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

Question

BlackTom AI · Accepted Answer

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

查看解析

登录即可查看完整答案

类似问题

Below are the results of an association study conducted by Saha, Morris and Kang (2019):Adjusted R2 = 0.689 Which of the following is incorrect?

In the multiple regression model, [math: yi=β1+β2xi+β3zi+ui]y_i=\beta _1+\beta _2x_i +\beta _3z_i+u_i, which of the following leads to improved precision on the estimates [math: β^2]\hatβ_2, (that is, smaller [math: se(β^2|x,z)]se(\hat{\beta}_2|x,\,z)?[Fill in the blank]

What is the consequence of including irrelevant variables (those that have no direct effect on the dependent variable) in your regression model?[Fill in the blank]

Question at position 19 Cause-and-Effect Models can have multiple independent variables.TrueFalse

更多留学生实用工具

考试浏览器助手

风格化写作助手

论文查重助手

文献引用助手

课堂转译助手

课堂笔记助手

Quiz搜索助手

学校历年真题

智能刷题助手

智能匹配练习

希望你的学习变得更简单