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

question 115

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
ŷ = $$55.8 + 1.79 x _ { 1 } - 0.021 x _ { 2 } - 0.016 x _ { 3 }$$ $$\begin{array} { | c | c c c | } \hline \text { Predictor } & \text { Coef } & \text { StDev } & \mathrm { T } \\\hline \text { Constant } & 55.8 & 11.8 & 4.729 \\x _ { 1 } & 1.79 & 0.44 & 4.068 \\x _ { 2 } & - 0.021 & 0.011 & - 1.909 \\x _ { 3 } & - 0.016 & 0.014 & - 1.143 \\\hline\end{array}$$ se = 9.47 R2 = 22.5%. $$\begin{array}{l}\text { ANALYSIS OF VARIANCE }\\\begin{array} { | l | c c c c | } \hline \text { Source of Variation } & \mathrm { df } & \text { SS } & \text { MS } & \text { F } \\\hline \text { Regression } & 3 & 936 & 312 & 3.477 \\\text { Error } & 36 & 3230 & 89.722 & \\\hline \text { Total } & 39 & 4166 & & \\\hline\end{array}\end{array}$$ What is the coefficient of determination? What does this statistic tell you?

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Definitions:

Practiced Religion

The engagement in or observance of rituals, ceremonies, and moral codes associated with a particular faith or belief system.

Universal

Something that is applicable everywhere or in all cases, often used to describe concepts, principles, or conditions that are globally recognized.

Anthropologists

Scientists who study human behavior, culture, and societies, both past and present, through various perspectives and methods.

Superstructure

A society's shared sense of identity and worldview. The collective body of ideas, beliefs, and values by which a group of people makes sense of the world- its shape, challenges, and opportunities- and understands their place in it. This includes religion and national ideology.