写一个python的正交实验各因素的离差平方和及自由度的计算代码

当然，我可以帮你提供一个实现正交实验各因素的离差平方和及自由度的Python代码。请看以下代码示例：

import numpy as np

# 设定正交试验的因素变量
A = [-1, -1, 1, 1]
B = [-1, 1, -1, 1]
C = [-1, 1, 1, -1]

# 构建正交试验方案矩阵
X = np.array([
    [1, 1, 1, 1], # 1代表中心值
    A,
    B,
    C,
    A*B,
    A*C,
    B*C,
    A*B*C
])

# 设定样本观测值向量
Y = np.array([3, 4, 5, 6, 6, 7, 8, 10])

# 计算各因素离差平方和及总离差平方和
SST = np.sum((Y - np.mean(Y)) ** 2)
SSA = np.sum((np.mean(Y[X[i,:] == 1]) - np.mean(Y)) ** 2 for i in range(X.shape[0]))
SSB = np.sum((np.mean(Y[X[i,:] == 1]) - np.mean(Y)) ** 2 for i in range(X.shape[0]) if np.sum(X[i,:]) == 2)
SSC = np.sum((np.mean(Y[X[i,:] == 1]) - np.mean(Y)) ** 2 for i in range(X.shape[0]) if np.sum(X[i,:]) == 2)
SSAB = np.sum((np.mean(Y[X[i,:] == 1]) - np.mean(Y)) ** 2 for i in range(X.shape[0]) if np.sum(X[i,:]) == 3 and sum(A*X[i,:]) == sum(B*X[i,:]))
SSAC = np.sum((np.mean(Y[X[i,:] == 1]) - np.mean(Y)) ** 2 for i in range(X.shape[0]) if np.sum(X[i,:]) == 3 and sum(A*X[i,:]) == sum(C*X[i,:]))
SSBC = np.sum((np.mean(Y[X[i,:] == 1]) - np.mean(Y)) ** 2 for i in range(X.shape[0]) if np.sum(X[i,:]) == 3 and sum(B*X[i,:]) == sum(C*X[i,:]))
SSABC = SST - SSA - SSB - SSC - SSAB - SSAC - SSBC

# 计算各因素对应的自由度
dfA = len(np.where(X[1,:] == 1)[0]) - 1
dfB = len(np.where(X[2,:] == 1)[0]) - 1
dfC = len(np.where(X[3,:] == 1)[0]) - 1
dfAB = dfA * dfB
dfAC = dfA * dfC
dfBC = dfB * dfC
dfABC = dfA * dfB * dfC
dfE = len(Y) - len(np.unique(X, axis=1).shape[1])

# 输出结果
print("SSA={:.2f}, dfA={}, MS(A)={:.2f}".format(SSA, dfA, SSA/dfA))
print("SSB={:.2f}, dfB={}, MS(B)={:.2f}".format(SSB, dfB, SSB/dfB))
print("SSC={:.2f}, dfC={}, MS(C)={:.2f}".format(SSC, dfC, SSC/dfC))
print("SSAB={:.2f}, dfAB={}, MS(AB)={:.2f}".format(SSAB, dfAB, SSAB/dfAB))
print("SSAC={:.2f}, dfAC={}, MS(AC)={:.2f}".format(SSAC, dfAC, SSAC/dfAC))
print("SSBC={:.2f}, dfBC={}, MS(BC)={:.2f}".format(SSBC, dfBC, SSBC/dfBC))
print("SSABC={:.2f}, dfABC={}, MS(ABC)={:.2f}".format(SSABC, dfABC, SSABC/dfABC))
print("SSE={:.2f}, dfE={}".format(SST-SSA-SSB-SSC-SSAB-SSAC-SSBC-SSABC, dfE))

注意：该代码实现的正交实验是按照3因素4水平设计进行的，如果需要进行其他设计，需要自己修改代码中的变量和自由度计算公式。