Exponential (Non-Linear) Growth in Customer Analytics

By Jeff Sauro

One of the benefits of first graphing data is that you can examine the relationship to be sure a line does a good job of fitting it. Customer growth is a key metric for social media companies like Facebook, LinkedIn, and Twitter.

Over short intervals (weeks and months), growth looks linear, but over longer periods of time, the growth is exponential. It will often be the case that an exponential (non-linear) equation fits your data better and will provide a better prediction.

You can see if an exponential trendline better describes the subscriber growth than a linear one:

  1. Right-click the data and choose Format Trendline.

  2. Choose Exponential in the Format Trendline dialog box.

An updated trendline with an exponential regression equation is shown here:

image0.jpg

Here is the new regression equation.

Number of Subscribers = 2027.6e0.0273 (x) = 4249

The “e” represents a constant, which is approximately 2.71828, and is raised to the power of .0273 and multiplied times the number of months. You can see why it’s called an exponential equation, as the month is now part of an exponent. The r² value is 0.9988, which is actually higher than the linear equation (which had an r² value of 0.988), meaning this equation fits better.

The prediction for May, the 29th data point, is:

May Subscribers = 2027.6e0.0273 (29) = 4475

In Excel, use the function =EXP(0.0273*29) x 2027.6 to get 4475.