CorrelationCorrelation

CorrelationCorrelation

Is a statistical procedure that estimates the Is a statistical procedure that estimates the linear relationship between two or more linear relationship between two or more variablesvariables

The value of r The value of r (matey?)(matey?)

Correlation = rCorrelation = r The value of r can range from -1 to 1The value of r can range from -1 to 1 If r = 0,then there is no correlation between the two If r = 0,then there is no correlation between the two

variablesvariables If r = 1 (or -1), then there is a perfect positive (or perfect If r = 1 (or -1), then there is a perfect positive (or perfect

negative) relationship between the two variablesnegative) relationship between the two variables

http://www.uic.edu/classes/psych/psych343f/lecture08.htm

MagnitudeMagnitude

The absolute value for the size of the The absolute value for the size of the correlation corresponds to the magnitude correlation corresponds to the magnitude (or strength) of the relationship(or strength) of the relationship -0.85 indicates a negative correlation and the -0.85 indicates a negative correlation and the

magnitude is |-0.85| magnitude is |-0.85| 0.85 0.85

DirectionDirection

Two types:Two types: Direct Correlation – Direct Correlation – positive correlation (positive positive correlation (positive

sign); as one variable increases the other variable will sign); as one variable increases the other variable will also increasealso increase

Inverse Correlation– Inverse Correlation– negative correlation (negative negative correlation (negative sign); as one variable increase the other variable will sign); as one variable increase the other variable will decreasedecrease

ExamplesExamples Direct (both variables are in the same Direct (both variables are in the same

direction)direction) Height and shoe sizeHeight and shoe size Education and incomeEducation and income Happiness and helpfulnessHappiness and helpfulness

Inverse (one variable is in the opposite Inverse (one variable is in the opposite direction of the corresponding variable)direction of the corresponding variable) Depression and happinessDepression and happiness Temperature and number of clothing articles wornTemperature and number of clothing articles worn

Correlation does Correlation does notnot imply Causation imply Causation

Children raised in homes with more Children raised in homes with more appliances tend to perform better in appliances tend to perform better in school. Therefore, appliances improve school. Therefore, appliances improve intelligence.intelligence.

http://btr.michaelkwan.com/2009/01/10/correlation-does-not-imply-causation/

SSCP MatrixSSCP Matrix

CP formulaCP formula = (Xi-Xbar)(Yi-Ybar)= (Xi-Xbar)(Yi-Ybar)

Variance-Covariance MatrixVariance-Covariance Matrix

Covariance – measure of how two Covariance – measure of how two variables varyvariables vary

Covariance formulaCovariance formula = = ∑∑ (Xi-Xbar)(Yi-Ybar) (Xi-Xbar)(Yi-Ybar)

df df

Correlation FormulaCorrelation Formula

Correlation = rCorrelation = r

An ExampleAn Example

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What is the correlation between shoe size and height in a sample of 4 individuals?