Chapter 5, Problem 9E

Savings-Mart (a chain of discount department stores) sells patio and lawn furniture. Sales are seasonal, with higher sales during the spring and summer quarters and lower sales during the fall and winter quarters. The company developed the following quarterly sales forecasting model: ${\hat{Y}}_{}$

t = 8.25 + 0.125 t − 2.75 D 1 t + 3.50 D 3 t

where ${\hat{Y}}_{}$

t = predicted sales  ( $ million )  in quarter  t $\text{8}.\text{25}=\text{quarterly sales }\left(\$\text{million}\right)\text{ when t}=0$ $\begin{array}{l}t=\text{time period }\left(\text{quarter}\right)\text{ where the fourth quarter of 2}00\text{2}=0,\\ \text{first quarter of 2}00\text{3}=\text{1},\text{second quarter of 2}00\text{3}=\text{2},\mathrm{...}\end{array}$ $\begin{array}{l}{D}_{1t}=\{\begin{array}{c}\text{1 for first-quarter observations}\\ 0\text{ otherwise}\end{array}\\ D_{2t}=\{\begin{array}{c}\text{1 for second-quarter observations}\\ 0\text{ otherwise}\end{array}\\ D_{3t}=\{\begin{array}{c}\text{1 for third-quarter observations}\\ 0\text{ otherwise}\end{array}\end{array}$

Forecast Savings-Marts sales of patio and lawn furniture for each quarter of 2010.