Compute simple linear regression via OLS with equation, r², standard error, and prediction.
Simple linear regression models the relationship between an independent variable X and a dependent variable Y as a straight line: Ŷ = β₀ + β₁X. This calculator estimates the coefficients by Ordinary Least Squares (OLS), which picks the line that minimizes the sum of squared residuals, the vertical distances between the points and the line. Alongside the coefficients, it shows r² (how much of Y's variation the model explains), the Pearson r, the standard error of estimate, and a section to predict Y from a new X. Just paste the x, y pairs (one per line, up to 200 points) and the equation appears instantly. It is the right tool for exploring trends, quantifying relationships and making quick predictions in data science, statistics, economics and schoolwork, all in the browser, without sending data to servers.
Simple linear regression fits a line Ŷ = β₀ + β₁X to your points, picking the slope (β₁) and intercept (β₀) that keep the line as close as possible to all the data at once. The criterion is Ordinary Least Squares (OLS): among all possible lines, it chooses the one that minimizes the sum of squared residuals, the vertical distances between each point and the line. The slope comes from β₁ = Σ(x−x̄)(y−ȳ) / Σ(x−x̄)², and the intercept from β₀ = ȳ − β₁·x̄.
Besides the coefficients, the tool computes r² (the coefficient of determination), which runs from 0 to 1 and tells you what fraction of Y's variation the line explains; the Pearson r, with the same sign as the slope; and the standard error of estimate, the typical spread of the points around the line. Everything is computed in 64-bit floating point, with up to 200 data pairs.
Example 1, the "Load example" dataset: (1, 2.1), (2, 4.0), (3, 5.9), (4, 8.2), (5, 9.8). The means are x̄ = 3 and ȳ = 6; summing, Σ(x−x̄)(y−ȳ) = 19.6 and Σ(x−x̄)² = 10, so β₁ = 19.6/10 = 1.96 and β₀ = 6 − 1.96 × 3 = 0.12. The line is Ŷ = 1.96X + 0.12, with r² ≈ 0.998 (the line explains nearly all the variation) and a standard error ≈ 0.167. Predicting X = 6: Ŷ = 1.96 × 6 + 0.12 = 11.88.
Example 2, study hours (X) and exam score (Y): (1, 53), (2, 54), (3, 56), (4, 57). Here β₁ = 1.4 and β₀ = 51.5, so Ŷ = 1.4X + 51.5, with r² = 0.98. The slope of 1.4 reads directly: each extra hour of study is associated with about 1.4 more points on the score. Predicting 5 hours: Ŷ = 1.4 × 5 + 51.5 = 58.5 points.
Linear regression is useful whenever you suspect an approximately straight relationship between two variables and want to quantify it or make predictions: sales versus ad budget, temperature versus energy use, dose versus response, study hours versus performance. The slope becomes an interpretable rate (how much Y changes per unit of X) and the line lets you estimate Y for new values of X.
There are important limits. The line only captures linear relationships, curved data needs a different model; the method is sensitive to outliers, which can pull the slope; and correlation is not causation, so a high r² does not prove that X causes Y. Extrapolating far beyond the range of your data is risky, and this tool handles a single X variable (simple regression), for several variables, use multiple regression in Python (scikit-learn) or R.
Paste the code into your HTML and the tool shows up on your page, without J-Kit's navigation and ads. It still runs in the browser of whoever visits your site.
<iframe
src="https://jkit.tools/embed/en-US/linear-regression-calculator"
width="100%"
height="600"
style="border:0"
loading="lazy"
title="Linear Regression Calculator"
></iframe>These references help contextualize formulas, standards, APIs and limitations used on this page. They do not replace professional validation when a result has legal, financial, medical or operational impact.
Simple linear regression is a statistical model that describes the relationship between an independent variable X and a dependent variable Y as a line, Ŷ = β₀ + β₁X. The slope β₁ tells you how much Y changes for each one-unit increase in X, and the intercept β₀ is the predicted value of Y when X is zero. It is the foundation of much of data analysis, used both to understand a relationship and to predict values.
One x, y pair per line. Maximum 200 pairs.
All data stays in your browser. No data is sent to any server.