关于regress函数的使用

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

1 P2 K2 b2 w' D2 T1 Z2 H; n这个是regress的使用说明，用来进行多元线性回归。
( r0 ^" n, e1 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.
% s3 ?8 l  y$ T, ~1 yType "help regress" for more information.
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- {! t5 j4 r# ?4 G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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4 \0 I$ ?% p5 N. C( n: H! ~. |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
3 _( \. b% p; ^               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.
+ @2 g& Z* G' j4 w7 L0 DB = REGRESS (Y,X)
) i8 C! }' }1 m/ A- P, Sreturns the vector B of regression coefficients in the
linear model Y = X*B.

X is an n-by-p design matrix, with rows
" J0 q1 T5 d" F+ ycorresponding to observations and columns to predictor variables.

0 Q6 F4 m4 P/ i( XY is an n-by-1 vector of response observations.
REGRESS
& Q3 @  e) O/ ?* X  V多元线性回归——用最小二乘估计法
B = REGRESS (Y,X) ，

返回值为线性模型Y = X*B的回归系数向量
     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）
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9 C9 M0 @1 J4 K( _0 ~[B,BINT] = REGRESS (Y,X)
& V( e6 k0 }+ E* }3 q: oreturns a matrix BINT of 95% confidence intervals for B.
: P2 L  a  e  J" v) |4 BBINT，B的95%的置信区间矩阵
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[B,BINT,R] = REGRESS (Y,X)
: n  F& E! K) B( i. p' hreturns a vector R of residuals.
1 v& c* D8 Z, f( B2 m3 R# @1 oR，残差向量
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9 ]8 n$ S5 j+ f' i% l3 e! r' K# c[B,BINT,R,RINT] = REGRESS (Y,X)
% A( A7 L; i- S; Mreturns a matrix RINT of intervals that
. A  Q8 v2 y/ ?4 R  s4 K. Ecan be used to diagnose outliers.

$ ]2 c- Z4 H1 i/ P# m: ?If 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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: s/ y2 p; u: O+ e6 \+ L7 l4 RThis is evidence that the I-th observation is an outlier.
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. o. \  `* |' VRINT，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
the R-square statistic, the F statistic and p value for the full model,and an estimate of the error variance.
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& O: s6 j" R( q$ L1 iSTATS，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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1 Y5 ]% M0 r3 O/ ^7 ^[...] = REGRESS (Y,X,ALPHA)
: C$ \) f  `1 p7 @- r4 I6 f, guses a 100*(1-ALPHA)% confidence level to compute BINT, and a (100*ALPHA)% significance level to compute RINT.
9 ?( p9 p3 G& h: e! l用100*(1-ALPHA)%的置信水平来计算BINT，
: y2 G+ H+ T# }& z4 n( `! W用(100*ALPHA)%的显著性水平来计算RINT

* K2 J( E) D9 `% T* w3 v! aX should include a column of ones so that the model contains a constant
# F5 ~0 X% X2 G8 s+ hterm.
5 Z  |% q# B1 \- l# qThe F statistic and p value are computed under the assumption
that the model contains a constant term, and they are not correct for
models without a constant.
9 W; z# ?# W# T& g' uThe R-square value is one minus the ratio of
9 H$ E) a& K' pthe error sum of squares to the total sum of squares.
  I# p: O+ Z5 U: \: Q* j4 uThis value can
3 _. |6 v: R1 o- L, c8 }/ F# ibe 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）

3 P6 n* R6 J6 h. S6 r. x1 ?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.
# M/ S5 `# S! R9 X8 t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”。

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。