SER (a.k.a. SEE) - How to determine n?

[dennis_cmpe]

In the following formula, how do you determine n in the question below? The question doesn't mention the sample size. The answers seems to indicate that n = 3.

SEE = (SSE/(n-2) )1/2

10. Paul Graham, FRM® is analyzing the sales growth of a baby product launched three years ago by a regional company. He assesses that three factors contribute heavily towards the growth and comes up with the following results:

Y=b+1.5X1+1.2X2 +3X3

Sum of Squared Regression [SSR] = 869.76
Sum of Squared Errors [SEE] = 22.12

Determine what proportion of sales growth is explained by the regression results.


a. 0.36
b. 0.98
c. 0.64
d. 0.55

Answer: C

Coefficient of Determination i.e. R2 explains proportion of variation explained by the regression.

R2 = SSR/SST
SEE = (SSE/(n-2) )1/2
SST = SSR + SSE.

Therefore, SSE = 489.29, SST = 1359.05, R2 = 0.64
​

 

[David Harper CFA FRM]

Hi Dennis,

I assume "Sum of Squared Errors [SEE] = 22.12" should be "Standard Error of Estimate [SEE] = 22.12"?
Which you correctly point out is, per Gujarati: SER

The answer is wrong. Per Gujarati,

SER^2 = RSS/[n-k] where [n-k] is degrees of freedom.
n is sample size, not given. Ergo, question cannot be answered.
k is the number of variables including the intercept; i.e., in this case, k= 4

so should be: SER^2 = RSS/[n-4], or
RSS = SER^2*[n-4]

agree, question implies n = 3, but that must be incorrect as multivariate regression has three explanatory variables.

David