Prediction · Exercise 21

Recently, the annual number of driver deaths per 100,000 for the selected age groups was as follows:

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

(a) For each age group, pick the midpoint of the interval for the x value. (For the 75+ group, use 80.)
(b) Using “ages” as the independent variable and “Number of driver deaths per 100,000” 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 of: ŷ = a + bx
(d) Find the correlation coefficient. Is it significant?
(e) Predict the number of deaths for ages 40 and 60.
(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, Introductory Statistics 2e · §12.5 Prediction · Exercise 21