- Simple regression
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Multiple regression
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Considerations variables
- Logic
- Fit
- Parsimony
- Stability
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Tests for relevance variables
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Statistically significance
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Overall fit: F test
- H0: B1 = B2 = Bn = 0
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Individual Beta t test
- H0: B1 = 0
- H0: B1 >= X
- H0: B1 =< X
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Partial F test
- H0: B1 = B2 = 0 out of a total of Bn
- H0: B1 = B2
- H0: B1 + B2 = 1
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Overall Practicality
- R squared: Coefficient of determination
- Adjusted R Squared
- Standard error of the regression
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Considerations for multiple variables
- Binary predictor (dummy variable)
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Interaction between variables
- Test significance of the coefficient of X1*X2
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Multicollinearity: indepencany of variables
- Test: Variance Inflation Factor (VIF)
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Conditions / assumptions / points of interest
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Residual errors
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Errors are normally distributed
- Test: Histrogram standardized residual
- Test: Normal probability plot of the residuals
- Test: Skewness and Kurtoisse
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Errors have constant variance: Homoscedastic
- Test: Scatterplot residuals (for simple regression)
- Test: Plot residuals against predicted Y values (multiple regression)
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Errors are independent (non autocorrelated)
- Test: graph Residuals
- Durbin Watson test
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Unusual observations
- Leverage
- Outliers
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Linearity
- Test: adding Xi^squared as variable
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Predictions
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Y
- Individual prediction
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Confidence interval Individual
- Simple regression
- Multiple regression
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Confidence interval Mean
- Simple regression
- Multiple regression
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Bi
- Individual prediction
- Confidence interval Individual