- CFA Exams
- CFA Level I Exam
- Topic 1. Quantitative Methods
- Learning Module 2. Multiple Regression
- Subject 8. Is R
^{2}Related to Statistical Significance?

###
**CFA Practice Question**

Which of the following are true?

II. When an additional variable is added to a model, adjusted R

III. k + 1 is the number of regression parameters.

IV. If k > 1, adjusted R

I. If k = 1, adjusted R

^{2}is greater than or equal to R^{2}.II. When an additional variable is added to a model, adjusted R

^{2}can decrease.III. k + 1 is the number of regression parameters.

IV. If k > 1, adjusted R

^{2}≤ R^{2}.Correct Answer: II and IV

II. Although SSE will decrease when an extra explanatory variable is included, so will the term (n - K - 1). Thus the tem SSE/(n - K) can increase or decrease.

III. k is the number of regression parameters.

IV. R

I. Adjusted-R

^{2}is always ≤ R^{2}.II. Although SSE will decrease when an extra explanatory variable is included, so will the term (n - K - 1). Thus the tem SSE/(n - K) can increase or decrease.

III. k is the number of regression parameters.

IV. R

^{2}is always ≥ adjusted R^{2}.###
**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. |