CFA Practice Question

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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,

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
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
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