Observations with extreme values for the independent variables in regression are known as what?

High leverage points are observations in regression analysis that have extreme values for the independent variables. These points can significantly influence the slope and position of the regression line due to their position in the predictor space. When a data point has values that are far removed from the rest of the data for the independent variables, it has high leverage. Therefore, when this point is used in the regression analysis, its influence is larger than that of the other points, which may make the model sensitive to its presence.

While outliers generally refer to points that deviate significantly from the overall trend of the data in terms of the dependent variable, high leverage points specifically focus on the extreme nature of the independent variable(s). This distinction is important in regression analysis, as high leverage points can lead to potential distortion in the interpretation of the model results. Residuals pertain to the differences between observed and predicted values, and data anomalies indicate unusual patterns without specifying their influence on regression analysis.