Coefficient of Determination. Are there any tricks to this?

[monsieuruzairo3]

Dear David,

Please note the following question. I have doubts on the options. I believe the question is flawed as incomplete information is given. Kindly confim

Kris, FRM® is analyzing the sales growth of a Two Wheelers launched two years ago Suzuki. Majorly 3 factors contributes to sales growth and following are the results:
Y = b + 1.6 X1 + 1.3 X2 + 4 X3
Sum of Squared Regression [SSR] = 880.5
Sum of Squared Errors [SEE = 25.5
Determine what proportion of sales growth is explained by the regression results.
A. 0.36
B. 0.98
C. 0.64
D. 0.56

Now If we take Sum of Squared errors and ignore SEE then R^2 = 880.5/Sum(880.5,25.5)
However if we assume that this is SEE and not Sum of squared errors then
N=24(2 years), K=3
SEE=sqrt(SSE/n-k-1)
25.5=sqrt(SSE/20)
SSE=13005
TSS=13005+880.5=13885.5
R^2 = 880.5/13885.5 = .0634 which doesnt match any of the option
Answer provided is D 0.56. Can you please explain how this is?
Best uzi

 

[David Harper CFA FRM]

Hi monsieuruzairo3, I do not either understand how 0.56 is the answer. Assuming the question wants R^2, I don't see even adjusted R^2 as nearly 0.56, on the assumptions.

Upon initial view, I have the same impulse as you: to think the 25.5 is meant to be a standard error of estimate (SEE; aka, standard error of regression, SER, in our current FRM authors). It the question really reads "Sum of Squared Errors [SEE]" that is incorrect, the SEE is not a "sum of squares ..."

But i get the same result. I agree totally that SSE (sum of squared errors; aka, SSR or RSS) = SEE^2*(n-4) = 13,005, which does not explain the 0.56; e.g., I totally agree that n-k-1 = n - 4 as we have 4 df here. Sorry, I cannot explain it, i end up same place as you ... I wonder if the question wants something other than (adjusted) R^2??

 

[ShaktiRathore]

working backwardly from the answer given .56=R^2 we assume then,
880.5/SSE+880.5 = .56
=>SSE+880.5=880.5/.56=1572.32=>SSE=1572.32-880.5=691.82
sqrt(SSE/n-k-1)=25.5
=>SSE/n-k-1=650.25
=>n-k-1=1.06
=>n-3-1~1
=>n-4=1=>n=5 which seems absurd since the numbers of observations are not just 5 but 24. Therefore there seems some fault with the Question whcih i am unable to figure out,.
SSE=691.82 , then SEE=sqrt(SSE/n-k-1)=sqrt(691.82/24-3-1)=sqrt(691.82/20)=34.91~35 may be the SEE should be 35.5 instead of 25.5 a printing mistake who knows but nevertheless there is something wrong somewhere.
thanks

 

[David Harper CFA FRM]

Thanks ShaktiRathore good to know i didn't miss something obvious Even if the question were to expect n = 24, I think that is insufficiently precise based only on "analyzing the sales growth of a Two Wheelers launched two years ago Suzuki." (why assume monthly?). Thanks,