During the installation of a large computer system, it is useful to know how long specific tasks will take, particularly programming changes. A great deal of effort is spent estimating the amount of time such tasks will take and learning how to effectively use such estimations. Having an accurate idea of the time required for these tasks is crucial for the effective planning and timely completion of the installation. The data set in DS I 2.2.5 relates one expert's time estimates for programming changes to the actual time the tasks took.
(a) Fit a linear regression model with actual time as the dependent variable and estimated time as the explanatory variable.
(b) What is the predicted increase in the actual time when the estimated time increases by 1 hour? Is the expert underestimating or overestimating the times? If the estimated time is 7 hours, what is the predicted value of the actual time the task will take?
(c) What does your model tell you about the time it will take to perform a task that is estimated at 15 hours?
(d) What is the estimate of the error variance?
(This problem is continued in Problems 12.3.7, 12.4.7, 12.5.6, 12.6.9, 12.7.5, and 12.9.7.)