Firms planning to build new plants or make additions to existing facilities have become very conscious of the energy efficiency of proposed new structures and are interested in the relation between yearly energy consumption and the number of square feet of building shell. The table on the next page 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.
a. Find the least squares estimates of the intercept β0, and the slope β1.
b. Investigate the usefulness of the model you developed in part a. Is yearly energy consumption positively linearly related to the shell area of the building? Test using α = .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 warehouse that will contain 8,000 square feet of shell area. Find the predicted value of energy consumption and associated 95% prediction 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 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