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Correlation and Causation

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Correlation and Causation

Part II – Correlation Coefficient

This video is designed to accompany

pages 19-24

in

Making Sense of Uncertainty

Activities for Teaching Statistical Reasoning

Van-Griner Publishing Company

Defining a Need

The Correlation Coefficient is simply a numerical way of summarizing the relationship you’d see between two variables that you could represent with a scatterplot.

Positive association.

How strong is it?

Formula for “r”

The Correlation Coefficient is “r” measures the strength of the linear relationship between two variables “x” and “y”.

Before we compute it …

It is only appropriate to compute r if the scatterplot of y versus x exhibits a linear trend

r will always be between -1 and 1.

r will be negative if the points in the scatterplot have a downward trend from left to right

r will be positive if the points in the scatterplot have an upward trend from left to right

The closer r is to 1 in absolute value the tighter the cluster of points about the linear trend and the stronger the association between x and y

If r is close to 0 then the association is weak.

Simple Scatterplot

Moderate, positive correlation?

Compute It!

Scatterplots Revisited

Got it!

Student Grades

LDL Levels

r = -0.93

r = 0.75

Time Spent Studying

Hours Exercised

Life Expectancy at Birth

Final Exam Score

Not appropriate to use r since plot is curved

r = 0.02

GNP per capita

Quiz Average

The correlation coefficient is the most common numerical measure of the strength of a straight line relationship between two variables that can represented by a scatterplot.