%% Ex.01
clear all; close all; clc;

data = load('zad1a.txt');
alfa = 0.09;
sigma = std(data);
N = length(data);

chi2_range = chi2inv([1-(alfa/2) alfa/2], N-1);
trust_range = sqrt(((N-1)*sigma^2)./chi2_range);

%% Ex.02
clear all; close all; clc;

a = 5;
m = 21;
X = zeros(31,1);
X(1) = 1;

for i = 2:31
    X(i) = mod(a*X(i-1),m);
end

subplot(2,1,1); hist(X);
subplot(2,1,2); scatter(X(1:30), X(2:31));

% Okres generatora to 6 (wartości powtarzają się co 6)
% Okres generatora można odczytać z wykresu rozrzutu
%% Ex.03
clear all; close all; clc;

data_learn = load('pomiar.ucz.txt');
data_learn = data_learn(:,2);

data_test = load('pomiar.tes.txt');
data_test = data_test(:,2);

data_learn_lvl_1 = load('pomiar.ucz.1.txt');
data_learn_lvl_1 = data_learn_lvl_1(:,2);

data_test_lvl_1 = load('pomiar.tes.1.txt');
data_test_lvl_1 = data_test_lvl_1(:,2);

data_learn_lvl_2 = load('pomiar.ucz.2.txt');
data_learn_lvl_2 = data_learn_lvl_2(:,2);

data_test_lvl_2 = load('pomiar.tes.2.txt');
data_test_lvl_2 = data_test_lvl_2(:,2);

data_learn_lvl_3 = load('pomiar.ucz.3.txt');
data_learn_lvl_3 = data_learn_lvl_3(:,2);

data_test_lvl_3 = load('pomiar.tes.3.txt');
data_test_lvl_3 = data_test_lvl_3(:,2);

N = length(data_test) + length(data_learn);
AVG = (sum(data_learn) + sum(data_test))/N;
AVG_TEST = mean(data_test);
TSS = sum((data_learn-AVG).^2) + sum((data_test-AVG).^2);
TSS_T = sum((data_test - AVG_TEST).^2);

RSS_LVL_1 = sum((data_learn-data_learn_lvl_1).^2) + sum((data_test-data_test_lvl_1).^2);
RSS_LVL_1_T = sum((data_test - data_test_lvl_1).^2);
R2_LVL_1_T = 1 - RSS_LVL_1_T/TSS_T;
RSE_LVL_1 = RSS_LVL_1 / (N - 1);
CP_LVL_1 = 1/N * (RSS_LVL_1 + 2*1*RSE_LVL_1^2);

RSS_LVL_2 = sum((data_learn-data_learn_lvl_2).^2) + sum((data_test-data_test_lvl_2).^2);
RSS_LVL_2_T = sum((data_test-data_test_lvl_2).^2);
R2_LVL_2_T = 1 - RSS_LVL_2_T/TSS_T;
RSE_LVL_2 = RSS_LVL_2 / (N-2);
CP_LVL_2 = 1/N * (RSS_LVL_2 + 2*2*RSE_LVL_2^2);

RSS_LVL_3 = sum((data_learn-data_learn_lvl_3).^2) + sum((data_test-data_test_lvl_3).^2);
RSS_LVL_3_T = sum((data_test-data_test_lvl_3).^2);
R2_LVL_3_T = 1 - RSS_LVL_3_T/TSS_T;
RSE_LVL_3 = RSS_LVL_3 / (N-2);
CP_LVL_3 = 1/N * (RSS_LVL_3 + 2*2*RSE_LVL_3^2);
%% Ex.04
close all; clear all; clc;

data = load('zad1b.txt');
mi = 5.6;
MEAN = mean(data);
alfa = 0.05;
freedom = length(data) - 1;

x0 = -6:0.01:6;
hold on;
plot(x0, tpdf(x0,freedom));
t_range = tinv([1-alfa/2 alfa],freedom);

line([t_range(1) t_range(1)], [0 tpdf(t_range(1), freedom)]);
line([t_range(2) t_range(2)], [0 tpdf(t_range(2), freedom)]);
t_test = (MEAN-mi)/std(data) * sqrt(freedom);
line([t_test t_test], [0 tpdf(t_test(1), freedom)], 'Color','r');