unbiasedness (or consistency, for that matter) of OLS estimated parameters. Yes, the estimated parameters can be affected by multicollinearity (different sign or highly sensitive to changes in the sample, but this is not “biased”). Any reference text will tell you that OLS is unbiased with multicollinearity. Some say that OLS remains B.L.U.E. – best linear unbiased estimator –even in the presence of multicollinearity.

 

[tickersu]

varunvajpayee wrote:
Heteroskedasticity and Serial correlation will result in type 1 error (small error term) where as multicollinearity will result in type 2 error (large error term).

The estimated SER is underestimated in the presence of heteroscedasticity, yes.
With serial correlation, though, the SER can be understated OR overstated. It merely depends if you have positive or negative serial correlation.
Multicollinearity does not affect the SER (error term is unaffected). However, it can inflate the standard errors of the estimated regression coefficients. But again, the SER is unaffected. This would mean that you’re more likely to make a Type II error only when testing estimated coefficients that are affected by the multicollinearity, but not for unaffected coefficients or the global F-test for the model.
I hope this helps.