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

question 19

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 5% significance level to infer that the cholesterol level and the age at death are negatively linearly related?

Understand the principles of ESP and paranormal claims in contrast to established sensory phenomena.

Acknowledge the physiological processes involved in sensory transduction.

Distinguish between different senses (e.g., olfaction, gustation) and their interconnectedness.

Identify factors affecting perception, including motivations and emotional state.

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Definitions:

Apraxia

Inability to make voluntary movements in the absence of paralysis or other motor or sensory impairment, especially an inability to make proper use of an object.

Arm Movements

The action or process of moving the arm, which involves muscular and skeletal systems.

Copying Drawing

A method used to assess cognitive and motor functions by replicating a reference image.

Corpus Callosum

A large bundle of nerve fibers that connects the left and right hemispheres of the brain, facilitating interhemispheric communication.