Traffic forecasters at the Minnesota Department of Transportation MNOOT (MDOT) use regression analysis to estimate weekday peak-hour

Question:

Traffic forecasters at the Minnesota Department of Transportation MNOOT (MDOT) use regression analysis to estimate weekday peak-hour traffic volumes on existing and proposed roadways. In particular, they model y, the peak-hour volume (typically, the volume between 7:00 and 8:00 A.M.), as a function of x1, the road's total volume for the day. For one project involving the redesign of a section of Interstate 494, the forecasters collected n = 72 observations of peak-hour traffic volume and 24-hour weekday traffic volume using electronic sensors that count vehicles. The data are saved in the file. (The first and last five observations are listed in the table.)

a. Construct a scatter plot for the data, plotting peak hour volume y against 24-hour volume x1. Isolated group of observation at the top of the scatter plot. Investigators discovered that all of these data points were collected at the intersection of Interstate 35W and 46th Street. (These are observations 55-72 in the table.) While all other locations in the sample were three-lane highways, this location was unique in that the highway widens to four lanes just north of the electronic sensor. Consequently, the forecasters decided to include a dummy variable to account for a difference between the I-35W location and all other locations.
b. Knowing that peak-hour traffic volumes have a theoretical upper bound, the forecasters hypothesized that a second-order model should be used to explain the variation in y. Propose a complete second-order model for E(y) as a function of 24-hour volume .V] and the dummy variable for location.
c. Using an available statistical software package, fit the model of part b to the data. Interpret the results. Specifically, is the curvilinear relationship between peak-hour volume and 24-hour volume different at the two locations?
d. Conduct a residual analysis of the model, part b. Evaluate the assumptions of normality and constant error variance and determine whether any outliers exist.