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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?

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?

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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I need help with d, e, and f. Please show step by step with the formulas and explian. 

BTU Area 3870000 30001 1371000 13530 2422000 26060 672200 6355 233100 4576 218900 24680 354000 2621 3135000 23350 1470000 18770 1408000 12220 2201000 25490 2680000 23680 337500 5650 567500 8001 555300 6147 239400 2660 2629000 19240 1102000 10700 423500 9125 423500 6510 1691000 13530 1870000 18860
Transcribed Image Text:BTU Area 3870000 30001 1371000 13530 2422000 26060 672200 6355 233100 4576 218900 24680 354000 2621 3135000 23350 1470000 18770 1408000 12220 2201000 25490 2680000 23680 337500 5650 567500 8001 555300 6147 239400 2660 2629000 19240 1102000 10700 423500 9125 423500 6510 1691000 13530 1870000 18860
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- STU ber of square feet of building shell. 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 Bo 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 warehouse 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 warchouse. What are these assumptions?
Transcribed Image Text: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- STU ber of square feet of building shell. 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 Bo 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 warehouse 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 warchouse. What are these assumptions?
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