Kostenloser Linear Regressions Slope Rechner
Berechnen Sie den slope of the least-squares regression line aus summary statistics. Kostenloser regression slope Rechner.
Steigung (b1)
2.000000
Slope (b1) vs Number of Pairs
Formel
How to Calculate the Regression Slope
Formula
b1 = [n*Sum(xy) - Sum(x)*Sum(y)] / [n*Sum(x^2) - (Sum(x))^2]
The slope of the least-squares regression line represents the predicted change in Y for a one-unit increase in X. A positive slope indicates a positive relationship; negative means Y decreases as X increases.
Lösungsbeispiel
n = 5, Sum(xy) = 2350, Sum(x) = 75, Sum(y) = 150, Sum(x^2) = 1175.
- 01Numerator = 5*2350 - 75*150 = 11750 - 11250 = 500
- 02Denominator = 5*1175 - 75^2 = 5875 - 5625 = 250
- 03Slope b1 = 500 / 250 = 2.0
- 04For each unit increase in x, y increases by 2 on average
Häufig Gestellte Fragen
What if the slope is zero?
A slope of zero means there is no linear relationship between X and Y. The best prediction for Y is simply the mean of Y, regardless of X.
Is the regression slope the same as correlation?
No. The slope depends on the scales of X and Y (it has units of Y/X). The correlation r is dimensionless and standardized between -1 and 1. They share the same sign but different magnitudes.
What does "least squares" mean?
The least-squares method finds the line that minimizes the sum of squared vertical distances (residuals) between observed Y values and predicted Y values. This gives the best linear unbiased estimate under certain assumptions.
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