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

question 73

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 $y =$ $$55.8 + 1.79 x _ { 1 } - 0.021 x _ { 2 } - 0.016 x _ { 3 }$$ $$\begin{array} { | c | c c c | } \hline \text { Predictor } & \text { Coef } & \text { StDev } & \text { T } \\\hline \text { Constant } & 55.8 & 11.8 & 4.729 \\x _ { 1 } & 1.79 & 0.44 & 4.068 \\x _ { 2 } & - 0.021 & 0.011 & - 1.909 \\x _ { 3 } & - 0.016 & 0.014 & - 1.143 \\\hline\end{array}$$ 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 1% significance level to infer that the average number of hours of exercise per week and the age at death are linearly related?

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Definitions:

Reflection

The process of introspectively considering one's thoughts, feelings, and actions, and the outcomes they lead to, for the purpose of learning and self-improvement.

Reinforcing

Strengthening a behavior or response by providing a reward or positive outcome after the behavior occurs, often used in learning and behavior modification techniques.

Sending

The act of transmitting information, messages, or goods from one place or person to another.

Proxemics

Involves the use of space as people interact.