Download (a) Find the linear regression model for this data. Consider x = GDP

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Regression Example
The data below shows, for several countries, the Gross Domestic Product (GDP) measured
in $1000 per person and the life expectancy in years for that country.
1.965
Life
Expectancy
72.68
1.087
71.33
4.448
72.53
0.462
69.75
6.591
76.47
1.225
71.66
1.786
72.66
2.137
70.66
2.64
73.6
GDP
(a) Find the linear regression model for this data.
Consider x = GDP and y = life expectancy.
(b) What is the correlation value between these two
variables?
(c) Use your model to estimate the life expectancy in a
country having GDP = $462 per person (i.e. x =
0.462)
(d) Calculate the residual for the prediction in (c).
(e) Use the model to estimate the life expectancy in a
country with GDP = $1800 per person and also for
a country with GDP = $8500 per person.
(f) One of the predictions in part (e) is not likely to be a reliable prediction. Which one?
Why?
Answers
(a) ŷ = 70.231+ 0.862x
(b) r = 0.8527
(c) 70.231+ 0.862(0.462) = 70.629 years
(d) 69.75 – 70.629 = -0.879 years
(e) 70.231+ 0.862(1.8) = 71.783 years
70.231+ 0.862(8.5) = 77.558 years
(f) The prediction for GDP = $8500 per year is not reliable because a GDP of $8500 per year
(i.e. x = 8.5) is outside the scope of the original data set.
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