Question

Q6

3 4 91 Q6. The following data show the quarterly sales of Amazing Graphics, Inc. for the years 1 through 3. Year Quarter Time Period (t) Sales (1000s) 1 2 4.1 6.0 6.5 5.8 5.2 6.8 7.4 3 6.0 510 5.6 13 3 117.5 13 128.8 From the above data, it could be concluded that both quarterly seasonal effects and linear trend in the sales pattern are present. A time series model was considered for this question and the estimated regression equation from Minitab is found as follows: Ý (Sales) = 4.52 1- 0.77 Quarter_2 + 0.83 Quarter_3+ 1.42 Quarter_4 + 0.2 t, where, y = Estimated or forecasted sales in periodt, t = time period (where t = 1 for Quarter 1 of year 1 and t = 12 for Quarter 4 of year 3), Quarter Slif time period t corresponds to the second quarter of the vear otherwise, Quarter 3 = { if time period t corresponds to the third quarter of the year otherwise, Quarter 4 = { u time period t corresponds to the fourth quarter of the year otherwise. a) (5pt) Please find the estimated sales for the first quarter for the next year (year 4). Please show your work. b) (5pt) Please find the estimated sales for the fourth quarter for the next year (year 4). Please show your work.

Answer 1

The regression equation is:

Sales = 4.52 - 0.77*Quarter 2 + 0.83*Quarter 3 + 1.42*Quarter 4 + 0.2*t

(a) Sales = 4.52 - 0.77*0 + 0.83*0 + 1.42*0 + 0.2*13

Sales = 7.12

(b) Sales = 4.52 - 0.77*0 + 0.83*0 + 1.42*1 + 0.2*16

Sales = 9.14

Please give me a thumbs-up if this helps you out. Thank you!