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Regression Interpretation Guide — Coefficients, p-values, R², Assumptions — GetCalcMaster

How to interpret linear regression output: coefficients, intercept, p-values, confidence intervals, R²/adjusted R², residuals, and key assumptions.

Regression output can look intimidating, but it’s mostly a structured summary: coefficient estimates, uncertainty, fit quality, and diagnostics. This guide focuses on what each part means and what can go wrong.

Open Statistics Calculator Use Notebook Guides

Important: Educational. For publishable analysis, use diagnostics, robust SEs where appropriate, and field-specific modeling practices.

What this calculator is

The Statistics Calculator is an interactive tool inside GetCalcMaster. It’s designed to help you explore scenarios, understand formulas, and document assumptions.

Key features

Explains coefficients as “holding other variables constant” effects
Clarifies p-values vs confidence intervals vs practical size
Covers R², adjusted R², and why R² always increases with more predictors
Lists the most important assumptions and quick diagnostics

Formula

Linear model:  Y = β0 + β1 X1 + β2 X2 + ... + ε
R² = 1 - SSE/SST
Adjusted R² = 1 - (1-R²)*(n-1)/(n-p-1)

Quick examples

If β1=2.5 for X1=hours studied, then +1 hour is associated with +2.5 points in score (holding other variables fixed).
If a 95% CI for β1 is [0.1, 4.9], the data are consistent with small to moderate positive effects.
A huge R² doesn’t guarantee the model is valid if residuals show patterns (nonlinearity, heteroskedasticity).

How to use it (quick steps)

Start with the question: what outcome (Y) and predictors (X) are in the model?
Interpret each coefficient as the expected change in Y per 1-unit change in X (holding others constant).
Use confidence intervals to assess plausible effect sizes (not only p-values).
Check fit (R²/adjusted R²) and residual plots for obvious violations.
Be cautious about causality unless the design supports it.