Simple & Multiple Linear Regression calculator

Fit simple and multiple linear regression models online. Calculate coefficients, R-squared, residuals, and prediction intervals.

What it does

Models how the mean of a continuous outcome changes with several predictors at once, isolating each one's association while holding the others fixed.

When to use it

You have a continuous outcome and two or more predictors — e.g. to adjust for confounders or compare several predictors' contributions.

Worked example

You want to know what drives the price a house sells for. The outcome is the sale price in pounds; the predictors might be floor area, number of bedrooms, age of the property and distance to the nearest station. The model gives you a number for each: "every extra square metre is worth £X, holding the others fixed".

Alternatives

• Logistic — the outcome is binary (yes/no)
• Poisson / Negative Binomial — the outcome is a count of events
• a mixed model — rows are clustered or repeated (patients within clinics, repeated measures)
• Ridge / Lasso — you have many predictors relative to sample size and prediction is the goal

How to read the output

Coefficient (b / Estimate)

Comparing observations that differ by 1 unit in the predictor, the estimated difference in the outcome — on the outcome's own scale, holding the other predictors fixed. This is association, not causation: from observational data, 'a 1-unit increase CAUSES…' is not licensed.

95% CI

The range of coefficient values compatible with your data. Excluding 0 means the direction is fairly determined. A CI that spans 0 means the effect is undetermined — not proven to be zero.

p-value

How surprising a coefficient at least this large would be IF the true effect were exactly zero. A small p means the data would be surprising under that assumption — not that the effect is probably real, and not the probability that chance produced it. p is not effect size or importance. With a large sample, a tiny b can be 'significant' — and the significance pill looks identical either way.

R² / Adjusted R²

Share of the outcome's variance the model explains. Adjusted R² penalises extra predictors — use it to compare models with different predictor counts. A low R² alongside a precise, meaningful coefficient is still a real finding; don't dismiss it for being 'too low'.

Intercept

The predicted outcome when every predictor is 0. Meaningless unless predictors are centred (0 may lie outside your data range).

How this calculator is validated · Which statistical test should I use?