Kostenloser Regressions Intercept Rechner
Berechnen Sie den y-intercept of a linear regression line aus slope und mean values.
Y-Intercept (b0)
7.5005
Y-Intercept (b0) vs Slope (b1)
Formel
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.
Lösungsbeispiel
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
Häufig Gestellte Fragen
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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