Eve Henderson, the product manager for ski apparel at MountainWear, has the responsibility of providing forecasts to top management of sales by quarter one year ahead. She wants to see if unemployment and income in the regions in which the clothes are marketed might be correlated to sales. Data for these variables and for sales are in Week 4 Case One Data.xls

Construct a time-series graph of the sales data for MountainWears line of ski apparel (see data in Week 4 Spring 2023 Case Study 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.

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)

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

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.

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

Use your models 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

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 models historical MAPE to the forecast MAPE you calculated in part f. Identify any differences.