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.
Multiple R 0.941828
Adjusted R2 0.863258
Standard Error 2.543272
Durbin-Watson test statistic = 0.7856
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
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?
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 +?