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Inverse Linear Regression

Inverse Linear Regression

Introduction

The goal:  fit bi-variate data (x,y) to the curve:

y = 1 / (a*x + b)

We will be able to use the linear regression model with the following transformation:

1/y = a* x + b

y’ = 1/y
x’ =  x
a’ = a
b’ = b

y’ = a’ * x’ + b’

Let’s illustrate this with an example.

Example

Fit the curve y = 1 / (a*x + b) to the data:

(-2, -1.43)
(-1, 0.4)
(0, 0.18)
(1, 0.11)
(2, 0.08)
(4, 0.05)

Transform the data to (x’, y’): x’ = x,  y’ = 1/y

(-2, -1/1.43 = 0.6693006993)
(-1, 1/0.4 = 2.5)
(0, 1/0.18 = 5.555555556)
(1, 1/0.11 = 9.090909091)
(2, 1/0.08 = 12.5)
(4, 1/0.05 = 20)

Regression analysis with the transformed data:

Slope (a,m) = 3.443917194
Intercept (b) = 5.861915862
r^2 = 0.998386787

1/y = 3.443917194 * x + 5.861915862

y = 1 / (3.443917194 * x + 5.861915862)

Note:  My next blog entry will be posted on September 2, 2019, 12:00 AM Pacific Daylight Time on Labor Day. 

Eddie

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