1. Plan for Today:
Chapter 14: Describing Relationships: Scatterplots and Correlation

2. Scatterplot:
Persons’ muscle mass and their age

3. Scatterplot: Basic principles to describe a scatterplot: 1) Form
e.g.: linear, non-linear, or not obvious
2) Direction
e.g.: Positive, negative, or none
3) Strength
e.g. :Strong, moderate, or weak

4. Scatterplot (Form):
Linear:
Non-linear:

5. Scatterplot (Direction):
Positive association:
Negative association:

6. Scatterplot (Strength):
Strong:
Weak:

7. Correlation:
The correlation r describes the direction and strength of a straight-line relationship.
-- Positive r indicates positive association. And negative r indicates negative association.
-- It always falls between -1 and 1.
-- It measures the strength of only straight-line association between two variables.
-- It won’t change when you change the units of the variables.

8. Correlation (Guidelines):
Strength
0.0 to 0.2
Very weak to negligible correlation
0.2 to 0.4
Weak, low correlation (not very significant)
0.4 to 0.7
Moderate correlation
0.7 to 0.9
Strong, high correlation
0.9 to 1.0
Very strong correlation
The same for the corresponding negative correlations.

9. Correlation (Straight-line):

10. Correlation (Outlier):
A researcher tried to find the relationship between the price for hot dog and soda at different area. But unfortunately, he had a typo.
Actual plot
Plot with typo
r= 0.47
r= -0.70

11. Correlation and Causation:

12. Correlation and Causation:X Y
Causation

13. Correlation and Causation:Z Y X ?
Common response

14. Correlation and Causation:Z Y X ?
Confounding