Regression analysis is used to quantify the relationship between one or more explanatory variables and a response variable.

The most common type of regression analysis is simple linear regression, which is used when an explanatory variable and a response variable have a linear relationship.

However, sometimes the relationship between an explanatory variable and a response variable is nonlinear.

In these cases it makes sense to use **polynomial regression**, which can account for the nonlinear relationship between the variables.

This tutorial explains how to perform polynomial regression in Excel.

**Example: Polynomial Regression in Excel**

Suppose we have the following dataset in Excel:

Use the following steps to fit a polynomial regression equation to this dataset:

**Step 1: Create a scatterplot.**

First, we need to create a scatterplot. Go to the **Charts **group in the **Insert **tab and click the first chart type in **Scatter**:

A scatterplot will automatically appear:

**Step 2: Add a trendline.**

Next, we need to add a trendline to the scatterplot. To do so, click on any of the individual points in the scatterplot. Then, right click and select **Add Trendline…**

A new window will pop up with the option to specify a trendline. Choose **Polynomial **and choose the number you’d like to use for **Order**. We will use 3. Then, check the box near the bottom that says **Display Equation on chart**.

A trendline with a polynomial regression equation will automatically appear on the scatterplot:

**Step 3: Interpret the regression equation.**

For this particular example, our fitted polynomial regression equation is:

y = -0.1265x^{3} + 2.6482x^{2} – 14.238x + 37.213

This equation can be used to find the expected value for the response variable based on a given value for the explanatory variable. For example, suppose x = 4. The expected value for the response variable, y, would be:

y = -0.1265(4)^{3} + 2.6482(4)^{2} – 14.238(4) + 37.213 = **14.5362**.