Use this linear regression calculator to estimate the best-fit linear relationship between a predictor and an outcome variable. Outputs include coefficients, R-squared, residual diagnostics, and prediction intervals.
Use template ->What is linear regression?
Linear regression is a statistical method for estimating the relationship between a dependent variable and one or more independent variables, assuming that relationship is approximately linear. It produces a best-fit line that minimizes the sum of squared prediction errors across the dataset.
It is one of the most widely used techniques in both statistics and applied analytics, partly because its outputs are interpretable and partly because many real-world relationships are close enough to linear over a relevant range that the model is a useful approximation.
Linear regression formula
ŷ = β₀ + β₁x
Where ŷ is the predicted value, β₀ is the intercept (the value of ŷ when x equals zero), and β₁ is the slope (the change in ŷ for each unit change in x). Both are estimated by minimizing the sum of squared residuals, which gives each observation equal weight.
How the linear regression calculator works
The calculator fits the line and returns coefficients, R-squared, and residual diagnostics alongside the scatter and regression plot. R-squared and coefficients are the entry point, but residual structure is the reliability signal. If residuals show a clear pattern rather than random scatter around zero, the linear assumption is incomplete and the model deserves scrutiny before its outputs are used.
Prediction intervals are most informative once the diagnostic picture looks reasonable. Reading coefficients without checking residuals first is a common way to over-trust an early result, particularly when the relationship in the data is not as clean as a high R-squared might suggest.
How linear regression is used in practice
Linear regression appears across industry in forecasting, relationship estimation, and hypothesis testing. In business analytics, it shows up in pricing models, demand forecasting, and performance attribution. In research, it is often the first modeling step when exploring a numeric outcome. The key discipline is treating diagnostics as integral to the result rather than optional extras that can be checked later.