# linear regression: evaluating regression models overview assumptions for linear regression...

Click here to load reader

Post on 19-Dec-2015

234 views

Embed Size (px)

TRANSCRIPT

- Slide 1
- Slide 2
- LINEAR REGRESSION: Evaluating Regression Models
- Slide 3
- Overview Assumptions for Linear Regression Evaluating a Regression Model
- Slide 4
- Assumptions for Bivariate Linear Regression Quantitative data (or dichotomous) Independent observations Predict for same population that was sampled
- Slide 5
- Assumptions for Bivariate Linear Regression Linear relationship Examine scatterplot Homoscedasticity equal spread of residuals at different values of predictor Examine ZRESID vs ZPRED plot
- Slide 6
- Checking for Homoscedasticity
- Slide 7
- Assumptions for Bivariate Linear Regression Independent errors Durbin Watson should be close to 2 Normality of errors Examine frequency distribution of residuals
- Slide 8
- Checking for Normality of Errors
- Slide 9
- Influential Cases Influential cases have greater impact on the slope and y-intercept Select casewise diagnostics and look for cases with large residuals
- Slide 10
- Slide 11
- Standard Error of the Estimate Index of how far off predictions are expected to be Larger r means smaller standard error Standard deviation of y scores around predicted y scores
- Slide 12
- Sums of Squares Total SS total squared differences of Y scores from the mean of Y Model SS total squared differences of predicted Y scores from the mean of Y Residual SS total squared differences of Y scores from predicted Y scores
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Coefficient of Determination r 2 is the proportion of variance in Y explained by X Adjusted r 2 corrects for the fact that the r 2 often overestimates the true relationship. Adjusted r 2 will be lower when there are fewer subjects.
- Slide 17
- Goodness of Fit Dividing the Model SS by the Total SS produces r 2 The ANOVA F-test determines whether the regression equation accounted for a significant proportion of variance in Y F is the Model Mean Square divided by the Residual Mean Square
- Slide 18
- Coefficients The Constant B under unstandardized is the y-intercept b 0 The B listed for the X variable is the slope b 1 The t test is the coefficient divided by its standard error The standardized slope is the same as the correlation
- Slide 19
- Example of Reporting a Regression Analysis The linear regression for predicting quiz enjoyment from level of statistics anxiety did not account of a significant portion of variance, F(1, 24) = 1.75, p =.20, r 2 =.07.
- Slide 20
- Take-Home Points The validity of a regression procedure depends on multiple assumptions. A regression model can be evaluated based on whether and how well it predicts an outcome variable.