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Problem

Given data (x_i, y_i), for i = 1, 2, ..., n which is known to approximate an exponential curve, find the best fitting exponential function of the form y(x) = ae^bx.

Assumptions

We will assume the model is correct and that the data is defined by two vectors x = (x_i) and y = (y_i).

Tools

We will use algebra and linear regression.

Process

Take the logarithm of the y values and define the vector φ = (φ_i) = (log(y_i)).

Now, find the least-squares curve of the form c₁ x + c₂ which best fits the data points (x_i, φ_i). See the Topic 6.1 Linear Regression.

Having found the coefficient vector c, the best fitting curve is

y = e^c₂ e^{c₁ x}.

Topic 6.3: Transformations to Linear Regression (HOWTO)

Problem

Assumptions

Tools

Process