Retail Sales for a Home Improvement Store in Quarters 1-4

question 1

Essay

Retail sales for a home improvement store in quarters 1-4 over a five-year period are shown (in millions of dollars) in the table below. $$\begin{array} { c | c | c | c | c } \hline { \text { Quarter } } \\\hline \text { Year } & 1 & 2 & 3 & 4 \\\hline 1 & 1.2 & 1.4 & 1.5 & 1.1 \\\hline 2 & 1.3 & 1.6 & 1.5 & 1.2 \\\hline 3 & 1.4 & 1.8 & 1.8 & 1.6 \\\hline 4 & 1.4 & 1.7 & 1.9 & 1.6 \\\hline 5 & 1.6 & 2.0 & 2.1 & 1.9 \\\hline\end{array}$$ a. Write a regression model that contains trend and seasonal components to describe the sales data.
b. Use least squares regression to fit the model.
c. Use the regression model to forecast the quarterly sales during Year 6. Give 95% prediction intervals for the forecasts.

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Definitions:

Decision Trees

A graphical representation of possible solutions to a decision based on various conditions, often used in strategic planning and decision making.

Expected Monetary Values

A statistical concept used in decision making under uncertainty, calculating the weighted average of all possible outcomes, considering their probabilities and monetary impacts.

Sequence of Decisions

A series of choices made over time, where each choice might be influenced by past decisions, expected to lead to a desired outcome.

Decision Tree

is a graphical tool used in decision-making, which represents different choices and their possible outcomes, including chance event outcomes, resource costs, and utility.