关于regress函数的使用

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

这个是regress的使用说明，用来进行多元线性回归。
( o5 N/ ]5 |8 w5 s5 _1 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.
: _5 d3 _5 @7 IType "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？

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
* e' Z# `, s" V1 x8 G* O, I               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
. ~8 q( A8 t# K" L1 m: I8 llinear model Y = X*B.
/ y) T: Z- [4 Q& X' n' r  K* g
X is an n-by-p design matrix, with rows
, M0 ?' |. Z: Xcorresponding to observations and columns to predictor variables.

" i1 E* ?) r8 d) Y+ ZY is an n-by-1 vector of response observations.
REGRESS
+ G: O/ b$ j5 A, I. ~. r9 i4 H8 I0 `0 q多元线性回归——用最小二乘估计法
+ y% R) M* Y) ^5 kB = REGRESS (Y,X) ，

- h; x, }! c- o+ K8 Y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）
5 ~8 i# r3 C5 Y" y
[B,BINT] = REGRESS (Y,X)
) o  ~+ N6 z  w! b+ i4 Q" oreturns a matrix BINT of 95% confidence intervals for B.
BINT，B的95%的置信区间矩阵

8 ~( h( P, X+ \  R, ][B,BINT,R] = REGRESS (Y,X)
returns a vector R of residuals.
R，残差向量

[B,BINT,R,RINT] = REGRESS (Y,X)
8 T# a$ A, K" k2 C- ?8 hreturns a matrix RINT of intervals that
can be used to diagnose outliers.
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0 z' X& X/ D! D! @If RINT(i,: ) does not contain zero,
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then the i-th residual is larger than would be expected, at the 5%
significance level.
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# t0 m1 R3 x; D% R5 i. l' vThis is evidence that the I-th observation is an outlier.

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）

[B,BINT,R,RINT,STATS] = REGRESS (Y,X)
  @. D% S% `  b8 G' k2 Lreturns a vector STATS containing
! ?: t' W, |( ^' M6 L# t( \the R-square statistic, the F statistic and p value for the full model,and an estimate of the error variance.

9 W/ G. R' R% u. E6 _, @3 CSTATS，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 B: j* S% Q3 q3 b. f3 W, }1 m7 q[...] = REGRESS (Y,X,ALPHA)
' n% B# w4 X$ _. z; B# d6 i9 fuses a 100*(1-ALPHA)% confidence level to compute BINT, and a (100*ALPHA)% significance level to compute RINT.
" i  t$ h- a, e" ]" M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

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
that the model contains a constant term, and they are not correct for
models without a constant.
* S9 ~$ Q5 r- Q9 v- g/ MThe 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.
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）

8 k. c0 W& @9 N" O7 ?4 O; M) sIf columns of X are linearly dependent, REGRESS sets the maximum
possible number of elements of B to zero to obtain a "basic solution",
& y$ p  G, p* S6 l. F% @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”。

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。