Reciprocal Regression Calculator (y=a+b/x)
Fit the reciprocal model y=a+b/x to your (x, y) data points by least squares. Get coefficients a and b, the coefficient of determination R-squared, a scatter plot with the fitted curve, and a residual table.
Input
Enter your (x, y) data points to fit the reciprocal model y=a+b/x by least squares.
One point per line. Separate x and y with a comma or a space (x must not be 0).
Result
Regression equation
y = 1.984367 + 10.020138/x
Intercept a
1.984367
Coefficient b
10.020138
R-squared
0.999969
Correlation r
0.999984
Data points
6
Scatter plot and fitted curve
Data points and residuals
| x | Observed y | Predicted y | Residual |
|---|---|---|---|
| 1 | 12 | 12 | -0 |
| 2 | 7 | 6.99 | 0.01 |
| 4 | 4.5 | 4.49 | 0.01 |
| 5 | 4 | 3.99 | 0.01 |
| 8 | 3.2 | 3.24 | -0.04 |
| 10 | 3 | 2.99 | 0.01 |
How it works
- Substituting u=1/x turns the model into the linear form y=a+b times u, so ordinary least squares gives the intercept a and the coefficient b.
- R-squared is computed from the residuals between the actual y and the model value yhat=a+b/x. Values closer to 1 indicate a better fit.
- Data points with x=0 are excluded because 1/x is undefined there.
- Enter one point per line, with x and y separated by a comma or whitespace. Lines that cannot be parsed as numbers are ignored.
Reviews
Tell us what you think of this calculator.
Write a review
- Home
Reciprocal Regression Calculator (y=a+b/x)