在多元线性回归中，如何用matlab求得各个变量的T统计值及其p值？
回归模型为y=c0+c1*x1+c2*x2+c3*x3如何求得c1 c2 c3的t统计值？
推荐回答（2个）
一般情况下，p值取0.05，如果想要更为精确，可以取0.01.
二、一元线性回归
2．1．命令 polyfit最小二乘多项式拟合
[p，S]=polyfit（x，y，m）
多项式y=a1xm+a2xm-1+…+amx+am+1
其中x=（x1，x2，…，xm）x1…xm为（n*1）的矩阵;
y为（n*1）的矩阵；
p=（a1，a2，…，am+1）是多项式y=a1xm+a2xm-1+…+amx+am+1的系数；
S是一个矩阵，仔桥用来估计预测误差.
2．2．命令 polyval多项式函数的预测值
Y=polyval（p，x）求polyfit所得的回归多项式在x处的预测值Y；
p是polyfit函数的返回值；
x和polyfit函数的x值相同。
2．3．命令 polyconf 残差个案次序图
[Y，DELTA]=polyconf（p，x，S，alpha）求polyfit所得的回归多项式在x处的预测值Y及预测值的显著性为1-alpha的置信区间DELTA；alpha缺省时为0.05。
p是polyfit函数的返回值；
x和polyfit函数的x值相同；
S和polyfit函数的S值相同。
2．4 命令 polytool（x，拦戚渗y，m）一元多项式回归命令
2．5．命令regress多元线性回归（可用于一元线性回归）
b=regress( Y, X )
[b, bint,r,rint,stats]=regress(Y,X,alpha)
b 回归系数
bint 回归系数的区间估计
r 残差
rint 残差置信区间
stats 用于检验回归模型的统计量，有三个数值：相关系数R2、F值、与F对应的概率p,相关系数R2越接近1，说明回归方程越显著；F > F1-α（k，n-k-1）时拒绝H0，F越大，说明回归方程越显著；与F对应的概率p 时拒绝H0，回归模型成立。
Y为n*1的矩阵；
X为（ones(n,1),x1,…,xm）的矩阵；
alpha显著性水平（缺省时为0.05）。
三、多元线性回归
3．1．命令 regress（见2。5）
3．2．命令 rstool 多元二项式回归
命令：rstool（x，y，’model’, alpha）
x 为n*m矩阵
y为 n维列向量
model 由下列4个模型中选择1个（用字符串输入，缺省时为线性模型）：
linear（线性）：
purequadratic（纯二次）：
interaction（交叉）：
quadratic（完全二次）：
alpha 显著性水平（缺省时为0.05）
返回值beta 系数
返回值rmse剩余标准差
返回值residuals残差
四、非线性回归
4．1．命令 nlinfit
[beta,R,J]=nlinfit(X,Y,’’model’,beta0)
X 为n*m矩阵
Y为 n维列向量
model为自定义函数
beta0为估计的模型系数
beta为回归系数
R为残差
J
4．2．命令 nlintool
nlintool(X,Y,’model’,beta0,alpha)
X 为n*m矩阵
Y为 n维列向量
model为自定义函数
beta0为估计的模型系数
alpha显著性水平（缺省时为0.05）
4．3．命令 nlparci
betaci=nlparci(beta,R,J)
beta为回归系数
R为残差
J
返回值为回归简脊系数beta的置信区间
4．4．命令 nlpredci
[Y,DELTA]=nlpredci(‘model’,X,beta,R,J)
Y为预测值
DELTA为预测值的显著性为1-alpha的置信区间；alpha缺省时为0.05。
X 为n*m矩阵
model为自定义函数
beta为回归系数
R为残差
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