Regression Plot

How to add a regression line and confidence band to a scatter plot in Licklider, and what the figure shows.

A regression plot is a scatter plot with an ordinary least squares regression line and a 95% confidence band overlaid. It shows the linear relationship between two continuous variables and the uncertainty around the estimated mean response.

How it differs from a scatter plot

A scatter plot shows the raw data points. A regression plot adds:

  • A fitted regression line — the OLS line of best fit through the data
  • A 95% confidence band — a shaded region around the line reflecting uncertainty in the estimated mean at each value of x

The confidence band narrows in the middle of the x-range (near the mean of x) and widens toward the extremes. It reflects uncertainty in the mean response, not the spread of individual observations around the line.

How to request it

Describe the analysis in the Chat. For example:

  • "Show a regression plot"
  • "Add a regression line to this scatter plot"
  • "Plot Y against X with a fitted line"

Licklider will display the scatter plot with the regression line and confidence band automatically.

What the figure shows

The regression line is computed from the data using ordinary least squares. The confidence band is derived from the slope, intercept, residual standard error, and the spread of x values.

The statistical results — coefficient, R², p-value, and standard error — are shown in the Inspector panel alongside the figure.

Minimum data requirement

A regression plot requires at least 10 observations. For fewer observations, the regression line and confidence band can be misleading and Licklider will not generate this chart type.

Regression line vs correlation

The regression line answers: how does y change with x? The correlation coefficient answers: how strongly are x and y related?

Licklider reports both alongside the regression plot. Pearson correlation is reported when the data is approximately bivariate normal; Spearman correlation is reported alongside when normality is in question.

What this page does not cover