Regression Calculator
Perform linear regression analysis with ease. This calculator computes the best-fit line using the least squares method, providing slope, intercept, R², correlation coefficient, and detailed step-by-step calculations. Visualize your data with a scatter plot and regression line, and make predictions for new x values.
What Is Linear Regression?
Linear regression is a statistical method used to model the relationship between a dependent variable (y) and one or more independent variables (x). The goal is to find the best-fit line that minimizes the sum of squared vertical distances (residuals) between the observed data points and the line — this is called the least squares method.
The Regression Equation
y = mx + b
where m is the slope and b is the y-intercept
Key Statistics
- Slope (m): The change in y for a 1-unit change in x.
- Intercept (b): The value of y when x = 0.
- R² (Coefficient of Determination): The proportion of variance in y explained by x. Ranges from 0 to 1 (higher is better).
- Correlation (r): The strength and direction of the linear relationship between x and y. Ranges from -1 to +1.
- SSE (Sum of Squared Errors): The sum of squared residuals — smaller values indicate a better fit.
How the Calculator Works
- Enter Data: Add (x, y) pairs one at a time or paste a list.
- Calculate: The calculator computes the regression line using the least squares method.
- View Results: See the slope, intercept, R², correlation, and SSE.
- Visualize: The scatter plot shows your data points and the regression line.
- Predict: Enter a new x value to predict the corresponding y value.
Why Use This Regression Calculator?
- Complete Analysis: Get all key regression statistics in one place.
- Step-by-Step: See the calculation process with intermediate values.
- Visual: Interactive scatter plot with the regression line.
- Prediction: Forecast y values for new x inputs.
- Free & Private: No registration, no data storage.
❓ Regression Calculator FAQ
What is linear regression?
Linear regression is a statistical method that models the relationship between a dependent variable (y) and an independent variable (x) using a straight line: y = mx + b.
What is the least squares method?
The least squares method finds the best-fit line by minimizing the sum of the squared vertical distances (residuals) between the observed data points and the line.
What does R² mean?
R² (coefficient of determination) measures how well the regression line fits the data. It ranges from 0 to 1, where 1 indicates a perfect fit and 0 indicates no linear relationship.
What is the difference between correlation (r) and R²?
Correlation (r) measures the strength and direction of the linear relationship (-1 to +1). R² is the square of r and represents the proportion of variance explained (0 to 1).
How do I interpret the slope?
The slope (m) tells you how much y changes when x increases by 1 unit. A positive slope means y increases as x increases; a negative slope means y decreases as x increases.
What is SSE?
SSE (Sum of Squared Errors) is the sum of the squared residuals (vertical distances between each data point and the regression line). A smaller SSE indicates a better fit.
Can I use this for prediction?
Yes! Enter a new x value in the prediction section, and the calculator will use the regression equation to predict the corresponding y value.
What if my data doesn't follow a linear pattern?
If the data is non-linear, the R² value will be low, indicating a poor fit. You may want to consider other regression models (polynomial, exponential, etc.) for non-linear data.
Is this calculator free?
Yes, this calculator is completely free to use. No registration or personal data storage is required. All calculations are performed in your browser.