quadratic loss by solving a standard least squares problem over training data matrix (1x14) in matlab

main.m
% Training data matrix
X = [1, 0.74, 0.86, -0.99, -0.38, -0.81, ...
    0.18, -0.12, -0.06, -0.17, -0.23, ...
    -0.05, -0.05, 0.26];

% Quadratic loss function
quadLoss = @(w, X) sum((X - w).^2);

% Solve standard least squares problem using fmincon
% Starting value of w is the mean of the training data
w0 = mean(X);
w = fmincon(@(w) quadLoss(w,X), w0);

% Display the estimated coefficient value
disp(w);
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In the code above, we define the training data matrix X as a 1x14 vector. We then define the quadratic loss function as quadLoss which takes a parameter w (the coefficient we want to estimate) and the training data matrix X. The function computes the sum of the squared differences between X and w.

We then use the built-in Matlab function fmincon to solve the least squares problem by minimizing the quadratic loss function quadLoss. The starting value of w is set to the mean of the training data X. Finally, we display the estimated coefficient value w.

Note that this implementation assumes a linear relationship between the input variables and the response variable. If a nonlinear relationship exists, additional transformations may need to be made to the input variables or a different loss function may need to be used.