Undergrad Can I Use a Natural Log Function for Least Square Fitting?

[JoJoQuinoa]

Hello,

I'm trying to follow Wolfram to do a least square fitting. There are multiple summations in the two equations to find the coefficients. Are the i's the same in this case?

Thanks!

 

[Mark44]

Hello,

I'm trying to follow Wolfram to do a least square fitting. There are multiple summations in the two equations to find the coefficients. Are the i's the same in this case?

Thanks!

In both equations, i is the index of all of the summations. These summations run for i = 1, 2, 3, and so on, up to n. Here n is the number of points you're fitting to the log curve.

 

[JoJoQuinoa]

@Mark44

Sorry I just looked at it and got confused again. So for coefficient b, can I write the numerator as
$\Sigma_{i=1}^n (n*y_i*ln(x_i)-y_i*ln(x_i))$.

 

[Mark44]

@Mark44

Sorry I just looked at it and got confused again. So for coefficient b, can I write the numerator as
$\Sigma_{i=1}^n (n*y_i*ln(x_i)-y_i*ln(x_i))$.

No. The formula shown in the Wolfram page for the numerator of b is
$$n\sum_{i =1}(y_i\ln(x_i)) - (\sum_{i = 1}y_i)(\sum_{i = 1}\ln(x_i)$$
You can't simplify things as you have done. You need to calculate all three summations. Once you have these numbers, multiply the first summation by n, multiply the second and third summations together, and then subtract as shown.

 

[Chestermiller]

Just plot y vs x, with x plotted on a log scale (by your graphics package). The result should be a straight line, and the graphics package should automatically determine the best least squares fit equation to the data.