Chapter 11, Problem 11.116ACI

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 number of square feet of building shell. The table below lists the energy consumption in British thermal units (a BTU is the amount of heat required to raise 1 pound of water 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.

1. a. Find the least squares estimates of the intercept β₀ and the slope β_1.
2. b. Investigate the usefulness of the model you developed in part a. Is yearly energy consumption posi1ively linearly related to 1he shell area of the building? Test using α = .10.
3. c. Find the observed significance level of the test of part b. Interpret its value.
4. d. Find the coefficient of determination r² and interpret its value.
5. e. A company wishes 1o build a new warehouse that will con1ain 8,000 square feel of shell area. Find the predicted value of energy consumption and associated 95% prediction interval. Comment on the usefulness of this interval.
6. f. The application of the model you developed in part a to the warehouse problem of part e is appropriate only if certain assumptions can be made about the new warehouse. What are these assumptions?

BTU/Year (thousands)	Shell Area (square feet)
3,870,000	30,001
1,371,000	13,530
2,422,000	26,060
672 200	6,355
233,100	4,576
218,900	24,680
354 000	2,621
3,135,000	23,350
1,470,000	18,770
1,408,000	12.220
2.201,000	25,490
2,680,000	23,680
337,500	5,650
567,500	8,001
555,300	6,147
239,400	2,660
2,629,000	19,240
1,102,000	10,700
423,500	9,125
423,500	6,510
1,691,000	13,530
1,870,000	18,860