lhomoscedasticité

Homoscedasticity refers to a statistical assumption where the variance of the errors in a regression model is constant across all levels of the independent variables. In simpler terms, it means that the spread of the data points around the regression line is roughly the same for all values of the predictor variables. This is often visually represented by a scatter plot where the points are evenly distributed around the regression line, without any discernible funnel or fan shape.

The opposite of homoscedasticity is heteroscedasticity, where the variance of the errors is not constant. This can lead to several problems in statistical analysis. When homoscedasticity is violated, the standard errors of the regression coefficients become biased, leading to inaccurate hypothesis tests and confidence intervals. This means that conclusions drawn from the model, such as which variables are statistically significant, might be incorrect.

Common methods for detecting heteroscedasticity include visual inspection of residual plots (plotting residuals against predicted values or independent variables) and statistical tests such as the Breusch-Pagan test or the White test. If heteroscedasticity is detected, several remedies can be applied. These include transforming the dependent variable (e.g., using a logarithmic transformation), using weighted least squares regression, or employing robust standard errors that are less sensitive to violations of the homoscedasticity assumption. Maintaining homoscedasticity is important for the validity of many standard statistical inference procedures in regression analysis.