关于regress函数的使用

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

  ~7 \. P. N: H) H5 y9 l5 V4 G这个是regress的使用说明，用来进行多元线性回归。
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.

1 c6 g2 x, g: B' J7 q: z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)
returns the vector B of regression coefficients in the
linear model Y = X*B.
( H) D' B/ b' z! u, Y; K. ?1 z- Y
X is an n-by-p design matrix, with rows
corresponding to observations and columns to predictor variables.

. X( v- w( ^" H' Y& Z: CY is an n-by-1 vector of response observations.
REGRESS
多元线性回归——用最小二乘估计法
0 }$ H" T7 q: C% P* }' y2 \6 \B = REGRESS (Y,X) ，

8 ]3 P: w4 Y" q* O- \7 T( X- _返回值为线性模型Y = X*B的回归系数向量
; E  L6 p5 m" K/ _- v5 t     X ，n-by-p 矩阵，行对应于观测值，列对应于预测变量
; C! U' w/ f+ y. C+ n# E     Y ，n-by-1 向量，观测值的响应（即因变量）

[B,BINT] = REGRESS (Y,X)
returns a matrix BINT of 95% confidence intervals for B.
% {% K( G2 \& kBINT，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

  i' `. i# @3 \" y, t[B,BINT,R,RINT] = REGRESS (Y,X)
returns a matrix RINT of intervals that
) O0 ~! V$ T( {! P) p* Ccan be used to diagnose outliers.
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/ x5 M5 J$ p) S- S0 [4 @If RINT(i,: ) does not contain zero,
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: |9 e( X: ~5 _& ~then the i-th residual is larger than would be expected, at the 5%
significance level.
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2 g% s% _7 y* d3 R9 c/ Y" [7 p- g; LThis is evidence that the I-th observation is an outlier.
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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）。
: M7 O7 |5 ?1 y5 _3 x# B3 e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
. {, X+ r- v0 j( ^& c4 L# Nthe R-square statistic, the F statistic and p value for the full model,and an estimate of the error variance.
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, @& a! \% s4 U, W- L' Z+ WSTATS，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）
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[...] = REGRESS (Y,X,ALPHA)
. S/ J7 X0 v* p0 o  N" t% z4 suses a 100*(1-ALPHA)% confidence level to compute BINT, and a (100*ALPHA)% significance level to compute RINT.
8 @3 Q; ^' z  J3 F# X用100*(1-ALPHA)%的置信水平来计算BINT，
. \7 z1 O; I$ l3 q2 y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
term.
% C( C$ u! V$ |0 t! B6 KThe F statistic and p value are computed under the assumption
0 }5 Z* c4 a' q" E# r4 E5 Q3 H$ Tthat the model contains a constant term, and they are not correct for
models without a constant.
3 S; z7 n" m3 q% j( eThe R-square value is one minus the ratio of
the error sum of squares to the total sum of squares.
, g1 T* i+ I9 l; `! {This value can
* Z( ^% S7 A0 q; h" S4 t! q' Dbe 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）

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.
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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8 U* [) x; \0 z6 m$ |- W/ X" SREGRESS 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。