Лаб 5 / z2

% задача 2. Написать m-файлы функции для реализации метода наименьших
% квадратов для построения нелинейной полиномиальной регрессии со
% степенным базисом (n = 3, 5, 7) и построить аппроксимирующие кривые.
clear
% точки по варианту (7)
x = [-0.5:0.04:1.5]
Y = [0.8381, 0.6434, 0.8021, 0.5503, 0.7475, 0.8743, 0.7827 0.9828, 0.7537, 0.5455, ...
0.6848, 0.9725, 0.8272, 0.8888, 0.9585, 0.5737, 0.7556, 0.7446 0.7009, 0.8001, ...
1.0066, 0.8044, 0.9543, 0.7044, 0.7818, 0.6713, 0.7297, 0.7109 0.7870, 0.7939, ...
0.6826, 0.7843, 0.7412, 0.6961, 0.6057, 0.6965, 0.5632, 0.3903 0.5605, 0.4690, ...
0.4037, 0.5651, 0.6047, 0.2716, 0.3140, 0.1634, 0.3118, -0.1071 0.2734, 0.1377, ...
0.1034];

n = 51;
y = Y';
k3 = 3;
k5 = 5;
k7 = 7;
Y3 = 0;
Y5 = 0;
Y7 = 0;
# k = 3
A = ones(n, k3);
for i = 1:n
for j = 2:k3
A(i, j) = x(i).^(j - 1);
end
end
b_ = inv(A' * A) * A' * y;
for i = 1:k3
Y3 = Y3 + b_(i)*x.^(i - 1);
end
#k = 5
A = ones(n, k5);
for i = 1:n
for j = 2:k5
A(i, j) = x(i).^(j - 1);
end
end
b_ = inv(A' * A) * A' * y;
for i = 1:k5
Y5 = Y5 + b_(i)*x.^(i - 1);
end
#k = 7
A = ones(n, k7);
for i = 1:n
for j = 2:k7
A(i, j) = x(i).^(j - 1);
end
end
b_ = inv(A' * A) * A' * y;
for i = 1:k7
Y7 = Y7 + b_(i)*x.^(i - 1);
end

plot(x,Y3,'m',x,Y5,'r',x,Y7,'g',x,y,'.')
y=y';
figure
plot(x,Y3-y,'m',x,Y5-y,'r',x,Y7-y,'g')