# Graphically detecting heteroscedasticity in OLS

I wonder how do I check heteroscedasticity in the OLS regression model using graph.

What kind of plot should I use? Plotting residual against what? Independent variables?

## 1 Answer

You can visually inspect for heteroscedasticity in the disturbances by plotting the regression residuals against the fitted values and then checking if you can discern some pattern to the spread of the residuals in the scatterplot. The idea here is that the variance (spread) of heteroscedastic errors $\varepsilon_i$, conditional on the explanatory variables $X_i$, is not constant:

$$Var(\varepsilon_i | X_i) \neq \sigma^2.$$

You can also explicitly test for heteroscedasticity in a linear regression by using statistical tests such as Breusch-Pagan or White.

• Can you explain more in details about Breusch-Pagan test? I understand the white test.
– Tom
Apr 10, 2018 at 7:26
• Breusch-Pagan is a Lagrange multiplier test that tests for a linear relationship between the variance of the disturbances and the predictors. The null hypothesis of homoscedasticity is examined by regressing the square of residuals on the explanatory variables. Apr 10, 2018 at 16:05