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The following seasonal regression was fitted with quarterly seasonal binaries beginning in the first quarter (Qtr4...

The following seasonal regression was fitted with quarterly seasonal binaries beginning in the first quarter (Qtr4 is omitted to avoid multicollinearity). Make a prediction for y_t in period (a) t=21; (b) t=8; (c) t=15 yt=213+11t-9 Qtr1+12 Qtr-15 Qtr3

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Answer #1

yt=213+11t-9 Qtr1+12 Qtr2 -15 Qtr3

Using Qtr vlues as 0/1 for the corresponding quarters (Q1=1 for first quarter sales, when Q2/Q3/Q4 will be 0).

a) y21 = 213

The table below shows the calculations of sales per quarter of the year, coefficient of Q4 always being 0 as per the model:

t Qtr1 Qtr2 Qtr3 Qtr4 yt
21 1 0 0 0 435
21 0 1 0 0 456
21 0 0 1 0 429
21 0 0 0 0 444

where yt is calculated using the regression equation above, plugging in the different values for Year/Qtr1/Qtr2/Qtr3/Qtr4 as per the year and quarter number.

b) Similarly, for t=8:

t Qtr1 Qtr2 Qtr3 Qtr4 yt
8 1 0 0 0 292
8 0 1 0 0 313
8 0 0 1 0 286
8 0 0 0 0 301

c) Similarly for t=15:

t Qtr1 Qtr2 Qtr3 Qtr4 yt
15 1 0 0 0 369
15 0 1 0 0 390
15 0 0 1 0 363
15 0 0 0 0 378
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