State Burglary Rates in 2005 (n = 50 states, k = 4 predictors) Abbrev State Burg

Question

State Burglary Rates in 2005 (n = 50 states, k = 4 predictors) Abbrev State Burglary AgeMed Bankrupt FedSpend HSGrad% Variable Definition AL Alabama 986 37.4 10.57 8619 80.9 Burglary 2005 burglary rate per 100,000 population AK Alaska 576 33.9 3.48 12885 91.7 AgeMed 2005 median age of population AZ Arizona 990 34.5 6.85 7309 85.7 Bankrupt 2005 corporate or individual bankruptcies filed per 1,000 population AR Arkansas 1094 37.0 11.01 7080 81.4 FedSpend 2004 federal spending per capita for all functions CA California 685 34.4 4.63 6474 80.3 HSGrad% 2005 public high school graduation rate CO Colorado 717 34.7 9.37 6533 89.2 CT Connecticut 444 39.3 4.36 8649 90.0 DE Delaware 648 37.9 5.22 6326 86.8 Range Names Cell Range FL Florida 956 39.5 6.16 7009 86.8 Burglary D7:D56 GA Georgia 940 34.3 9.13 6247 85.7 AgeMed E7:E56 HI Hawaii 857 38.5 3.52 9651 87.3 Bankrupt F7:F56 ID Idaho 547 34.6 8.51 6437 89.1 FedSpend G7:G56 IL Illinois 597 35.6 8.43 6043 87.3 HSGrad% H7:H56 IN Indiana 676 36.1 12.63 6079 87.2 IA Iowa 615 38.6 6.29 6505 89.9 KS Kansas 731 36.1 8.28 6993 91.4 KY Kentucky 625 37.5 9.67 7649 78.9 LA Louisiana 1005 35.4 8.10 7298 80.2 ME Maine 481 41.2 5.01 8248 87.2 MD Maryland 660 37.1 6.31 11645 87.0 MA Massachusetts 537 38.2 4.10 8279 87.5 MI Michigan 637 36.9 8.77 5981 88.5 MN Minnesota 550 36.7 4.98 5644 92.7 MS Mississippi 953 35.5 8.12 7695 79.9 MO Missouri 703 37.4 9.11 7947 85.4 MT Montana 379 40.2 6.32 8085 92.1 NE Nebraska 562 36.2 6.95 6751 89.7 NV Nevada 991 35.2 10.11 5469 86.6 NH New Hampshire 382 39.5 4.64 6124 91.9 NJ New Jersey 472 38.0 5.67 6353 87.0 NM New Mexico 1047 36.2 6.53 10437 81.0 NY New York 368 37.5 5.69 7484 85.6 NC North Carolina 1185 36.2 4.94 6467 84.0 ND North Dakota 301 39.1 5.57 9513 90.0 OH Ohio 846 37.6 11.82 6388 87.9 OK Oklahoma 1000 36.5 11.20 7562 85.2 OR Oregon 837 37.0 9.09 6084 88.7 PA Pennsylvania 439 39.7 6.35 7649 86.3 RI Rhode Island 506 38.4 5.37 7630 84.0 SC South Carolina 1034 37.1 3.66 7158 83.0 SD South Dakota 409 37.0 5.40 8564 88.5 TN Tennessee 1020 37.3 11.05 7701 81.8 TX Texas 979 33.2 5.32 6308 78.2 UT Utah 637 28.5 9.07 5728 92.7 VT Vermont 545 40.7 4.16 7456 90.0 VA Virginia 386 37.2 5.97 12150 86.1 WA Washington 977 36.7 7.56 7228 91.5 WV West Virginia 602 40.7 9.76 8364 82.4 WI Wisconsin 433 37.9 6.89 5728 90.5 WY Wyoming 541 39.1 6.44 8673 90.9 SUMMARY OUTPUT Regression Statistics Multiple R 0.653709912 R Square 0.427336649 Adjusted R Square 0.37643324 Standard Error 187.6729919 Observations 50 ANOVA df SS MS F Significance F Regression 4 1182733.285 295683.3212 8.39505 0.0000379 Residual 45 1584951.835 35221.15189 Total 49 2767685.12 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept 4198.580801 799.3395051 5.252562615 0.000004 2588.62839 5808.533 2588.628 5808.5332 AgeMed -27.35396133 12.56873865 -2.176348964 0.034818 -52.6687004 -2.03922 -52.6687 -2.0392222 Bankrupt 17.48931356 12.40328598 1.410054851 0.165398 -7.49218677 42.47081 -7.49219 42.470814 FedSpend -0.01238993 0.017607623 -0.703668485 0.485265 -0.0478535 0.023074 -0.04785 0.0230736 HSGrad% -29.03138499 7.126829715 -4.073534257 0.000185 -43.3855569 -14.6772 -43.3856 -14.677213 Required: Use the assigned range names in all formulas. The assigned range names and related cell references are provided in cells J15:K19. A What is the estimated regression equation?       Burglary=4.198.5808-27.3539-27.3539AgeMed+17.4893Bankrupt-0.0124FedSpend-29.0314HSGradRate B Make a prediction for Burglary when: AgeMed 35 years Bankrupt 7 per 1,000 966.7 FedSpend $      6,000 HSGrad% 80% C Provide the null and alternative hypotheses (H0 and H1) to assess the overall fit of the observed predictors. 4159.672 H1 4198.581 H0 D Refer to the partial ANOVA table below. Source SS df MS Regression 1,182,733 4 295,683 Residual 1,584,952 45     35,221       Total 2,767,685 49 Assume an alpha () of .05 for your analysis. D(1) What is the critical value to test the hypotheses for overall fit? -1.67655 D(2) What is the F test statistic to test the hypotheses for overall fit? D(3) What is your decision rule using the critical value method of testing the hypotheses for overall fit? D(4) State your conclusion as to the overall fit of the predictors used in the regression model. E Refer to the regression analysis output Assume an alpha () of .05 for your analysis. Assume the null hypothesis is that the coefficients of all of the predictors equal zero, indicating that none of the predictors relate to the expected burglary rate (Y) E(1) What is the critical value to use in testing whether the coefficients of any of the predictors is significantly different from zero, which would indicate that predictor is related to the burglary rate. E(2) State your decision rule. E(3) Which coefficients, if any, are significantly different from zero? F Which predictor