1. CORRELATION AND REGRESSION Research Methods University of Massachusetts at Boston ©2006 William Holmes

2. ASSUMPTIONS OF CORRELAITON AND REGRESSION Continuous measures (counts, distance, duration, scale scores) Adequate sample size (20+) Normally distributed data Linear relationship between variables

3. ASSESSING ASSUMPTIONS Measurement—review measurement properties. Sample Size—examine how many cases there are. Normality of distribution—examine frequency distribution, bar chart, or statistics. Linearity—examine scattergram or statistics.

4. SCATTERGRAMS N=12, r=.46, Y=0.1+1.09X

5. CORRELATION Measured by correlation coefficient, “r” Varies from –1 to +1 Zero means no correlation Close to –1 or +1 means strong relationship Negative r means as one increases the other decreases Positive r means as one increases the other also increases

6. EXAMPLE CORRELATION TABLE

7. REGRESSION ANALYSIS Estimates prediction equation, Y=a+BX “Y” is variable to be predicted “a” is constant to adjust for differences in scaling of measures “B” is regression coefficient “X” is variable used to make prediction

8. REGRESSION EXAMPLE: 1

9. REGRESSION EXAMPLE: 2 Motivation=0.609 +0.664(Knowledge)