Residual Plot

How to generate a residual plot in Licklider, what it shows, and how to use it to check regression assumptions.

A residual plot shows the residuals from a regression model plotted against the fitted values. It is used to check whether the assumptions of the regression are met — particularly whether the residuals are randomly distributed around zero.

What residuals are

A residual is the difference between the observed value and the value predicted by the model. For each observation:

residual = observed y − fitted y

If the model fits well, residuals should be scattered randomly above and below zero with no systematic pattern. Systematic patterns indicate that the model is missing something — for example, that the true relationship is non-linear, or that the variance changes across the range of fitted values.

What the figure shows

The x-axis shows the fitted values from the model. The y-axis shows the residuals. A horizontal reference line at zero is included.

If the assumptions of the regression hold:

  • Points should be scattered randomly above and below the reference line
  • The spread of residuals should be roughly constant across the range of fitted values (homoscedasticity)
  • No curved or systematic pattern should be visible

When it is available

Residual plots are available for:

  • Simple linear regression (one predictor) — residuals are computed from the fitted OLS line
  • Non-linear regression (4PL, 3PL, Hill) — residuals are returned by the fitting engine alongside the fitted curve

Residual plots for logistic regression and multiple linear regression (more than one predictor) are not currently supported.

This current scope is intentional. The public residual-plot surface is limited to cases where a single fitted-value axis gives a relatively direct visual reading of misspecification or changing spread. More complex model families require additional diagnostic views that are not yet exposed in this figure contract.

How to request it

After fitting a regression model, request the residual plot in the Chat:

  • "Show the residual plot"
  • "Show residuals vs fitted"
  • "Check the regression assumptions"

What the Inspector shows

The Inspector panel alongside the residual plot shows the model type used and the number of observations. For simple linear regression, the residual standard error is also reported.

The residual standard error is included because it gives a compact summary of the typical residual size in the same units as the outcome, complementing the visual pattern in the plot.

Interpreting patterns

Random scatter around zero No evidence of model misspecification. The linearity and homoscedasticity assumptions are plausible.

Curved pattern (funnel or arc) The true relationship may be non-linear. Consider fitting a non-linear model or transforming the predictor.

Increasing spread (fan shape) Variance increases with fitted values — a violation of homoscedasticity. Log-transforming the outcome may stabilize the variance.

Outlying residuals Individual observations far from zero warrant investigation. They may indicate data entry errors, extreme biological responses, or protocol deviations.

Licklider cannot determine automatically whether a visible pattern is substantively important, whether a transformed model is the scientifically right next step, or whether an outlying residual is a meaningful signal or an error. A residual plot is one diagnostic view, not a complete proof that the model is valid or invalid.

Even when points look roughly random, that does not guarantee that every regression assumption is satisfied. Residual plots are best read together with model context and, where relevant, other diagnostics.

Design Rationale & References

This page follows a simple rule: model-checking figures should make the mismatch between fitted values and observed data visible before users place too much confidence in a regression result. That is why the plot uses residuals versus fitted values with a zero reference line, and why the page emphasizes pattern reading over a single pass/fail summary.

Residuals-versus-fitted is a standard diagnostic view because it helps reveal nonlinearity, changing variance, and other systematic departures that are hard to see from coefficients alone [1, 2]. The current support is limited to simpler regression surfaces because those cases are easier to read directly without implying a more complete diagnostic suite than the product currently exposes.

The page also avoids treating the residual plot as a standalone validator. That boundary is intentional: diagnostic plots help identify potential model problems, but they do not decide on their own which scientific correction is appropriate.

  1. Anscombe, F. J., & Tukey, J. W. (1963). The Examination and Analysis of Residuals. Technometrics, 5(2), 141-160. https://doi.org/10.1080/00401706.1963.10490071
  2. Fox, J. (2016). Applied Regression Analysis and Generalized Linear Models (3rd ed.). Sage.

What this page does not cover