An air conditioning company responds to calls concerning problems with air conditioners by sending a repair person to the home of the caller. There have been complaints about lengthy delays between the time the call is received and the time when the repair person reports to the home. The manager of the company would like to develop a method to estimate the length of time the customer will have to wait before receiving service. Data is obtained by taking a random sample of 15 calls for service for each backlog situation in which 0, 1, 2, 3, or 4 previous callers are waiting for service and then recording the number of minutes it took for the service person to reach the customer.

a. Plot the data, and assess whether fitting a regression model relating response time to backlog would be appropriate.
b. Fit a regression line relating the response time to the backlog of previous calls.
c. Fit a regression line relating the logarithm of response time to the backlog of previous calls.
d. Which of the two regression lines appears to be most appropriate?

Backlog 00 0 0 00 0 0 0 0 0 00 Resp time 2 3 5 6 8 10 13 15 16 20 24 27 32 3 42 Resp. time 12 23 51 36 48 112 123 163 172 120 252 237 212 245 246 Backlog 22 22 2 2 2 2 222 Resp, time 42 38 105 156 158 210 183 215 216 320 324 278 332 375 412 Backlog 333 33 33 3 3 3 33 3 3 Resp. time 62 73 58 126 208 270 313 45 416 320 324 427 432 435 442 Backlog 44 4 4 4 4 4 4 44 4 4 444 Resp. time 82 93 105 206 278 310 313 415 316 420 424 527 532 635 642