Linear Regression Intercept Calculator Formula

Understand the math behind the linear regression intercept calculator. Each variable explained with a worked example.

Use the Linear Regression Intercept Calculator

Formulas Used

Intercept (b0)

intercept = y_mean - slope * x_mean

y at x=0

equation_check = y_mean - slope * x_mean

y at x = x_mean

y_at_mean_x = y_mean

Variables

VariableDescriptionDefault
y_meanMean of y30
x_meanMean of x15
slopeSlope (b1)2

How It Works

How to Calculate the Regression Intercept

Formula

b0 = y_mean - b1 * x_mean

The y-intercept is the predicted value of Y when X = 0. The regression line always passes through the point (x_mean, y_mean). Once you have the slope b1, computing b0 is straightforward. The full regression equation is: Y = b0 + b1*X.

Worked Example

Mean of y = 30, mean of x = 15, slope = 2.

y_mean = 30x_mean = 15slope = 2
  1. 01b0 = y_mean - b1 * x_mean
  2. 02b0 = 30 - 2 * 15
  3. 03b0 = 30 - 30 = 0
  4. 04Regression equation: Y = 0 + 2*X = 2X

Ready to run the numbers?

Open Linear Regression Intercept Calculator