11.118 Energy efficiency of buildings. Firms conscious of the energy efficiency of proposed new structures are interested in the relation between yearly energy consumption and the num- BTU ber of square feet of building shel. The table (next page) lists the energy consumption in British thermal units (a BTU is the amount of heat required to raise 1 pound of wa- ter 1°F) for 22 buildings that were all subjected to the same climatic conditions Consider a straight-line model relating BTU consumption, y, to building shell area, x. a. Find the least squares estimates of the intercept B and the slope B1. b. Investigate the usefulness of the model you developed in part a. Is yearly energy consumption positively lin- early related to the shell area of the building? Test using a -.10. c. Find the observed significance level of the test of part b. Interpret its value. d. Find the coefficient of determination r² and interpret its value. e. A company wishes to build a new warchouse that will contain 8,000 square feet of shell area. Find the predicted value of energy consumption and associated 95% predic- tion interval. Comment on the usefulness of this interval. f. The application of the model you developed in part a to the warehouse problem of part e is appropri- ate only if certain assumptions can be made about the new warehouse. What are these assumptions?