1. Correlation

2. Correlation  Is a statistical procedure that estimates the linear relationship between two or more variables

3. The value of r (matey?)  Correlation = r  The value of r can range from -1 to 1  If r = 0,then there is no correlation between the two variables  If r = 1 (or -1), then there is a perfect positive (or perfect negative) relationship between the two variables http://www.uic.edu/classes/psych/psych343f/lecture08.htm

4. Magnitude  The absolute value for the size of the correlation corresponds to the magnitude (or strength) of the relationship -0.85 indicates a negative correlation and the magnitude is |-0.85|  0.85 -0.85 indicates a negative correlation and the magnitude is |-0.85|  0.85

5. Direction  Two types: Direct Correlation – positive correlation (positive sign); as one variable increases the other variable will also increase Direct Correlation – positive correlation (positive sign); as one variable increases the other variable will also increase Inverse Correlation– negative correlation (negative sign); as one variable increase the other variable will decrease Inverse Correlation– negative correlation (negative sign); as one variable increase the other variable will decrease

6. Examples  Direct (both variables are in the same direction) Height and shoe size Height and shoe size Education and income Education and income Happiness and helpfulness Happiness and helpfulness  Inverse (one variable is in the opposite direction of the corresponding variable) Depression and happiness Depression and happiness Temperature and number of clothing articles worn Temperature and number of clothing articles worn

7. Correlation does not imply Causation  Children raised in homes with more appliances tend to perform better in school. Therefore, appliances improve intelligence. http://btr.michaelkwan.com/2009/01/10/correlation-does-not-imply-causation/

8. SSCP Matrix  CP formula = (Xi-Xbar)(Yi-Ybar) = (Xi-Xbar)(Yi-Ybar)

9. Variance-Covariance Matrix  Covariance – measure of how two variables vary  Covariance formula = ∑ (Xi-Xbar)(Yi-Ybar) df = ∑ (Xi-Xbar)(Yi-Ybar) df

10. Correlation Formula  Correlation = r

11. An Example ☻☺ What is the correlation between shoe size and height in a sample of 4 individuals?