# Exponential Regression

An exponential regression is the process of finding the equation of the exponential function that fits best for a set of data. As a result, we get an equation of the form $y=a{b}^{x}$ where $a\ne 0$ .

The relative predictive power of an exponential model is denoted by ${R}^{2}$ . The value of ${R}^{2}$ varies between $0$ and $1$ . The more close the value is to $1$ , the more accurate the model is.

Example:

Consider the set of data. Determine the exponential regression for the set.

$\left(0,3\right),\left(1,7\right),\left(2,10\right),\left(3,24\right),\left(4,50\right),\left(5,95\right)$

Enter the $x$ -coordinates and $y$ -coordinates in your calculator and do an exponential regression. The equation of the function that best approximates the points is $y=3.0465{\left(1.988\right)}^{x}$ .

Plot the graph. You should get a graph like this.