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.

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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
  2. 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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