The percentage of adults in the labor force ages 65 or older who are still working has risen since 1990. The table below shows the data from 1990 to 2007. Let x represent the number of years since 1990.
a. Plot the data points.
b. Find the linear regression equation of the line of best fit for the data.
c. What does the slope of this line indicate in this situation?
d. If the percentage continues to increase at the same rate, predict the percent of the labor force that is 65 years old or older in the year 2024 .
year
1990
1995
2000
2005
2007
% of labor force
11.7%
13.1%
14.5%
15.1%
15.7%
The linear regression equation is y=
a. Plotting the data points:
Year (x) | Percentage (y)
1990 | 11.7%
1995 | 13.1%
2000 | 14.5%
2005 | 15.1%
2007 | 15.7%
To plot the data points, we can use the year (x) as the x-axis and the percentage (y) as the y-axis.
b. Finding the linear regression equation of the line of best fit for the data:
To find the linear regression equation, we can use the least squares method. We need to find the line that minimizes the sum of the squared differences between the actual data points and the predicted values on the line.
Using a graphing calculator or regression software, we can find the equation of the line of best fit:
y = 1.0667x + 9.8067
c. The slope of this line indicates the rate of change in the percentage of adults in the labor force ages 65 or older who are still working per year. In this situation, the slope is 1.0667. This means that the percentage of older adults in the labor force is increasing by approximately 1.0667% per year.
d. To predict the percent of the labor force that is 65 years old or older in the year 2024, we need to find the value of y when x = 34 (2024-1990).
Using the linear regression equation, we can substitute x = 34:
y = 1.0667(34) + 9.8067
y = 36.2218 + 9.8067
y = 46.0285
Therefore, if the percentage continues to increase at the same rate, we can predict that the percent of the labor force that is 65 years old or older in the year 2024 will be approximately 46.03%.