Carpet City wants to develop a means to forecast its carpet sales. The store manager believes that the store’s sales are directly related to the number of new housing starts in town. The manager has gathered data from county records on monthly house construction permits and from store records on monthly sales. These data are as follows:
Monthly Carpet ......Monthly Construction
Sales (1,000 yd.) ..... Permits
5 ............ 21
10 ............ 35
4 ............ 10
3 ............ 12
8 ............ 16
2 ............ 9
12 ............ 41
11 ............ 15
9 ............ 18
14 ............ 26
a. Develop a linear regression model for these data and forecast carpet sales if 30 construction permits for new homes are filed.
b. Determine the strength of the causal relationship between monthly sales and new home construction by using correlation.