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 themselves, Badeaux sampled 20 recent shipments to determine what if any relationship exists between shipping costs and package weight. The data are contained in the file 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 an alpha value of 0.05, to determine whether the population correlation coefficient is significantly different from zero.
c. Determine the simple linear regression model for this data. Plot the simple linear regression model together with the data. Would a nonlinear model better fit the sample data?
d. Now develop a nonlinear model and plot the model against the data. Does the nonlinear model provide a better fit than the linear model developed in part c?