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,

semifragile, and durable. Costs for several 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 semifragile

cargo

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a) Provide the appropriate regression equation for this problem which requires the use of dummy

variables. Note that the number of dummy variables needed is always the number of categories

(in this case 3) minus 1. (5 points)

b) Interpret each of the coefficients including the intercept (6 points; 2 points for each coefficient).

Hint: these coefficients can be interpreted as means (averages).

c) Which cargo is most costly? (2 points)

Which cargo is least costly? (2 points)

d) Assess the fit of the data. Hint: look at the R-square and interpret it as a percentage of the

variation explained by the model. (2 points). How could you improve the fit of the model (1

point).

e) Predict the cost of a semifragile cargo. (4 points)