Question

(b) Explain with brief reasons whether the following statements are true, false, or uncertain: [12] (i) The weighted least squares method is preferred to the ordinary least squares (OLS) method when an important variable is omitted from the model. (ii) The OLS estimators are no longer BLUE (best linear unbiased estimators) under the situation of the heteroskedasticity. (iii) The adjusted $R^2$ will not decrease if an additional explanatory variable is introduced into the model. (iv) We impose assumptions on the dependent variable and the random error term in linear regression models using the least squares principle. We do not need to impose assumptions on the explanatory variables since they are random variables. (v) For linear models, it is always appropriate to use $R^2$ as a measure of how well the estimated regression equation fits the data. (vi) Interval estimates based on the least squares principle are certain to include the true value of the estimated parameter.

          (b) Explain with brief reasons whether the following statements are true, false, or uncertain: [12]
(i) The weighted least squares method is preferred to the ordinary least squares (OLS) method when an important variable is omitted from the model.
(ii) The OLS estimators are no longer BLUE (best linear unbiased estimators) under the situation of the heteroskedasticity.
(iii) The adjusted $R^2$ will not decrease if an additional explanatory variable is introduced into the model.
(iv) We impose assumptions on the dependent variable and the random error term in linear regression models using the least squares principle. We do not need to impose assumptions on the explanatory variables since they are random variables.
(v) For linear models, it is always appropriate to use $R^2$ as a measure of how well the estimated regression equation fits the data.
(vi) Interval estimates based on the least squares principle are certain to include the true value of the estimated parameter.

b explain with brief reasons whether the following statements are true false or uncertain 12 i the weighted least squares method is preferred to the ordinary least squares ols method when an 55817

Added by Alberto M.

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