Question8 Including irrelevant regressors in multiple regression typically: Select one alternative: a) Increases variance of estimates b) Biases coefficients c) Reduces variance of estimates d) Leaves [math] unchanged ResetMaximum marks: 0.5 Flag question undefined

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When we discuss including irrelevant regressors in a multiple regression model, we need to examine how OLS estimates are affected across the options.
Option a) Increases variance of estimates: This is true. Adding irrelevant regressors does not improve the information about the true underlying relationships, and it tends to inflate the standard errors of the estimated coefficients due to multicollinearity and wasted degrees of freedom, thereby increasing the variance of the estimates.
Option b) Biases coefficients: Under the classical OLS assumptions, including an irrelevant regressor does not bias the coefficients of the included variables (the estimators remain unbiased for the true parameters). However, it can inflate variances; bias is not the correct characterization here.
Option c) Reduces variance of estimates: This is incorrect. The presence of unnecessary regressors typically worsens precision, not improves it. The variance of the estimated coefficients tends to go up rather than down when useless predictors are added.
Option d) Leaves R^2 unchanged: In fact, R^2 cannot decrease when you add regressors, even if they are irrelevant; it either increases or stays the same. However, subtracting adjusted R^2 may reveal a reduction in model quality, and the statement about R^2 being unchanged is not accurate in general.

In summary, the key effect of including irrelevant regressors is a rise in the variance (standard errors) of the estimated coefficients, not a reduction in variance, not bias in the coefficients under standard assumptions, and not an unchanged R^2. Therefore, option a) is the correct characterization among the given choices.

Question8 Including irrelevant regressors in multiple regression typically: Select one alternative: a) Increases variance of estimates b) Biases coefficients c) Reduces variance of estimates d) Leaves [math] unchanged ResetMaximum marks: 0.5 Flag question undefined

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