关于regress函数的使用

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• [b,bint,r,rint,stats] = regress(y,X)
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& C7 F: Y. i7 x( o& H0 S# U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.
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9 m5 X* j; h  D! u9 ~# c9 j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？

( ^# y- c- }+ w! P0 @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
) F6 g1 P% R' b               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.
  G+ n0 \1 w4 I9 k! UB = REGRESS (Y,X)
returns the vector B of regression coefficients in the
linear model Y = X*B.

X is an n-by-p design matrix, with rows
corresponding to observations and columns to predictor variables.
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Y is an n-by-1 vector of response observations.
REGRESS
多元线性回归——用最小二乘估计法
  b) I5 j! }- x7 W& ~( ?( n0 dB = REGRESS (Y,X) ，

返回值为线性模型Y = X*B的回归系数向量
" E8 l$ }/ T- F+ B9 {     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）

[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

5 N4 t* F, W3 n, p1 k4 L$ }8 C[B,BINT,R] = REGRESS (Y,X)
returns a vector R of residuals.
R，残差向量

+ n/ F5 Y7 S  J[B,BINT,R,RINT] = REGRESS (Y,X)
2 D/ i$ l4 ]/ `/ g0 O) w  e$ Hreturns a matrix RINT of intervals that
1 y0 d. v" ?: B- H/ y/ hcan be used to diagnose outliers.
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1 s* V; _/ Q; s: ?6 k* P/ wIf 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.

9 f( }1 p0 V' n% h: s4 PThis 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）。
5 N$ E. y3 A4 m5 f  B2 p$ [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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1 l2 _& D- f; j: @' [& H- @1 o4 Y[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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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）
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[...] = REGRESS (Y,X,ALPHA)
+ J9 G+ _3 @% P$ i1 puses 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，
: O0 e; ^4 `# C. q& D0 W/ L& S: j8 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
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% ]% {5 x$ G* D' G3 }4 k/ Y8 ZThe 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.
3 a, e1 h- Y' ]/ D: }) sThe R-square value is one minus the ratio of
1 Z3 n$ L- }  S8 T5 f, q, o$ i0 lthe error sum of squares to the total sum of squares.
! @( Z4 I( X" N  BThis value can
( {0 q( i9 v1 A0 I" j! g6 L! j% Cbe 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
- t9 w! A3 k+ O: p, |* J5 {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.
6 b# U/ Y# f& b  \$ {; r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。