Linear Regression Calculator

You can use this Linear Regression Calculator to find out the equation of the regression line along with the linear correlation coefficient. It also produces the scatter plot with the line of best fit. Enter all known values of X and Y into the form below and click the "Calculate" button to calculate the linear regression equation. Click on the "Reset" to clear the results and enter new data.

Reference

The Linear Regression Calculator uses the following formulas:

The equation of a simple linear regression line (the line of best fit) is y = mx + b,

Slope m: m = (n*∑x_i y_i - (∑x_i)*(∑y_i)) / (n*∑x_i² - (∑x_i)²)

Intercept b: b = (∑y_i - m*(∑x_i)) / n

Mean x: x̄ = ∑x_i / n

Mean y: ȳ = ∑y_i / n

Sample correlation coefficient r: r = (n*∑x_iy_i - (∑x_i)(∑y_i)) / Sqrt([n*∑x_i² - (∑x_i)²][n*∑y_i² - (∑y_i)²])

-1 < r < +1

Where:

n  is the total number of samples,

x_i (x₁, x₂, ... ,x_n) are the x values,

y_i (y₁, y₂, ... ,y_n) are the y values,

∑x_i  is the sum of x values,

∑y_i  is the sum of y values,

∑x_i y_i  is the sum of products of x and y values

∑x_i²  is the sum of squares of x values

∑y_i²  is the sum of squares of y values

You may also be interested in our Quadratic Regression Calculator or Gini Coefficient Calculator

You can use this Linear Regression Calculator to find out the equation of the regression line along with the linear correlation coefficient. It also produces the scatter plot with the line of best fit. Enter all known values of X and Y into the form below and click the "Calculate" button to calculate the linear regression equation. Click on the "Reset" to clear the results and enter new data.

Reference

The Linear Regression Calculator uses the following formulas:

The equation of a simple linear regression line (the line of best fit) is y = mx + b,

Slope m: m = (n*∑x_i y_i - (∑x_i)*(∑y_i)) / (n*∑x_i² - (∑x_i)²)

Intercept b: b = (∑y_i - m*(∑x_i)) / n

Mean x: x̄ = ∑x_i / n

Mean y: ȳ = ∑y_i / n

Sample correlation coefficient r: r = (n*∑x_iy_i - (∑x_i)(∑y_i)) / Sqrt([n*∑x_i² - (∑x_i)²][n*∑y_i² - (∑y_i)²])

-1 < r < +1

Where:

n  is the total number of samples,

x_i (x₁, x₂, ... ,x_n) are the x values,

y_i (y₁, y₂, ... ,y_n) are the y values,

∑x_i  is the sum of x values,

∑y_i  is the sum of y values,

∑x_i y_i  is the sum of products of x and y values

∑x_i²  is the sum of squares of x values

∑y_i²  is the sum of squares of y values

You may also be interested in our Quadratic Regression Calculator or Gini Coefficient Calculator