Regression Intercept Calculator Formula
Understand the math behind the regression intercept calculator. Each variable explained with a worked example.
Formulas Used
Y-Intercept (b0)
intercept = mean_y - slope * mean_xVariables
| Variable | Description | Default |
|---|---|---|
slope | Slope (b1) | 0.8333 |
mean_x | Mean of x (x-bar) | 15 |
mean_y | Mean of y (y-bar) | 20 |
How It Works
Regression Intercept
The y-intercept is the predicted value of y when x equals zero. The regression line always passes through the point (x-bar, y-bar).
Formula
b0 = y-bar - b1 × x-bar
The intercept may not have a meaningful interpretation if x = 0 is outside the range of observed data. The regression equation is: y-hat = b0 + b1 × x.
Worked Example
With slope = 0.8333, mean x = 15, mean y = 20.
slope = 0.8333mean_x = 15mean_y = 20
- 01b0 = 20 - 0.8333 × 15
- 02b0 = 20 - 12.5 = 7.5005
- 03Regression equation: y-hat = 7.50 + 0.833x
Ready to run the numbers?
Open Regression Intercept Calculator