Refer to the Journal of Transportation Engineering (May 2013) study of the lane utilization of a highway, Exercise 12.13. Recall that the dependent variable in the analysis was lane utilization y, measured as the percentage of vehicles in the lane. The researchers used two independent variables used to model y:x₁ total traffic flow (total number of vehicles per hour) and x₂ = HGV flow (number of heavy-goods vehicles per hour). An analysis of traffic data collected over several weeks for different sections of Lane 1 of the M42 highway yielded the following results:
ŷ = .976 - .0000285x₁ - .002004x₂, R² = .70

a. Interpret the value of R² for this model.

b. Assuming n = 2,000 observations, conduct a test of overall model utility. Use

c. Use the β estimates to draw a sketch of the estimated relationship between lane utilization and total traffic flow.

d. Use the β estimates to draw a sketch of the estimated relationship between lane utilization and HGV flow.

Data from Exercise 12.13

The lane utilization of a highway is measured by how the traffic flow in one direction is distributed among the available lanes. A lane utilization model for highways in the United Kingdom was developed in the Journal of Transportation Engineering (May 2013). The TRAINWAIT dependent variable in the analysis was lane utilization y, measured as the percentage of vehicles in the lane. Previous studies used a quadratic model for lane utilization as a function of x = total traffic flow (total number of vehicles per hour)