Linear Regression Calculator
Equation
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R-Squared
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Prediction
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Standard Error
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Simple Linear Regression
Simple linear regression fits a straight line (y = mx + b) to paired data points using the least squares method. The slope (m) represents the average change in Y for each one-unit increase in X. The intercept (b) is the predicted Y value when X equals zero.
R-squared measures how well the line fits the data, ranging from 0 to 1. An R-squared of 0.85 means the line explains 85% of the variance in Y. Higher R-squared indicates a better fit. The standard error of the regression estimates the typical size of prediction errors.
The least squares method minimizes the sum of squared vertical distances between data points and the fitted line. This calculator computes the slope as: (n*SumXY - SumX*SumY) / (n*SumX2 - SumX*SumX), and the intercept as: MeanY - Slope*MeanX. You can use the fitted equation to predict Y values for new X values, though predictions far outside your data range (extrapolation) should be treated with caution.
Frequently Asked Questions
What does R-squared tell me?
R-squared indicates the proportion of variance in Y explained by X. An R-squared of 0.90 means 90% of the variation in Y is predicted by the linear relationship with X. Higher values indicate better predictive power.
Can I use regression for prediction?
Yes, within the range of your data (interpolation). Predictions outside your data range (extrapolation) become increasingly unreliable. Always consider whether a linear model is appropriate for your data.
What are the assumptions of linear regression?
The relationship should be approximately linear, residuals should be normally distributed with constant variance, observations should be independent, and there should be no significant outliers unduly influencing the results.
How many data points do I need?
A minimum of 10-20 data points is recommended for simple linear regression. With fewer points, the results may be unreliable. More data generally gives more stable and trustworthy estimates.