Question5 Which statement is true regarding adjusted [math]? Select one alternative: a) Always increases when new variables are added b) Penalises inclusion of irrelevant regressors c) Equals [math] when all variables are significant d) Unaffected by number of regressors ResetMaximum marks: 0.5 Flag question undefined

Question

BlackTom AI · Accepted Answer

Question5 asks about the adjusted [math] statistic in the context of regression.
Option a) 'Always increases when new variables are added'—This is not true in general. While R^2 can increase with more predictors, adjusted R^2 incorporates a penalty for adding variables that do not meaningfully improve fit. If the new variable has little or no explanatory power, the penalty can cause adjusted R^2 to stay the same or even decline.
Option b) 'Penalises inclusion of irrelevant regressors'—This statement correctly captures the purpose of adjusted R^2. The adjustment reduces the impact of adding variables that do not contribute substantial explanatory power, helping to prevent overfitting by favoring a more parsimonious model.
Option c) 'Equals R^2 when all variables are significant'—This claim is misleading. Although all variables being significant can improve fit, adjusted R^2 is not generally equal to R^2 even in that scenario; adjusted R^2 is R^2 adjusted downward by a penalty term that depends on the number of predictors and observations. Therefore, equality is not guaranteed,
  and in practice adjusted R^2 remains less than or equal to R^2, with equality not being a universal property.
Option d) 'Unaffected by number of regressors'—This is false. The whole point of the adjusted measure is to account for the number of regressors; as more regressors are added (especially those with weak predictive power), the adjustment changes, often reducing the statistic when the added variables do not improve the model adequately.
In summary, a is incorrect because the adjusted statistic can decrease with extraneous variables; b is correct because it describes the core idea of the adjustment; c is misleading since equality with R^2 is not a general rule; d is incorrect since the adjustment explicitly depends on the number of regressors.

View Explanation

Log in for full answers

Similar Questions

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

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]

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?

More Practical Tools for Students Powered by AI Study Helper

Homework AI Solver

Stylized AI Paper Writer

Plagiarism Checker Assistant

Citation AI Academic Writing Tool

In-Class Translation Assistant

AI Note Generator

AI Quiz Answers

Past Exam Questions from University Test Bank

Smart Practice Assistant

Adaptive Practice

Making Your Study Simpler