Prob 13.38

# Prob 13.38 - Rawdata Risk y 12 24 13 56 28 51 18 31 37 15...

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Raw data Page 1 Risk, y Age, x1 Pressure, x2 Smoker, x3 y = risk (% chance) 12 57 152 No x1 = age (years) 24 67 163 No x2 = pressure 13 58 155 No x3 = smoker 56 86 177 Yes = no if non-smoker 28 59 196 No = yes if smoker 51 76 189 Yes 18 56 155 Yes 31 78 120 No 37 80 135 Yes 15 78 98 No 22 71 152 No 36 70 173 Yes 15 67 135 Yes 48 77 209 Yes 15 60 199 No 36 82 119 Yes 8 66 166 No 34 80 125 Yes 3 62 117 No 37 59 207 Yes

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model data Page 2 y x1 x2 x3 y = risk (% chance) 12 57 152 0 x1 = age (years) 24 67 163 0 x2 = pressure 13 58 155 0 x3 = smoker 56 86 177 1 = 0 if non-smoker 28 59 196 0 = 1 if smoker 51 76 189 1 18 56 155 1 31 78 120 0 Find by multiple regression ( 37 80 135 1 the equation that best fits all 15 78 98 0 22 71 152 0 Y = b0 +b1x1 + b2x2 + b3x3 36 70 173 1 15 67 135 1 where Y is the expected valu 48 77 209 1 15 60 199 0 36 82 119 1 8 66 166 0 34 80 125 1 3 62 117 0 37 59 207 1
model data Page 3 (using the method of least squares) of the data, of the form 3 ue of risk calculated from the regression equation.

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Risk, y Age, x1 Pressure, x2 Smoker, x3 y = risk (% chance) 12 57 152 0 24 67 163 0 13 58 155 0 56 86 177 1 28 59 196 0 51 76 189 1 18 56 155 1 31 78 120 0 37 80 135 1 15 78 98 0 22 71 152 0 36 70 173 1 15 67 135 1 48 77 209 1 15 60 199 0 36 82 119 1 8 66 166 0 34 80 125 1 3 62 117 0 37 59 207 1 Conclusion: None of the simple linear regressions are good models because the R^2's are so low. 50 55 60 65 0 10 20 30 40 50 60 f(x) = 1x - 42.8 R² = 0.42 Age Risk, y 80 100 120 140 0 10 20 30 40 50 60 f(x) = 0.18x - 0.81 R² = 0.15 Press Risk, y 0 0 10 20 30 40 50 60 f(x) = 19.7x + 17.1 R² = 0.46 Smok Risk, y
x1 = age (years) x2 = pressure x3 = smoker = 0 if non-smoker = 1 if smoker 70 75 80 85 90 e, x1 160 180 200 220 sure, x2 1 ker, x3

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SUMMARY OUTPUT Regression Statistics Multiple R 0.93 R Square 0.87
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