A recent study found that “absolute income mobility,” defined as the percent of children who earn more than their parents, declined in a linear way in the 20th century. The following table of selected data points shows the absolute income mobility for cohorts born in various years between 1940 and 1984.

(a) Find a linear equation for the mobility in terms of t, the number of years since 1900, using the data for 1940 and 1984.
(b) Repeat part (a), using the data for 1960 and 1984.
(c) Find the equation of the least squares line using all the data. Then plot the data and the three lines from parts (a)–(c) on a graphing calculator.
(d) Discuss which of the three lines found in parts (a)–(c) best describes the data, as well as to what extent a linear model accurately describes the data.
(e) Find the correlation coefficient.

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Year 1940 1945 1950 1955 1960 Mobility 91.5 86.4 78.5 69.6 62.3 Year 1965 1970 1975 1980 1984 Mobility 59.3 61.0 58.6 50.0 50.3