Analysis of a Central Composite (Response Surface) Experiment - Residual Plots Tab
Analyzing Central Composite Designs
Select the Residual plots tab of the Analysis of a Central Composite (Response Surface) Experiment dialog box to access options to generate various diagnostic plots of the raw residuals and/or the studentized deleted residuals. Note that these results are for the currently specified model. You can specify a new model via the Model tab. Note that for plots involving residuals, either the raw residual values or the studentized deleted residuals are used depending on whether the Plot raw residuals option button or the Plot studentized deleted residuals option button (see below) is selected.
- Plot raw residuals
- If the Plot raw residuals option button is selected, residual plots will use the raw residuals on the dependent variable for each case or run as the values to be plotted.
- Plot studentized deleted residuals
- If the Plot studentized deleted residuals option button is selected, residual plots will use the studentized deleted residuals on the dependent variable for each case or run as the values to be plotted.
- Histograms
- Use the options in the Histograms group box to plot either a Histogram of residuals or a Histogram of predicted values.
- Histogram of residuals
- Click the Histogram of residuals button to produce a histogram of the selected residual values (Raw or Studentized deleted, see above), given the current model. The ANOVA analysis assumes that the residual values follow the normal distribution. Note that this plot also shows the fitted normal distribution curve.
- Histogram of predicted values
- Click the Histogram of predicted values button to produce a histogram of predicted values, given the current model, showing the frequency distribution of the predicted values for the dependent variable. Note that this plot also shows the fitted normal distribution curve.
- Probability plots of residuals
- The Probability plots of residuals groups box contains three options from which to select probability plots: Normal plot, Half-normal plot, and Detrended normal plot.
- Normal plot
- Click the Normal plot button to produce a Normal Probability Plot of the Residuals, which plots the Expected Normal Values and corresponding probabilities against the selected Residual values (Raw or Studentized deleted, see above) of the dependent variable for each case or run.
The so-called normal probability plot is a common tool to assess how closely a set of observed values (residuals in this case) follows a theoretical distribution. In this plot the actual residual values are plotted along the horizontal x-axis; the vertical y-axis shows the expected normal values for the respective values, after they were rank-ordered. If all values fall onto a straight line, you can be satisfied that the residuals follow the normal distribution.
- Half-normal plot
- Click the Half-normal plot button to produce a Half-Normal Probability Plot of the Residuals, which plots the Expected Half-Normal Values and corresponding probabilities against the raw residual values (Raw or Studentized deleted) of the dependent variable for each case or run.
- Detrended normal plot
- Click the Detrended normal plot button to produce a Detrended Normal Probability Plot of the Residuals, which plots the Deviations from Expected values against the raw residual values (Raw or Studentized deleted) of the dependent variable for each case or run.
- Scatterplots
- The Scatterplots group box contains five options from which to select scatterplots: Predicted vs. residual values, Observed vs. predicted values, Observed vs. residual values, Residuals vs. deleted residuals, and Residuals vs. case numbers.
- Predicted vs. residual values.
- Click the Predicted vs. residual values button to produce a Predicted vs. Residual Values Plot, which plots the selected residuals (Raw or Studentized deleted, see above) against the Predicted Values of the dependent variable for each case or run.
- Observed vs. predicted values.
- Click the Observed vs. predicted values button to produce an Observed vs. Predicted Values Plot, which plots the Observed Values against the Predicted Values of the dependent variable for each case or run.
- Observed vs. residual values.
- Click the Observed vs. residual values button to produce an Observed vs. Residual Values Plot, which plots the selected residuals (Raw or Studentized deleted) against the Observed Values of the dependent variable for each case or run.
- Residuals vs. deleted residuals.
- Click the Residuals vs. deleted residuals button to produce a Residuals vs. Deleted Residuals Plot, which plots the Studentized Deleted Residuals against the Raw Residuals of the dependent variable for each case or run.
- Residuals vs. case numbers.
- Click the Residuals vs. case numbers button to produce a Residuals vs. Case Numbers Plot, which plots the selected residuals (Raw or Studentized deleted) against the Case numbers for each case or run.