Linear Regression Calculator
Calculate the best-fit regression line, slope, intercept, correlation coefficient, R-squared value, residuals, and predicted values from your data.
Enter Data Points
Add at least two valid X and Y coordinate pairs.
Enter one pair per line. Separate X and Y using a comma, tab, semicolon, or space.
Regression Results
Review the equation, model strength, and prediction statistics.
Your results will appear here
Enter paired numerical data and select Calculate Linear Regression to analyze the relationship between X and Y.
Scatter Plot and Best-Fit Line
| # | X | Observed Y | Predicted Y | Residual |
|---|
What Is a Linear Regression Calculator?
A linear regression calculator analyzes the relationship between two numerical variables. It creates a straight line that best represents the pattern in your data and provides an equation that can be used for interpretation and prediction.
The calculator treats X as the independent or explanatory variable and Y as the dependent or response variable. It applies the least-squares method to minimize the squared differences between observed Y values and values predicted by the regression line.
Regression Equation
Generate the best-fit equation in the standard form ŷ = a + bx, where a is the intercept and b is the slope.
Model Strength
Review the correlation coefficient and R-squared value to understand the direction and strength of the linear relationship.
Value Prediction
Enter a new X value to estimate the corresponding Y value using the calculated regression equation.
How to Use the Linear Regression Calculator
Enter Paired Data
Add each independent X value with its corresponding dependent Y value. At least two valid pairs are required.
Calculate the Model
Select the calculate button to generate the regression equation, slope, intercept, correlation, R², and residuals.
Review and Predict
Explore the chart, inspect predicted values, download the analysis, or estimate Y for a new X value.
Linear Regression Formula
Simple linear regression creates a straight-line equation using the least-squares method:
Understanding the Regression Results
A positive slope indicates that Y generally increases as X increases. A negative slope indicates that Y generally decreases as X increases. A slope close to zero suggests little linear change in Y as X changes.
The correlation coefficient, represented by r, ranges from -1 to 1. Values near 1 indicate a strong positive linear relationship, while values near -1 indicate a strong negative linear relationship. Values near zero indicate a weak linear relationship.
R-squared ranges from 0 to 1 and measures how much of the variation in Y is explained by the regression line. A higher R-squared value indicates that the line fits the observed data more closely, but it does not automatically prove causation or guarantee accurate predictions outside the observed range.
Frequently Asked Questions
The slope represents the expected change in Y when X increases by one unit. For example, a slope of 2.5 means the predicted Y value increases by approximately 2.5 units for every one-unit increase in X.
There is no universal R-squared threshold. An acceptable value depends on the subject, data quality, natural variability, and purpose of the analysis. Higher values normally indicate a closer fit, but model assumptions must also be considered.
No. Correlation shows that two variables move together, but it does not establish that one variable causes changes in the other. Other variables, study design, and supporting evidence must be evaluated.
Yes. The calculator accepts positive values, negative values, zero, integers, and decimal numbers for both X and Y.
A residual is the difference between an observed Y value and the Y value predicted by the regression equation. Smaller residuals generally indicate a closer fit for individual data points.
It can estimate Y values from new X values using the regression equation. Predictions are normally more dependable within the range of the original data. Extrapolating far beyond that range may produce unreliable results.
No. The regression calculations are performed in your browser using JavaScript. The entered values do not need to be uploaded or stored on the server.