1. Chapter 7: Scatterplots, Association, and Correlation
“You can observe a lot by watching.”
Yogi Berra

2. Scatterplots Most common and effective display of data
Observe patterns, trends, relationships, and outlying values
Observe the relationship between two quantitative variables
Ask whether there is an association between the two variables.

3. Scatterplots Look at the direction of the points Look at the form
Positive
Negative
Look at the form
Linear
Non-linear
Look at how much scatter the plot has
Look for any outliers
Points that stand away from the overall pattern

4. Scatterplots – TI Tips

5. Roles for Variables Explanatory Variable Response Variable
Predictor variable
x-axis
Response Variable
y-axis
Roles that we choose are based upon how we think about the variables
The variables may or may not explain anything or respond to anything

6. Correlation Conditions
Measures the strength of the linear association between two quantitative variables.
Quantitative Variable Condition
Know the variables’ units and what they measure
Strength Enough Condition
Know that the correlation is linear
Outlier Condition
Report the correlation with and without the outlier(s).

7. Finding the Correlation
Always check the conditions first.

8. Correlation Properties
Sign gives the direction of the association
Between -1 and +1
Treats x and y symmetrically
No units
Not affected by change in units, scale, or center
Measures strength of linear association
Sensitive to outliers

9. Strengthening Scatterplots
When a scatterplot shows a non-linear form that consistently increases or decreases, we can straighten the form by re-expressing one or both variables.

10. What Can Go Wrong??
Don’t say “Correlation” when you mean “Association.”
Association
Vague term
Describes relationship between two variables
Correlation
Precise term
Describes the linear relationship between quantitative variables

11. What Can Go Wrong?? Check the Conditions!
Don’t correlate categorical variables.
Be sure the association is linear.
Don’t confuse Correlation with Causation!!!
Don’t try to explain correlation by saying that the predictor variable has caused the response variable to change.
Watch out for Lurking variables!!
Hidden variable simultaneously affecting both variables

12. Let’s Try Lunch! (Pg 133 #13) Variables: Conditions
Calories: average number of calories a child consumed during lunch
Time: average number of minutes a child spent at the table when lunch was served.
Conditions
Quantitative: both calories and time are quantitative
Straight enough: scatterplot looks linear
Outlier: There are a few stray points, but the none are very far from the rest of the points

13. Lunchtime!!

14. Lunchtime!! The correlation coefficient is Interpretation:
The scatterplot shows a negative direction, with lower calories going with higher times.
The plot is generally straight with a moderate amount of scatter.
The correlation coefficient of indicates a linear association.
A few cases stand out with lower times related to higher calorie intake, as well as a few with higher times related to lower calorie intake.