ISyE 6414 Regression Analysis Homework 5 solution


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A regional express delivery company conducted a study to investigate the relationship
between 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). By using
the attached comma-deliminated data file HW5ShipmentData.csv and α = 0.05, answer
Questions 1–7. Submit all relevant outputs and your R codes (if you used R).

1. Produce the matrix plot, and interpret the possible relations among all variables.
2. Solve the first-order model, i.e., y = β0+β1×1+β2×2+. Also, produce the ANOVA
table. Is the model useful (significant) as a whole, i.e., apply an F-test. Are the
predictors significant? You can perform the hypothesis tests by considering p-values

3. Calculate R2 by using appropriate ANOVA table quantities. Justify your result by
referring to the R2 quantity found in your output.
4. Check the random error assumptions for the first-order model, in particular, check
whether E() = 0 or not, the normality, and the identical distribution (variance)
assumptions. What are your conclusions?

5. Find a 95% confidence interval for the mean response when the predictors Weight
= 6 and Distance = 150.
6. Find a 95% prediction interval for a single future observation when the predictors
Weight = 6 and Distance = 150.

7. Now consider the following full second-order model for the same problem, i.e.,
y = β0 + β1×1 + β2×2 + β3x
1 + β4x
2 + β5x1x2 + . Is this full model better than the
reduced model in Question 2? Answer by performing the partial F-test.

A consulting firm markets a computerized system for monitoring road construction bids to
various state departments of transportation. The firm wants to compare the mean annual
maintenance costs accrued by the system users in three different states: Kansas, Kentucky, and Texas.

Answer Questions 8–10 by using the attached HW5StateCostData.csv
and α = 0.05.
8. Solve the linear regression model to study whether the qualitative variable “State”
with three categories is significant or not? What is your base level?

9. Write down the model and the dummy variables in the model. What does β0
correspond to in terms of expected costs?

10. By using the hypothesis in Question 8, discuss whether the expected costs in each
state are identical or not.