Weighted Logarithmic Regression Calculator

Fit a logarithmic model y = a + b ln(x) to frequency-weighted data points using weighted least squares. Get the coefficients a and b, the coefficient of determination R squared, the correlation, and the total weight, plus a scatter plot with the fitted curve.

Input

Enter (x, y, weight) data points with a frequency for each, and the tool fits the logarithmic model y = a + b ln(x) by weighted least squares.

Data points (x, y, weight)

One point per line. Separate x, y, and weight with a comma or space. Omit the weight to treat it as 1. x and weight must be positive.

Result

Weighted logarithmic regression equation

y = 2.112116 + 1.76666 ln(x)

Intercept a

2.112116

Coefficient b

1.76666

R squared

0.998

Correlation r

0.999

Total weight

Data points

Scatter plot and fitted curve

Data points and predictions

x	y	Weight	Predicted y
1	2	3	2.112
2	3.4	5	3.337
4	4.6	4	4.561
8	5.8	6	5.786
16	6.9	2	7.01

How it works

Each data point carries a frequency (weight), and the model y = a + b ln(x) is fitted with weighted least squares.
Substituting u = ln(x) turns the model into a weighted straight-line fit y = a + b u, solved through the weighted normal equations for a and b.
Because ln(x) is taken, x values must be positive, and the weights must be positive as well.
R squared is computed from the weighted residual sum of squares relative to the weighted mean; values closer to 1 indicate a better fit.
Enter one point per line as x, y, and weight separated by commas or spaces. Omit the weight to treat it as 1.

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