Math113 Fitting Lines to Data Points

The table below gives the projected life expectancy (life span) of a person born in the United States for select birth years from 1920 and through 2018 according to the CDC.

Year	1920	1930	1940	1950	1960	1970	1980	1990	2000	2004	2010	2015	2018
Years since 1900
Life Span	54.1	59.7	62.9	68.2	69.7	70.8	73.7	75.4	76.8	77.5	78.7	78.7	78.8

First, fill in the empty row of the table labelled Years since 1900 with the number of years since 1900. E.g. the year 1960 is 60 years since 1900. We will consider this row of data our independent variable \(x.\)

It’s almost always a good idea to offset the data we’re using as our independent variable like this to (1) make computations simpler, and (2) to make the labels on any figures we product less cluttered and easier to read.
Using technology — likely either your TI graphing calculator or Desmos — plot a scatter-plot of this data using Years since 1900 as the independent variable \(x\) and Life Span as the dependent variable \(y.\)
Graphs these two lines on the plot containing the scatter-plot.

\( y = \frac{1}{5}x+56 \)

\( y = \frac{1}{4}x+50 \)
You should see that each of these two lines appear to fit the data pretty well, but there must be a line that fits the data better. In your TI calculator or Desmos, manually play with the parameters (slope and \(y\)-intercept ) of the equation of a line to find a line that, to your estimation, appears to fit the data best.

If you already know about linear regression try this exercise anyways to see how close your estimation come to the regression line. We’ll calculate the regression line altogether as a class in a moment. At the very least, don’t spoil it for the members of your group!