is the strongest predictor of burglary rates? State Burglary Rates in 2005 (n = 50 states, k = 4 predictors) Abbrev State Burglary AgeMed Bankrupt FedSpend HSGrad% Variable Definition AL Alabama 986 37.4 10.57 8619 80.9 Burglary 2005 burglary rate per 100,000 population AK Alaska 576 33.9 3.48 12885 91.7 AgeMed 2005 median age of population AZ Arizona 990 34.5 6.85 7309 85.7 Bankrupt 2005 corporate or individual bankruptcies filed per 1,000 population AR Arkansas 1094 37.0 11.01 7080 81.4 FedSpend 2004 federal spending per capita for all functions CA California 685 34.4 4.63 6474 80.3 HSGrad% 2005 public high school graduation rate CO Colorado 717 34.7 9.37 6533 89.2 CT Connecticut 444 39.3 4.36 8649 90.0 DE Delaware 648 37.9 5.22 6326 86.8 Range Names Cell Range FL Florida 956 39.5 6.16 7009 86.8 Burglary D7:D56 GA Georgia 940 34.3 9.13 6247 85.7 AgeMed E7:E56 HI Hawaii 857 38.5 3.52 9651 87.3 Bankrupt F7:F56 ID Idaho 547 34.6 8.51 6437 89.1 FedSpend G7:G56 IL Illinois 597 35.6 8.43 6043 87.3 HSGrad% H7:H56 IN Indiana 676 36.1 12.63 6079 87.2 IA Iowa 615 38.6 6.29 6505 89.9 KS Kansas 731 36.1 8.28 6993 91.4 KY Kentucky 625 37.5 9.67 7649 78.9 LA Louisiana 1005 35.4 8.10 7298 80.2 ME Maine 481 41.2 5.01 8248 87.2 MD Maryland 660 37.1 6.31 11645 87.0 MA Massachusetts 537 38.2 4.10 8279 87.5 MI Michigan 637 36.9 8.77 5981 88.5 MN Minnesota 550 36.7 4.98 5644 92.7 MS Mississippi 953 35.5 8.12 7695 79.9 MO Missouri 703 37.4 9.11 7947 85.4 MT Montana 379 40.2 6.32 8085 92.1 NE Nebraska 562 36.2 6.95 6751 89.7 NV Nevada 991 35.2 10.11 5469 86.6 NH New Hampshire 382 39.5 4.64 6124 91.9 NJ New Jersey 472 38.0 5.67 6353 87.0 NM New Mexico 1047 36.2 6.53 10437 81.0 NY New York 368 37.5 5.69 7484 85.6 NC North Carolina 1185 36.2 4.94 6467 84.0 ND North Dakota 301 39.1 5.57 9513 90.0 OH Ohio 846 37.6 11.82 6388 87.9 OK Oklahoma 1000 36.5 11.20 7562 85.2 OR Oregon 837 37.0 9.09 6084 88.7 PA Pennsylvania 439 39.7 6.35 7649 86.3 RI Rhode Island 506 38.4 5.37 7630 84.0 SC South Carolina 1034 37.1 3.66 7158 83.0 SD South Dakota 409 37.0 5.40 8564 88.5 TN Tennessee 1020 37.3 11.05 7701 81.8 TX Texas 979 33.2 5.32 6308 78.2 UT Utah 637 28.5 9.07 5728 92.7 VT Vermont 545 40.7 4.16 7456 90.0 VA Virginia 386 37.2 5.97 12150 86.1 WA Washington 977 36.7 7.56 7228 91.5 WV West Virginia 602 40.7 9.76 8364 82.4 WI Wisconsin 433 37.9 6.89 5728 90.5 WY Wyoming 541 39.1 6.44 8673 90.9 SUMMARY OUTPUT Regression Statistics Multiple R 0.653709912 R Square 0.427336649 Adjusted R Square 0.37643324 Standard Error 187.6729919 Observations 50 ANOVA df SS MS F Significance F Regression 4 1182733.285 295683.3212 8.39505 0.0000379 Residual 45 1584951.835 35221.15189 Total 49 2767685.12 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept 4198.580801 799.3395051 5.252562615 0.000004 2588.62839 5808.533 2588.628 5808.5332 AgeMed -27.35396133 12.56873865 -2.176348964 0.034818 -52.6687004 -2.03922 -52.6687 -2.0392222 Bankrupt 17.48931356 12.40328598 1.410054851 0.165398 -7.49218677 42.47081 -7.49219 42.470814 FedSpend -0.01238993 0.017607623 -0.703668485 0.485265 -0.0478535 0.023074 -0.04785 0.0230736 HSGrad% -29.03138499 7.126829715 -4.073534257 0.000185 -43.3855569 -14.6772 -43.3856 -14.677213 Required: Use the assigned range names in all formulas. The assigned range names and related cell references are provided in cells J15:K19. A What is the estimated regression equation?       Burglary=4.198.5808-27.3539-27.3539AgeMed+17.4893Bankrupt-0.0124FedSpend-29.0314HSGradRate B Make a prediction for Burglary when: AgeMed 35 years Bankrupt 7 per 1,000 966.7 FedSpend $      6,000 HSGrad% 80% C Provide the null and alternative hypotheses (H0 and H1) to assess the overall fit of the observed predictors. 4159.672 H1 4198.581 H0 D Refer to the partial ANOVA table below. Source SS df MS Regression 1,182,733 4 295,683 Residual 1,584,952 45     35,221       Total 2,767,685 49 Assume an alpha () of .05 for your analysis. D(1) What is the critical value to test the hypotheses for overall fit? -1.67655 D(2) What is the F test statistic to test the hypotheses for overall fit? D(3) What is your decision rule using the critical value method of testing the hypotheses for overall fit? D(4) State your conclusion as to the overall fit of the predictors used in the regression model. E Refer to the regression analysis output Assume an alpha () of .05 for your analysis. Assume the null hypothesis is that the coefficients of all of the predictors equal zero, indicating that none of the predictors relate to the expected burglary rate (Y) E(1) What is the critical value to use in testing whether the coefficients of any of the predictors is significantly different from zero, which would indicate that predictor is related to the burglary rate. E(2) State your decision rule. E(3) Which coefficients, if any, are significantly different from zero? F Which predictor is the strongest predictor of burglary rates?

