Nonlinear regression is a regression technique that is used when the relationship between a predictor variable and a does not follow a linear pattern.

The following step-by-step example shows how to perform nonlinear regression in Excel.

Step 1: Create the Data

First, let’s create a dataset to work with:

Step 2: Create a Scatterplot

Next, let’s create a scatterplot to visualize the data.

First, highlight the cells in the range A1:B21. Next, click the Insert tab along the top ribbon, and then click the first plot option under Scatter:

The following scatterplot will appear:

Step 3: Add a Trendline

Next, click anywhere on the scatterplot. Then click the + sign in the top right corner. In the dropdown menu, click the arrow next to Trendline and then click More Options:

In the window that appears to the right, click the button next to Polynomial. Then check the boxes next to Display Equation on chart and Display R-squared value on chart.

This produces the following curve on the scatterplot:

Note that you may need to experiment with the value for the Order of the polynomial until you find the curve that best fits the data.

Step 4: Write the Regression Equation

From the plot we can see that the equation of the regression line is as follows:

y = -0.0048x⁴ + 0.2259x³ – 3.2132x² + 15.613x – 6.2654

The tells us the percentage of the variation in the response variable that can be explained by the predictor variables.

The R-squared for this particular curve is 0.9651. This means that 96.51% of the variation in the response variable can be explained by the predictor variables in the model.