Linear Regression Calculator – Line of Best Fit in 2 Easy Steps
Linear Regression Calculator
Free linear regression calculator – find the line of best fit (Y = mX + b) by entering your independent (X) and dependent (Y) variables.
Variable X (Independent)
Enter values separated by commas or new lines.
Variable Y (Dependent)
Must have the exact same number of values as X.
Use this free linear regression calculator to find the line of best fit for your data in seconds.
Quick answer
Simple linear regression fits Y = mX + b with slope m = Σ(x − x̄)(y − ȳ) ÷ Σ(x − x̄)² and intercept b = ȳ − m·x̄. Example: X = 1, 2, 3, 4, 5 and Y = 2, 4, 5, 4, 5 give Y = 0.6X + 2.2 with R² = 0.6, meaning 60% of the variation in Y is explained by X. This linear regression calculator shows the equation, slope, intercept and R².
Table of Contents
Linear regression is the simplest way to describe how one variable changes with another: how sales rise with ad spend, how exam scores relate to study hours, or how temperature affects energy use. The result is a straight line that best fits your points.
Our free linear regression calculator uses the least-squares method. Paste your X and Y values (comma or line separated), click calculate and get the equation of the line, the slope, the y-intercept and R².
Linear Regression Formulas
| Value | Formula |
|---|---|
| Slope (m) | Σ(x − x̄)(y − ȳ) ÷ Σ(x − x̄)² |
| Intercept (b) | ȳ − m·x̄ |
| Line of best fit | Ŷ = mX + b |
| R² (coefficient of determination) | 1 − SSres ÷ SStot |
Worked Example
- Means: x̄ = 3, ȳ = 4.
- Σ(x − x̄)(y − ȳ) = (−2)(−2) + (−1)(0) + 0 + (1)(0) + (2)(1) = 6.
- Σ(x − x̄)² = 4 + 1 + 0 + 1 + 4 = 10.
- Slope m = 6 ÷ 10 = 0.6; intercept b = 4 − 0.6·3 = 2.2.
- Equation: Y = 0.6X + 2.2, R² = 0.6.
How to read R²
- R² = 1: all points lie on the line.
- R² around 0.6: a moderate linear relationship.
- R² near 0: the line explains almost none of the variation.
How to Use the Linear Regression Calculator
Get your regression line in two steps.
Step 1: Enter Your X and Y Values
Paste the independent values into Variable X and the dependent values into Variable Y, separated by commas or new lines. Both lists must have the same number of values. Click Calculate Equation.
Step 2: Read the Regression Report
The Regression Analysis Report shows the line of best fit equation, the slope, the y-intercept and R². Use Share or Download to save the results.
Using the Equation to Predict
Once you have Y = 0.6X + 2.2, plug in a new X to predict Y. For X = 6, Ŷ = 0.6·6 + 2.2 = 5.8. Be careful predicting far outside your data range – the relationship may not stay linear.
Assumptions to Keep in Mind
- The relationship should look roughly linear on a scatter plot.
- Residuals (errors) should be random, without a pattern.
- Outliers can pull the line strongly – check them before trusting the result.
- Correlation is not causation: a good fit does not prove X causes Y.
Check the strength of the relationship with the Pearson Correlation Calculator, or for ranked data use the Spearman’s Rank Correlation Calculator.
Frequently Asked Questions
What does a linear regression calculator do?
It finds the straight line Y = mX + b that best fits your data using least squares, plus the slope, intercept and R².
What is R² in linear regression?
R² is the share of the variation in Y explained by X, from 0 to 1. Higher means a better fit.
How many data points do I need?
At least two, but use as many as you can – more points give a more reliable line.
Can I paste data from Excel?
Yes. Copy a column and paste it; values on new lines are accepted.
What is the difference between regression and correlation?
Correlation measures the strength of a relationship; regression gives the equation to predict Y from X.
Is the linear regression calculator free?
Yes. It is free, runs in your browser and needs no sign-up.