## Description

For all of the problems in this assignment, please submit the relevant outputs and your

R codes (if you used R). In addition, unless otherwise indicated, assume that α = 0.05.

Consider the regional express delivery company problem that you studied in HW5. To

remind you, we had defined: the cost of shipment, y (in dollars), and the variables that

control the shipping charge: package weight, x1 (in pounds), and distance shipped, x2

(in miles).

We used the data set HW5ShipmentData.csv. Answer Questions 1–4.

1. Solve the complete model: y = β0+β1×1+β2×2+β3x

2

1+β4x1x2+. Which predictors

are significant? You can perform the hypothesis tests by considering p-values only.

2. What is the effect of a one-mile increase in distance on the cost of shipment when

the weight is held constant at 5 pounds?

3. Check the random error assumptions for the complete model, in particular, check

whether E() = 0 or not, the normality, and the identical distribution (variance)

assumptions. What is your conclusion?

4. You checked random error assumptions for the reduced model, y = β0+β1×1+β2×2+

, in HW5. What would you conclude when you compare the error assumptions

of the reduced model and the error assumptions of the complete model? You can

refer to the HW5 solutions that we posted.

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5. After running a linear regression model, y ∼ x1 + x2 + x3 with a sample of 24

observations, the model adequacy was investigated, and the Durbin–Watson test

statistic was found to be 0.829. Check the independence assumption of the errors

by applying the Durbin–Watson test (test for both positive correlation and negative

correlation). Assume level α = 0.10.

Consider the hospital stay problem that you studied in HW4 by using

homework04Hospital.csv data. To remind you, we had defined: y = monthly labor

hours required; x1 = monthly X-ray exposures; x2 = monthly occupied bed days; and

x3 = average length of patients’ stays (in days). Answer Questions 6–8.

6. Do you identify potentially unusual observations? Answer by producing and listing

standardized residual and Cook’s distance measure for each observation.

2

7. Consider the solution you obtained for this problem (you can refer to the HW4

solutions that we posted). Can you identify counterintuitive results in the solutions

by considering the estimated coefficients and their standard errors? Why is that?

8. Produce the variance inflation factor (VIF) for each predicting variable and comment on the results.