What distribution is assumed for the error term ɛ in regression analysis?

In regression analysis, it is commonly assumed that the error term (denoted ɛ) follows a normal distribution. This assumption is fundamental because it allows for the derivation of various statistical properties and tests. The normality of the errors provides the basis for inference about the regression coefficients using t-tests and F-tests, as these tests rely on the properties of the normal distribution to produce reliable results regarding hypothesis testing and confidence intervals.

When the error term is assumed to be normally distributed, it implies that residuals (the differences between observed and predicted values) will also be normally distributed, thus enabling regression analysis to produce valid statistical conclusions. Furthermore, the assumption of normality helps in ensuring that the estimates of regression coefficients are unbiased and normally distributed themselves, particularly when the sample size is large due to the central limit theorem.

In contrast, other distributions such as exponential, uniform, and binomial do not hold the same validity for modeling the errors in regression contexts and fail to provide the necessary statistical properties needed for reliable inference. Therefore, the correct answer reflects the foundational assumption of normality for the error term in regression analysis.