An Actuary Wanted to Develop a Model to Predict How $x _ { 1 }$

question 36

Essay

An actuary wanted to develop a model to predict how long individuals will live. After consulting a number of physicians, she collected the age at death (y), the average number of hours of exercise per week ( $x _ { 1 }$ ), the cholesterol level ( $x _ { 2 }$ ), and the number of points by which the individual's blood pressure exceeded the recommended value ( $x _ { 3 }$ ). A random sample of 40 individuals was selected. The computer output of the multiple regression model is shown below:
THE REGRESSION EQUATION IS $y =$ $55.8 + 1.79 x _ { 1 } - 0.021 x _ { 2 } - 0.016 x _ { 3 }$ $$\begin{array} { | c | c c c | } \hline \text { Predictor } & \text { Coef } & \text { StDev } & \mathrm { T } \\\hline \text { Constant } & 55.8 & 11.8 & 4.729 \\x _ { 1 } & 1.79 & 0.44 & 4.068 \\x _ { 2 } & - 0.021 & 0.011 & - 1.909 \\x _ { 3 } & - 0.016 & 0.014 & - 1.143 \\\hline\end{array}$$ S = 9.47 R-Sq = 22.5%. $$\begin{array}{l}\text { ANALYSIS OF VARIANCE }\\\begin{array} { | l | c c c c | } \hline \text { Source of Variation } & \text { df } & \text { SS } & \text { MS } & \text { F } \\\hline \text { Regression } & 3 & 936 & 312 & 3.477 \\\text { Error } & 36 & 3230 & 89.722 & \\\hline \text { Total } & 39 & 4166 & & \\\hline\end{array}\end{array}$$ Is there enough evidence at the 10% significance level to infer that the model is useful in predicting length of life?

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Definitions:

Computer-mediated Groups

Teams or groups that interact primarily through digital technologies rather than face-to-face.

Face-to-face Groups

Social or work groups that interact directly and in person, as opposed to virtually or remotely.

Communication Medium

The method or technology used to convey messages between individuals or groups.

Web Media

Digital forms of communication and content delivery over the Internet, including websites, streaming services, and social media platforms.