1. Scatterplots, Association, and Correlation
Chapter 7
Scatterplots, Association, and Correlation

2. Goals Understand Association Understand Correlation
Work with and interpret scatterplots
Distinguish between association and causation

3. Car Weight v. Gas Mileage

4. Questions What is the general pattern of the data?
Does there appear to be a association between car weight and gas mileage?
What type of function would best fit the data?
Any unusual data values?

5. Marriage Ages

6. Marriage Ages ctd.
Association type?
Strength:
Center:
Spread:

7. Variable Roles Response variable
The dependent variable (frequently y).
Explanatory variable or predictor variable
The independent variable (frequently x).
used to predict or explain the values of the response variable.

8. Sketch a plot Drug dosage and degree of pain relief.
Calories consumed and weight loss.
Hours of sleep and score on a test.
Shoe size and grade point average.
Time for a mile run and age.

9. Correlation
Correlation measures the strength of the linear relationship between two quantitative variables.
A correlation is a specific type of association between two variables.

10. Car data
From the course webpage, select Car Data from Fathom Data Files.

11. Correlation Coefficient ctd.
The correlation coefficient is known as r.
What is the biggest value of r?
What is the smallest value of r?
What value(s) correspond to a strong association between two variables?
What value(s) correspond to a weak association between two variables?

12. Correlation Coefficient Formula

13. Unusual data points
There are 3 types of unusual data points you will find in a scatterplot. Each can have a dramatic effect on the correlation value.
Outlier
Influential Observation
High Leverage Point

14. Outlier

15. Influential Observation

16. High Leverage Point

17. Standardized Graph
From the course webpage, select Bird Data from Fathom Data Files.

18. Association v. Causation
The following examples all have a strong association indicated by r. Which of these are likely to have causation?
Drug dosage and degree of pain relief.
Calories consumed and weight loss.
Ice cream consumption and number of drownings.
Number of fire trucks that respond to a call and the cost of the damage.

19. Chapter 7 Objectives
Understand and distinguish between the terms association, correlation, and causation.
Know how to make a scatterplot
Know how to find a correlation between two variables.