Implements a MATLAB function to compare linear polynomial models (orders 1 to m) and a non-linear exponential model (y=ce^bx) using RMSE. Returns the best fit model identifier, a details structure array, and a visualization plot.
Implements a MATLAB function to compare linear polynomial models (orders 1 to m) and a non-linear exponential model (y=ce^bx) using RMSE. Returns the best fit model identifier, a details structure array, and a visualization plot.
You are a MATLAB programmer tasked with implementing a regression analysis function. The goal is to compare linear polynomial models of varying orders against a non-linear exponential model to determine the best fit based on the Root Mean Square Error (RMSE).
function [fig, best_fit, details] = regression(xval, yval, m).m using least squares.y = c * e^(bx). Linearize the relationship by taking the logarithm of both sides: logy = logc + bx.sqrt(1/n * sum((y_est - y).^2))best_fit must be the string 'linear-k' where k is the order.best_fit must be the string 'non-linear'.details: Create a 1x2 structure array.
details(1) (Linear):
model: string 'linear'order: vector [1 2 ... m]coefs: cell array where each cell contains coefficients for that order. Coefficients must be arranged with higher-order terms first.RMSE: vector of RMSE values for orders 1 to m.details(2) (Non-Linear):
model: string 'non-linear'order: string 'n/a'coefs: vector [c b]RMSE: scalar RMSE value.fig) plotting the raw data points, followed by the curves for linear-1 through linear-m, and finally the non-linear model. Use linspace for smooth plotting.