y =  degree_reg(V, b1f);
k = build_plot_disp_loss(V, b1f, y);

function y=lin_reg(V, bf)
    a = [sum(V) length(V);
         sum(V.^2) sum(V)];
    b = [sum(bf) sum(V .* bf)]';
    x = a\b;
    a = x(1);
    b = x(2);
    y = a * V + b;
end

function y = square_reg(V, bf)
    a = [sum(V.^2) sum(V) length(V);
         sum(V.^3) sum(V.^2) sum(V);
         sum(V.^4) sum(V.^3) sum(V.^2)];
    b = [sum(bf) sum(V .* bf) sum(V.^2 .* bf)]';
    x = a\b;
    a = x(1);
    b = x(2);
    c = x(3);
    y = a * V.^2 + b * V + c;
end

function y = degree_reg(V, bf)
    a = [length(V) sum(log(V));
         sum(log(V)) sum(log(V).^2)];
    b = [sum(log(bf)) sum(log(bf).*log(V))]';
    x = a\b;
    a = exp(x(1));
    b = x(2);
    y = a * V.^b;
end

function y = loss_fn(bf, res)
    y = 1/length(bf) * sum(abs((bf - res)./bf));
end

function loss = build_plot_disp_loss(V, bf, res)
    loss = loss_fn(bf, res);
    disp("loss is: " + loss * 100 + "%");
    figure('Color', 'w');
    plot(V, bf, 'r');
    hold on;
    plot(V, res, 'b');
end