18. The following summary statistics were obtained from a study that used regression analysis to investigate the relationship between pavement deflection and surface temperature of the pavement at various locations on a state highway.

Here x
temperature (°F) and y
deflection adjustment factor (y  0):

n
15
xi
1425
yi
10.68

x2 i
139,037.25
xi yi
987.645

y2 i
7.8518

(Many more than 15 observations were made in the study;

the reference is “Flexible Pavement Evaluation and Rehabilitation,” Transportation Eng. J., 1977: 75–85.)

a. Compute
ˆ1,
ˆ0, and the equation of the estimated regression line. Graph the estimated line.

b. What is the estimate of expected change in the deflection adjustment factor when temperature is increased by 1°F?

c. Suppose temperature were measured in °C rather than in

°F. What would be the estimated regression line? Answer part

(b) for an increase of 1°C. [Hint: °F
(9/5)°C 32;

now substitute for the “old x” in terms of the “new x.”]

d. If a 200°F surface temperature were within the realm of possibility, would you use the estimated line of part (a)

to predict deflection factor for this temperature? Why or why not?