Regression Calculator

Least-squares linear regression: slope, intercept, r, R², standard error and predictions, with the scatter plot and fitted line.

Your result will appear here

Fill in the fields and press Calculate, or pick one of the examples.

About the Regression Calculator

Fits the least-squares line $y = a + bx$ to paired data — the line that minimises the sum of squared vertical distances to the points — and reports how well it fits through r and R².

Enter an x value to get a prediction from the fitted line. The scatter plot shows the data with the line.

Limitations

Linear model only. A high R² does not show that x causes y, and predictions far outside the range of the data (extrapolation) are unreliable.

How to use it

Enter the X values and the Y values in matching order.
Optionally enter an x to predict y.
Press Calculate.

Example

X: 1 2 3 4 5, Y: 2 4 5 4 5

→ y = 2.2 + 0.6x, R² = 0.6

Formulas used

b = \frac{\sum (x_i - \bar{x})(y_i - \bar{y})}{\sum (x_i - \bar{x})^{2}},\qquad a = \bar{y} - b\bar{x}

Slope and intercept of the least-squares line.

R^{2} = 1 - \frac{\sum (y_i - \hat{y}_i)^{2}}{\sum (y_i - \bar{y})^{2}}

Share of the variation in y explained by the line.

Correlation CalculatorPearson and Spearman correlation coefficients for paired data, with r² and a plain-language strength description.Data VisualizerTurn a data set into a histogram, box plot, bar chart, line chart or scatter plot, with a fitted normal curve and shape analysis.Slope CalculatorSlope, angle of inclination and the equation of the line through two points in slope-intercept and general form.

About the Regression Calculator

Limitations

How to use it

Formulas used

Related tools

About the Regression Calculator

Limitations

How to use it

Formulas used