SEE formula is different when using t-stats versus an f-stat?

CFA Level II Quant
#1

SEE = √SSE/n-2, correct? What is SEE = √SSE/n-k-1 for?

#2

The first formula is used in simple linear regression (only 1 dependent variable) and the second formular is used in multiple linear regression (2 or more dependent variables). The first case uses T-stat to test for the only slope significance, but on mutiple linear regression we use F-stat to test for the significance of the whole pack of dependent variables slopes at once where at least 1 dependent variable is significant. Thus, the SEE formula denominator adjusts of the quantity of variables in the model.

In fact n-k-1 is just a generalized representation that also applies for simple linear regression. If you have only 1 variable (k=1), then:

n-k-1 = n-1-1 = n-2

2 Likes
#3

Nicely explained, thank you.

#4

The whole pack of slopes.

Not dependent variables (there’s only one of those).

And not the whole pack of coefficients, because we specifically exclude the intercept.

1 Like
#5

That’s right, subtle but significant mistake (no pun intended, lol).

I just corrected it, thanks!

#6

My pleasure.