A regional express delivery service company conducted a study to investigate the relationship between the cost of shipping a package, the package weight, and the distance shipped.

Twenty packages were randomly selected from among the large number received for shipment and an analysis of the shipping cost was conducted for each package.

1. Estimate a simple linear regression model involving shipping cost and package weight

2. Interpret the slope coefficient as well as the R²

3. Add another explanatory variable – distance shipped – to the model. Estimate and interpret this expanded model

4. How does the R² for this model compare to that of the simple regression? Explain any difference between the two R² values

5. Suppose that one of the managers of this company is trying to decide whether to add an interaction term involving the weight and the distance shipped. Why would the manager want to add such a term?

6. Estimate and interpret the revised model

7. Compare the R² as well.