Beta Regression is a Generalised Linear Model (GLM) for outcomes that are continuous proportions or rates strictly between 0 and 1. Use it whenever the dependent variable is bounded on (0, 1) and ordinary linear regression would produce nonsensical predictions (negative values or values above 1). Typical applications include the proportion of items answered correctly on an exam, the fraction of habitat covered by a species, or the share of household income spent on food.

Logistic regression handles a binary 0/1 outcome and models the probability of a single success. Beta regression handles a continuous proportion like 0.32 or 0.78 and models the expected mean on the (0, 1) scale. If the outcome is recorded as a fraction or percentage divided by 100, use Beta; if it is a yes/no event, use logistic.

The standard Beta density is undefined at 0 and 1. Two practical options exist: (a) apply the Smithson and Verkuilen (2006) transformation y' = (y(n − 1) + 0.5)/n to nudge boundary values just inside the interval, or (b) fit a zero-inflated, one-inflated, or zero-and-one-inflated Beta model that accommodates the boundary values directly. This calculator applies option (a) automatically when needed.

Coefficients are on the logit scale. A positive β means the linear predictor — and therefore the expected proportion — increases with the predictor. To convert to a proportion at a chosen X, compute μ̂ = exp(β₀ + β₁X) / (1 + exp(β₀ + β₁X)). The exponentiated coefficient exp(β₁) is the multiplicative effect on the odds of the proportion.

φ governs how tightly the data cluster around the mean. The variance of y is μ(1 − μ)/(1 + φ); larger φ implies smaller variance and more concentrated proportions, while smaller φ implies wider scatter. Reporting φ alongside the coefficients is recommended for full transparency.

Ferrari and Cribari-Neto (2004) defined pseudo-R² as the squared Pearson correlation between the linear predictor η̂ = β₀ + β₁X and the link-transformed response g(y). It ranges from 0 to 1 and is interpreted in the same direction as OLS R² — larger means a better fit — though the absolute scale differs from least-squares R².

For a single predictor, a practical minimum is 30 observations. For multiple predictors, aim for at least 10–20 cases per coefficient. Bias and standard-error stability improve markedly above n = 50.

Report the coefficient (β), standard error, z-statistic, p-value, link function, precision φ̂ and pseudo-R². Example: "A Beta regression with logit link was fitted; X significantly predicted Y, β = 0.42, SE = 0.11, z = 3.82, p < .001, pseudo-R² = .31, φ̂ = 28.4."

The calculator is designed for educational use, teaching demonstrations, and exploratory analysis. For peer-reviewed publication we recommend cross-validating the estimates in dedicated software such as the betareg package in R (Cribari-Neto & Zeileis, 2010). You may cite this tool as: STATS UNLOCK. (2026). Beta Regression Calculator. https://statsunlock.com.

A non-significant coefficient (p > α) does not prove the absence of an effect. It indicates that the data, at your chosen alpha and sample size, do not provide sufficient evidence to reject the null hypothesis of no effect. Consider a power analysis and look at the confidence interval — a wide CI that crosses zero suggests an under-powered design rather than a true null.