If we want to show a regression model for quarterly sales, why would u ommit n-1 dumy variables??
I wrote an article on dummy variables that may be of some help here: http://financialexamhelp123.com/dummy-variables/
Great! Thanks, S2000 Magician
My pleasure.
Great magician
It might be worth adding that you would use n dummy variables in the case where you don’t fit an intercept. However, fitting an intercept gives nicer interpretations to the estimated coefficients (and the CFA exam doesn’t cover regressions through the origin (no intercept fit)). To see why we like fitting the intercept, recall a model with a qualitative variable that has 3 groups (A, B, and C).
E(y) = bo + b1x1 + b2x2
Coding scheme
x1 = 1 if A; 0 if other
x2= 1 if B; 0 if other
As magician pointed out in his article, you’ve now identified all the classes. We can verify this with a table.
Class x1 x2
A 1 0
B 0 1
C 0 0
If we plug in 0 for x1 and 0 for x2 (representing group C), we see that the equation simplifies to E(y) = b0. We can say that the intercept is equal to the mean of Y for group C.
If we plug in 1 for x1 and 0 for x2 (represents group A), we see that the equation simplifies to E(y) = b0 + b1. Referencing that b0= mean of Y for group C, we can see that b1 must equal the difference in means between group A and group C; (mean A) - (mean C) = b1.
If we plug in 0 for x1 and 1 for x2 (represents group B), we see that the equation simplifies to E(y) = b0 + b2. Doing the same as we previously did, we can see that b2 represents the difference in means between group B and group C; (mean B) - (mean C) = b2.
If we don’t include bo in our model, we need to include another coefficient, say, b3. The model would look like this:
E(y) = b1x1 + b2x2 + b3x3
Coding scheme
x1 = 1 if A; 0 if other
x2= 1 if B; 0 if other
x3= 1 if C; 0 if other
Class x1 x2 x3
A 1 0 0
B 0 1 0
C 0 0 1
We would lose the very nice interpretations of the coefficients (they would just represent means, rather than differences between means and we can’t make comparisons as easily as our first model with the intercept). You can use the same algebraic procedure to verify this case as well.
The technical point of all of this: if we fit an intercept, n-1 dummy variables will sufficiently identify each group (here, using n groups will cause perfect collinearity as mentioned in S2000’s article).
The practical point: if we fit the intercept, the coefficients allow us to more easily make comparisons between groups (and make more meaningful interpretations from the model).
Hopefully this example adds an additional perspective to reference with S2000’s article.
tickersu, you are an absolute SAVAGE!!
I prefer to point out that I’ve helped teach and privately tutor some of this material (non-CFA related), and I’ve also taken additional coursework in these areas. There’s a tremendous amount of information out there, but getting experience with it is key (and I enjoy learning it, which is always a plus).
I’m glad when someone finds it helpful!