- CFA Exams
- CFA Level I Exam
- Study Session 2. Quantitative Methods (1)
- Reading 5. Multiple Regression
- Subject 8. Is R
^{2}Related to Statistical Significance?

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**CFA Practice Question**

Which one(s) is (are) true?

II. If k > 5, R

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

I. Adjusted R

^{2}can be negative.II. If k > 5, R

^{2}≥ adjusted R^{2}.III. When an additional variable is added to a model, adjusted R

^{2}can decrease.A. II and III

B. I and III

C. I, II and III

**Explanation:**I. Adjusted R

^{2}can actually be negative if the correlation between the dependent variable and the independent variables is sufficient low.

II. If k > 1, R

^{2}≥ adjusted R

^{2}.

III. When a new independent variable is added, adjusted R

^{2}can decrease if adding that variable has only a small effect on R

^{2}. Mathematically, 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.

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**User Contributed Comments**
7

User |
Comment |
---|---|

murli |
Simply, mid point of the middle most class |

art1997 |
R-squared negative ??? nonsence |

snider |
Adjusted R-square could be negative if the correlation between the dependent variable and the independent variables is sufficient low. |

volkovv |
Adjusted R-square = 1-[(n-1)/(n-k-1)]*(1-R^2). If R^2 is very small, it is possible for adjusted R^2 to be negative. |

simonjdp |
No, Since (n-1)/(n-k-1) will always be <= 1 for n,k >= 0 and since 1-R^2 will also always < 1, adjusted R^2 can never be negative. Do the math. |

Ruan |
No... (n-1)/(n-k-1) will always be >=1, eg n=9,k=2 then: (9-1)/(9-2-1) = 1.333333, so yes a adj Rsq can be Negative |

fanfanli |
Agree with Ruan but think of n=5 k=8 and you will see how it can be negative |