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.

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?

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BTU/Year (thousands) Shell Area (square feet) 30,001 13,530 26,060 6,355 4,576 24,680 2,621 23,350 18,770 12,220 25,490 23,680 5,650 8,001 6,147 2,660 19,240 10,700 9,125 6,510 13,530 18,860 3,870,000 1,371,000 2,422,000 672,200 233,100 218,900 354,000 3,135,000 1,470,000 1,408,000 2,201,000 2,680,000 337,500 567,500 555,300 239,400 2,629,000 1,102,000 423,500 423,500 1,691,000 1,870,000