There are a number of underlying assumptions about the dependent and independent variables, and their relationship, which affect the statistical procedures such as LSE and significance tests used for linear regression. These assumptions, listed here, need to be tested at the different stages of the regression process.
Normality: Variables and their combination are assumed to follow the normal distribution.
Linearity is assumed, as is evident from the name (linear regression).
Homoscedasticity: Variance of dependent variable should not vary across range of predictor variables.
Residuals (errors, i.e., predicted minus observed values) are assumed to be independent. The prediction errors should be uncorrelated, otherwise it suggests some unexplained, systematic relationship in the dependent variable.
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