Figure 1
OLS model estimation for an example data subset. The subset arises from a choice in categories at the left sidebar (Project 02, forest ecosystems, upper soil layer, and sensor type CS655). Zoom in to the main data cloud is activated. Further options are a robust MM-type estimator, and visualization of row IDs. The user can browse and upload their own dataset. The application is organized in five panels. The first one shows the current OLS model fit (scatter plot accompanied by 95% confidence interval for the model estimate). A potential outlier point is brushed.
Figure 2
MM-type model estimation for an example data subset. Same data subset as in Figure 1 is visualised. Switching to the robust MM-type estimator enhances the coefficient of determination as the outlier point #2 (brushed point) does loose leverage on model estimation. The model equation and r2 are comparable to the OLS estimate without point #2, which does refer to y = 0.062 + 0.87×, r2 = 59. Applying visualisation of the row IDs facilitates identifying leverage and outlier points with the model diagnostic plots (panel Diagnostics).
Figure 3
Model diagnostic plots for OLS estimator. The model diagnostic plots are applied to answer the following questions: (1) Do the model residuals have non-linear patterns? (2) Are the model residuals normally distributed? (3) Are the model residuals spread equally along the ranges of predictors? (4) Which are the influential outliers? Facing these questions helps testing underlying assumptions for OLS and in the end is beneficial for detection of outlier and leverage points (e.g. point #2).
Figure 4
Model diagnostic plots for MM-type estimator (further explanation see caption Figure 3).
Figure 5
Interpretation of standardised residuals vs. robust distance. The plot divides the value range in four regions marked by lines and coloured points: (1) Regular, (2) Outlier, (3) Leverage, (4) Outlier and Leverage. Points in the fourth category are of major importance as they are outlier points, influencing the model fit if removed from estimation.