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 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). An analysis of traffic data collected over several weeks for different sections of Lane 2 of the 4-lane M25 highway yielded the following results:

ŷ = .46 - .0000764x + .00000000627x₂, R² = .73

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. A graph of the data for another lane of the M25 highway is shown below. Hypothesize a polynomial model that you believe will fit the data.

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0.8 0.6 0.4 0.2 1000 2000 3000 4000 5000 6000 7000 8000 9000 Total traffic flow (veh/h) Lane utilization factor