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Regression analysis is based on the assumption that the dependent variable is distributed according some function of the independent variables together with independent identically distributed random errors. If the error terms were not stochastic then some of the properties of the regression analysis are not valid.
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ViviThe stochastic error term in regression analysis represents the variability in the dependent variable that is not explained by the independent variables. It captures the random fluctuations or unobserved factors that affect the dependent variable but are not included in the model. The error term is assumed to be normally distributed with a mean of zero and constant variance in classical linear regression models. Understanding and modeling the stochastic error term is crucial for assessing the reliability and accuracy of the regression results.
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