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:

Maintenance

The routine tasks and repairs conducted to keep equipment, buildings, or machinery in working order and prevent its deterioration.

Utilities

Services provided to the public or households such as water, electricity, natural gas, sewage treatment, and telecommunications, often subject to government regulations and possibly eligible for tax deductions in certain business contexts.

Rental Expenses

Costs incurred in the operation, maintenance, and improvement of a property rented out, which can often be deducted for tax purposes.

Deductible

The amount paid out of pocket by the policyholder before an insurance company pays a claim.