Retailer Best Buy sells computers, software, music, cameras, and other electronic goods. The data for this exercise are the quarterly gross profits of Best Buy, in millions of dollars from 1995 through 2011. The data table includes a column named Time that indicates the date of each quarter. Managers at Best Buy expect that there is a substantial increase in profits during the holiday season, but they would like to have a measure of the size of this effect. (These data also appear in Example 27.3; this exercise takes you through an alternative analysis of the same time series.)
Motivation
(a) Explain why it would be useful to have an estimate of the size of the seasonal effect on profits.
Method
(b) Examine the timeplot of gross profits at Best Buy. Does the magnitude of the seasonal effect appear to change over time?
(c) Examine the timeplot of the natural log of gross profits at Best Buy. Does this transformation apparently stabilize the size of the seasonal variation?
(d) Let D1, D2, and D3 be dummy variables that identify observations in the first, second, and third quarters. If we add these variables to a trend model that uses the gross profits as the response, will the model represent the effects of the seasonal pattern? What if we use the log of gross profits as the response?
Mechanics
(e) Fit a segmented trend with three dummy variables to the natural log of gross profits at Best Buy. To ft a segmented trend, use two variables for the time trend. The variable Time and a vari-able Segment defined to measure the number of years since 2002:

The multiple regression should have Time, Segment, and three dummy variables for the quarters. Interpret the coefficients of the dummy variables, Time, and Segment.
(f) Does the regression capture all of the dependence in the residuals, or does substantial residual autocorrelation remain?
(g) Revise the model to remedy problems or improve the ft and summarize the statistical significance of the model€™s estimates.
Message
(h) Show a ft of your model with the actual data, on the scale of the original data. (A plot such as this will show how well the model does or does not capture the seasonal variation.)
(i) What are the estimated seasonal effects? Interpret (without esoteric terminology) the seasonal component in this model.
(j) Would you recommend forecasting 2012 with this model, or would you limit its use to estimating the seasonal effects?

Transcribed Image Text:

if Time 2002 otherwise Segment- Time-2002