Suppose we regress student’s ATAR scores on parent’s education and parent’s income. If we run the regression again but also include the student’s height as an additional regressor:[Fill in the blank]

Question

BlackTom AI · Accepted Answer

In this question, we’re adding height as an additional regressor to a regression of ATAR on parent education and parent income, so we need to think about R^2 vs adjusted R^2 behavior when a regressor is added.
Option a: 'The R^2 for the regression will either increase or decrease.' In ordinary least squares, the regular R^2 cannot decrease when you add a regressor; it either stays the same or increases because it’s the fraction of variance explained by the model and more predictors can only explain more or the same amount of variance. So this statement is not accurate as written, since a decrease is not possible for R^2 itself.
Option b: 'The adjusted R^2 for the regression will either stay the same or increase.' This is the standard property of adjusted R^2: it includes a penalty for adding additional regressors that do not improve the fit sufficiently. If the height variable provides useful information beyond what is already captured by parental education and income, adjusted R^2 will rise; if not, it may stay the same. Therefore this statement correctly captures the usual behavior.
Option c: 'Both (a) and (b) are true.' Since (a) is incorrect about R^2 potentially decreasing, this combination cannot be correct.
Option d: 'The adjusted R^2 for the regression will decrease.' As noted, adjusted R^2 can decrease if the new regressor adds little explanatory power relative to its penalty, but it is not guaranteed to decrease; it can stay the same or increase. So this statement is not universally true.

Suppose we regress student’s ATAR scores on parent’s education and parent’s income. If we run the regression again but also include the student’s height as an additional regressor:[Fill in the blank]

查看解析

登录即可查看完整答案

类似问题

Adjusted R squared is use to account for which?

What is the relationship between Adjusted R-Square and R-Square?

What is the relationship between Adjusted R-Square and R-Square?

At times, adjusted R^2 is used instead of R^2 in order

Why is the adjusted R2 more informative than the R2?

Why may we opt for the adjusted r2 instead of the multiple r2 when assessing model fit of multiple linear regression?

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