The I-85 Carpet Outlet 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 of monthly house construction permits and from store records on monthly sales. These data are as follows:
Monthly Carpet Sales Monthly Construction
(1000s yd) Permits
5 ...........17
12 .........30
6 ...........12
5 ...........14
8 ...........18
4 ...........10
14 .........38
9 ...........20
9 ...........16
16 .........31
a. Develop a linear regression model for this data and forecast carpet sale if 25 construction permits for new homes are filed.
b. Determine the strength of the causal relationship between monthly sales and new home construction using correlation.