STA 2023Section 9.1Correlation

Correlation

Types of Correlation

Constructing a Scatterplot Example 1: The data below are the temperatures on

randomly chosen days during a summer class and the number of absences on those days. Construct a scatter plot for the data.

Temperature

72 85 91 90 88 98 75 100 80

Number of absences

3 7 10 10 8 15 4 15 5

Correlation Coefficient

Example 2: Use the data from example 1 do calculate the correlation coefficient.

Steps: Press 2nd, then 0 to enter the catalog. Scroll down until you see DiagnosticOn. Press enter to copy the command to the home screen. Then press enter. You only need to do this once to setup your calculator to find r.

Go to your list and enter your data in List 1 and List 2. Exit from the list. Then, press STAT, arrow over to CALC and

choose 4: LinReg(ax+b) With the command copied type “L1,L2” after it. On the read out, look at the very last line for r.

Temperature

72 85 91 90 88 98 75 100 80

Number of absences

3 7 10 10 8 15 4 15 5

Testing a Population Correlation Coefficient After calculating the correlation coefficient, we

want to know if we can make an inference based on the data we have.

To determine whether the population correlation coefficient is significant, we use the critical values in Table 11.

If |r|is greater than the critical value, there is enough evidence to decide that the correlation is significant.

Example 3: Using the data from example 1 and the result from example 2, is the correlation coefficient significant?

Hypothesis Testing for a Population Correlation Coefficient

Correlation and Causation The fact that two variables are strongly

correlated does not imply a cause-and-effect relationship between the variables.

If a significant correlation exists, a researcher should ask the following: Is there a direct cause-and-effect relationship? Is there a reverse cause-and-effect relationship? Does another factor influence the two variables? It the relationship just coincidence?