Power Regression Analysis

00:00 5 marks

Consider a real dataset that demonstrates a non-linear relationship between an independent variable \(x\) and a dependent variable \(y\). Describe the process of performing a power regression analysis to model this relationship in the form \(y = ax^b\). Explain how the value of the exponent \(b\) influences the growth rate of \(y\) with respect to \(x\).

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Hint

To perform power regression, transform the relationship into a linear form using logarithms, then apply linear regression techniques to the transformed data.

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To perform power regression for \(y = ax^b\), first, linearize the equation by taking logarithms: \(\ln(y) = \ln(a) + b\ln(x)\). Then, perform linear regression on the transformed variables \(\ln(x)\) and \(\ln(y)\) to find the slope \(b\) and intercept \(\ln(a)\). The exponent \(b\) determines the growth rate. If \(b > 1\), growth is accelerating; if \(0 < b < 1\), growth is decelerating.

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