Residuals and Causation

A group of biologists is studying the population of wolves and the population of deer in a particular region. The biologists compared the populations each month for 2 years. After analyzing the data, the biologists found that as the population of wolves increases, the population of deer decreases.

• Has correlation and the variables cause a change in the other variable.

• Has correlation but there may be another factor that is the cause of the change in the variables.

Researchers at an auto insurance company are studying the ages of its policyholders and the number of accidents per 100 policyholders. The researchers compared each year of age from 16 to 65. After analyzing the data, the researchers found that as age increases, the number of accidents per 100 policyholders decreases.

• Has correlation and the variables cause a change in the other variable.

• Has correlation but there may be another factor that is the cause of the change in the variables.

Educational researchers are investigating the relationship between the number of musical instruments a student plays and a student’s grade in math. The researchers conducted a survey asking 110 students the number of musical instruments they play and went to the registrar’s office to find the same 110 students’ grades in math. The researchers found that students who play a greater number of musical instruments tend to have a greater average grade in math.

• Has correlation and the variables cause a change in the other variable.

• Has correlation but there may be another factor that is the cause of the change in the variables.

Researchers are studying the relationship between the median salary of a police officer in a city and the number of violent crimes per 1000 people. The researchers collected the police officers’ median salary and the number of violent crimes per 1000 people in 84 cities. After analyzing the data, researchers found that a city with a greater police officers’ median salary tends to have a greater number of violent crimes per 1000 people.

• Has correlation and the variables cause a change in the other variable.

• Has correlation but there may be another factor that is the cause of the change in the variables.

The owner of a ski resort is studying the relationship between the amount of snowfall in centimeters during the season and the number of visitors per season. The owner collected information about the amount of snowfall and the number of visitors for the past 30 seasons. After analyzing the data, the owner determined that seasons that have more snowfall tend to have more visitors.

• Has correlation and the variables cause a change in the other variable.

• Has correlation but there may be another factor that is the cause of the change in the variables.

Government researchers are studying the relationship between the amount of gas used and the number of miles driven in a month. The researchers found that the months with a higher average amount of gas used tend to have more miles driven.

• Has correlation and the variables cause a change in the other variable.

• Has correlation but there may be another factor that is the cause of the change in the variables.

• A

• B

• C

Which graph indicates the model for the data is a good fit?

• Graph A

• Graph B

Which description matches the residual graph

• The actual points and predicted points coincide

• The residual plot suggests a good fit for a linear model

• The residual plot suggests a good fit for a non-linear model

Which description matches the residual graph

• The actual points and predicted points coincide

• The residual plot suggests a good fit for a linear model

• The residual plot suggests a good fit for a non-linear model