Average Cost

A consumer advocacy group was interested in the cost of hiring a removalist and how that related to the distance from source to destination. A random sample of removalist jobs was obtained, with the costs and distances summarised below.

(a) Obtain a 95% confidence interval for the slope coefficient in this regression .
(b) Use the above confidence interval to formally test if the true distance rate is $1.50 per kilometre.
(c) Briefly explain why the intercept term in this model can be interpreted as a “truck loading/unloading fee” for a removalist job.

(d) What is the estimated difference in average cost for moving 300 km versus moving 200 km?
(e) How much of the variability in removalist cost is left unexplained after accounting for the effect of distance?

(f) The 4 th observation has the values (x , y) = (584, 1125.6).
(i) What is the predicted cost for a distance of 584 km? (Round your answer to one dp.)
(ii) What is the observed residual for this point? (Round your answer to one dp)
(iii) Did this removalist job cost more or less than expected? Briefly explain why.
(g) Obtain an interval that has 95% probability of containing the cost for a removalist job for a distance of 584 km.
Use the values for S, n, x and S xx from the data summary or Minitab printout.
Please refer to the alternate t-table if necessary.
State your final answer in a meaningful sentence.