Question: An engineering firm is interested in investigating whether the variability in the cost of small projects (defined as projects under $10 million) can be accounted for, in part, by differences in the number of direct engineering consulting hours billed. A random sample of 24 small projects was randomly selected from small projects performed over the past two years. The number of engineering consulting hours billed for each project, along with the project's cost, was recorded. The results are shown below:
a. Develop a simple linear regression model to explain the variation in total project cost based on the number of billed consulting hours.
b. Construct and interpret a 95% confidence interval estimate for the regression slope coefficient.
c. Provide a 95% confidence interval for the average value of y when xp = 3,500.
d. Provide a 95% prediction interval for total project cost for a particular project with 3,500 billed consulting hours.