Outliers · Exercise 13

A researcher is investigating whether population impacts homicide rate. He uses demographic data from Detroit, Michigan, to compare homicide rates and the population.

$$\begin{array}{cc}\text{Population Size}& \text{Homicide Rate per 100,000 People}\\ \text{558,724}& \text{8.6}\\ \text{538,584}& \text{8.9}\\ \text{519,171}& \text{8.52}\\ \text{500,457}& \text{8.89}\\ \text{482,418}& \text{13.07}\\ \text{465,029}& \text{14.57}\\ \text{448,267}& \text{21.36}\\ \text{432,109}& \text{28.03}\\ \text{416,533}& \text{31.49}\\ \text{401,518}& \text{37.39}\\ \text{387,046}& \text{46.26}\\ \text{373,095}& \text{47.24}\\ \text{359,647}& \text{52.33}\end{array}$$

(a) Use a calculator to construct a scatter plot of the data. What is the independent variable? Why?
(b) Use the calculator’s regression function to find the equation of the least-squares regression line. Add this to your scatter plot.
(c) Discuss what the following mean in context:
(a) The slope of the regression equation
(b) The y-intercept of the regression equation
(c) The correlation coefficient, r
(d) The coefficient of determination, r^2
(d) Do the data provide convincing evidence that there is a linear relationship between population size and homicide rate? Carry out an appropriate test at a significance level of 0.05 to help answer this question.

Its source prints no answer for this problem, so there's nothing to check against.

OpenStax, Statistics · §12.5 Outliers · Exercise 13