1. LESSON 6: REGRESSION 2/21/12 EDUC 502: Introduction to Statistics

2. Review Critical Values Correlation

4. Regression Just as in correlation we want to find the relationship In fact we are even going to get a Pearson r out of it The difference with regression is that we want to predict scores on one variable using another And we often have an idea of the direction of the effect even though we can’t prove causation with regression

5. Regression Equation Y’ = bX + a This allows us to predict how someone will do on Y if we know their X score b is the slope and a is the intercept (i.e. where the regression line meets the y-axis) We won’t be calculating these by hand

6. Errors in Predicting Y The standard error around the regression line gives us an estimate of the average error between our actual Y values and the predicted Y value (which is on the regression line) This is inversely related to r So the better we do at predicting the smaller those errors are

7. Proportion of Variance Accounted For One of the things we want to know from a regression is how much of the variance in Y have we accounted for by using X To do this we simply square our r value to get r 2

8. Reporting Correlation and Regression Example with n = 25 Correlation  Bivariate correlation indicated there was a significant relationship between study time and test scores, r(23) =.86, p <.001, showing that as study time increases test scores increase. Regression  A linear regression was run to establish if study time predicts test scores. Study time had a significant positive relationship with test scores r =.86, F(1,24) = 65.32, p <.001 and an r 2 =.74.