Linear Regression Calculator
Linear regression online with coefficients, p-values, R squared, residual plots and 95 percent CIs.
When to use it
Use to predict a continuous outcome Y from a single continuous predictor X. Returns the slope, intercept, R-squared, and significance tests, plus diagnostic plots that tell you whether the linear assumption is reasonable.
When NOT to use it
Do not use for binary outcomes (use logistic regression). Do not use for count outcomes (use Poisson or negative binomial). Do not use when residuals show a clear curve in the residual-versus-fitted plot; consider polynomial terms or a transformation. For multiple predictors use the Multiple Regression tool.
What you get
Slope and intercept with their standard errors, t-statistics, p-values, and 95 percent confidence intervals; R-squared and adjusted R-squared; the F test of the model; the regression equation written out; a residual-versus-fitted plot, a normal Q-Q plot of residuals, and the fitted line on a scatter of the raw data.
Worked example
Fifteen-pair height (m) and mass (kg) dataset, American women aged 30 to 39 (R built-in `women`).
1.47, 1.50, 1.52, 1.55, 1.57, 1.60, 1.63, 1.65, 1.68, 1.70, 1.73, 1.75, 1.78, 1.80, 1.83 52.21, 53.12, 54.48, 55.84, 57.20, 58.57, 59.93, 61.29, 63.11, 64.47, 66.28, 68.10, 69.92, 72.19, 74.46
Expected output: intercept = -39.062, slope = 61.272, r = 0.9946
Source: Becker, R. A., Chambers, J. M. and Wilks, A. R. (1988). The New S Language. Wadsworth and Brooks (source of R `women`). Reproduced as the introductory simple-LM example in Draper, N. R. and Smith, H. (1998), Applied Regression Analysis, 3rd ed., Wiley, ch. 1.
How to interpret the output
The slope is the expected change in Y per one-unit increase in X. The intercept is the expected Y when X equals zero (often not biologically meaningful, do not over-interpret). R-squared is the proportion of variance in Y explained by X; its square root is the absolute Pearson correlation. A significant F (or equivalently a significant slope t) means X has a non-zero linear effect on Y at the chosen alpha. Cross-checked against R lm() on the 15-pair height-mass `women` dataset (Becker, Chambers and Wilks 1988; Draper and Smith 1998 ch. 1).
Common pitfalls
- Reporting only R-squared; always report the slope, its CI, and the p.
- Inferring causation from a high R-squared (regression measures association).
- Extrapolating predictions far outside the observed X range.
- Ignoring the residual-versus-fitted plot when it shows a U-shape (linear model is wrong).
Try it in StatVeda
The Simple Linear Regression engine runs entirely in the browser. No signup, no install, no data sent to a server. Paste your data, hit Run, copy the output.
Open Simple Linear RegressionReferences
- Snedecor, G. W. and Cochran, W. G. (1989). Statistical Methods, 8th edition. Iowa State University Press, Ames. Chapter 9.
- Draper, N. R. and Smith, H. (1998). Applied Regression Analysis, 3rd edition. John Wiley and Sons, New York.
- Kutner, M. H., Nachtsheim, C. J., Neter, J. and Li, W. (2005). Applied Linear Statistical Models, 5th edition. McGraw-Hill, New York.