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Regression diagnostics and assumptions
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- 1Things to consider:sample size
no multicollinearity
no outliers - 2AssumptionsNormality of residuals
linearity of relationship
no heteroscedasticity of residuals
independence of residuals - 3Sample Size influences:power of significance tests (F and t)
stability of regression co-efficient over repeated sampling
15-20 per predictor
50+8*predictors - 4Multicollinearity what?exists when two or more predictor variable correlate highly (>0.7)
e.g. age in years and age in months should correlate perfectly - 5Multicollinearity why is it bad?Makes it difficult to interpret importance of predictor variables, and prevents stable regression co-efficients from being found.
- 6two measures of collinenearity:tolerance = 1 - squared multiple correlation of predictors
variance inflation factor = 1/tolerance - 7Outliers:can radically disturb the regression line of best fit
- 8statistics to check for outliers 1Distance - measure outliers in the DV e.g. standardized residuals. Values greater than 3 are outliers
- 9statistics to check for outliers 2leverage (h) - measures outliers in the IV. Values greater than (3*(predictos+1))/N are outliers
- 10statistics to check for outliers 3Cook's D - a measure of influence which is the joint contribution of distance and leverage. Values above 1 generally problematic
- 11Assumption 1Normality of Residuals
- 12How normality works for regressionlinear regression attempts to minimise errors in the prediction of the Y variable.
Error (residuals)= Ypred - Y actual
for significance tests to give good p-values, residuals must be normally distributed about the predicted values of Y - 13Assumption 2Linearity of relationship
- 14what is a non linear relationshipwhen there isn't a random relationship between the residuals and the predicted values of Y.
- 15Assumption 3No heteroscedasticity of residuals
- 16wtf is heteroscedasticity?(different dispersion of residuals)
The variance of the residuals should be roughly equal along all values of the predicted variable
use scatter plot - 17Assumption 4Independence of residuals
- 18wtf is independence of residuals?any two residuals in the analysis should not correlate with each other (aka zero autocorrelation)
- 19How to test independence of residuals?Durbin-Watson statistic
2 = uncorrelated good
>2 negatively correlated
<2 residuals positively correlated
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- whiffy bum RM2 Fichas sobre Regression diagnostics and assumptions, creado por James Rowland el 31/03/2016.
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- James Rowland
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