General plots / Linear regression plot
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Points are the raw data and the solid line is the least-squares fit; the darker band is the confidence band for the mean (uncertainty of the line itself) and the lighter dashed band is the prediction interval (where a new observation is expected; always wider).
R² is the share of variance in y explained by the model. For a straight line the P value tests whether the slope is zero; for polynomials it is the overall F test. The coefficient table lists estimates, standard errors, t, P and confidence intervals.
For data spanning orders of magnitude you can fit on a log10 scale (e.g. power-law relationships); with a group column each group is fitted separately by default, so slopes can be compared.
Regression describes association only; check residuals and subject knowledge to judge whether the model fits. Outliers can strongly influence a least-squares line.
Ordinary least squares (OLS); coefficients, standard errors, t, P, R² and the F test match statsmodels OLS; confidence and prediction bands match get_prediction().summary_frame(), using the t(1 − α/2, n − p) quantile.
Up to 20,000 points and 12 groups.
Send us your data and research question and you will receive a written plan within 1 working day: analysis steps, parameter rationale, deliverables and timeline. Quoted per project.