Prediction · Exercise 22

shows the life expectancy for an individual born in the United States in certain years.

$$\begin{array}{cc}\text{Year of Birth}& \text{Life Expectancy}\\ \text{1930}& \text{59.7}\\ \text{1940}& \text{62.9}\\ \text{1950}& \text{70.2}\\ \text{1965}& \text{69.7}\\ \text{1973}& \text{71.4}\\ \text{1982}& \text{74.5}\\ \text{1987}& \text{75}\\ \text{1992}& \text{75.7}\\ \text{2010}& \text{78.7}\end{array}$$

(a) Decide which variable should be the independent variable and which should be the dependent variable.
(b) Draw a scatter plot of the ordered pairs.
(c) Calculate the least squares line. Put the equation in the form of: ŷ = a + bx
(d) Find the correlation coefficient. Is it significant?
(e) Find the estimated life expectancy for an individual born in 1950 and for one born in 1982.
(f) Why aren’t the answers to part e the same as the values in that correspond to those years?
(g) Use the two points in part e to plot the least squares line on your graph from part b.
(h) Based on the data, is there a linear relationship between the year of birth and life expectancy?
(i) Are there any outliers in the data?
(j) Using the least squares line, find the estimated life expectancy for an individual born in 1850. Does the least squares line give an accurate estimate for that year? Explain why or why not.
(k) What is the slope of the least-squares (best-fit) line? Interpret the slope.

Its source prints no answer for this problem, so there's nothing to check against.

OpenStax, Introductory Statistics 2e · §12.5 Prediction · Exercise 22