Question

Some of the toll highways in the United States are “functional”. In other words, the toll costs are a function of the mileage. Back around the year 2000, the Florida Turnpike from north of Orlando to outside West Palm Beach used a card system. The toll cost per user was then based on where the driver started and ended their journey. The table below represents the toll schedule at that time.

Mile Marker   236   193 152 142 133 116 109 99 93 88

Toll Cost 0 4.10 6.50 7.10 7.60 8.70 9.10 9.60 10.00 10.90

Is there a correlation between the miles driven and cost on the Florida Turnpike? If so, what would be the function, i.e. equation, that would relate those two variables? Can you determine an approximate cost per mile? Can you predict the hypothetical cost for driving 100 miles?

a) Construct a scatterplot. Based on the scatterplot, what would you say about the possible correlation between the two variables? Does there appear to be a strong pattern?

b) Calculate the correlation coefficient. Based on that result, can you conclude that there is a significant linear correlation between the two variables? Why or why not?

c) Construct the linear regression equation.

d) Can you use this equation to make a prediction? If not, explain why not. If so, then make the prediction as indicated.

Answer 1

(a)      

Yes, there appears to be a strong relationship between miles driven and cost

(b)      

R^2 = 0.9894, so the correlation coefficient is R = 0.9947. This confirms a high degree of correlation between miles driven and cost.

(c)      

It is Cost = 0.0682 * Miles driven + 0.5455   

(d)       

Cost per mile driven = $0.0682    

Yes, we can use the equation to make predictions.

Cost for driving 100 miles = 0.0682 * 100 + 0.5455 = $7.37