Question 1040374: 9. (14 pts) Life expectancy at birth is the estimated lifespan of a baby born in a particular year (given the conditions of that time period). Based on data retrieved from http://www.indexmundi.com/facts/united-states/life-expectancy-at-birth the following chart of U.S. life expectancy for males has been prepared.
img src= http://d2vlcm61l7u1fs.cloudfront.net/media%2F73f%2F73fe8e89-e840-4194-85c2-0c891fa17698%2FphpJRNuLz.png
The regression line is y = 0.2052x – 336.5, where x = birth year and y = U.S. life male expectancy, in years. The value of r2 is 0.9809.
(a) Use the regression line to estimate the U.S. life expectancy of a male baby born in 1970, to the nearest tenth of a year. Show some work.
(b) Use the regression line to predict the U.S. life expectancy of a male baby born in 2020, to the nearest tenth of a year. Show some work.
(c) What is the slope of the regression line and what are the units of measurement? In a sentence, interpret what the slope is telling us, in the context of this real-world application.
(d) What is the value of the correlation coefficient, r? Also, interpret its value: Looking at the graph and the size of r, do you judge the strength of the linear relationship to be very strong, moderately strong, somewhat weak, or very weak?
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! y = 0.2052x – 336.5
=(0.2052)(1970)-336.5=67.7 years
y=(0.2052)(2020)-336.5=78.0 years
slope of the line is 0.2052, and the units are rise/run which is age(in years)/year of birth
The real-world application is that age of male children born increases 0.336.5, a third of a year, for every year their birth is delayed. Or, male children born 10 years later will be expected to live about 3.4 years longer than their counterparts.
r=sqrt(0.9809)=0.99. This is a very high correlation and I would say the strength of the linear relationship is very strong.
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