Introduction to the Correlation Coefficient, r

http://www.stattucino.com/berrie/dsl/correlation.html

 

Objectives:

            To study scatter plots with various sample sizes and r-values to gain a feel for the strength of a linear relationship from a scatter plot.

 

 Exercise 1

• Choose a sample size and an r-value and watch the scatter plot.

• Choose the same sample size with the opposite r-value and observe the scatter plot.
• Note how the two compare.
• Repeat this for different r-values.
• Answer: Explain what the sign of the r-value tells you about the scatter plot.

 

Exercise 2

• Choose a sample size and a high positive r-value. Observe the scatter.
• Choose the same sample size and a low positive r-value (close to 0). Observe the scatter.
• Note how the two compare.
• Repeat this for negative r-values.
• Answer: Explain what you notice is the difference between r-values that have “large” absolute values and “small” absolute values.

 

Exercise 3

• Choose a small sample size and a high r-value. Observe the scatter.
• Choose a large sample size and the same r-value from before. Observe the scatter.
• Note how the two compare.
• Repeat this for different positive r-values or for negative r-values.
• Answer: How does the sample size effect the look of a scatter plot for a given r-value?