- CFA Exams
- CFA Level I Exam
- Topic 1. Quantitative Methods
- Learning Module 10. Simple Linear Regression
- Subject 4. Hypothesis Testing of Linear Regression Coefficients
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,F = 4,675/[2,176/(15 - 2)] = 27.93.
Since the calculated value exceeds the critical value, the regression is significant.
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 |