Modeling peak-hour roadway traffic. Traffic forecastersat

QUESTION:

Problem 157SE

Modeling peak-hour roadway traffic. Traffic forecastersat the Minnesota Department of Transportation(MDOT) use regression analysis to estimate weekdaypeak-hour traffic volumes on existing and proposedroadways. In particular, they model y, the peak-hourvolume (typically, the volume between 7:00 and 8:00a.m.), as a function of x1, the road’s total volume for theday. For one project involving the redesign of a section ofInterstate 494, the forecasters collected n = 72 observations of peak-hour traffic volume and 24-hour weekdaytraffic volume using electronic sensors that count vehicles. The data are saved in the file. (The first and last fiveobservations are listed in the table.)

a. Construct a scatterplot for the data, plotting peak-hour volume y against 24-hour volume x1. Note theisolated group of observations at the top of the scatterplot. Investigators discovered that all of these datapoints were collected at the intersection of Interstate35W and 46th Street. (These are observations 55–72in the table.) While all other locations in the samplewere three-lane highways, this location was uniquein that the highway widens to four lanes just north ofthe electronic sensor. Consequently, the forecastersdecided to include a dummy variable to account fora difference between the I-35W location and all otherlocations.

b. Knowing that peak-hour traffic volumes have a theoretical upper bound, the forecasters hypothesized thata second-order model should be used to explainthe variation in y. Propose a complete second-ordermodel for E(y) as a function of 24-hour volume x1 andthe dummy variable for location.

c. Using an available statistical software package, fitthe model of part b to the data. Interpret the results.Specifically, is the curvilinear relationship betweenpeak-hour volume and 24-hour volume different atthe two locations?

d. Conduct a residual analysis of the model, part b.Evaluate the assumptions of normality and constanterror variance and determine whether any outliers exist.