Interstate 90 is the longest of the east-west U.S. interstate highways with its 3,112 miles stretching from Boston, MA at I-93 on the eastern end to Seattle WA at the Kingdome on the western end. It travels across 13 northern states; the number of miles and number of intersections in each of those states is listed below.

State No. of Inter Miles
WA 57 298
ID 15 73
MT 83 558
WY 23 207
SD 61 412
MN 52 275
WI 40 188
IL 19 103
IN 21 157
OH 40 244
PA 14 47
NY 48 391
MA 18 159

a. Construct a scatter diagram of the data.

b. Find the equation for the line of best fit using x= miles and y=intersections.

c. Using the equation found in part (b), estimate the average number of intersections per mile along I-90.

d. Find a 95% confidence interval for β1.

e. Explain the meaning of the interval found in part d.