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REGRESS Multiple linear regression using least squares.
: m \/ ], A8 C9 R. N5 ]7 UB = REGRESS (Y,X)
+ A8 U3 l3 }" }. b, Z7 D2 creturns the vector B of regression coefficients in the
/ b# s3 k/ g* e8 ]4 I) S8 ?" g alinear model Y = X*B.
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X is an n-by-p design matrix, with rows
0 I5 u9 q }3 _* \2 \) ]corresponding to observations and columns to predictor variables.
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Y is an n-by-1 vector of response observations.
3 ~8 q) U% J; z7 F, E# uREGRESS& y$ V+ P- {" k& }! F( O7 [# P
多元线性回归——用最小二乘估计法1 S# D, P0 p3 r* G- e
B = REGRESS (Y,X) ，
3 w- {: s4 B+ t( v4 ^4 P5 |# o, e# V* y8 S& |4 K
返回值为线性模型Y = X*B的回归系数向量
4 {" g8 ^3 t. K. J: j X ，n-by-p 矩阵，行对应于观测值，列对应于预测变量1 I! i. o/ _6 O7 R
Y ，n-by-1 向量，观测值的响应（即因变量）
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[B,BINT] = REGRESS (Y,X) - l- O- S8 y' _* P! |
returns a matrix BINT of 95% confidence intervals for B.
* W' ~% c3 Z9 t$ \BINT，B的95%的置信区间矩阵
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[B,BINT,R] = REGRESS (Y,X)
) n9 }/ d R* o3 xreturns a vector R of residuals.# [+ p; }. }4 |, T
R，残差向量
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[B,BINT,R,RINT] = REGRESS (Y,X)
7 M$ ]+ u- P+ ~ J$ K$ k0 U# breturns a matrix RINT of intervals that6 r, s8 S. P( M7 \6 N. m' k
can be used to diagnose outliers.
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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%" j+ @" U7 a- Q$ i! |, ?
significance level.
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3 E! C9 F3 N3 w; gThis is evidence that the I-th observation is an outlier.. h O% r6 [! d& |+ g
6 W, @5 J) l9 |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）。% q- _1 r* _9 Q6 k' ]! ^6 L
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）3 O' F+ r% d7 y# ]9 q6 h6 n
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[B,BINT,R,RINT,STATS] = REGRESS (Y,X) : w6 F7 s6 z* ?) I
returns a vector STATS containing
, M& a3 U, D$ v; D# [" bthe R-square statistic, the F statistic and p value for the full model,and an estimate of the error variance.3 a3 N- v5 Q% e& N" E& H1 H6 K
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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）4 ^: }/ z1 I3 n9 _
, }' m2 ]6 m1 e[...] = REGRESS (Y,X,ALPHA) ( y. p, D0 j7 a3 G
uses a 100*(1-ALPHA)% confidence level to compute BINT, and a (100*ALPHA)% significance level to compute RINT.
, k6 o# A& s/ l& h3 X用100*(1-ALPHA)%的置信水平来计算BINT，
9 \0 R& z% U- R用(100*ALPHA)%的显著性水平来计算RINT( z* v) f: I( ^/ U5 V
! N5 P8 B) d& ?6 H/ Y6 [" IX should include a column of ones so that the model contains a constant
! H+ x& [, A( _; I2 dterm., { B p N4 L) b3 f1 Y' a2 W7 z
The F statistic and p value are computed under the assumption1 T; g* y; V# ?; U/ N
that the model contains a constant term, and they are not correct for* }7 K- q$ q P7 X( C' g
models without a constant.7 ^" t6 F2 Y% o' W# [) j
The R-square value is one minus the ratio of/ [: c% s# m+ G: f
the error sum of squares to the total sum of squares.; V' H% }% x* M+ v/ n5 ~
This value can
3 H2 o( x O- x9 E0 {4 qbe negative for models without a constant, which indicates that the model is not appropriate for the data.
; {% Z( R) b+ g1 V. I8 @# G+ sX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）
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If columns of X are linearly dependent, REGRESS sets the maximum+ O$ s: E. i- W: g/ |3 l
possible number of elements of B to zero to obtain a "basic solution",2 @. ~5 V2 P# b) |
and returns zeros in elements of BINT corresponding to the zero elements of B.
. r% q* O" M+ y5 @% r$ I" J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”。. q' G. x2 |2 b/ C. W# n& _ e% l! t
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REGRESS treats NaNs in X or Y as missing values, and removes them. REGRESS
9 }3 x* @/ u0 t$ S3 Z) U: P将X或者Y中的NaNs当作缺失值处理，并且移除它们。 |
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发表于 2020-4-14 10:34
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