Chapter 14.8, Problem 14.46ACI

Graphing calculator sales. The next table presents the quarterly sales index for one brand of graphing calculator at a campus bookstore. The quarters are based on an academic year, so the first quarter represents fall; the second, winter; the third, spring; and the fourth, summer. Define the time variable as t = 1 for the first quarter of 2011, t = 2 for the second quarter of 2011, etc. Consider the following seasonal dummy variables:

     $\begin{array}{l}{Q}_1=\{\begin{array}{cc}1& \text{if}\text{Quarter}1\\ 0& \text{Otherwise}\end{array}\\ Q_2=\{\begin{array}{cc}1& \text{if}\text{Quarter}2\\ 0& \text{Otherwise}\end{array}\\ Q_3=\{\begin{array}{cc}1& \text{if}\text{Quarter}3\\ 0& \text{Otherwise}\end{array}\end{array}$

a. Write a regression model for E (Y_t) as a function of t₁ Q₁, Q₂, and Q₃.

b. Find and interpret the least squares estimates and evaluate the usefulness of the model.

c. Which of the assumptions about the random error component is in doubt when a regression model is fit to time series data?

d. Find the forecasts and the 95% prediction intervals for the 2016 quarterly sales. Interpret the result.