Life Expectancy an Actuary Wanted to Develop a Model to Predict

question 49

Essay

Life Expectancy
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 (x₁),the cholesterol level (x₂),and the number of points that the individual's blood pressure exceeded the recommended value (x₃).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 + 1.79x₁− 0.021x₂− 0.061x₃ ​ S = 9.47 ​ R−Sq = 22.5% ANALYSIS OF VARIANCE ​ ​
-{Life Expectancy Narrative} Is there enough evidence at the 5% significance level to infer that the cholesterol level and the age at death are negatively linearly related?

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Definitions:

Exponential Distribution

A statistical distribution used to model time between events in a process that occurs continuously and independently at a constant average rate.

Poisson Distribution

A mathematical representation that quantifies the odds of various event frequencies occurring within a predetermined span of time or space.

Average Time

The mean time taken for a process or event, calculated by summing the total times recorded and dividing by the number of events.

Arrival Rate

In operations, it refers to the frequency at which tasks, customers, or entities arrive at a system or facility, typically measured in units per time period.