Graphing calculator sales. The table (next page) 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. Data for Exercise 14.46 Year First Quarter Second Quarter Third Quarter Fourth Quarter 2016 438 398 252 160 2017 464 429 376 216 2018 523 496 425 318 2019 593 576 456 398 2020 636 640 526 498 Define the time variable as t = 1 for the first quarter of 2016, t = 2 for the second quarter of 2016, etc. Consider the following seasonal dummy variables: Q1 = e 1 if Quarter 1 0 otherwise Q2 = e 1 if Quarter 2 0 otherwise Q3 = e 1 if Quarter 3 0 otherwise

a. Write a regression model for E1Yt2 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 2021 quarterly sales. Interpret the result