Linear Regression Calculator

The Least-Squares Method

This tool fits a straight line y = mx + b through your data points by minimizing the sum of squared vertical distances between each point and the line - the standard "least squares" approach. It computes the slope first, then derives the intercept from the slope and the data's mean values.

Worked Example

Using the five points shown in the placeholder - (1,2), (2,3), (3,5), (4,4), (5,6) - the mean of x is 3 and the mean of y is 4. For each point, multiply (x minus mean x) by (y minus mean y): (-2)(-2)=4, (-1)(-1)=1, (0)(1)=0, (1)(0)=0, (2)(2)=4. Summing gives 9 (the numerator). The denominator sums (x minus mean x) squared: 4+1+0+1+4 = 10. Slope = 9/10 = 0.9. Intercept = mean y minus slope times mean x = 4 - 0.9x3 = 1.3. The fitted line is y = 0.9x + 1.3.

Checking the Fit

Predicted values at each x: 2.2, 3.1, 4.0, 4.9, 5.8. Squared residuals: 0.04, 0.01, 1.00, 0.81, 0.04, summing to 1.90. Total variance in y (sum of (y minus mean y) squared) is 10. R-squared = 1 - 1.90/10 = 0.81, meaning the line explains 81% of the variation in y. The correlation coefficient r = square root of 0.81 = 0.9 (positive, since the slope is positive).

Reading the Chart

Orange dots mark your actual data points; the blue line is the fitted regression line extended slightly past the min and max x values in your dataset for visual clarity.

Minimum Data Requirement

At least 2 valid (x, y) pairs are required - with only one point, there's no way to calculate a meaningful slope, and the tool will ask for more data instead of guessing.