simple linear regression equation from stata

Software packages usually default to a homoscedastic model, even though such a model may be less accurate than a heteroscedastic model. For example, the variance of expenditure is often larger for individuals with higher income than for individuals with lower incomes. Heteroscedasticity allows the variance to be dependent on x, which is more accurate for many real scenarios. In the homoscedastic model, it is assumed that the variance of the error term is constant for all values of x. One instance in which robust estimation should be considered is when there is a strong suspicion of heteroscedasticity. The Huber loss function is a robust alternative to standard square error loss that reduces outliers' contributions to the squared error loss, thereby limiting their impact on regression estimates.Īpplications Heteroscedastic errors Robust regression methods are designed to limit the effect that violations of assumptions by the underlying data-generating process have on regression estimates.įor example, least squares estimates for regression models are highly sensitive to outliers: an outlier with twice the error magnitude of a typical observation contributes four (two squared) times as much to the squared error loss, and therefore has more leverage over the regression estimates. are not robust to assumption violations). Standard types of regression, such as ordinary least squares, have favourable properties if their underlying assumptions are true, but can give misleading results otherwise (i.e. A regression analysis models the relationship between one or more independent variables and a dependent variable. In robust statistics, robust regression seeks to overcome some limitations of traditional regression analysis.

Specialized form of regression analysis, in statistics Part of a series on

Simple linear regression equation from stata