Linear Regression Intercept Calculator
Calculate the y-intercept (b0) of the least-squares regression line from the means of x and y and the slope.
Intercept (b0)
0.000000
Intercept (b0) vs Mean of y
Formula
## 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.
Exemplo Resolvido
Mean of y = 30, mean of x = 15, slope = 2.
- 01b0 = y_mean - b1 * x_mean
- 02b0 = 30 - 2 * 15
- 03b0 = 30 - 30 = 0
- 04Regression equation: Y = 0 + 2*X = 2X
Perguntas Frequentes
Does the intercept always have a meaningful interpretation?
Not always. If X = 0 is outside the range of observed data, the intercept is an extrapolation and may not be meaningful. For example, predicting weight at height = 0 is nonsensical.
Can the intercept be negative?
Yes. A negative intercept means the regression line crosses the y-axis below zero. This is common when the relationship has a positive slope but the data range does not include x = 0.
Why does the regression line pass through (x_mean, y_mean)?
This is a mathematical property of least-squares regression. The formula b0 = y_mean - b1*x_mean guarantees this. Substituting x_mean into the equation gives y = b0 + b1*x_mean = y_mean.
Aprender