Regression ques from 2008 practice exam 1

[madinthemind]

Hi,

I have a question about the 2008 practice exam (1), ques 10. The ques is as follows:

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

I thought the sum of squared errors would be the same as the residual sum of squares and took SST = SSR + SEE = 869.76+22.12 = 891.88. Hence, R^2 = SSR/SST = 869.76/891.88 = 0.98 i.e. b.

However, the ans and explanation given at the back says:

(b) Incorrect. The candidate will choose this if he/she confuses SEE with SSE in the calculation explained in choice 'c'.
(c) Correct. R^2 = SSR/SST, SEE = [SSE/(n-2)]^1/2. SST = SSR + SSE. Therefore, SSE = 489.29, SST = 1359.05, R^2 = 0.64.

My first ques is, what exactly is the sum of squared errors, if it's different from the residual sum of squares.

Secondly, the formula for SEE (in c) looks somewhat like the standard error of regression for a 2 variable model. However, in this case the SER would have been [SSE/(n-4)]^1/2, correct?

Three, n is not given. So, I don't see how we can get from the SEE to the SSE using the formula given in c. What they've seemed to have done is just squared the SEE to get the SSE.

Could you please help out?

Thanks!

 

[David Harper CFA FRM]

madinthemind,

This question is *terrible* and your answer and issues are *correct* ...

The problem means to say:
"Standard error of estimate (SEE) = 22.12"

Then SEE = SQRT[SSE / d.f.], and df = n - k
i..e, it's only SEE = SSE/(n-2) in the two-variable (univariate) regression

so, in this case, with three explanatory variables, SEE = SQRT[SSE / (n-4)]; i.e., k = 4 b/c we "lose" 3 partial slope coefficients and the intercept
so: SSE = SEE^2 * (N-4)

Re: "n is not given". Agreed, as n is not given, we can't get to SSE

so it's a mess...your instincts are good...

the above is valid but "old" notation before FRM switched the stat to Gujarati, so the equivalences are:
old SSR = new ESS (sum of squared regression to explained sum of squares)
old SSE = new RSS (sum of squared errors to residual sum of squares)
old SST = new TSS (sum of squared total to total sum of squares)
old SEE = new SER (standard estimate of error = standard error of regression)

e.g., SER = SQRT[RSS/df] = SQRT[RSS/(n-k)]

David