Linear Regression Calculator
Calculate linear regression with step-by-step solutions. Find slope, intercept, correlation coefficient (r), and R-squared with scatter plot visualization.
Formula:y = mx + b
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What is Linear Regression?
Linear regression is a statistical method for modeling the relationship between a dependent variable (y) and one or more independent variables (x). Simple linear regression uses one independent variable and finds the line y = bx + a that best fits the data by minimizing the sum of squared differences between observed and predicted values.
Linear regression finds the best-fitting straight line through a set of data points. Use our free calculator to calculate the slope, intercept, correlation coefficient (r), and R-squared value. Simply enter your x,y data points and get the regression equation with detailed step-by-step calculations and an interactive scatter plot.
Key Facts About Linear Regression
- *The regression line minimizes the sum of squared residuals (least squares)
- *Slope (b) tells you how much y changes for each unit increase in x
- *Intercept (a) is the predicted y value when x equals zero
- *Correlation coefficient (r) ranges from -1 to +1, measuring linear relationship strength
- *R-squared (R^2) is the proportion of variance in y explained by x
- *R^2 = r^2 for simple linear regression
- *Residuals are the differences between actual and predicted y values
- *A perfect fit has R^2 = 1 and all residuals equal zero
Frequently Asked Questions
What is R-squared and how do I interpret it?
R-squared (R^2) measures how well the regression line fits the data. It ranges from 0 to 1, representing the proportion of variance in y explained by x. An R^2 of 0.85 means 85% of the variation in y is explained by the linear relationship with x. Higher values indicate better fit.
What is the difference between r and R^2?
The correlation coefficient (r) measures the strength and direction of the linear relationship (-1 to +1). R-squared (R^2) is simply r^2 and represents the proportion of explained variance (0 to 1). R^2 is always positive while r preserves the direction.
How do I interpret the slope?
The slope (b) tells you the change in y for each one-unit increase in x. If the slope is 2.5, then y increases by 2.5 units for every 1-unit increase in x. A negative slope means y decreases as x increases.
What are residuals?
Residuals are the differences between the actual y values and the predicted y values from the regression line. Residual = Actual y - Predicted y. The regression line minimizes the sum of squared residuals (least squares method).
Practice Linear Regression
Test your skills with practice problems
Practice with 6 problems to test your understanding.
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How this works
Formulas follow standard definitions from the NIST Digital Library of Mathematical Functions and classical textbook derivations. Calculations run entirely in your browser. Where a closed-form solution exists, it is used; where an iterative or numerical method is required, the implementation is named on the page.
Sources
- [1]NIST Digital Library of Mathematical FunctionsAcademicdlmf.nist.govAccessed Apr 21, 2026
Joseph OrdunaFounder & Software Engineer
Full-stack software engineer specializing in embedded systems, web architecture, and AI/ML. Founder of Practical Web Tools. Built the gesture-controlled drone IP acquired by KD Interactive (Aura Drone, sold on Amazon).