关于regress函数的使用

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• [b,bint,r,rint,stats] = regress(y,X)
  

这个是regress的使用说明，用来进行多元线性回归。
9 R  N+ g& A1 y第一个问题：regress的第三个参数为置信水平，可填可不填，但是不管我填写与否，都会有一个warning：R-square and the F statistic are not well-defined unless X has a column of ones.
Type "help regress" for more information.
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* R+ B7 H: n1 t' _第二个问题：r是预测值和真实值的差，r'*r应该是残差平方和吗？它能够用来评价回归模型的好坏吗？
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第三个问题：stats是一个数组，The vector stats contains the R2 statistic along with the F and p values for the regression
               很多网上的使用说明，包括matlab的help都只提到了stats数组的3个成员，但是我使用regress函数后stats有4个成员，请问另外一个是代表什么问题
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ExxNEN

REGRESS Multiple linear regression using least squares.
B = REGRESS (Y,X)
. J% e( L: u6 `( nreturns the vector B of regression coefficients in the
8 ~0 J  B& s3 f0 ~9 Y) clinear model Y = X*B.
. R9 t8 i8 T# a& L
X is an n-by-p design matrix, with rows
corresponding to observations and columns to predictor variables.
8 r. U4 O, X9 A- v: ?. p
Y is an n-by-1 vector of response observations.
( _6 ?  C! G# P& b$ ^5 QREGRESS
5 Z& g3 Z6 A( o/ w' R多元线性回归——用最小二乘估计法
# }2 ]+ i1 x, v, D, j* w- NB = REGRESS (Y,X) ，

返回值为线性模型Y = X*B的回归系数向量
) l2 [; j# O& V' D2 Y3 b$ L: U! q( L+ X5 T     X ，n-by-p 矩阵，行对应于观测值，列对应于预测变量
     Y ，n-by-1 向量，观测值的响应（即因变量）

[B,BINT] = REGRESS (Y,X)
7 {, U4 c! _' X- Y, \, |% Jreturns a matrix BINT of 95% confidence intervals for B.
BINT，B的95%的置信区间矩阵

[B,BINT,R] = REGRESS (Y,X)
returns a vector R of residuals.
R，残差向量
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' R4 x0 r( U) G[B,BINT,R,RINT] = REGRESS (Y,X)
returns a matrix RINT of intervals that
can be used to diagnose outliers.

If RINT(i,: ) does not contain zero,
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then the i-th residual is larger than would be expected, at the 5%
significance level.

- W1 L0 c) o* h& GThis is evidence that the I-th observation is an outlier.

RINT，区间矩阵，该矩阵可以用来诊断异常（即发现奇异观测值，译者注）。
如果RINT(i，：)所定区间没有包含0，则第i个残差在默认的5%的显著性水平比我们所预期的要大，这可说明第i个观测值是个奇异点（即说明该点可能是错误而无意义的，如记录错误等，译者注）
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[B,BINT,R,RINT,STATS] = REGRESS (Y,X)
returns a vector STATS containing
9 x! H, E; `& D: e/ n$ N4 cthe R-square statistic, the F statistic and p value for the full model,and an estimate of the error variance.

STATS，向量，包括R方统计量，F统计量，总模型的p值（还不清楚）和方差的一个估计（还不清楚）

[...] = REGRESS (Y,X,ALPHA)
& h7 d* F2 n. R, ^6 v8 |/ wuses a 100*(1-ALPHA)% confidence level to compute BINT, and a (100*ALPHA)% significance level to compute RINT.
% ]' Z+ e8 u2 E& z* H( S用100*(1-ALPHA)%的置信水平来计算BINT，
+ q( e# Z- e! ]. m用(100*ALPHA)%的显著性水平来计算RINT

4 m% ^, Z! T. Y& z1 `X should include a column of ones so that the model contains a constant
0 M! W; f9 M1 q& Q5 `# Qterm.
9 H/ d  \6 T0 H$ OThe F statistic and p value are computed under the assumption
$ E8 q5 t! y7 v) D( F/ W, Rthat the model contains a constant term, and they are not correct for
models without a constant.
The R-square value is one minus the ratio of
the error sum of squares to the total sum of squares.
4 K2 D9 y3 T  P, |# Q0 t# h0 yThis value can
1 f. }) _6 T5 ]) p; x9 X8 M& kbe negative for models without a constant, which indicates that the model is not appropriate for the data.
X应该包含一个全“1”的列，这样则该模型包含常数项。F统计量和p值是在模型有常数项的假设下计算的，如果模型没有常数项，则计算得的F统计量和p值是不正确的。The R-square value is one minus the ratio of the error sum of squares to the total sum of squares.（此句无法把握，请高手帮忙~~!）若模型没有常数项，则这个值可以为负值，这也表明这个模型对数据是不合适的。（即数据不适合用多元线性模型，译者注）

& H/ R6 n& n, e9 a4 ZIf columns of X are linearly dependent, REGRESS sets the maximum
possible number of elements of B to zero to obtain a "basic solution",
and returns zeros in elements of BINT corresponding to the zero elements of B.
1 W5 M( T0 z; A( I. g如果X的列是线性相关的，则REGRESS将使B的元素中“0”的数量尽量多，以此获得一个“基本解”，并且使B中元素“0”所对应的BINT元素为“0”。
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REGRESS treats NaNs in X or Y as missing values, and removes them. REGRESS
将X或者Y中的NaNs当作缺失值处理，并且移除它们。