linear regression calculator

Enter matching X and Y values to calculate the best-fit line, correlation, and prediction.

X values (comma, space, or new-line separated)

Y values (same number of values as X)

Predict Y for X (optional)

What this calculator does

This tool computes a simple linear regression using your dataset. It finds the straight line that best explains how Y changes with X, using the least-squares method. In practical terms, you can use it to estimate trends, make quick forecasts, and measure relationship strength between two numeric variables.

How linear regression works

Simple linear regression models a relationship using: ŷ = b₀ + b₁x

b₁ (slope): expected change in Y when X increases by 1.
b₀ (intercept): expected value of Y when X = 0.
r: correlation coefficient, from -1 to +1.
R²: percent of Y variation explained by X.

Output included in this page

Regression equation
Slope and intercept
Correlation coefficient (r)
Coefficient of determination (R²)
RMSE (root mean squared error)
Optional prediction for a custom X value

How to use the calculator

Enter all X values in the first box.
Enter the matching Y values in the second box.
Optionally add a value for “Predict Y for X.”
Click Calculate Regression.

You can separate values with commas, spaces, or line breaks. Just make sure X and Y contain the same number of points.

Interpreting your results

1) Slope

A positive slope means Y tends to increase as X increases. A negative slope means Y tends to decrease. The magnitude tells you how quickly Y changes.

2) Intercept

The intercept is the predicted Y value at X = 0. In some domains this has real meaning; in others, it’s just a mathematical anchor point.

3) Correlation and R²

Correlation near +1 or -1 indicates a strong linear relationship. R² closer to 1 means your line explains more of the variation in data. Low R² often suggests either weak linear relationship or missing variables.

Best practices and limitations

Use linear regression when the relationship is roughly straight-line.
Watch for outliers; one extreme value can distort the model.
Correlation does not prove causation.
Predictions are most reliable within the range of observed X values.
If X values are all identical, regression is undefined (no slope can be fit).

Example use cases

Estimating monthly revenue growth from ad spend.
Relating study hours to exam score.
Forecasting energy usage from temperature.
Checking whether process time changes with workload.

Final thought

Linear regression is one of the most useful first-pass statistical tools because it is fast, interpretable, and practical. Use this calculator to get a clean baseline model, then refine with more advanced methods when your data needs them.