Question

Since the time series has trend and seasonal pattern, to forecast the quarterly sales of the textbook, the following regression equation was found: stack y t with overparenthesis on top equals 2120 space minus 620 space Q t r 1 space minus space 1320 space Q t r 2 space plus space 290 space Q t r 3 space plus space 24 space t , where Q t r 1 , Q t r 2and Q t r 3 are dummy variables corresponding to Quarters 1, 2 and 3, and t = time period. The sales in Quarter 4 of the next year are predicted to be

Answer 1

Y(2)= 2120+ 48= 2168

Explanation:

The given equation is

Yt= 2120 - 620 Qtr 1 t -1320 Qtr 2 t + 290 Q tr3 t + 24 t

Taking the quarter 1 , 2 and 3 to be dummy variable the predicted sales for the 4th qtr are

Yt= 2120 - 620 Qtr 1(0) -1320 Qtr 2(0) + 290 Q tr3 (0) + 24 (1)

Y(1)= 2120 + 24 = 2144 ( for year =1)

Y(2)= 2120+ 48= 2168 ( for year =2)

Y(3)= 2120 + 72= 2192 ( for year =3)

where t is the number of years.

So for the next year the fourth quarter sales are predicted to be 2168.