Exponential Regression Calculator Documentation

Exponential model

In exponential regression the following equation is used:

$y = a \cdot exp(b \cdot x)$

An exponential function is used to describe processes with rapid growth of decay of some quantity. Examples include growth of bacteria, radioactive decay, chemical reaction kinetics.

Fig. 3. Exponential fit illustration

Data input

In the table on the left side of the application type data: x and y variables. You can add rows if you want to introduce more data. You can also paste dataset from Excel worksheet by LCTRL+C (Copy) and LCTRL-V (Paste) shortucts.

Exporting results

The calculations are performed automatically, after you put the data to 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 the 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 = a · e^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 Coefficient B0 corresponds to ln(a) and coefficient B1 corresponds to b. line will be ln(y) = B₀ + B₁ · x, where B₀ is the intercept and B₁ is the slope.

   Coefficient B₀ corresponds to ln(a) and coefficient B₁ corresponds to b.

A tutorial on working with the Curve Fitting Tool: https://youtu.be/dd2gJ-KSkTU