The Fresh Detergent Case

Enterprise Industries produces Fresh, a brand of liquid detergent. In order to more effectively manage its inventory, the company would like to better predict demand for Fresh. To develop a prediction model, the company has gathered data concerning demand for Fresh over the last $84$ sales periods. Each sales period is defined as one month. The variables are as follows:

Demand $=$ Y $=$ demand for a large size bottle of Fresh $($in $100,000)$

Price $=$ the price of Fresh as offered by Ent. Industries

AIP $=$ the average industry price

ADV $=$ Ent. Industries Advertising Expenditure $($in $$100,000)$ to Promote Fresh in the sales period.

DIFF $=$ AIP $-$ Price $=$ the "price difference" in the sales period

Period Price AIP ADV

Jan. $2023$ $$9\mathrm{.}20$ $$6\mathrm{.}95$ $$13\mathrm{.}5$

Feb. $2023$ $$9\mathrm{.}4$ $$6\mathrm{.}60$ $$14\mathrm{.}3$

Mar. $2023$ $$9\mathrm{.}10$ $$7\mathrm{.}05$ $$14\mathrm{.}2$