Highway traffic volume. A study in Transportation Engineering (Vol. 2, 2020) assessed the impact of snowfall and cold temperature on classified vehicle volume variation using five years of Weigh-in-Motion (WIM) data recorded at a highway near Leduc in Alberta, Canada. The total vehicle volume was recorded as well as the snowfall categories (SC1 (SC1 = 0 cm), SC2 (0 6 SC2 6 = 3 cm) and SC3 (SC3 7 3 cm)).

a. Consider a model for the mean total vehicle volume, E(y), that allows for different means depending on the snowfall categories. Create the appropriate number of dummy variables for snowfall categories. (Use SC1 as the base level.)

b. Write the equation of the model, part

a, incorporating the dummy variables.

c. In terms of the b’s in the model, what is the mean total vehicle volume contributed by SC2?

d. In terms of the b’s in the model, what is the difference between the total vehicle volume contributed by SC2 and contributed by SC1?

e. One theory posits that SC3 will achieve the lowest mean total vehicle volume, but that there will be no difference between the mean total vehicle volume contributed by SC2 and SC1. If this theory is true, give the expected signs of the b’s in the model.

f. The researcher found the b estimate for the dummy variable for SC2 to be negative but not significantly different from 0 (p-value 6 .100). The b estimate for the dummy variable for SC3 was also negative but significantly different from 0 (p-value 7 .000). Do these results support the information provided in part e? Applying the Concepts—Intermediate