Regression Plot

A regression plot adds a fitted line and confidence band to a scatter plot, making the linear model the primary message. This commits the figure to a specific claim: X predicts Y. All regression plots require assumption diagnostics, disclosure of the regression model parameters, and —for observational data —explicit acknowledgment that prediction is not causation.

STEP 1 —When to Use

Use a regression plot when: linear regression is the primary analysis (not just an annotation on a scatter); you want to display the fitted model with its uncertainty (confidence band); you are predicting Y from X and the linear model has been validated.

Regression diagnostics are required before generating a regression plot: linearity, homoscedasticity, normality of residuals, and absence of influential outliers must be checked (see Regression Diagnostics Guard, 4.7.1).

[Image placeholder: Regression plot with scatter (n=55) and fitted OLS line. 95% confidence band shown as shaded region around line. Rﾂｲ=0.61, equation shown as annotation. Residual plot inset (small, bottom right) showing no pattern. Legend: "OLS regression: Y = 2.3X + 14.1 (Rﾂｲ = 0.61, 95% CI for slope: [1.8, 2.8])."]

Regression plot with confidence band, Rﾂｲ, equation annotation, and residual diagnostic inset —all required for a fully transparent regression figure.

STEP 2 —Journal Requirement

Regression equation (intercept, slope) and Rﾂｲ must be stated in the legend or as a figure annotation.
95% CI for the slope must be reported.
Regression assumption checks must be referenced in the Methods section.
Confidence band type: "95% confidence band for the mean response" (not for individual predictions —this requires a prediction interval).
For observational data: "This regression is descriptive/associative. Causality is not implied."

STEP 3 —Licklider Implementation

Input

Two continuous variables
Regression model type: OLS (default), robust (Huber), weighted, or polynomial (degree specified)
Causation declaration: associative (default) or causal (requires basis)

Output

Scatter points + fitted regression line
95% confidence band for the mean (shaded, semi-transparent)
Equation and Rﾂｲ annotated on the figure
95% CI for slope in legend
Regression diagnostics summary linked (from 4.7.1 check results)
Causation disclosure auto-inserted in legend based on declaration

[Image placeholder: Licklider regression plot. Scatter + OLS line + 95% confidence band. Annotation: "Y = 2.3X + 14.1, Rﾂｲ = 0.61." Legend: "Slope = 2.3 (95% CI [1.8, 2.8]). The regression is descriptive; no causal relationship between X and Y is claimed. Assumption checks: residuals normal (Shapiro-Wilk p = 0.38), homoscedastic (Breusch-Pagan p = 0.42), no influential points (max Cook's D = 0.09)."]

Licklider regression plot: fitted line with 95% confidence band, Rﾂｲ, equation, slope CI, and full assumption check summary in legend.

STEP 4 —Draft Output (Draft / Needs review)

OLS regression of [Y] on [X] (n = 55): Y = 2.3X + 14.1 (Rﾂｲ = 0.61).
Slope = 2.3 (95% CI [1.8, 2.8]), t(53) = 9.1, p < 0.001.
The shaded region shows the 95% confidence band for the mean response.
Regression assumptions were verified: residuals were normally distributed
(Shapiro-Wilk: W = 0.97, p = 0.38), homoscedastic (Breusch-Pagan: p = 0.42),
and no influential points were detected (max Cook's D = 0.09).
This regression is descriptive; no causal relationship is implied.