Regression Lesson 16 Predicting Outcomes Predictions l Based

Regression Lesson 16

Predicting Outcomes Predictions l Based on what has happened in past n Predict length of stay (LOS) in hospital after a heart attack l Use mean LOS as predictor n More information better prediction l Predictors: age, gender, smoker, treatment, etc. n Regression: l Predictor(s) Outcome ~ n

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 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 ~ n

Describing Lines Intercept: = 2 If X = 2, then Y = 4 Slope: = 1 8 Y 6 4 2 0 0 2 4 8 6 X 10 12

Regression Correlation l Measures strength of relationship n Regression l Predict value of variable l Predictor (X) outcome (Y) n Multiple predictor variables (Xn) l More complex model, but. . . l Same logic and basic process n Regression equation l Defines regression line ~ n

Regression Coefficients 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 n n ei = residual or error • Theoretical, not used in calculation ~

Regression Model outcomei = model + error or

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

Assessing Fit of Model n n Model = regression line R 2 l Coefficient of determination l Goodness of Fit F test l Is regression model better predictor than mean? l If p <. 05: model better predictor of Y than the mean ~ l n

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 n Annual fee: $500 l Intercept (b 0) Extra $10 for each l Slope (b 1) ~

Regression Models n Simple regression l n Multiple regression l

Correlation Coefficients n b 0 l l l n b 1 l n is the intercept value of the Y when all Xs = 0 where regression plane crosses the Y-axis regression coefficient for predictor variable 1 (X 1) b 2 l regression coefficient for predictor variable 2 (X 2) ~

Interpreting Regression Model summary l R = r (correlation coefficient) 2 l R = % variance explained by model n ANOVA (analysis of variance) l F test l Tests H 0: model = mean as predictor. *H 1 : model better predictor l Sig. : <. 05 then model is better predictor than mean ~ n

Regression in SPSS 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) n Only one for simple regression u do not use options ~ u

SPSS: Multiple Regression n Data entry l 1 column per variable, like simple Menus l Analyze Regression Linear Dialog box l Dependent Outcome variable l Independent(s) Predictor variables l Method: Stepwise l Options ~