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:

a. Write a regression model for E(Yt) as a function of t, 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.

if Quarter 1 lo otherwise S1 if Quarter 2 Qi Q2= otherwise Si if Quarter 3 Q3 lo otherwise U . Second Quarter First Fourth Quarter Third Quarter Year Quarter 2011 2012 2013 2014 2015 438 464 523 593 636 398 429 496 576 640 252 376 425 456 160 216 318 398 498 526