Question: Projecting residential electricity customers. To satisfy the Public Service Commission's energy conservation requirements, an electric utility company must develop a reliable model for projecting the number of residential electricity customers in its service area. The first step is to study the effect of changing population on the number of electricity customers. The information shown in the next table was obtained for the service area from 2000 to 2009. Since a service area with 0 population obviously would have 0 residential electricity customers, one could argue that regression through the origin is appropriate.
(a) Fit the model y = β1x + ε to the data.
(b) Is there evidence that x contributes information for the prediction of y? Test using α = .01.
(c) Now fit the more general model y = β0 + β1x + ε to the data. Is there evidence (at α = .01) that x contributes information for the prediction of y?
(d) Which model would you recommend?
