How to Linearize and Fit Data Points in MATLAB?

[hunter55]

Homework Statement

For the given set of data, find the least-square curve:
A) f(x)=Ce^Ax, by using the change of variable X=x, Y=ln(y), and C=e^B to linearize the data points.

B) f(x) = 1/(Ax+B), by using the change of variable X=x and Y = 1/y to linearize the data points.

x : [ -1 0 1 2 3]
y : [ 6.62 3.94 2.17 1.35 0.89]

I need the MATLAB code on how to do these 2 problems I am confused and which curve gives a better fit. ??

Homework Equations

This is the only code i know but idk how to do it with the question they are asking i need to pertain it to that

function C = poly(X,Y,M)
n=length(X);
B=zeros(1:M+1);
F=zeros(n,M+1);
for k=1:M+1
F(:,k)=X'.^(k-1);
end
A=F'*F;
B=F'*Y';
C=A\B;
C=flipud(C);

The Attempt at a Solution

These are the coefficients:
-0.0458x^3
0.5225x^2
-2.1567x
3.9040

I am confused with what the question is asking i know I am suppose to have a ans for part A and B

 

[Nok1]

Think about what a change of variable is, then figure out how to apply that to the data.

Aka, when you make a substitution for y=ln(y), that just means you take your y list, and just take the ln of that. That now because the new measurement for what used to be the y-axis.

Does that make sense?

 

[Mene]

but idk how to do it with the question they are asking

I would approach this problem by first understanding the goal of curve fitting and the method being used. Curve fitting is a process of finding a mathematical function that best represents a set of data points. In this case, we are using the least-square method, which minimizes the sum of the squared errors between the actual data points and the predicted values from the curve.

For part A, we are asked to find the least-square curve in the form of f(x)=Ce^Ax. To linearize the data points, we can use the change of variable X=x, Y=ln(y), and C=e^B. This transformation will convert the original equation into a linear form, which can be solved using the code provided. Once we have the coefficients, we can use them to generate the curve and compare it to the original data points to determine the fit.

Similarly, for part B, we need to use the change of variable X=x and Y=1/y to linearize the data points for the equation f(x) = 1/(Ax+B). Again, once we have the coefficients, we can use them to generate the curve and compare it to the original data points.

To determine which curve gives a better fit, we can use a metric such as the coefficient of determination (R^2) or the root mean square error (RMSE). A higher R^2 value or a lower RMSE value indicates a better fit.

As for the MATLAB code, I would suggest starting by defining the variables X and Y with the given data points. Then, use the provided code to calculate the coefficients for both parts A and B. Finally, use the coefficients to generate the curves and compare them to the original data points. You can also calculate the R^2 or RMSE values to determine the better fit.