*62*

**Exponential regression** is a type of regression model that can be used to model the following situations:

**1. Exponential growth:** Growth begins slowly and then accelerates rapidly without bound.

**2. Exponential decay:** Decay begins rapidly and then slows down to get closer and closer to zero.

The equation of an exponential regression model takes the following form:

y = ab^{x}

where:

**y:**The response variable**x:**The predictor variable**a, b:**The regression coefficients that describe the relationship betweenÂ*x*and*y*

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

**Step 1: Create the Data**

First, letâ€™s create a fake dataset that contains 20 observations:

**Step 2: Take the Natural Log of the Response Variable**

Next, we need to create a new column that represents the natural log of the response variableÂ *y*:

**Step 3: Fit the Exponential Regression Model**

Next, weâ€™ll fit the exponential regression model. To do so, click theÂ **Data** tab along the top ribbon, then click **Data Analysis** within theÂ **Analysis** group.

*If you donâ€™t see Data Analysis as an option, you need to first load the Analysis ToolPak.*

In the window that pops up, clickÂ **Regression**. In the new window that pops up, fill in the following information:

Once you clickÂ **OK**, the output of the exponential regression model will be shown:

The overall F-value of the model is 204.006 and the corresponding p-value is extremely small, which indicates that the model as a whole is useful.

Using the coefficients from the output table, we can see that the fitted exponential regression equation is:

**ln(y) = 0.9817 + 0.2041(x)**

ApplyingÂ *e* to both sides, we can rewrite the equation as:

**y = 2.6689 * 1.2264 ^{x}**

We can use this equation to predict the response variable,Â *y*, based on the value of the predictor variable,Â *x*. For example, ifÂ *x* = 14, then we would predict thatÂ *y* would beÂ **46.47**:

y = 2.6689 * 1.2264^{14} = 46.47

**Bonus:** Feel free to use this online Exponential Regression Calculator to automatically compute the exponential regression equation for a given predictor and response variable.

**Additional Resources**

How to Perform Simple Linear Regression in Excel

How to Perform Multiple Linear Regression in Excel

How to Perform Quadratic Regression in Excel

How to Perform Polynomial Regression in Excel