- CFA Exams
- CFA Level I Exam
- Study Session 2. Quantitative Methods (1)
- Reading 4. Introduction to Linear Regression
- Subject 5. Testing the significance of a regression coefficient

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**CFA Practice Question**

In a regression, the sum of squared errors (SSE) equaled 2,176 and the regression sum of squares (RSS) equaled 4,675. the regression had a single independent variable and a sample size of 15. Based on the information given, is the overall regression significant at the 95% confidence level, and what is the value of the relevant test statistic?

A. No, 2.15

B. No, 4.67

C. Yes, 27.93

**Explanation:**The overall significance of a regression is judged by the F-statistic. In this case, only one independent co-efficient is estimated. Thus, the degrees of freedom are 1, and 13 (= 15 - 2) for numerator and denominator respectively. For alpha = 5%, the critical value is 4.67. The calculated test statistic is,

Since the calculated value exceeds the critical value, the regression is significant.

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**User Contributed Comments**
9

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

danlan |
Any one can help me on this one? |

armanaziz |
F =( RSS/1)/[SSE/(n-2)] Just memorize and lookup in F Table... |

mirco |
There is another way, should you not remember this formula (though more time consuming). For a simple regression F-statistic is simply the sqare of the t-statistic. So: 1) Calculate coefficient of correlation: R^2=SSR/SST=SSR/(SSR+SSE) 2) Test the significance of correlation: t=(r*(n-2)^.5)/(1-r^2)^.5 3) F=t^2 |

fedor5 |
should we memorize F-table for the exam? |

nsmwaura |
sounds rocket science... I am taking my chances |

AkuK |
to armanaziz i think we should memorize F=(RSS/k)/[SSE/(n-k-1)] shouldnt we? i saw Qs with 2 ks... |

Hishy |
Does F = t squared? I dont remember reading that |

Allstats |
This is an easy one; all the results are >2 thus it is significant,so the answer is C. |

chriswwu |
@Allstats what you said is only true for t-stat, not for F-stat |