Решение: Расчет произведений разностей Xᵢ * Yᵢ

Для выполнения пунктов 1.3 – 1.8 произведем расчеты на основе ранее вычисленных отклонений \(X_i = (x_i - \bar{x})\) и \(Y_i = (y_i - \bar{y})\). 1.3 Расчет произведений разностей \(X_i \cdot Y_i\): \[X_1 \cdot Y_1 = (-0,58) \cdot (-4,875) = 2,8275\] \[X_2 \cdot Y_2 = 3,42 \cdot 14,725 = 50,3595\] \[X_3 \cdot Y_3 = 1,22 \cdot (-5,975) = -7,2895\] \[X_4 \cdot Y_4 = (-1,28) \cdot 3,325 = -4,256\] \[X_5 \cdot Y_5 = 2,22 \cdot 4,925 = 10,9335\] \[X_6 \cdot Y_6 = 0,82 \cdot 1,925 = 1,5785\] \[X_7 \cdot Y_7 = 0,82 \cdot 3,225 = 2,6445\] \[X_8 \cdot Y_8 = (-3,18) \cdot (-7,375) = 23,4525\] \[X_9 \cdot Y_9 = 0,42 \cdot 2,925 = 1,2285\] \[X_{10} \cdot Y_{10} = 1,42 \cdot (-5,175) = -7,3485\] \[X_{11} \cdot Y_{11} = (-3,58) \cdot (-9,575) = 34,2785\] \[X_{12} \cdot Y_{12} = (-0,38) \cdot 4,225 = -1,6055\] \[X_{13} \cdot Y_{13} = (-0,88) \cdot 0,225 = -0,198\] \[X_{14} \cdot Y_{14} = 3,92 \cdot 6,425 = 25,186\] \[X_{15} \cdot Y_{15} = 1,52 \cdot (-2,575) = -3,914\] \[X_{16} \cdot Y_{16} = (-3,58) \cdot 10,825 = -38,7535\] \[X_{17} \cdot Y_{17} = (-3,58) \cdot 10,825 = -38,7535\] \[X_{18} \cdot Y_{18} = 3,42 \cdot (-12,375) = -42,3225\] \[X_{19} \cdot Y_{19} = (-2,58) \cdot (-13,375) = 34,5075\] \[X_{20} \cdot Y_{20} = 0,12 \cdot (-2,275) = -0,273\] 1.4 Расчет суммы произведений \(\sum X \cdot Y\): \[\sum X \cdot Y = 2,8275 + 50,3595 - 7,2895 - 4,256 + ... - 0,273 = 39,227\] 1.5 и 1.6 Расчет квадратов \(X^2\) и их суммы \(\sum X^2\): \[X_1^2 = 0,3364; X_2^2 = 11,6964; X_3^2 = 1,4884; X_4^2 = 1,6384; X_5^2 = 4,9284;\] \[X_6^2 = 0,6724; X_7^2 = 0,6724; X_8^2 = 10,1124; X_9^2 = 0,1764; X_{10}^2 = 2,0164;\] \[X_{11}^2 = 12,8164; X_{12}^2 = 0,1444; X_{13}^2 = 0,7744; X_{14}^2 = 15,3664; X_{15}^2 = 2,3104;\] \[X_{16}^2 = 12,8164; X_{17}^2 = 12,8164; X_{18}^2 = 11,6964; X_{19}^2 = 6,6564; X_{20}^2 = 0,0144\] \[\sum X^2 = 108,972\] 1.7 и 1.8 Расчет квадратов \(Y^2\) и их суммы \(\sum Y^2\): \[Y_1^2 = 23,7656; Y_2^2 = 216,8256; Y_3^2 = 35,7006; Y_4^2 = 11,0556; Y_5^2 = 24,2556;\] \[Y_6^2 = 3,7056; Y_7^2 = 10,4006; Y_8^2 = 54,3906; Y_9^2 = 8,5556; Y_{10}^2 = 26,7806;\] \[Y_{11}^2 = 91,6806; Y_{12}^2 = 17,8506; Y_{13}^2 = 0,0506; Y_{14}^2 = 41,2806; Y_{15}^2 = 6,6306;\] \[Y_{16}^2 = 117,1806; Y_{17}^2 = 117,1806; Y_{18}^2 = 153,1406; Y_{19}^2 = 178,8906; Y_{20}^2 = 5,1756\] \[\sum Y^2 = 1144,482\]