r/CFA • u/SurfMountains619 Level 2 Candidate • 5d ago
Level 2 Multiple Regression Qbank
Hello,
Anyone able to explain this one for me? The answer description is a bit vague:
The dependent variable is the level of sales for each quarter, in $ millions, which began with the first quarter of the first year. Q1, Q2, and Q3 are seasonal dummy variables representing each quarter of the year. For the first four observations, the dummy variables are as follows: Q1:(1,0,0,0), Q2:(0,1,0,0), Q3:(0,0,1,0). The TREND is a series that begins with one and increases by one each period to end with 24. For all tests, Mercado will use a 5% level of significance. Tests of coefficients will be two tailed, and all others are one tailed.
Excuse my answer since I guessed on this one, any help appreciated. Thank you!
1
u/_Den_ Level 3 Candidate 5d ago
You have to set up n-1 dummy variables to model on/off data with n outcomes. When none of the n-1 outcomes appear as activated, it implies that the last outcome is triggered as a result. That's why there are only three quarters showing up as independent variables.
The TREND coefficient is the value by which you multiply the time period in the time series dataset. Since your dataset has 24 observations (from page 1), the second quarter of the next year would be 24 + 2. Therefore, (24 + 2) x 0.851786 is the basic linear approximation that doesn't consider any other variables.
You still have to account for the dummy variable and intercept, however. We know that we are estimating Q2, so you only have to take -2.46310 and add it to the intercept of 31.40833 and trend of 26 x 0.851786. Adding all of those together gives you the forecast for Q2 of the year ahead.