Model quality, parameter estimates, and predicted by observed

The output first summarizes the model quality statistics and the parameter estimates for different quantiles at .25, .50, and .75.

Figure 1. Model quality and parameter estimates by different quantiles charts
Model quality and parameter estimates by different quantiles charts

For each quantile, more details are given to the parameter estimates in terms of the hypothesis test statistics and the confidence intervals.

Figure 2. Quantile = 0.25 chart
Quantile = 0.25 chart
Figure 3. Quantile = 0.50 chart
Quantile = 0.50 chart
Figure 4. Quantile = 0.75 chart
Quantile = 0.75 chart

The Plot of the Estimated Parameters chart can be created in the presence of multiple quantiles. It compares the quantile regression models with the ordinary linear regression model fitted with the same predictors. Note that the coefficients estimated by linear regression remain the same at different quantiles, while it is not true in general for quantile regression. The estimated confidence intervals are also superimposed onto the chart for comparison. Usually, the prediction lines are plotted for covariates, and the prediction tables are created for factors.

Figure 5. Plot of the Estimated Parameters chart
Plot of the Estimated Parameters chart

The Predicted by Observed chart compares the predicted values and the observed values for different quantiles.

Figure 6. Predicted by Observed chart
Predicted by Observed chart