Question

The average remaining lifetimes for women of various ages in a certain country are given in the following table. (A graphing calculator is recommended.) Average Remaining Lifetimes for Women Age (x) Years (y) 0 79.0 15 64.7 35 45.3 65 19.0 75 11.5 (a) Find the equation of the least-squares line for the data. (b) Use the equation from part (a) to estimate the remaining lifetime of a woman of age 28. (c) Is the procedure in part (b) an example of interpolation or extrapolation?

Answer 1

To find the equation of the least-squares line for the data, calculate the mean of the x and y values. Then, use the mean values to calculate the slope and y-intercept of the line. Substitute 28 for x in the equation to estimate the remaining lifetime for a woman of age 28. This is an example of interpolation.

Step-by-step explanation:

To find the equation of the least-squares line for the data, we first need to calculate the mean of the x-values and the mean of the y-values. Then, we calculate the sum of the products of the differences between each x-value and the mean of the x-values, and the corresponding y-value and the mean of the y-values. Next, we calculate the sum of the squares of the differences between each x-value and the mean of the x-values. Finally, we use these values to calculate the slope and y-intercept of the least-squares line, giving us the equation of the line

Using the equation from part (a), we can estimate the remaining lifetime of a woman of age 28 by substituting 28 for x in the equation and solving for y.

The procedure in part (b), where we estimate the remaining lifetime of a woman of age 28 using the equation from part (a), is an example of interpolation. Interpolation is the estimation of values within the range of known data points.