Chap014 - CHAPTER 14 MULTIPLE REGRESSION AND CORRELATION...

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C HAPTER 14 M ULTIPLE R EGRESSION AND C ORRELATION A NALYSIS 1. a. Multiple regression equation b. the Y -intercept c. $374,748 found by Y = 64,100 + 0.39(796,000) + 9.6(6940) - 11,600(6.0) 2. a. Multiple regression equation b. One dependent, four independent c. A regression coefficient d. 0.002 e. 105.014, found by Y = 11.6 + 0.4(6) + 0.286(280) + 0.112(97) + 0.002(35) 3. a. 497.736, found by Y = 16.24 + 0.017(18) + 0.0028(26,500) + 42(3) + 0.0012(156,000) + 0.19(141) + 26.8(2.5) b. Two more social activities. Income added only 28 to the index; social activities added 53.6. 4. a. 30.69 cubic feet b. A decrease of 1.86 cubic feet, down to 28.83 cubic feet. c. Yes, logically, as the amount of insulation increases and outdoor temperature increases, the consumption of natural gas decreases. 5. a. 19 b. 3 c. 0.318 found by 21/66 d. 1.732, found by 45 (19 (3 1)) - + Chapter 14 138
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6. a. 26 b. 5 c. 0.3 found by 60/200 d. 2.65 found by 140 (26 (5 1)) - + 7. a. Source DF SS MS F Regression 3 7,500 2500 18 Error 18 2,500 138.89 Total 21 10,000 b. H o : β 1 = β 2 = β 3 = 0 H 1 : Not all β ‘s are 0 Reject H o if F > 3.16 Reject H o . Not all net regression coefficients equal zero. c. For X 1 for X 2 for X 3 H o : β 1 = 0 H o : β 2 = 0 H o : β 3 = 0 H 1 : β 1 0 H 1 : β 2 0 H 1 : β 3 0 t = - 4.00 t = 1.50 t = - 3.00 Reject H o if t > 2.101 or t < - 2.101 Delete variable 2, keep 1 and 3 8. a. Source DF SS MS F Regression 5 1500 300 9.00 Error 15 500 33.33 Total 20 2000 b. H o : β 1 = β 2 = β 3 = β 4 = β 5 = 0 H 1 : Not all β ‘s are 0 Reject H o if F > 2.90 Reject H o . Not all of the regression coefficients are zero. c. For X 1 for X 2 for X 3 for X 4 for X 5 H o : β 1 = 0 H o : β 2 = 0 H o : β 3 = 0 H o : β 4 = 0 H o : β 5 = 0 Chapter 14 139
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H 1 : β 1 0 H 1 : β 2 0 H 1 : β 3 0 H 1 : β 4 0 H 1 : β 5 0 t = 4.00 t = - 0.833 t = 1.00 t = - 3.00 t = 4.00 Reject H o if t > 2.131 or t < - 2.131 Delete variable 2 then rerun, perhaps delete variable 3 also. 9. a. n = 40 b. 4 c. R 2 = 750/1250 = 0.60 d. 1234 500/35 3.7796 y S S = = e. H o : β 1 = β 2 = β 3 = β 4 = 0 H 1 : Not all β ‘s equal 0 H o is rejected if F > 2.65 750/ 4 13.125 500/35 F = = H o is rejected. At least one β i does not equal zero. 10. H o : β 1 = 0 H o : β 2 = 0 H 1 : β 1 0 H 1 : β 2 0 H o is rejected if t < - 2.074 or t > 2.074 2.676 4.779 0.56 t = = 0.880 1.239 0.710 t - = = - The second variable can be deleted. 11. a. n = 26 b. R 2 = 100/140 = 0.7143 c. 1.4142, found by 2 d. H o : β 1 = β 2 = β 3 = β 4 = β 5 = 0 H 1 : Not all β ‘s are 0 Reject H o if F > 2.71 Computed F = 10.0. Reject H o . At least one regression coefficient is not zero. e.
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Chap014 - CHAPTER 14 MULTIPLE REGRESSION AND CORRELATION...

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