Hello,
Different methods weight the residuals differently while Fitting the curve, leading to a different curve, which is responsible for the change in the R^2 value.
- The LAR scheme finds a curve that minimizes the absolute difference of the residuals, rather than the squared differences. Therefore, extreme values have a lesser influence on the fit.
- The Bisquare method minimizes a weighted sum of squares, where the weight given to each data point depends on how far the point is from the fitted line. Points near the line get full weight. Points farther the line get reduced weight. Points that are farther from the line than would be expected by random chance get zero weight.
Thus a dataset with large number of outliers leads to more variation in R^2.
Refer to the following link for further information:
- https://www.mathworks.com/help/stats/coefficient-of-determination-r-squared.html(Coefficient of Determination (R-Squared))
- https://www.mathworks.com/help/curvefit/fit.html(Fit)
- https://www.mathworks.com/matlabcentral/answers/183690-what-is-the-difference-between-lar-and-the-bisquare-remain-robust-in-regression-curve-fitting-tool(Difference between LAR and Bisquare)
- https://www.mathworks.com/matlabcentral/answers/314961-curve-fitting-what-does-lar-do?s_tid=srchtitle(LAR)
