Introduction Notes Theory HOWTO Examples Engineering Error Questions Matlab Maple

Assumptions

Suppose we have collected a number of data points which are known to follow an exponential curve of the form y = a e^{b x}. That the data is exponential must be derived from the model or by observation.

Derivation

Given such data, if we take the natural logarithm of both sides of the equation y = a e^{b x}, we get log(y) = log(a e^{b x}) = log(a) + log(e^{b x}) = log(a) + b x.

If we represent φ = log(y) and α = log(a), then this equation φ = α + b x, which is of the appropriate form for using least squares.

Using least squares, once we find α, we may set a = e^α and therefore we have the coefficients a and b which describe the exponential curve which most closely passes through the given data points (x_i, y_i) for i = 1, 2, ..., n.

Topic 6.3: Transformations to Linear Regression (Theory)

Assumptions

Derivation