- CFA Exams
- CFA Level I Exam
- Study Session 2. Quantitative Methods (1)
- Reading 5. Multiple Regression
- Subject 2. Testing the Significance of a Regression Coefficient

###
**CFA Practice Question**

Which of the following statements is FALSE with respect to the computation and interpretation of the F-statistic for a multiple linear regression model?

II. A high F-statistic is an indication that the model explains a high degree of the variation in the dependent variable.

III. The F-statistic helps reveal if at least one of the regression coefficients is significant.

IV. The F-statistic requires two sets of degrees of freedom in order for it to be tested.

I. The F-statistic will increase as the mean sum of squares of the error term increase as well.

II. A high F-statistic is an indication that the model explains a high degree of the variation in the dependent variable.

III. The F-statistic helps reveal if at least one of the regression coefficients is significant.

IV. The F-statistic requires two sets of degrees of freedom in order for it to be tested.

A. I and III

B. I and II

C. I only

**Explanation:**The F-statistic will decrease as the mean sum of squares of the error term increases. The F-statistic is the ratio of mean sum of squares of the regression to the mean sum of the squares of the error terms. Thus, the mean sum of squares of the errors is in the denominator. An increase in the denominator value will cause the value of the term to decline.

###
**User Contributed Comments**
12

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

tany |
Why is IV wrong? I would have thought you need two degrees of freedom (df1=k, df2=n-(k+1))for the F to be calculated (and tested)?can anyone help? |

tany |
sorry for the stupid comment :-) |

mazen1967 |
why iii is wrong |

pochuevalex |
iii) is wrong cause F stat is used to determine if ALL regression coefficients are significant |

tim2 |
iii) isn't wrong, I think. If you read reading 12 section 7 it says the F test tests the null hypothesis that all coefficients are zero. In other words if you reject the null then it indicates at least one of the coefficents appears to be non zero, as in iii |

Dieckmann |
i don't agree with tim2. |

uviolet |
I agree with pchuevalex on why III is wrong. F stat is a global test and not to test individual variables. |

Hishy |
I still don't get why IV is wrong |

StJohnDale |
The notes seem to refer to "All" |

MathewBinu |
F-test = MSR/MSE = (SSR/k)/ SSE/(n-k-1) so based on the formula two sets of df are needed, k and n-k-1. |

ericczhang |
If you go to a statistical package and run some regressions and F-tests, you'll notice that sometimes regressions with statistically insignificant coefficients will pass a F-test. This basically means that your MSR/MSE is big, even though each individual regression coefficient are not statistically significant. Thus III is wrong. |

Bernie90 |
"To test the null hypothesis that all of the slope coefficients in the multiple regression model are jointly equal to 0 against the alternative hypothesis that at least one slope coefficient is not equal to 0 we must use an F-test" III. is definitely true... in analysis you would literally say "The F-statistic is larger than the critical value at xx level of significance and therefore we reject the null hypothesis that all slope coefficients are jointly 0 in favour of the alternative hypothesis that at least one slope coefficient differs significantly from 0" |