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Regression

Learn how to predict the length of stay (LOS) in the hospital after a heart attack using regression analysis. Use predictor variables such as age, gender, smoker, and treatment to improve the accuracy of the prediction.

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Regression

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  1. Regression Lesson 12

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

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

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

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

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

  7. Regression Coefficients • Give slope & intercept of regression line • b1(or b) • Slope (or gradient) • Amount Y changes, when  X by 1 • b0(or a) • Intercept • Value of Y when X = 0 • ei = residual or error • Theoretical, not used in calculation ~

  8. Regression Model outcomei = model + error or

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

  10. Assessing Fit of Model • Model = regression line • R2 • Coefficient of determination • Goodness of Fit • F test • Is regression model better predictor than mean? • If p < .05: model better predictor of Y than the mean ~

  11. Regression Equation & Prediction • My yearly YMCA costs • Y = my total annual cost • X = # premium classes taken • Each pilates or tae kwan do class • Annual fee: $500 • Intercept (b0) • Extra $10 for each • Slope (b1) ~

  12. Regression Models • Simple regression • Multiple regression

  13. Correlation Coefficients • b0 • is the intercept • value of the Y when all Xs = 0 • where regression plane crosses the Y-axis • b1 • regression coefficient for predictor variable 1 (X1) • b2 • regression coefficient for predictor variable 2 (X2) ~

  14. Interpreting Regression • Model summary • R = r (correlation coefficient) • R2 = % variance explained by model • ANOVA (analysis of variance) • F test • Tests H0: model = mean as predictor. *H1 : model better predictor • Sig.: < .05 then model is better predictor than mean ~

  15. Regression in SPSS • Data entry • 1 column per variable, like correlation • Menus • Analyze  Regression Linear • Dialog box • Outcome variable  Dependent • Predictor variable  Independent(s) • Only one for simple regression • do not use options ~

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

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