Convenience Shopping For each of two service stations operated by a national petroleum refiner, we have the daily sales in the convenience store located at the service station. The data for each day give the sales at the store (in dollars) and the number of gallons of gas sold. For Site 1, the data cover 283 days; for Site 2, the data cover 285 days.
(a) Would it be appropriate for management of this chain of service stations to rate the operators of the convenience stores based on a two-sample comparison of the sales of the convenience stores during these two periods, or would such a comparison be confounded by different levels of traffic (as measured by the volume of gas sold)?
(b) Perform the two-sample
-test to compare the sales of the two service stations. Summarize this analysis, assuming that there are no lurking variables.
(c) Compare the sales at the two sites using an analysis of covariance. Summarize the comparison of sales based on this analysis. Use a dummy variable coded as 1 for Site 1 and 0 otherwise. (Assume for the moment that the model meets the conditions for the MRM.)
(d) Compare the results from parts (b) and (c). Do they agree? Explain why they agree or differ. You should take into account the precision of the estimates and your answer to part (a).
(e) Does the estimated multiple regression used in the analysis of covariance meet the similar variances condition?
(f) Suppose an analyst fit the simple regression of sales in the convenience store on gas sales, ignoring the distinction between the two sites. Does this pooling of all the data together affect the relationship between sales in the store and gas sales?