Comparing Convenience Store Sales: A Multiple Regression Analysis

To compare the sales of the two stations while including Volume in the analysis, we can use a multiple regression model with Sales as the response variable, Volume as the predictor variable, and Site as a categorical variable.

The regression model can be written as:

Sales = β0 + β1Volume + β2Site

Where β0 is the intercept, β1 is the coefficient for Volume, and β2 is the coefficient for Site.

The analysis of this model would provide us with estimates of β0, β1, and β2, as well as their standard errors, t-values, and p-values.

Based on this analysis, we can summarize the comparison of sales between the two stations as follows:

• If the coefficient for Volume (β1) is positive and statistically significant, it would indicate that there is a positive relationship between gas sales and convenience store sales. In other words, as the number of gallons of gas sold increases, so does the dollar sales of the convenience store.
• If the coefficient for Site (β2) is statistically significant, it would indicate that there is a difference between the two stations in terms of their average sales, after controlling for the effect of Volume.
• If the coefficient for Site (β2) is positive, it would indicate that the station with Site=1 (for example) has higher average sales than the station with Site=2, after controlling for the effect of Volume.
• The magnitude of the coefficients (β1 and β2) would provide us with an idea of the strength of the relationship between the predictor variables and the response variable, and the direction of the relationship (positive or negative).

Overall, the analysis would allow us to compare the sales of the two stations while taking into account the number of gallons of gas sold, and to identify any differences between the stations that cannot be attributed to differences in gas sales alone.