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 said: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!
No. The formula shown in the Wolfram page for the numerator of b isJoJoQuinoa said:@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))##.
The natural log function, also known as the logarithm with base e, is a mathematical function that is the inverse of the exponential function. It is denoted as ln(x) and is commonly used to solve exponential equations.
The natural log function can be used to fit data by transforming the data into a linear form. This is done by taking the natural log of both the independent and dependent variables. The resulting linear equation can then be used to find the best-fit line for the data.
One advantage of using the natural log function for data fitting is that it can handle a wide range of data, including both small and large values. It also helps to reduce the influence of outliers and makes the data easier to interpret.
No, the natural log function is most commonly used for data that follows an exponential growth or decay pattern. It may not be suitable for other types of data, such as linear or quadratic relationships.
The goodness of fit for a natural log function can be determined by calculating the coefficient of determination, also known as R-squared. This value represents the proportion of the variation in the data that is explained by the natural log function. A higher R-squared value indicates a better fit for the data.