A 10-year study conducted by the American Heart Association provided data on how age, blood pressure, and smoking relate to the risk of strokes. Data from a portion of this study follow. Risk is interpreted as the probability (times 100) that a person will have a stroke over the next 10-year period. For the smoker variable, 1 indicates a smoker and 0 indicates a nonsmoker. Risk 19 35 17 57 30 53 12 25 31 27 25 39 25 60 41 35 32 42 36 5 43 Age 78 66 63 79 72 80 61 81 80 70 61 77 68 73 67 65 66 59 76 81 Blood Pressure 145 138 176 187 215 203 116 171 161 147 113 184 100 153 189 112 157 180 132 123 Smoker 1 0 1 1 1 0 0 1 0 1 0 0 0 0 HO 1 0 1 1 H 1 0 a. Develop an estimated regression equation that can be used to predict the risk of stroke given the age and blood pressure level. Enter negative value as negative number. Use Table 4 in Appendix B. The regression equation is (to 4 decimals) Risk = 8 = R = R-sq adj = Analysis of Variance SOURCE Regression Residual Total + Age + (to 4 decimals) (to 4 decimals) (to 4 decimals) DF Blood Pressure SS MS (to 2 decimals) (to 2 decimals) F (to 2 decimals) p-value (to 4 decimals) b. Consider adding two independent variables to the model developed in part (a), one for the interaction between age and blood pressure level and the other for whether the person is a smoker. Develop an estimated regression equation using these four independent variables. Enter negative value as negative number. Use Table 4 in Appendix B. The regression equation is (to 4 decimals) Risk = 8 = R = R-sq adj= = Analysis of Variance SOURCE Regression Residual Total + Age + (to 4 decimals) (to 4 decimals) (to 4 decimals) DF Blood Pressure + SS MS (to 2 decimals) (to 2 decimals) F (to 2 decimals) Smoker + p-value (to 4 decimals) AgeBlood Press c. At a .05 level of significance, test to see whether the addition of the interaction term and the smoker variable contribute significantly to the estimated regression equation developed in part (a). Use Table 4 in Appendix B. What is the value of the F test statistic? (to 2 decimals) P-value is - Select your answer - + so the addition of the two independent variables - Select your answer statistically significant. I Entries in the table give F values, where a is the area or probability in the upper tail of the F distribution. For example, with 4 numerator degrees of freedom, 8 denominator degrees of freedom, and a .05 area in the upper tail, F05 = 3.84. Denominator Degrees of Freedon 2 Area in oppe 1 2 39.86 161.45 647.79 4052.18 4999.34 199 50 799 48 4 230.16 233.99 236.77 921.83 937.11 948 20 5763.96 5858.95 1928.33 924 929 933 19.25 19.30 19.33 19.35 916 19.16 19.00 38.51 39.00 39.17 39.25 39.30 39.33 39.36 98.50 99,00 99.16 5.46 9.55 30.03 53 50 215.71 224.58 864.15 899 60 403.53 5624.26 5.39 5.34 9.28 9.12 9.01 2016 28.71 28.24 27.01 5.28 8.94 4.19 4.11 4.05 4.01 003 02 0:40 16.69 15.98 15.52 15.21 0.00 8.89 2767 3.98 DAUN 4.98 227 4.00 685 10.46 Numerator Degrees of Freedom 59.44 238.88 95664 5980.95 027 19.37 39.37 27.40 3.95 0.00 14.80 3.94 000 4.66 3.92 201 15 14.55 62.05 62.26 62 53 62.79 63.01 63.30 60.19 241.88 6122 61.74 245.95 248.02 249.26 250.10 251.14 252.20 253.04 254.19 963.28 968.63 984.87 993.08 998.09 1001.40 1005.60 1009.79 1013.16 1017.76 5022.40 6055.93 6156.97 6208.66 6239.86 6260.35 6286.43 631297 6333.92 6362.80 20 3.324 15 643 9.72 19.45 3.84 20% 086 4,20 14.02 25 30 850 13.91 40 19.46 39.46 39A7 26.50 3.82 Ov 13.84 26.41 3.80 244 13.75 29 047 19.48 39.48 5.15 8.31 26.32 3.79 0000 13.65 19.49 39,49 20 19.49 39.50 99.50 5.13 8.33 xu 3.76 206 12 47 TABLE 4 F DISTRIBUTION (Continued) Denominator Degree of Freedom + Numerator Degrees of Freedom 5 6 7 8 9 3.46 3.29 3.18 3.11 3.05 3.01 15 20 25 8 9 8 Fadg 1228