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_x

Variables

VariableDescriptionDefault
slopeSlope (b1)0.8333
mean_xMean of x (x-bar)15
mean_yMean 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
  1. 01b0 = 20 - 0.8333 × 15
  2. 02b0 = 20 - 12.5 = 7.5005
  3. 03Regression equation: y-hat = 7.50 + 0.833x

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