You wanted to develop a model to predict how long individuals will live. After consulting a number of physicians, you collected the age at death (y), the average number of hours of exercise per week (x1), the cholesterol level (x2), and the number of points that the individual's blood pressure exceeded the recommended value (x3). A random sample of 40 individuals was selected. The computer output of the multiple regression model is shown below.
THE REGRESSION EQUATION IS
y = 55.8 +1.79x1 - 0.021x2 - 0.016x3
Predictor Coef StDev T
Constant 55.8 11.8 4.729
X1 1.79 0.44 4.068
X2 -0.021 0.011 -1.909
X3 -0.016 0.014 -1.143
S = 9.47 R-Sq = 22.5%
ANALYSIS OF VARIANCE
Source of Variation df SS MS F
Regression 3 936 312 3.477
Error 36 3230 89.722
Total 39 4166
A. Is there enough evidence at the 10% significance level to infer that the model is useful in predicting length of life?
B. Is there enough evidence at the 1% significance level to infer that the average number of hours of exercise per week and the age at death are linearly related?
C. What is the coefficient of determination? What does this statistic tell you?
D. Interpret the coefficient b1
The solution provides step by step method for the calculation of regression analysis. Formula for the calculation and Interpretations of the results are also included.