关于regress函数的使用

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• [b,bint,r,rint,stats] = regress(y,X)
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. C8 F$ J* o/ \/ G$ [7 k( g( a这个是regress的使用说明，用来进行多元线性回归。
" t2 t# v9 w# _. t- R5 R2 O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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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

ExxNEN

REGRESS Multiple linear regression using least squares.
B = REGRESS (Y,X)
$ P0 Q( \- y4 V0 g( r, \, p4 _+ F: Areturns the vector B of regression coefficients in the
! k! K* J1 @* M" Alinear model Y = X*B.
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X is an n-by-p design matrix, with rows
2 S/ `6 S# q5 l# Ncorresponding to observations and columns to predictor variables.

1 C/ I# M  t6 f! u$ hY is an n-by-1 vector of response observations.
9 y5 j6 ^( m: c. R8 NREGRESS
( z+ A  i) e* L; p( R7 ?: k多元线性回归——用最小二乘估计法
B = REGRESS (Y,X) ，
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返回值为线性模型Y = X*B的回归系数向量
% V% _) m' n. O. @4 b2 p$ K     X ，n-by-p 矩阵，行对应于观测值，列对应于预测变量
3 U: @& Q0 O7 B% e( _! h& `     Y ，n-by-1 向量，观测值的响应（即因变量）

5 h9 g  Z9 k& R/ J9 A$ y7 ^[B,BINT] = REGRESS (Y,X)
: e7 X! b7 V* h, m9 preturns a matrix BINT of 95% confidence intervals for B.
) \9 y6 v; y0 Y% Z% ?/ @' s2 ZBINT，B的95%的置信区间矩阵

3 I$ g, X4 H& ~( U[B,BINT,R] = REGRESS (Y,X)
returns a vector R of residuals.
R，残差向量

( b3 d$ a' b5 _4 \# h- _! o. a[B,BINT,R,RINT] = REGRESS (Y,X)
returns a matrix RINT of intervals that
can be used to diagnose outliers.
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3 }3 K' Z5 w' H4 z# JIf RINT(i,: ) does not contain zero,

then the i-th residual is larger than would be expected, at the 5%
significance level.
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3 m2 F) h8 f$ t) Z0 N) oThis is evidence that the I-th observation is an outlier.

" L( p, s9 |4 ~+ U& l; V* hRINT，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）。
) c& k# o5 T7 E' B, y5 V8 }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）

[B,BINT,R,RINT,STATS] = REGRESS (Y,X)
returns a vector STATS containing
the 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)
% c% e% ~* I& {& J. ]/ @uses a 100*(1-ALPHA)% confidence level to compute BINT, and a (100*ALPHA)% significance level to compute RINT.
' [# w. ~+ v8 w+ Y8 k* f" y用100*(1-ALPHA)%的置信水平来计算BINT，
4 H/ p3 i3 s; j. L( Z# R用(100*ALPHA)%的显著性水平来计算RINT

X should include a column of ones so that the model contains a constant
1 V$ q. D0 ^8 D- H" x  o- k8 n: Eterm.
# G4 K. F; t  ~/ d: D/ k8 YThe F statistic and p value are computed under the assumption
that the model contains a constant term, and they are not correct for
6 t( ]; M+ D% pmodels without a constant.
) K2 q7 ^2 X% A. NThe R-square value is one minus the ratio of
the error sum of squares to the total sum of squares.
This value can
/ }$ r; }3 I9 _8 q4 _1 ube negative for models without a constant, which indicates that the model is not appropriate for the data.
' [' D+ J" ]8 C1 n" Q% hX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）
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5 o! S7 b, Y5 ?4 b3 \# w) m+ `If 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.
( N1 E4 n5 G% v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”。

( q7 ~: o6 Z* uREGRESS treats NaNs in X or Y as missing values, and removes them. REGRESS
0 ^! n* L' ~, q$ t) U+ P; J7 Y& H% Z将X或者Y中的NaNs当作缺失值处理，并且移除它们。