Regression Lesson 11

The General Linear Model n Relationship b/n predictor & outcome variables form straight line l Correlation, regression, t-tests, analysis of variance l Other more complex models ~

Describing Lines n All lines defined by simple equation l Relationship b/n X and Y l Only 2 points required n Slope (or gradient) l Amount Y changes, when X increases by 1 n Intercept l Value of Y when X = 0 ~

Describing Lines = 2 Y X = 1 Intercept: Slope: If X = 2, then Y =4

Regression n Correlation l Measures strength of relationship n Regression l Predict value of variable l Predictor (X)  outcome (Y) n Data from correlational studies l PASW uses independent & dependent variables l Even though NOT experimental ~

Regression Model n Linear model l outcome i = model + error n Regression line l Best-fit straight line describing relationship between X and Y l Method of least squares n Regression equation l Defines regression line ~

Regression Coefficients n Give slope & intercept of regression line n b 1 (or b) l Slope (or gradient) l Amount Y changes, when  X by 1 n b 0 (or a) l Intercept l Value of Y when X = 0  i = residual or error Theoretical, not used in calculation ~

Regression Model outcome i = model + error or

Describing Lines b 0 = 2 Y X b 1 = 1 Intercept: Slope: If X = 2, then Y =4

Method of Least Squares Residuals (  i ) l Like deviation score l Error between predicted score & actual score n Best fit line l Minimizes residuals ~

Assessing Fit of Model n Model = regression line nR2nR2 l Coefficient of determination l Square root = Pearson’s r l n Goodness of Fit l R 2 x 100 = % variance explained by regression line l Higher %  better fit ~

Regression & ANOVA n ANOVA = analysis of variance l Statistical test: F test l Compares systematic (MS M ) and unsystematic variance (MS R ) l l In regression l

F test n Ratio of variances l MS M = Variance explained by model u Systematic variance l MS R = residual variance (error) u Unsystematic variance n If model predicts well, then l MS M >> MS R l F >> 1 l Regression model better predictor of Y than the mean ~

Regression Equation & Prediction n My yearly YMCA costs l Y = my total annual cost l X = # premium classes taken u Each pilates or tae kwan do class n Annual fee: $500 l Intercept (b 0 ) n Extra $10 for each l Slope (b 1 ) ~

Simple Regression in PASW n Data entry l 1 column per variable, like correlation n Menus l Analyze  Regression  Linear n Dialog box l Outcome variable  Dependent l Predictor variable  Independent(s) u Only one for simple regression u do not use options ~

PASW: Regression Dialog Box

PASW Output Not interested in this, not part of analysis

PASW Output

Interpreting Simple Regression n Model summary l R = r (correlation coefficient) l R 2 = % variance explained by model n ANOVA (analysis of variance) l F test l Tests H 0 : model = mean as predictor. l Sig.: <.05 then model is better predictor than mean ~

Interpreting Simple Regression n Coefficients (B) l Constant = b 0 l Predictor = b 1 l Sig.: same info as in ANOVA table ~