**Cubic regression** is a regression technique we can use when the relationship between a predictor variable and a response variable is non-linear.

The following step-by-step example shows how to fit a cubic regression model to a dataset in Excel.

**Step 1: Create the Data**

First, let’s create a fake dataset in Excel:

**Step 2: Perform Cubic Regression**

Next, we can use the following formula in Excel to fit a cubic regression model in Excel:

=LINEST(B2:B13, A2:A13^{1,2,3})

The following screenshot shows how to perform cubic regression for our particular example:

Using the coefficients in the output, we can write the following estimated regression model:

ŷ = -32.0118 + 9.832x – 0.3214x^{2} + 0.0033x^{3}

**Step 3: Visualize the Cubic Regression Model**

We can also create a scatterplot with the fitted regression line to visualize the cubic regression model.

First, highlight the data:

Then click the **Insert** tab along the top ribbon and click the first option within the **Insert Scatter (X, Y)** option in the **Charts** group. This will produce the following scatterplot:

Next, click the green plus sign in the top right corner of the chart and click the arrow to the right of **Trendline**. In the dropdown menu that appears, click **More Options**…

Next, click the **Polynomial** trendline option and select **3** for the order. Then check the box next to “Display Equation on chart”

The following trendline and equation will appear on the chart:

Notice that the equation in the chart matches the equation that we calculated using the **LINEST()** function.

**Additional Resources**

How to Perform Simple Linear Regression in Excel

How to Perform Multiple Linear Regression in Excel

How to Perform Polynomial Regression in Excel