Homoscedasticity (which means “same variance”) is an important assumption in linear regression models. It refers to a situation where the error term—the random noise in the relationship between the independent and dependent variables—has a constant variance across all levels of the independent variables. In other words, the spread of the residuals remains consistent, no matter what value the predictors take.
When homoscedasticity holds, the model produces more reliable standard errors, p-values, and confidence intervals, because the error variance is stable across all levels of the predictor.
When the homoscedasticity assumption is violated, the error variance changes with the value of the predictors. This condition is called heteroscedasticity. With this condition, the model can still produce unbiased estimates, but it can distort the standard errors, which in turn affects confidence intervals and hypothesis tests. The severity of the impact depends on the degree of heteroscedasticity.
Assess homoscedasticity using a residuals vs. fitted values plot. You want to see a consistent vertical spread of the residuals across the full range of fitted values, as shown below.
