g1583MarchenkoDZ1Var7

% 1583 Марченко С.А. вариант VII
x = [156 165 415 894 465 163 496 131 566 561 562 354];
y = [526 414 561 561 456 321 648 654 321 456 464 456];

% 1)
avr_x = mean(x)
avr_y = mean(y)

% 2)
sigma_x_2 = mean(x.^2) - avr_x^2;
sigma_x = sqrt(sigma_x_2)
sigma_y_2 = mean(y.^2) - avr_y^2;
sigma_y = sqrt(sigma_y_2)

% 3)
xy = zeros(1, 12);
for i = 1:1:12
xy(i) = x(i)*y(i);
end

b1 = (mean(xy) - avr_x * avr_y) / sigma_x_2
b0 = avr_y - b1 * avr_x
y_domik = b0 + b1 * x

% 4)
e = b1 * avr_x / avr_y

% 5)
r_xy = (mean(xy) - avr_x * avr_y) / (sqrt(sigma_x_2 * sigma_y_2))

% 6)
R_xy = r_xy^2

% 7)
A = 1/12 * sum(abs((y - y_domik) / avr_y))

% 8)
% k1 = 1, k2 = 10, F_t = 4.96
F_f = R_xy / (1 - R_xy) * 10

% 9)
% alpha = 0.05, k1 = 10, t_t = 2.26
S_y = sqrt(sum((y - y_domik).^2) / 10)
S_b0 = S_y * sqrt(sum(x.^2) / sum((x - avr_x).^2))
S_b1 = S_y / sqrt(sum((x - avr_x).^2))
t_b0 = abs(b0) / S_b0
t_b1 = abs(b1) / S_b1

S_r_xy = sqrt((1 - R_xy) / 10)
t_r_xy = r_xy / S_r_xy

% 10)
delta_b0 = 2.26 * S_b0
delta_b1 = 2.26 * S_b1
%b_volna0 = b0 +- delta_b0;
%b_volna1 = b1 +- delta_b1;

% 11)
x_zvezda = 0
y_zvezda = b0 + b1 * x_zvezda

S_y_zvezda = sqrt(sum((y - y_domik).^2) / 10) * sqrt(1 + 1/12 + (x_zvezda - avr_x)^2 / sum((x - avr_x).^2))
delta_y_zvezda = 2.26 * S_y_zvezda
%y_volna_zvezda = y_zvezda +- delta_y_zvezda;