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

Scatterplot: Persons’ muscle mass and their age

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

Scatterplot (Form): Linear: Non-linear:

Scatterplot (Direction): Positive association: Negative association:

Scatterplot (Strength): Strong: Weak:

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.

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.

Correlation (Straight-line):

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

Correlation and Causation:

Correlation and Causation: X Y Causation

Correlation and Causation: Z Y X ? Common response

Correlation and Causation: Z Y X ? Confounding