Question

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

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