A large school system is planning a renovation of a number of schools, all built prior to 1940. While making estimates for the budget, it was necessary to forecast the likely cost of renovation based on accumulated experience in past similar jobs. The cost data on old jobs has been updated to current conditions using the Engineering News-Record index. Data are as follows:
(a) Assume that the expected cost of renovation is linear with the number of rooms. Estimate the regression line and show the relationship on a plot with the data. Estimate σ and plot lines 1 standard deviation each side of the mean value function. Estimate and plot 1-standard-deviation confidence limits on the mean value.
(b) If the first job to be studied contains 32 rooms, use the results of (a) to make statements about its
expected cost and the standard deviation of this figure. Note that a single forecast of the random variable, i.e., cost, is desired.
(c) Data on the number of stories are given. Repeat the analysis using number of stories to predict the cost. The job contains three stories. Which independent variable-number of rooms or number of stories- gives a "more reliable" prediction of cost?