- CFA Exams
- CFA Level I Exam
- Study Session 2. Quantitative Methods (1)
- Reading 4. Introduction to Linear Regression
- Subject 7. Analysis of variance (ANOVA)

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**CFA Practice Question**

Which of the following statements is (are) true with respect to an F-statistic when analyzing a regression model?

II. The t-statistic will not be effective in testing the validity of a linear multiple regression as a whole.

III. In all cases, the calculated F-statistic is simply the square of the calculated t-statistic.

IV. F-statistic is calculated to determine if the coefficients of a linear multiple regression equation are, in aggregate, significant.

I. The calculated F-statistic will decrease as the mean sum of squares of the error terms increases relative to the mean sum of the squares of the regression.

II. The t-statistic will not be effective in testing the validity of a linear multiple regression as a whole.

III. In all cases, the calculated F-statistic is simply the square of the calculated t-statistic.

IV. F-statistic is calculated to determine if the coefficients of a linear multiple regression equation are, in aggregate, significant.

Correct Answer: I, II and IV

III is incorrect because the calculated F-statistic is the square of the calculated t-statistic only when dealing with a simple linear regression.

I is correct because the calculated F-statistic is equal to MSS

_{R}/MSS_{E}. As MSS_{E}increases, F_{calc}will decrease.###
**User Contributed Comments**
2

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

vi2009 |
II is true ... F-statistics give more weight to test validity of linear multiple regression by testing for weightage of error due explained error by the regresssion model = > someone please confirm. Thanks |

ericczhang |
The t-statistic only tells you about one coefficient, whereas the F-statistic tells you about the entire linear multiple regression. That's why II is true. Although there are certain special cases where the t-stat is equivalent to a F-stat. |