Curve Fitting || Fitting of Exponential Curve || y =ae^bx||Easy Explanation||@curiousabhi550

Curve Fitting || Fitting of Exponential Curve || y =ae^bx||Easy Explanation|| @curiousabhi550
Curve Fitting || Fitting of Exponential Curve || y =ae^bx||Easy Explanation|| @curiousabhi550

Curve Fitting
Fitting of Exponential Curve using Method of Least Squares
y = ae^bx
IN THIS VIDEO

To fit an exponential curve to a set of data points, you can use nonlinear regression. This process involves finding the parameters that best fit the exponential equation to the data. The general form of an exponential equation is:

y = ae^(bx)

Here's how you can fit an exponential curve to your data points:

Gather your data: Collect a set of data points in the form (x, y) that you want to fit the exponential curve to.
Take the natural logarithm: Take the natural logarithm (ln) of the y-values for each data point. This helps linearize the exponential equation.
Set up the linear equation: Define a new variable, z, as ln(y), and rewrite the exponential equation as:

z = ln(a) + bx
Now, you have a linear equation in the form:
z = c + bx
where c = ln(a).
Linear regression: Perform linear regression on the transformed data points (x, z). This will determine the values of b and c in the linear equation.

Calculate the parameters: Once you have the values of b and c, you can calculate the original parameters a and b using the following equations:

a = e^c
b = b

Formulate the equation: Plug the calculated parameters (a and b) into the exponential equation: y = ae^(bx).
By following these steps, you will obtain the equation of the exponential curve that best fits your data points. It's important to note that fitting an exponential curve requires careful consideration of the nature of your data and whether an exponential relationship is appropriate.

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RELATED KEYWORDS
Curve Fitting y=ae^bx | Method of Least Squares| Curve Fitting of Exponential Curve