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The Exponential regression is used to find an exponential curve based on your data and which best suits the data you are studying. There are various regressions which helps us draw a line (linear regression), parabola (quadratic regression) or a cubic curve (cubic regression) and Exponential regression is similar to those methods.
There are some datasets that grow rapidly at first then slows down, or grows slowly at first then start accelerating rapidly. In such cases, there is not line or a parabola that can depict the data perfectly and here, Exponential regression can be a best fit. Some of the examples of such data can be and investment growth, temperatures, etc.
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Exponential regression too has a response variable (y) which is observed as a count and an explanatory variable (x). The exponential regression equation reads y = a * bˣ, where a ≠ 0 and b > 0, b ≠ 1. The coefficients a and b are to be chosen in such a way that they correspond to the Exponential regression curve that is a best fit for your dataset (x₁, y₁), …, (xₙ, yₙ)
As we learned the exponential fit equation, we will see how to calculate exponential regression for the collected da in this section.
Exponential regression formula for the data (x, y) is:
y = exp(c) * exp(m * x)
Where m is the slope and c is the intercept of the linear regression model fitted to the data (x, ln(y)). See the next section to check the details of the derivation.
Standards for interpreting correlation coefficient r:
0.7＜|r|≦1 strong correlation
0.4＜|r|＜0.7 moderate correlation
0.2＜|r|＜0.4 weak correlation
0≦|r|＜0.2 no correlation
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There are various Exponential regression online calculators also that minimize your efforts and also help you to get your exponential fit for the data.
In this example, let’s take some random coo-ordinates: (0,3),(1,7),(2,10),(3,24),(4,50),(5,95)
Now, you can enter these x-coordinates and y-coordinates in your Exponential regression calculator and.
The equation of the function that best approximates the points is y=3.0465(1.988)xy=3.0465(1.988)x
And when you plot the graph for the above data, it will look something like this: