Linear regression calculator for data points. Find the best-fit line, correlation coefficient, R-squared, and predictions with step-by-step solutions.
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Calculate the equation of the best-fit line for your data using least squares regression. Get slope, intercept, correlation coefficient (r), R-squared, standard error, and make predictions. Includes scatter plot visualization with regression line.
Linear regression is a statistical method for modeling the relationship between a dependent variable and one or more independent variables. Simple linear regression finds the best-fitting straight line (ŷ = b₀ + b₁x) through data points by minimizing the sum of squared residuals. It's fundamental to predictive modeling and data analysis.
Regression Equation
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R-squared, also called the coefficient of determination, indicates how well the regression line fits your data. An R² of 0.85 means 85% of the variance in Y is explained by X. Values closer to 1 indicate a better fit, while values near 0 suggest the model doesn't explain the data well.
The correlation coefficient (r) measures the strength and direction of the linear relationship between variables, ranging from -1 to 1. R² is simply r squared, which gives the proportion of variance explained. Unlike r, R² is always positive and doesn't indicate direction.
While you technically need at least 2 points to fit a line, meaningful statistical analysis requires more. Generally, you should have at least 10-20 data points, and preferably more, to get reliable results. The standard error calculation requires n > 2.
Don't use linear regression when: the relationship isn't linear (check the scatter plot), there are significant outliers, the data shows heteroscedasticity (non-constant variance), or the observations aren't independent. In these cases, consider other methods or data transformations.