32.              South Shore Construction builds permanent docks and seawalls along the southern shore of Long Island, New York. Although the firm has been in business only five years, revenue has increased from $308,000 in the first year of operation to $1,084,000 in the most recent year. The following data show the quarterly sales revenue in thousands of dollars:

 

 

Quarter 1	Year 1 20	Year 2 37	Year 3 75	Year 4 92	Year 5 176
2	100	136	155	202	282
3	175	245	326	384	445
4	13	26	48	82	181

 

a.             Construct a time series plot. What type of pattern exists in the data?

b.             Use an Excel or LINGO model with dummy variables as follows to develop an equa- tion to account for seasonal effects in the data. Qtr1 = 1 if Quarter 1, 0 otherwise; Qtr2 = 1 if Quarter 2, 0 otherwise; Qtr3 = 1 if Quarter 3, 0 otherwise.

c.              Let Period = 1 to refer to the observation in quarter 1 of year 1; Period = 2 to refer to the observation in quarter 2 of year 1; . . . and Period = 20 refer to the observation in quarter 4 of year 5. Using the dummy variables defined in part (b) and Period, develop an equation to account for seasonal effects and any linear trend in the time series. Based upon the seasonal effects in the data and linear trend, compute estimates of quarterly sales for year 6.

 

 

TABLE 15.18 FOOD AND BEVERAGE SALES FOR THE VINTAGE RESTAURANT ($1000s)