# Linear regression assumptions

I have read that we make the following assumption for linear regression:
1. Linearity (correct functional form)
2. Constant error variance (homoskedasticity)
3. Independent error terms (no autocorrelation)
4. Normality of error terms
5. No multicollinearity
6. Exogeneity (no omitted variable bias)

So are these assumptions specific to Linear Regression or applicable for all types of regression techniques like Support Vector Regression, Lasso and Ridge regression, Stepwise regression etc.

• These are typical assumptions in OLS for finding a minimum-variance unbiased estimator of the parameters and performing inference (confidence intervals, p-values) on the parameters. These assumptions are not, however, necessary for other forms of regression. Lasso, for instance, will tend to find groups of correlated predictors and give nonzero parameter estimates for only one variable per group. This doesn't mean that Lasso requires correlated predictors, but Lasso tolerates correlated predictors. – Dave Mar 11 at 15:10
• @Dave, +1 for most of it, but I'm not sure whether Lasso will tend to zero out all but one from a correlated group? At least, in the case of an actual duplicated column, lasso will split the coefficient evenly across the two. – Ben Reiniger Mar 11 at 16:27
• @BenReiniger You may be right about what happens when Lasso encounters duplicated columns, but I'd still say that it's the case that Lasso tends to zero-out all but one of a group of predictors with tight correlation. That may not always happen, but it does tend to. – Dave Mar 11 at 16:31