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

question 106

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 5% significance level to infer that the number of points by which the individual's blood pressure exceeded the recommended value and the age at death are negatively linearly related?

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Definitions:

Acquiring Information

The process of obtaining knowledge or data from various sources, through reading, observation, or research.

Spreading Activation

A theory in cognitive psychology that suggests ideas in the brain are connected in a network, and thinking about one concept triggers the recall of associated concepts.

Nodes

In network theory, points at which lines or pathways intersect or branch, which can refer to elements in a network or connections in a neural network.

Abstraction

The process of extracting the underlying essence or general patterns from specific instances or material representations, often used in the fields of art, mathematics, and philosophy.