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.