# Exponential Regression in Python (Step-by-Step)

Exponential regression is a type of regression 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 = abx

where:

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

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

### Step 1: Create the Data

First, let’s create some fake data for two variables: x and y:

```import numpy as np

x = np.arange(1, 21, 1)
y = np.array([1, 3, 5, 7, 9, 12, 15, 19, 23, 28,
33, 38, 44, 50, 56, 64, 73, 84, 97, 113])
```

### Step 2: Visualize the Data

Next, let’s create a quick scatterplot to visualize the relationship between x and y:

```import matplotlib.pyplot as plt

plt.scatter(x, y)
plt.show()``` From the plot we can see that there exists a clear exponential growth pattern between the two variables.

Thus, it seems like a good idea to fit an exponential regression equation to describe the relationship between the variables as opposed to a linear regression model.

### Step 3: Fit the Exponential Regression Model

Next, we’ll use the polyfit() function to fit an exponential regression model, using the natural log of y as the response variable and x as the predictor variable:

```#fit the model
fit = np.polyfit(x, np.log(y), 1)

#view the output of the model
print(fit)

[0.2041002  0.98165772]
```

Based on the output, the fitted exponential regression equation can be written as:

ln(y) = 0.9817 + 0.2041(x)

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

y = 2.6689 * 1.2264x

We can use this equation to predict the response variable, y, based on the value of the predictor variable, x. For example, if x = 12, then we would predict that y would be 30.897:

y = 2.6689 * 1.226412 = 30.897

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