Question 5 Find the estimated multiple regression equation that predict \"risks\

Question

Question 5

Find the estimated multiple regression equation that predict "risks" using all three possible independent variables. Find the coefficient of tje joint variables and the coefficient of each variable individually. Please do the same for the Adjusted R square (joint and individually )

Risk Age Pressure Smoker 12 57 152 No 24 67 163 No 13 58 155 No 56 86 177 Yes 28 59 196 No 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

Explanation / Answer

First code th given datd in smoker column

No = 0 and yes = 1

By using minitab command Stat>>>Regression>>>Regression...

We get the following output

Regression Analysis: Risk versus Age, Pressure, Smoker

The regression equation is
Risk = - 91.8 + 1.08 Age + 0.252 Pressure + 8.74 Smoker

Predictor Coef SE Coef T P
Constant -91.76 15.22 -6.03 0.000
Age 1.0767 0.1660 6.49 0.000
Pressure 0.25181 0.04523 5.57 0.000
Smoker 8.740 3.001 2.91 0.010

S = 5.75657 R-Sq = 87.3% R-Sq(adj) = 85.0%

Analysis of Variance

Source DF SS MS F P
Regression 3 3660.7 1220.2 36.82 0.000
Residual Error 16 530.2 33.1
Total 19 4190.9

Since all the p-values < 0.05 so all the variables are important for prediction of "risk".

R2 = 87.3% So the regressors explain about 87.3% variation in risk when we used this multiple regression model.

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