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

question 31

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%. $$\begin{array}{l}\text { ANALYSIS OF VARIANCE }\\\begin{array} { | l | c c c c | } \hline \text { Source of Variation } & \mathrm { df } & \text { SS } & \text { MS } & \text { F } \\\hline \text { Regression } & 3 & 936 & 312 & 3.477 \\\text { Error } & 36 & 3230 & 89.722 & \\\hline \text { Total } & 39 & 4166 & & \\\hline\end{array}\end{array}$$ 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:

Capital Lease

A lease agreement in which the lessee essentially buys an asset and borrows the funds through the lease, recording the asset and the liability on their balance sheet.

Implicit Interest Rate

An interest rate inferred from leasing transactions or other contractual arrangements, calculated based on the present value of payments and the initial value of the leased asset.

Present Value Factors

A mathematical formula used to determine the present value of a series of future cash flows by applying a specific discount rate.

Capital Lease

A lease classified as a purchase by the lessee for accounting purposes, where the lessee essentially buys the leased asset.