# Quant Forecasts

Manuel Mercado, CFA has performed the following two regressions on sales data for a given industry. He wants to forecast sales for each quarter of the upcoming year.

Model ONE
Regression Statistics
Multiple R 0.941828
R2 0.887039
Standard Error 2.543272
Observations 24

Durbin-Watson test statistic = 0.7856

ANOVA
df SS MS F Significance F
Regression 4 965.0619 241.2655 37.30006 9.49E−09
Residual 19 122.8964 6.4682
Total 23 1087.9583

Coefficients Standard Error t-Statistic
Intercept 31.40833 1.4866 21.12763
Q1 −3.77798 1.485952 −2.54246
Q2 −2.46310 1.476204 −1.66853
Q3 −0.14821 1.470324 −0.10080
TREND 0.851786 0.075335 11.20848

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.

Using Model ONE, what is the sales forecast for the second quarter of the next year?

A)

\$46.31 million.

B)

\$51.09 million.

C)

\$56.02 million.

Explanation

The estimate for the second quarter of the following year would be (in millions):

31.4083 + (−2.4631) + (24 + 2) × 0.851786 = 51.091666.

Why was each variable used in the equation? Specifically the (24+2) and the " *.085176) instead of +?

It included the intercept because you always include the intercept.

It included the Q2 coefficient because it’s for a second quarter; presumably the dummy variable Q2 is 1 for a second quarter and zero for a first, third, or fourth quarter.

It used (24 + 2) presumably because the data were gathered through the last quarter of the last year, so that 24 was the value of the TREND variable for the last quarter of the last year, and, therefore, (24 + 2) will be the value of the TREND variable for the second quarter of the next year. It multiplies 0.851786 by (24 + 2) because 0.851786 is the slope coefficient for the TREND variable; that’s how slope coefficients for variables work: you multiply them by the value of the corresponding variable.

The proper value for the TREND variable is a unclear from the vignette. While it’s easy to see what they intended it to be (and why) given the guideline answer, I see nothing in the vignette that would steer one unmistakably to that reasoning.

Where did you get this question?

This was a Kaplan question, hopefully actual questions won’t be too similar to this. Thanks for pointing out the variables though!

My pleasure.

Welcome to the world of third party question banks.

The questions on the real exam will be clear. Extremely clear.