Assumptions of Linear regression
No or little multicollinearity
No auto-correlation
Linear relationship
Homoscedasticity
Relationship between the independent and dependent variables needs to be linear and additive
check for outliers
tested with scatter plots
Multivariate normality
checked with a histogram or a Q-Q-Plot.
linear regression analysis requires all variables to be multivariate normal
Tested with
Tested with
checked with a goodness of fit test
occurs when the independent variables are too highly correlated with each other.
Variance Inflation Factor (VIF)
Tolerance
Correlation matrix
Tested with
Tested with
T < 0.1
T < 0.01
might be multicollinearity there in the data
multicollinearity is certainly there in the data
correlation coefficients need to be smaller than 1
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VIF > 10
VIF <= 4
multicollinearity not present
certainly multicollinearity is there among variables
occurs when the residuals are not independent from each other.
Condition Index
values > 30 indicate strong multicollinearity.
Values of 10-30 indicate a mediocre multicollinearity in the linear regression
Durbin-Watson test
analyses linear autocorrelation and only between direct neighbors, which are first-order effects.
Check if the residuals are equal across the regression line
Can be checked using scatter plot
There should be no correlation between the residual (error) terms
error terms must have constant variance.
The error terms must be normally distributed.