ISyE 6414 Regression Analysis Homework 6 solution

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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.
*****

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.