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

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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*

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Scatterplot Y X 65 73 88 515 2530 Plots one variable against the other A 30 88 Hours Studied Exam Grade B 5 65 C 25 88 D 15 73 E 15 65 Hours Studied Exam Grade

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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

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Form of a CorrelationNon-linear Linear Nonlinear correlation Linear correlation

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

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

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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.”

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Pearson’s Correlation Coefficient – Strength of a Positive Correlation

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Pearson’s Correlation Coefficient – Strength of a Negative Correlation

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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 11 1310 1817 1213 1614

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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

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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

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