Question

# If the errors in the CLR model are not normally distributed, although the OLS estimator is...

1. If the errors in the CLR model are not normally distributed, although the OLS estimator is no longer BLUE, it is still unbiased.
2. In the CLR model, βOLS is biased if explanatory variables are endogenous.
3. The value of R2 in a multiple regression cannot be high if all the estimates of the regression coefficients are shown to be insignificantly different from zero based on individual t tests.
4. Suppose the CNLR applies to a simple linear regression y = β1 + X2β2 + ε, and you obtained the OLS results 0.73 with standard error 0.2 from a data set. Since β2OLS is unbiased, the sampling distribution of β2OLS is distributed around 0.73 with standard error 0.2.
5. In the CLR model, y = X1β1 + X2β2 + ε (population) and y = X1β1OLS + X2β2OLS + e (sample), β2OLS can be obtained when the residuals from a regression of y on X1 alone are regressed on the set of residuals obtained when each column of X2 is regressed on X1.

Statement 1 is true as normality plays no role in unbiasedness.Normality is required only to derive distribution of OLS estimators.

Statement 2 is true that OLS estimator are biased if explanatory variables are endogeneous.

Statement 3 is False as in case of muticollinearity R2 can be high even when coefficient are insignificant

Statement 4 is False as sampling distribution of β2OLS  is distributed around its expected value i.e β2 and not a particular sample value of β2OLS

Statement 5 is correct. Because in this process we are purifying Y and X2 of the influence of X1.Here residuals indicate their purified value on which simple regression model can be applied.

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