Barbara Lynch is the product manager for a line of skiwear produced by HeathCo Industries and privately branded for sale under several different names, including Northern Slopes and Jacque Monri. A new part of Ms. Lynch’s job is to provide a quarterly forecast of sales for the northern United States, a region composed of 27 states stretching from Maine to Washington. A 10-year sales history is shown:
a. Because Ms. Lynch has so many other job responsibilities, she has hired you to help with the forecasting effort. First, she would like you to prepare a time-series plot of the data and to write her a memo indicating what the plot appears to show and whether it seems likely that a simple linear trend would be useful in preparing forecasts.
b. In addition to plotting the data over time, you should estimate the least-squares trend line in the form:
c. Do your regression results indicate to you that there is a significant trend to the data? Explain why or why not.
d. On the basis of your results, prepare a forecast for the four quarters of 2008.
e. A year later, Barbara gives you a call and tells you that the actual sales for the four quarters of 2008 were: Q1 334,271, Q2 328,982, Q3 317,921, and Q4 350,118. How accurate was your model? What was the root-mean-squared error?