Multiple regression assumptions diagnostic
How can we test regression assumptions? Before performing regression analysis, it is important to check regression assumptions like multicollinerity, normality, linearity, autocorrelation, and homoskasticity.
1. Normally distribution
It refers to the normal distribution of residuals or error terms.
It can be tested using either graphical methods by histogram, predicted probability (p-p) plots and plotted points or statistical methods by using kurtosis and skewness values.
Statistical methods are better than graphical methods.
A data is normally distributed when the skewness and kurtosis values are between -2 and 2.
2. Multicollinearity
It refers to the relationship between independent variables or predictors.
That is, predictors should not be highly correlated.
It can be checked by using either correlation coefficient between independent variables, using Tolerance and variance inflation factors (VIF) values of variables or eigenvalue values.
That is, there is no multicollinearity among independent variables (multicollinearity assumption is not violated) if the correlation coefficient is less than 0.8 or tolerance is above 0.1 and VIF is below 5.
3. Linearity
It refers to the linear relationship between independent and outcome variables.
In a scatter plot, linearity can be checked if points conform to a diagonal fitted line.
If the assumption of multicollinearity and normality are not violated, don't worry about linearity.
4. Homoscedasticity
Homoscedasticity refers to the constant variance of error terms.
Its opposite is heteroscedasticity.
If it fails (heteroscedastic), additional predictors are required to explain results, or transform the data using logarithm, square root, ....
Homoscedastic if residuals evenly distributed between -2 and 2.
5. Autocorrelation
It refers to independence of observation.
The independent variable is said to be autocorrelated when the current value of Y is dependent on its previous value.
It can be checked by using Durbin-Watson test (DW).
If DW = 2 or approaches to 2, there is no autocorrelation.
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