Explanation / Answer

B. Estimated regression equation is as follows

Bulglary= 4198.580801- 27.35396133*AgeMed+17.48931356*Bankrupt-0.01238993*FedSpend -29.03138499*HSGrad%

Given the data of independent variable Estimated Bulglary would be

Bulglary=4198.580801- 27.35396133*35+17.48931356*7-0.01238993*6000-29.03138499*80 Bulglary= 966.76697

D(2) F test =Mean of square for model/ Mean of square for error. It is given that Mean of square for model=295683 and mean of square for error=35221 Then F=295683/35221=8.395

D(3) Reject Null hypothesis if test statistics is greater than critical value or otherwise accept the null hypothesis.

D(4) As in our case test statistics is greater than the critical value then reject the null hypothesis. That the predictors are overall fitted.

E(1) Critical value can be provided by the F table. As the null hypothesis which is supposed in this case that the coefficient of every independent variables i.e. H0:a1=a2=a3=a4=0 H1:otherwise H1 is provides that predictor is related to Bulglary.

E(2) From the ANNOVA table if p value for the F test is less than the significance level in this case 0.05 then reject the null hypothesis.

E(3): The coefficient of AgeMed and HSGrade is different from zero as their p value is less than 0.05.

F. HSGrade% is the strongest predictor as it is different frim zero and the absolute value of coefficient is greatest than all others.

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