Suppose that a regional express delivery service company wants to estimate the cost of shipping a package (Y) as a function of cargo type, where cargo type includes the following possibilities: fragile, semi fragile, and durable. Costs for 15 randomly chosen packages of approximately the same weight and same distance shipped, but of different cargo types, are provided in the file P10_28.xlsx.
a. Estimate an appropriate multiple regression equation to predict the cost of shipping a given package.
b. Interpret the estimated regression coefficients. You should find that the estimated intercept and slope of the equation are sample means. Which sample means are they?
c. According to the estimated regression equation, which cargo type is the most costly to ship? Which cargo type is the least costly to ship?
d. How well does the estimated equation fit the given sample data? How do you think the model’s goodness of fit could be improved?
e. Given the estimated regression equation, predict the cost of shipping a package with semi fragile cargo.