%% Data input

clear,clc
diameter = [36,28,28,41,19,32,22,38,25,17,31,20,25,19,39,33,17,37,23,39]; % [inches]
board_feet = [192,113,88,294,28,123,51,252,56,16,141,32,86,21,231,187,22,205,57,265]; % [inches^3]

%% Built-in Matlab functions for linear fit

scatter(diameter,board_feet,'filled')
xlabel('Diameter')
ylabel('Board-feet')

coeffs = polyfit(diameter, board_feet, 1);
% Get fitted values
x = linspace(min(diameter), max(diameter), 200);
y = polyval(coeffs, x);
% Plot the fitted line
hold on;
plot(x, y, 'r-', 'LineWidth', 2);

linear_fit = fitlm(diameter,board_feet,'y~x1')
linear_fit.Rsquared.Ordinary

%% Try some of our models

fit1 = fitlm(diameter,board_feet,'y~x1^3-x1^2-x1-1')
fit1.Rsquared.Ordinary

fit2 = fitlm(diameter,board_feet,'y~x1^3-x1^2-x1')
fit2.Rsquared.Ordinary

fit3 = fitlm(diameter,board_feet,'y~x1^2-x1')
fit3.Rsquared.Ordinary

fit4 = fitlm(diameter,board_feet,'y~x1^2-x1-1')
fit4.Rsquared.Ordinary

fit5 = fitlm(diameter,board_feet,'y~x1^2-1')
fit5.Rsquared.Ordinary

%% Plot residuals for the various fits

figure, plotResiduals(fit4,'fitted')
xlabel('Diameter'), ylabel('Residuals')

%%
figure,
subplot(2,2,1), plotResiduals(fit1,'fitted')
xlabel('Diameter'), ylabel('Residuals for y~x1^3')

subplot(2,2,2), plotResiduals(fit2,'fitted')
xlabel('Diameter'), ylabel('Residuals for y~x1^3+1')

subplot(2,2,3), plotResiduals(fit3,'fitted')
xlabel('Diameter'), ylabel('Residuals for y~x1^2+1')

subplot(2,2,4), plotResiduals(fit4,'fitted')
xlabel('Diameter'), ylabel('Residuals for y~x1^2')