### Problem on using multiple linear regression for forecasting

The following problem shows students how using indicator variables can
help model seasonal demand patterns and improve forecasting ability.

The data in the following data files (in SPSS, text, and
Excel format, respectively): bikesales. sav , bikesales.txt, bikesales.xls, contains quarterly sales of
a particular mountain bike for the previous four years at a bicycle
shop in Switzerland. The bike sales exhibit a positive trend but with
strong seasonal patterns, with bike sales being higher in the spring
and summer quarters than in the winter and fall quarters. The shop
owner wishes to forecast sales for next year to ensure that there is
sufficient inventory to meet demand.

- How can you display the data graphically to demonstrate the
seasonal pattern in sales?
- If you fit a simple linear regression model with "sales" as the
response (dependent) variable and "period" as the predictor
(independent) variable, how can you tell this model fits poorly?
- Fit a multiple linear regression model that incorporates the
seasonality. (
*Hint:* consider dummy indicator variables.)
- How many bikes should be stocked each quarter of the coming year
to be reasonably sure of meeting demand? (
*Hint:* consider the
relative costs of over-estimating and under-estimating demand.)

*Last updated: April, 2012*

*© 2012, Iain Pardoe*