Regression Intercept Calculator
Calculate the y-intercept of the least-squares regression line from the slope and mean values of x and y.
Y-Intercept (b0)
7.5005
Y-Intercept (b0) vs Slope (b1)
公式
## 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.
计算示例
With slope = 0.8333, mean x = 15, mean y = 20.
- 01b0 = 20 - 0.8333 × 15
- 02b0 = 20 - 12.5 = 7.5005
- 03Regression equation: y-hat = 7.50 + 0.833x
常见问题
Does the intercept always have meaning?
Not always. If x = 0 is outside the range of your data, the intercept is an extrapolation and may not be meaningful. For example, predicting weight at zero height makes no sense.
Can the intercept be negative?
Yes. A negative intercept simply means the regression line crosses the y-axis below zero. This is perfectly valid mathematically, though it may or may not make sense contextually.
Should I force the intercept through zero?
Only if there is a strong theoretical reason (e.g., zero input must give zero output). Forcing through zero changes the slope estimate and can increase residual error. Use F-test to compare models.
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