11.26 Architectural firm billings. A summary of firms engaged in commercial architecture in the Indianapolis, Indiana, area provides firm characteristics, including total annual billing in the current year, total annual billing in the previous year, the number of architects, the number of engineers, and the number of staff employed in the firm.6 Consider developing a model to predict current total billing using the other four variables.

  1. (a) Using numerical and graphical summaries, describe the distribution of current and past year total billing and the number of architects, engineers, and staff.

  2. (b) For each of the 10 pairs of variables, use graphical and numerical summaries to describe the relationship.

  3. (c) Carry out a multiple regression. Report the fitted regression equation and the value of the regression standard error s.

  4. (d) Analyze the residuals from the multiple regression. Are there any concerns?

  5. (e) A firm did not report its current total billing but had $1 million in billing last year and employs three architects, one engineer, and 17 staff members. What is the predicted total billing for this firm?

  6. (f) This analysis utilized the data from all commercial firms in the Indianapolis area that responded to the survey. Provide justification for the use of inference under this setting.