Diagnostic Results
Interactive Q-Q Plot
Normality Tests
| Test | Statistic | p-value | Decision |
|---|
Shapiro-Wilk and Lilliefors values are practical browser approximations. Confirm critical decisions with specialist statistical software.
Interpretation
Residual and Quantile Details
| # | Group | Label | Observed | Predicted | Raw residual | Selected residual | Sorted residual | Theoretical quantile | Probability | Deviation | Outlier |
|---|
Formula Used
Raw residual: eᵢ = yᵢ − ŷᵢ Standardized residual: zᵢ = (eᵢ − ē) / sₑ Internally studentized residual: rᵢ = eᵢ / [s √(1 − hᵢ)] Plotting position: pᵢ = (i − a) / (n + 1 − 2a) Theoretical quantile: qᵢ = F⁻¹(pᵢ) Q-Q reference line: y = intercept + slope × q Q-Q correlation: r = Corr(qᵢ, e(i)) Q-Q R²: r²
How to Use
Choose observed and predicted values or enter residuals directly. Paste rows, upload a file, or load the example dataset. Include optional labels, groups, leverage, and Cook’s distance values.
Select the residual definition and reference distribution. Adjust plotting positions, transformations, confidence envelopes, and outlier rules. Then create the interactive diagnostic plot.
Review normality tests, summary statistics, and highlighted tail departures. Compare groups using the group column. Export the plot, table, or complete PDF report.
Example Data Format
| observed | predicted | label | group | leverage | cooks |
|---|---|---|---|---|---|
| 12.1 | 11.7 | A01 | Model A | 0.08 | 0.01 |
| 14.8 | 15.2 | A02 | Model A | 0.11 | 0.02 |
| 18.6 | 18.0 | A03 | Model A | 0.07 | 0.01 |
Frequently Asked Questions
What does a Q-Q plot of residuals show?
It compares ordered residuals with theoretical distribution quantiles. Near-linear points support the chosen distribution. Curvature indicates skewness, unusual tails, or outliers.
Must residuals be perfectly normal?
No. Small departures are common in practical models. Serious tail departures matter most for inference and prediction intervals.
Which residual type should I use?
Raw residuals suit simple exploration. Standardized residuals support scale-free comparison. Studentized residuals better reveal influential observations.
What is the confidence envelope?
It shows expected sampling variation around the theoretical pattern. Points outside it deserve investigation. The envelope is not a strict acceptance rule.
What causes an S-shaped Q-Q plot?
An S-shape often indicates tail-weight differences. Heavy tails bend both extremes away. Light tails usually bend them inward.
Can I compare several models?
Yes. Add a group value for each row. Each group receives a separate Q-Q trace and summary.
Why do test results disagree?
Normality tests emphasize different departures. Sample size also changes sensitivity. Use tests together with the visual pattern.
How are percentage residuals calculated?
They use residual divided by observed value. Rows with zero observed values are protected. Interpret large percentages cautiously.
Can non-normal distributions be checked?
Yes. Choose Student’s t, logistic, exponential, uniform, or Laplace. Distribution parameters can be fitted or entered manually.
What does Q-Q correlation measure?
It measures linear agreement between sample and theoretical quantiles. Values near one indicate stronger distributional agreement. Tail problems may still remain.
Are browser normality tests exact?
Some are exact formulas, while others use approximations. Confirm regulated or high-stakes work with dedicated statistical software. Preserve the exported data.