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

question 8

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 10% significance level to infer that the model is useful in predicting length of life?

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Definitions:

Meissner Corpuscles

Specialized nerve endings in the skin responsible for sensitivity to light touch.

Two-Point Discrimination

The ability to discern two separate points of contact on the skin, a measure of tactile sensory resolution.

Dermal Papillae

Small, nipple-like extensions of the dermis into the epidermis that increase surface area for oxygen and nutrient transfer between these layers.

Phasic Receptors

Sensory receptors that quickly respond to stimuli but then adapt and decrease their response over time.