Exponential Regression Models

We now consider how to perform exponential regression, i.e. regression based on the following equation:

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Our goal is to calculate the values of the coefficients α and β which minimize the sum of the squares of the observed y values minus the values of y predicted by the regression model.

We explore both linear and nonlinear exponential regression models as well as describe how to perform exponential regression using Real Statistics capabilities.

Topics

Advanced topic

References

Foth, R. (2024) Modeling exponential relationships with regression
https://pimaopen.pressbooks.pub/topicsinmathematics/chapter/5-4-modeling-exponential-relationships-with-regression

Abramson, J. (2024) Exponential and logarithmic regressions
https://math.libretexts.org/Workbench/1250_Draft_3/06%3A_Exponential_and_Logarithmic_Functions/6.09%3A_Exponential_and_Logarithmic_Regressions

Libre Texts (2024) Nonlinear regression
https://math.libretexts.org/Workbench/Numerical_Methods_with_Applications_(Kaw)/6%3A_Regression/6.04%3A_Nonlinear_Regression

Geeks for Geeks (2024) Non-linear regression with examples
https://www.geeksforgeeks.org/non-linear-regression-examples-ml/

7 thoughts on “Exponential Regression Models”

  1. Hi Charles,
    I am grateful for your valuable support. I seek your guidance for a case of nonlinear regression y = f (x). Measurement data for y and x are collected. Based on previous studies, the relationship is expected to be: y=(exp(a+(b/x)+c*log(x))). Also, it was indicated that y values for clusters of x are following a lognormal distribution round the midpoint of each cluster.
    Would you please provide your advice and guidance on the approach for calculating the fitting parameters and the standard error for y estimates.
    Best regards,
    Samir

    Reply

    • Hello Samir,
      I don’t see a straightforward transformation. You can try to estimate the parameters a, b, and c by minimizing the residuals from your sample data using Solver.
      You can get standard errors using bootstrapping.
      Charles

      Reply

      • Hello Charles,
        Thank you very much for the highly acknowledged advice. I’ll try this approach.
        Best regards,
        Samir

        Reply

  3. Dear Charles,

    I have 2 sets of data (decrease concentration of substance s1 with time and decrease concentration of substance s2 with time), which I described by exponential decay curve Conc (s1)=a1+a2*exp(-k*t) and Conc (s2)=a1+a2*exp(-k*t). I got the parameters from exponential curves: a1, a2 and k for both substances. Now was asked to compare these parameters (a1 for substance 1 and 2; a2 and k) to show that they are similar or different. My question is: which statistical test can I do to answer this question?

    Thank you,
    Anna

    Reply

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