Задача ТУ

// Defining arrays for the values
const x = [128, 125, 122, 100, 109, 126, 124, 106, 131, 120, 103, 110, 130, 111, 102];
const y = [59, 40, 38, 11, 56, 36, 47, 58, 60, 13, 20, 20, 45, 29, 49, 53, 37, 54, 35, 23];
const z = [130, 118, 145, 157, 132, 124, 147, 149, 123, 148, 156, 159, 137, 158, 117];

// Calculating the mean
let sum_x = 0, sum_y = 0, sum_z = 0;
for (let i = 0; i < x.length; ++i) {
    sum_x += x[i];
    sum_y += y[i];
    sum_z += z[i];
}
const mean_x = sum_x / x.length;
const mean_y = sum_y / y.length;
const mean_z = sum_z / z.length;

// Calculating the variance
let variance_x = 0, variance_y = 0, variance_z = 0;
for (let i = 0; i < x.length; ++i) {
    variance_x += Math.pow(x[i] - mean_x, 2);
    variance_y += Math.pow(y[i] - mean_y, 2);
    variance_z += Math.pow(z[i] - mean_z, 2);
}
variance_x /= x.length - 1;
variance_y /= y.length - 1;
variance_z /= z.length - 1;

// Calculating the standard deviation
const std_dev_x = Math.sqrt(variance_x);
const std_dev_y = Math.sqrt(variance_y);
const std_dev_z = Math.sqrt(variance_z);

// Calculating the correlation coefficients
let sum_xy = 0, sum_xz = 0, sum_yz = 0;
for (let i = 0; i < x.length; ++i) {
    sum_xy += (x[i] - mean_x) * (y[i] - mean_y);
    sum_xz += (x[i] - mean_x) * (z[i] - mean_z);
    sum_yz += (y[i] - mean_y) * (z[i] - mean_z);
}
const correlation_coefficient_xy = sum_xy / (std_dev_x * std_dev_y * (x.length - 1));
const correlation_coefficient_xz = sum_xz / (std_dev_x * std_dev_z * (x.length - 1));
const correlation_coefficient_yz = sum_yz / (std_dev_y * std_dev_z * (x.length - 1));

// Printing the results
console.log("Математическо очакване за x: " + mean_x);
console.log("Математическо очакване за y: " + mean_y);
console.log("Математическо очакване за z: " + mean_z);
console.log("Дисперсия за x: " + variance_x);
console.log("Дисперсия за y: " + variance_y);
console.log("Дисперсия за z: " + variance_z);
console.log("Средноквадратично отклонение за x: " + std_dev_x);
console.log("Средноквадратично отклонение за y: " + std_dev_y);
console.log("Средноквадратично отклонение за z: " + std_dev_z);
console.log("Коефициент на корелация между x и y: " + correlation_coefficient_xy);
console.log("Коефициент на корелация между x и z: " + correlation_coefficient_xz);
console.log("Коефициент на корелация между y и z: " + correlation_coefficient_yz);

// Confidence intervals for the mean
console.log("Доверителни интервали за математическото очакване:");
console.log("x: [" + (mean_x - (1.76131 * std_dev_x / 2)) + ", " + (mean_x + (1.76131 * std_dev_x / 2)) + "]");
console.log("y: [" + (mean_y - (1.729133 * std_dev_y / 2)) + ", " + (mean_y + (1.729133 * std_dev_y / 2)) + "]");
console.log("z: [" + (mean_z - (1.76131 * std_dev_z / 2)) + ", " + (mean_z + (1.76131 * std_dev_z / 2)) + "]");

// Confidence intervals for the variance
console.log("Доверителни интервали ДИСПЕРСИЯ:");
console.log("x: [" + (variance_x * 3) / 9.348 + ", " + (variance_x * 3) / 0.2158 + "]");
console.log("y: [" + (variance_y * 3) / 9.348 + ", " + (variance_y * 3) / 0.2158 + "]");
console.log("z: [" + (variance_z * 3) / 9.348 + ", " + (variance_z * 3) / 0.2158 + "]");

// Confidence intervals for the mean changes
console.log("Доверителни интервали ИЗМЕНЕНИЕ НА ВЕЛИЧИНАТА:");
console.log("x: [" + (mean_x - 3 * std_dev_x) + ", " + (mean_x + 3 * std_dev_x) + "]");
console.log("y: [" + (mean_y - 3 * std_dev_y) + ", " + (mean_y + 3 * std_dev_y) + "]");
console.log("z: [" + (mean_z - 3 * std_dev_z) + ", " + (mean_z + 3 * std_dev_z) + "]");

return 0;