Lecture 17: Correlations – Describing Relationships Between Two Variables 2011, 11, 22

Learning Objectives 1. Construct and interpret scatterplots 2. Understand properties of a correlation: direction, strength, form 3. Compute and interpret Pearson correlation coefficient (r) by hand** 4. Difference between correlation and causation*

Scatterplot Y X Plots one variable against the other A Hours Studied Exam Grade B 5 65 C D E Hours Studied Exam Grade

Direction of a Correlation Positive Correlation: The more hours I studied, the better grade I’ll have Negative Correlation: Number of beer you had the night before midterm and your midterm grade

Form of a CorrelationNon-linear Linear Nonlinear correlation Linear correlation

Strength of a Correlation How spread out the dots around the line Stronger ――――――――――――  Weaker

Strength of a Correlation Perfect “+” Perfect “-” IQ Shoe Size

Pearson’s Correlation Coefficient – Measure the Strength of Correlation Notation  Population:  ( rho)  Sample: r Properties  Between -1 to +1  Sign of a correlation coefficient r = 1.0 “perfect positive corr.” r = 0.0 “no relationship” r = -1.0 “perfect negative corr.”

Pearson’s Correlation Coefficient – Strength of a Positive Correlation

Pearson’s Correlation Coefficient – Strength of a Negative Correlation

How to Compute the Pearson correlation coefficient (r)? By hand  Step 1: Compute SS X & SS Y  Step 2: Sum of the Products (SP)  Step 3: Compute r XY

Correlation Doesn’t Equal to Causation Given a correlation of ice cream consumption and cases of drowning, you may speculate “ice cream cause drowning?” r =0.70

Lab 17 Correlation – Recap Scatter plot and fitting line Properties of a correlation  Direction (Positive; negative)  Form (Linear; nonlinear)  Strength (Weak vs. Strong) Compute and interpret Pearson’s correlation coefficient (r) Difference between correlation and causation