Badeaux Brothers Louisiana Treats ships packages of Louisiana coffee, cakes, and Cajun spices to individual customers around the United States. The cost to ship these products depends primarily on the weight of the package being shipped. Badeaux charges the customers for shipping and then ships the product itself. As a part of a study of whether it is economically feasible to continue to ship products itself, Badeaux sampled 20 recent shipments to determine what, if any, relationship exists between shipping costs and package weight. These data are in the file called Badeaux.
a. Develop a scatter plot of the data with the dependent variable, cost, on the vertical axis and the independent variable, weight, on the horizontal axis. Does there appear to be a relationship between the two variables? Is the relationship linear?
b. Compute the sample correlation coefficient between the two variables. Conduct a test, using a significance level of 0.05, to determine whether the population correlation coefficient is significantly different from zero.
c. Badeaux Brothers has been using a simple linear regression equation to predict the cost of shipping various items. Would you recommend it use a second-order polynomial model instead? Is the second-order polynomial model a significant improvement on the simple linear regression equation?
d. Badeaux Brothers has made a decision to stop shipping products if the shipping charges exceed $100. The company has asked you to determine the maximum weight for future shipments. Do this for both the first- and second-order models you have developed.