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Basic Question 8 of 11
Which of the following are true?
II. When an additional variable is added to a model, adjusted R2 can decrease.
III. k + 1 is the number of regression parameters.
IV. If k > 1, adjusted R2 ≤ R2.
I. If k = 1, adjusted R2 is greater than or equal to R2.
II. When an additional variable is added to a model, adjusted R2 can decrease.
III. k + 1 is the number of regression parameters.
IV. If k > 1, adjusted R2 ≤ R2.
User Contributed Comments 7
| User | Comment |
|---|---|
| johans | you would expect if it is N-k-1 instead of N-k that adjusted R^2 < R^2 if k = 1 ... |
| solnce | Both an intercept and slope coeffiecients are regression parameters. |
| katybo | or also "regression coefficients" |
| bmeisner | I have to agree with johans, given the equation, adjusted R^2 ought to be <= R^2 even if k=1. This is because the fraction (n-1)/(n-k-1) is just (n-1)/(n-2) which gives a number less than 1. |
| annwwar | (n-1)/(n-2) > 1 for n>2 |
| weiw | Why III is wrong. K is the number of independent variables and K+1 should be the regression parameters, am I right? |
| ericczhang | Yeah I count the constant as a regression parameter so k+1 should be the number of parameters. I think this is just a case giving them the answer that they think it's right. |
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Learning Outcome Statements
evaluate how well a multiple regression model explains the dependent variable by analyzing ANOVA table results and measures of goodness of fit;
CFA® 2025 Level II Curriculum, Volume 1, Module 2.