Exponential Regression Calculator Documentation

Exponential Model

In exponential regression, the following equation is used:

An exponential function is used to describe processes with rapid growth or decay of some quantity. Examples include:

• Growth of bacteria
• Radioactive decay
• Chemical reaction kinetics

Fig. 1. Exponential fit illustration

Data Input

In the table on the left side of the application, input your data: x and y variables. You can add rows if you need to introduce more data. You can also paste a dataset from an Excel worksheet using Ctrl+C (Copy) and Ctrl+V (Paste) shortcuts.

Exporting Results

The calculations are performed automatically after entering the data into the table. You will see the plot with the fitted curve and parameters describing the quality of fit. The axes of the graph can be changed, as well as the title of the plot. You can export the results to a .txt file.

How to Calculate the Exponential Regression Formula

1. Prepare Your Data
   Collect your data points, consisting of pairs of x (independent variable) and y (dependent variable) values. Ensure that you have at least two data points to perform the regression.

2. Transform the Data
   To linearize the exponential relationship, take the natural logarithm of the y values. This will transform the exponential equation:

   $$y = e \cdot exp(bx)$$

   into a linear form:

   $$ln(y) = ln(a) + bx$$

   The transformed equation is now suitable for linear regression, where ln(y) is treated as the dependent variable.

3. Perform Linear Regression
   Use the linear regression method on your transformed data (x, ln(y)) to find the best-fit line. The equation of the line will be:

   $$ln(y) = B_0 + B_1x$$

   where $B_0$ is the intercept and $B_1$ is the slope.

   • Coefficient $B_0$ corresponds to ln(a) and coefficient $B_1$ corresponds to b.

Tutorial on Working with the Curve Fitting Tool

For more information, watch this tutorial:
Working with the Curve Fitting Tool