1. Construct a time-series graph of the sales data for MountainWear's line of ski apparel (see data in Week 4 Fall 2022 Case One Data.xls). Does there appear to be a seasonal pattern and/or trend in the sales data? Explain why you think there is or is not seasonality and/or trend in the data.

Period	Sales $	Inc	NRUR
Mar-09	153907	475	6.9
Jun-09	127732	534	6.5
Sep-09	93209	574	6.5
Dec-09	118203	622	6.4
Mar-10	145611	667	6.3
Jun-10	129976	702	6.2
Sep-10	95219	753	6.3
Dec-10	105210	796	6.5
Mar-11	164592	858	6.8
Jun-11	113201	870	7.9
Sep-11	105932	934	8.3
Dec-11	132182	1010	8
Mar-12	174200	1066	8
Jun-12	152918	1096	8
Sep-12	132290	1162	8
Dec-12	152419	1187	7.8
Mar-13	182764	1207	7.5
Jun-13	162921	1242	7.1
Sep-13	132961	1279	6.9
Dec-13	152971	1318	6.5
Mar-14	193271	1346	6.2
Jun-14	172312	1395	5.5
Sep-14	152281	1443	5.3
Dec-14	192314	1528	5
Mar-15	221938	1613	4.8
Jun-15	219223	1646	4.7
Sep-15	182342	1694	4.5
Dec-15	201921	1730	4.4
Mar-16	253901	1755	4.2
Jun-16	243976	1842	4
Sep-16	203338	1832	3.9
Dec-16	246723	1882	3.8
Mar-17	265532	1914	3.5
Jun-17	223008	2027	3.5
Sep-17	219976	1989	3.4
Dec-17	243338	2056	3.4
Mar-18	274456	2032	3.3
Jun-18	253382	2204	3.2
Sep-18	227764	2190	3.1
Dec-18	241138	2342	3.1

1. Develop a multiple regression model for sales as a function of different quarters, income (INC) and unemployment (NRUR).You can define as following: a dummy variable Q1 = 1 for each first quarter and Q1 = 0 otherwise; a dummy variable Q2 = 1 for each second quarter and Q2 = 0 otherwise; and a dummy variable Q3 = 1 for each third quarter and Q3 = 0 otherwise. Identify the regression equation for your model:

SALES = b0 + b1(Q1) + b2(Q2) + b3(Q3) + b4(INC) + b5(NRUR)

3. Do the signs on the coefficients make sense? Explain why.

4. Identify whether the five variable coefficients in your model are statistically different from zero, using a 95 percent confidence level and a one-tailed test.

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

6. Use your model's forecast of SALES (SF2) for the four quarters of 2019 to calculate the MAPE for the forecast period.

PERIOD	SALES ($)	SF2
2019Q1	322988
2019Q2	290875
2019Q3	256882
2019Q4	275400

7. Include a time-series plot of SALES (for 2009Q1 through 2018Q4) and SF2 (for 2019Q1 through 2019Q4) from your model created in part b to illustrate how SALES and SF2 compare. Compare your model's historical MAPE to the forecast MAPE you calculated in part f. Identify any differences.