Free Linear Regression Slope Calculator
Calculate the slope (b1) of the least-squares regression line from summary statistics.
Slope (b1)
2.000000
Mean of x15.0000
Mean of y30.0000
Slope (b1) vs Number of Pairs
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.
Example Calculation
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
Frequently Asked Questions
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