关于regress函数的使用

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

; N! d6 ?! Y( a  }这个是regress的使用说明，用来进行多元线性回归。
4 R* g5 r+ X) z  d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.
5 ~+ w/ y# }3 v' `, z$ \; ^Type "help regress" for more information.
: b* s! t5 b; n, q* C
- t- q# b% b, o# M& j' x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？

2 ~8 j! P; @/ t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
4 v$ {7 p7 J( {) \               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)
returns the vector B of regression coefficients in the
* g! Q; N8 V% a; V" N. Xlinear model Y = X*B.

X is an n-by-p design matrix, with rows
corresponding to observations and columns to predictor variables.
0 D* e1 J* L; h4 c, c- A8 v, x
Y is an n-by-1 vector of response observations.
9 s, v) C# g/ C* w! n7 [' \; E6 GREGRESS
$ S6 m% T) G* b6 m多元线性回归——用最小二乘估计法
9 l% S: D: f- r: r) oB = REGRESS (Y,X) ，
. z1 n0 n) |5 A
返回值为线性模型Y = X*B的回归系数向量
9 x8 _3 S+ J# ]/ _4 {# k  a     X ，n-by-p 矩阵，行对应于观测值，列对应于预测变量
5 n- o9 `1 P9 s     Y ，n-by-1 向量，观测值的响应（即因变量）
, E! v8 Q2 _. t6 `3 R+ i
: a+ n5 w- V. _- |! b6 t& f: g' u# z[B,BINT] = REGRESS (Y,X)
returns a matrix BINT of 95% confidence intervals for B.
( a, p6 A4 U$ O) eBINT，B的95%的置信区间矩阵
& B) ?- X- b3 K/ G
[B,BINT,R] = REGRESS (Y,X)
0 E4 h' Z( c/ Z5 ^& lreturns a vector R of residuals.
R，残差向量
4 C( a# h  q0 D8 X% b0 l6 U; `8 _' q
[B,BINT,R,RINT] = REGRESS (Y,X)
returns a matrix RINT of intervals that
( L- h" I% {! D% Z/ r' o1 q9 Ycan be used to diagnose outliers.

/ o& _6 A9 @, P( SIf RINT(i,: ) does not contain zero,

then the i-th residual is larger than would be expected, at the 5%
significance level.

" x( f( P6 O" L0 L8 P/ X, NThis is evidence that the I-th observation is an outlier.
* }1 l/ O+ K% z. \
$ c# s, F# c3 v  C  m8 YRINT，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）

[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）

9 l/ ]" Y6 `: d/ g* M[...] = REGRESS (Y,X,ALPHA)
uses a 100*(1-ALPHA)% confidence level to compute BINT, and a (100*ALPHA)% significance level to compute RINT.
用100*(1-ALPHA)%的置信水平来计算BINT，
用(100*ALPHA)%的显著性水平来计算RINT
5 Q5 U) v# Q0 B
X should include a column of ones so that the model contains a constant
term.
The F statistic and p value are computed under the assumption
3 _2 e6 _+ T) o# c# R  Ythat 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.
This value can
be negative for models without a constant, which indicates that the model is not appropriate for the data.
! D0 R- t* B/ T% A& @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）

If columns of X are linearly dependent, REGRESS sets the maximum
* `( K; Z2 v% j$ t  Ipossible 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.
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”。
2 p) S: t" W6 \' ]$ U- D  h$ s  Q( {6 X
6 p1 x0 u0 i+ q5 ZREGRESS treats NaNs in X or Y as missing values, and removes them. REGRESS
9 e9 c0 \0 W' ]; a: s将X或者Y中的NaNs当作缺失值处理，并且移除它们。