Question

A sociologist recorded the estimated life expectancies of women born in Center City. Use the data from women born in 1970 and 2000 to create a linear model that predicts the life expectancy, in years, (y) of a female born in a given year (x).

Year
Born
Life Expectancy
(years)
1960
66.1
1970
67.6
1980
70.1
1990
71.9
2000
74.0
2010
75.9

Which equation represents this linear model?
y = 0.213x – 352.7
y = 0.213x – 358.4
y = 4.695x – 9181.6
y = 4.695x – 9322.4

Answer 1

Use the points (1970, 67.6) and (2000, 74.0).

Slope m = (74.0 − 67.6)/(2000 − 1970) = 6.4/30 = 0.213333... ≈ 0.213.

Intercept b = 67.6 − 0.213333...·1970 = −352.666... ≈ −352.7.

So the linear model is y = 0.213x − 352.7.