A company that sells musical instruments has been in business for five years. During that time, sales of pianos increased from 12 units in the first year to 77 units in the most recent year. The firm's owner wants to develop a forecast of piano sales for the coming year. The quarterly sales data follow. Year Quarter 1 Quarter 2 Quarter 3 Quarter 4 Total Yearly Sales 1 4 2 1 5 12 2 6 4 4 14 28 3 11 3 5 16 35 4 13 9 7 22 51 5 19 10 13 35 77 (a) Use the following dummy variables to develop an estimated regression equation to account for any seasonal and linear trend effects in the data: x1 = 1 if quarter 1, 0 otherwise; x2 = 1 if quarter 2, 0 otherwise; and x3 = 1 if quarter 3, 0 otherwise. (Let t = 1 denote the time series value in quarter 1 of year 1; t = 2 denote the time series value in quarter 2 of year 1; and t = 20 denote the time series value in quarter 4 of year 5. Round your numerical values to two decimal places.) t = __________________________ (b)Compute the quarterly forecasts for next year. (Round your answers to the nearest integer.) forecast for quarter 1 :_____________ pianos forecast for quarter 2 :_____________ pianos forecast for quarter 3 :_____________ pianos forecast for quarter 4 :_____________ pianos
