In Chapter 4, you worked with data on sales for a line of skiwear that is produced by HeathCo Industries. Barbara Lynch, product manager for the skiwear, has the responsibility of providing forecasts to top management of sales by quarter one year ahead. One of Ms. Lynch’s colleagues, Dick Staples, suggested that unemployment and income in the regions in which the clothes are marketed might be causally connected to sales. If you worked the exercises in Chapter 4, you have developed three bivariate regression models of sales as a function of time (TIME), unemployment (NRUR), and income (INC). Data for these variables and for sales are as follows:

Period	Sales	Inc	NRUR		Period	Sales	Inc	NRUR
Mar-07	72,962	218	8.4		Mar-12	174,200	1,066	8
Jun-07	81,921	237	8.2		Jun-12	182,556	1,096	8
Sep-07	97,729	263	8.4		Sep-12	198,990	1,162	8
Dec-07	142,161	293	8.4		Dec-12	243,700	1,187	8.9
Mar-08	145,592	318	8.1		Mar-13	253,142	1,207	9.6
Jun-08	117,129	359	7.7		Jun-13	218,755	1,242	10.2
Sep-08	114,159	404	7.5		Sep-13	225,422	1,279	10.7
Dec-08	151,402	436	7.2		Dec-13	253,653	1,318	11.5
Mar-09	153,907	475	6.9		Mar-14	257,156	1,346	11.2
Jun-09	100,144	534	6.5		Jun-14	202,568	1,395	11
Sep-09	123,242	574	6.5		Sep-14	224,482	1,443	10.1
Dec-09	128,497	622	6.4		Dec-14	229,879	1,528	9.2
Mar-10	176,076	667	6.3		Mar-15	289,321	1,613	8.5
Jun-10	180,440	702	6.2		Jun-15	266,095	1,646	8
Sep-10	162,665	753	6.3		Sep-15	262,938	1,694	8
Dec-10	220,818	796	6.5		Dec-15	322,052	1,730	7.9
Mar-11	202,415	858	6.8		Mar-16	313,769	1,755	7.9
Jun-11	211,780	870	7.9		Jun-16	315,011	1,842	7.9
Sep-11	163,710	934	8.3		Sep-16	264,939	1,832	7.8
Dec-11	200,135	1,010	8		Dec-16	301,479	1,882	7.6

a. Now you can expand your analysis to see whether a multiple-regression model would work well. Estimate the following model:

b. Test to see whether the coefficients you have estimated are statistically different from zero, using a 95 percent confidence level and a one-tailed test.

c. What percentage of the variation in sales is explained by this model?

d. Use this model to make a sales forecast (SF1) for 2017Q1 through 2017Q4, given the previously forecast values for unemployment (NRURF) and income (INCF) as follows:

Period	NRURF (%)	INC ($ Billions)	SF1
Mar-17	7.6	1,928
Jun-17	7.7	1,972
Sep-17	7.5	2,017
Dec-17	7.4	2,062

e. Actual sales for 2017 were: Q1 = 334,271; Q2 = 328,982; Q3 = 317,921; Q4 = 350,118. On the basis of this information, how well would you say the model worked? The graph below shows that the model follows the general upward trend in the sales data but fails to take into account the seasoality.

What is the mean absolute percentage error (MAPE)?

f. Plot the actual data for 2017Q1 through 2017Q4 along with the values predicted for each quarter based on this model.