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**Power regression** is a type of non-linear regression that takes on the following form:

**y = ax ^{b}**

where:

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

This type of regression is used to model situations where the response variable is equal to the predictor variable raised to a power.

The following step-by-step example shows how to perform power regression for a given dataset in Excel.

**Step 1: Create the Data**

First, letâ€™s create some fake data for two variables: x and y.

**Step 2: Transform the Data**

Next, letâ€™s take the natural log of both x and y by using the **=LN(number)** formula:

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

Next, weâ€™ll fit a regression model to the transformed data.

To do so, click the **Data** tab along the top ribbon. Then click the **Data Analysis** option within the **Analyze** section.

If you donâ€™t see this option available, you need to first load the Analysis ToolPak.

In the dropdown window that appears, click **Regression** and then clickÂ **OK**. Then fill in the following information:

Once you clickÂ **OK**, the regression output will automatically appear:

The overall F-value of the model is 254.2367 and the corresponding p-value is extremely small (4.61887e-12), which indicates that the model as a whole is useful.

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

**ln(y) = 0.15333 + 1.43439ln(x)**

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

**y = e**^{ 0.15333 + 1.43439ln(x)}**y = 1.1657x**^{1.43439}

We can use this equation to predict the response variable,Â *y*, based on the value of the predictor variable,Â *x*.

For example, if *x* = 12, then we would predict that *y* would beÂ **41.167**:

y = 1.1657(12)^{1.43439} = 41.167

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

**Additional Resources**

How to Perform Multiple Linear Regression in Excel

How to Perform Exponential Regression in Excel

How to Perform Logarithmic Regression in Excel