关于regress函数的使用

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

) o! @& q, F# Z3 ^, N3 J这个是regress的使用说明，用来进行多元线性回归。
2 g. P- m, v. X$ N9 [+ j+ D9 m5 u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.

9 x# h3 z$ r/ u5 L4 X2 x' l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？

8 G- s; l" x8 i- T( g! ^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
0 U5 \. i0 W8 Z5 a  }               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.
9 ^" t" F$ c4 m8 m# g/ g/ j5 _* hB = REGRESS (Y,X)
returns the vector B of regression coefficients in the
# ~5 B; Q2 f4 w6 Dlinear model Y = X*B.
$ Y" [1 e- w6 c9 P5 _5 W# m
/ c  D2 s; }" E5 v4 ?: UX is an n-by-p design matrix, with rows
corresponding to observations and columns to predictor variables.
2 o0 G' X) ^# l. O3 |/ j
8 ?5 \0 D$ n$ T; aY is an n-by-1 vector of response observations.
, d5 N& h* X- o3 Z5 t' {REGRESS
4 U( @) y+ {% T5 q' F4 c1 l多元线性回归——用最小二乘估计法
B = REGRESS (Y,X) ，
- B1 N" A3 K; G5 b! Q
" o4 E. u. p% O0 t8 p+ w' N返回值为线性模型Y = X*B的回归系数向量
# s9 \! V4 I: B1 \  u     X ，n-by-p 矩阵，行对应于观测值，列对应于预测变量
1 h. e/ d8 m( i     Y ，n-by-1 向量，观测值的响应（即因变量）
8 F. G+ ^$ C$ v3 w
0 I# R5 P! T$ t" r7 a  N/ i[B,BINT] = REGRESS (Y,X)
returns a matrix BINT of 95% confidence intervals for B.
BINT，B的95%的置信区间矩阵
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[B,BINT,R] = REGRESS (Y,X)
returns a vector R of residuals.
R，残差向量

[B,BINT,R,RINT] = REGRESS (Y,X)
returns a matrix RINT of intervals that
9 V8 q* q& q8 t4 g5 _/ u8 m* r: e  ]9 Dcan be used to diagnose outliers.
6 h. T) m6 f6 K, ~% y
. I6 j8 B: a5 J9 C. w/ RIf RINT(i,: ) does not contain zero,
! a, H/ l# C3 a. Z* P- O
2 E' v) L$ b1 a& @4 ^then the i-th residual is larger than would be expected, at the 5%
significance level.
3 T  C: \5 S% {9 J
This 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）。
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）

! J1 S9 K: w3 N" y: H, q' g" E5 t4 a[B,BINT,R,RINT,STATS] = REGRESS (Y,X)
* d' B2 B  A4 u9 R2 ?: s4 o' treturns 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)
+ G& W9 C* M: j4 }$ \uses a 100*(1-ALPHA)% confidence level to compute BINT, and a (100*ALPHA)% significance level to compute RINT.
# i* z& G) ]- I- J用100*(1-ALPHA)%的置信水平来计算BINT，
9 n6 Z! l' T; j- g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
  `9 L; S2 ~- V8 w* K0 N* lterm.
8 t- J, \2 w5 l4 bThe F statistic and p value are computed under the assumption
) @- P  k- Z* P% Kthat the model contains a constant term, and they are not correct for
models without a constant.
# [; k+ j2 [' D+ A8 B7 K& D! @The R-square value is one minus the ratio of
the error sum of squares to the total sum of squares.
9 H6 P: f- e+ [7 cThis value can
  f7 G- F3 d2 l1 S& a$ {5 ?! T% Xbe 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）

. _7 k% v( w  ^If columns of X are linearly dependent, REGRESS sets the maximum
possible number of elements of B to zero to obtain a "basic solution",
: v' ^" u9 [: s- L, rand returns zeros in elements of BINT corresponding to the zero elements of B.
& ^; q& L2 A! v4 Z9 Y. m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。