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