Prediction (Optional) · Exercise 20

Recently, the annual numbers of driver deaths per 100,000 people for the selected age groups are as follows:

$$\begin{array}{cc}\text{Age (years)}& \text{Number of Driver Deaths (per 100,000 people)}\\ \text{16–19}& \text{38}\\ \text{20–24}& \text{36}\\ \text{25–34}& \text{24}\\ \text{35–54}& \text{20}\\ \text{55–74}& \text{18}\\ \text{75+}& \text{28}\end{array}$$

(a) For each age group, pick the midpoint of the interval for the x value. For the 75+ group, use 80.
(b) Using age as the independent variable and number of driver deaths per 100,000 people as the dependent variable, make a scatter plot of the data.
(c) Calculate the least-squares (best–fit) line. Put the equation in the form ŷ = a + bx.
(d) Find the correlation coefficient. Is it significant?
(e) Predict the number of deaths for ages 40 years and 60 years.
(f) Based on the given data, is there a linear relationship between age of a driver and driver fatality rate?
(g) What is the slope of the least-squares (best-fit) line? Interpret the slope.

OpenStax, Statistics · §12.4 Prediction (Optional) · Exercise 20