谁有多元回归的程序，急需啊！

小瑞儿

谁有多元回归的程序，急需啊！

zhenc

我也 急需，有的请发  29897815@QQ.COM    多谢

小瑞儿

zhenc 发表于 2012-8-26 09:49
我也 急需，有的请发      多谢

现在找到了没

liwenhui

多元线性回归的就是简单的矩阵计算，matlab中有现成regress函数可以调用，你要程序干什么？
根据最小二乘原理，
Y=XB+E中系数向量的估计值为b=inv(x'x)*x'y

matlab中的源代码是：

2. function [b,bint,r,rint,stats] = regress(y,X,alpha)
   
3. %REGRESS Multiple linear regression using least squares.
   
4. %   B = REGRESS(Y,X) returns the vector B of regression coefficients in the
   
5. %   linear model Y = X*B.  X is an n-by-p design matrix, with rows
   
6. %   corresponding to observations and columns to predictor variables.  Y is
   
7. %   an n-by-1 vector of response observations.
   
8. %
   
9. %   [B,BINT] = REGRESS(Y,X) returns a matrix BINT of 95% confidence
   
10. %   intervals for B.
    
11. %
    
12. %   [B,BINT,R] = REGRESS(Y,X) returns a vector R of residuals.
    
13. %
    
14. %   [B,BINT,R,RINT] = REGRESS(Y,X) returns a matrix RINT of intervals that
    
15. %   can be used to diagnose outliers.  If RINT(i,:) does not contain zero,
    
16. %   then the i-th residual is larger than would be expected, at the 5%
    
17. %   significance level.  This is evidence that the I-th observation is an
    
18. %   outlier.
    
19. %
    
20. %   [B,BINT,R,RINT,STATS] = REGRESS(Y,X) returns a vector STATS containing, in
    
21. %   the following order, the R-square statistic, the F statistic and p value
    
22. %   for the full model, and an estimate of the error variance.
    
23. %
    
24. %   [...] = REGRESS(Y,X,ALPHA) uses a 100*(1-ALPHA)% confidence level to
    
25. %   compute BINT, and a (100*ALPHA)% significance level to compute RINT.
    
26. %
    
27. %   X should include a column of ones so that the model contains a constant
    
28. %   term.  The F statistic and p value are computed under the assumption
    
29. %   that the model contains a constant term, and they are not correct for
    
30. %   models without a constant.  The R-square value is one minus the ratio of
    
31. %   the error sum of squares to the total sum of squares.  This value can
    
32. %   be negative for models without a constant, which indicates that the
    
33. %   model is not appropriate for the data.
    
34. %
    
35. %   If columns of X are linearly dependent, REGRESS sets the maximum
    
36. %   possible number of elements of B to zero to obtain a "basic solution",
    
37. %   and returns zeros in elements of BINT corresponding to the zero
    
38. %   elements of B.
    
39. %
    
40. %   REGRESS treats NaNs in X or Y as missing values, and removes them.
    
41. %
    
42. %   See also LSCOV, POLYFIT, REGSTATS, ROBUSTFIT, STEPWISE.
    
43. 
    
44. %   References:
    
45. %      [1] Chatterjee, S. and A.S. Hadi (1986) "Influential Observations,
    
46. %          High Leverage Points, and Outliers in Linear Regression",
    
47. %          Statistical Science 1(3):379-416.
    
48. %      [2] Draper N. and H. Smith (1981) Applied Regression Analysis, 2nd
    
49. %          ed., Wiley.
    
50. 
    
51. %   Copyright 1993-2009 The MathWorks, Inc.
    
52. %   $Revision: 1.1.8.3 $  $Date: 2011/05/09 01:26:41 $
    
53. 
    
54. if  nargin < 2
    
55.     error(message('stats:regress:TooFewInputs'));
    
56. elseif nargin == 2
    
57.     alpha = 0.05;
    
58. end
    
59. 
    
60. % Check that matrix (X) and left hand side (y) have compatible dimensions
    
61. [n,ncolX] = size(X);
    
62. if ~isvector(y) || numel(y) ~= n
    
63.     error(message('stats:regress:InvalidData'));
    
64. end
    
65. 
    
66. % Remove missing values, if any
    
67. wasnan = (isnan(y) | any(isnan(X),2));
    
68. havenans = any(wasnan);
    
69. if havenans
    
70.    y(wasnan) = [];
    
71.    X(wasnan,:) = [];
    
72.    n = length(y);
    
73. end
    
74. 
    
75. % Use the rank-revealing QR to remove dependent columns of X.
    
76. [Q,R,perm] = qr(X,0);
    
77. p = sum(abs(diag(R)) > max(n,ncolX)*eps(R(1)));
    
78. if p < ncolX
    
79.     warning(message('stats:regress:RankDefDesignMat'));
    
80.     R = R(1:p,1:p);
    
81.     Q = Q(:,1:p);
    
82.     perm = perm(1:p);
    
83. end
    
84. 
    
85. % Compute the LS coefficients, filling in zeros in elements corresponding
    
86. % to rows of X that were thrown out.
    
87. b = zeros(ncolX,1);
    
88. b(perm) = R \ (Q'*y);
    
89. 
    
90. if nargout >= 2
    
91.     % Find a confidence interval for each component of x
    
92.     % Draper and Smith, equation 2.6.15, page 94
    
93.     RI = R\eye(p);
    
94.     nu = max(0,n-p);                % Residual degrees of freedom
    
95.     yhat = X*b;                     % Predicted responses at each data point.
    
96.     r = y-yhat;                     % Residuals.
    
97.     normr = norm(r);
    
98.     if nu ~= 0
    
99.         rmse = normr/sqrt(nu);      % Root mean square error.
    
100.         tval = tinv((1-alpha/2),nu);
     
101.     else
     
102.         rmse = NaN;
     
103.         tval = 0;
     
104.     end
     
105.     s2 = rmse^2;                    % Estimator of error variance.
     
106.     se = zeros(ncolX,1);
     
107.     se(perm,:) = rmse*sqrt(sum(abs(RI).^2,2));
     
108.     bint = [b-tval*se, b+tval*se];
     
109. 
     
110.     % Find the standard errors of the residuals.
     
111.     % Get the diagonal elements of the "Hat" matrix.
     
112.     % Calculate the variance estimate obtained by removing each case (i.e. sigmai)
     
113.     % see Chatterjee and Hadi p. 380 equation 14.
     
114.     if nargout >= 4
     
115.         hatdiag = sum(abs(Q).^2,2);
     
116.         ok = ((1-hatdiag) > sqrt(eps(class(hatdiag))));
     
117.         hatdiag(~ok) = 1;
     
118.         if nu > 1
     
119.             denom = (nu-1) .* (1-hatdiag);
     
120.             sigmai = zeros(length(denom),1);
     
121.             sigmai(ok) = sqrt(max(0,(nu*s2/(nu-1)) - (r(ok) .^2 ./ denom(ok))));
     
122.             ser = sqrt(1-hatdiag) .* sigmai;
     
123.             ser(~ok) = Inf;
     
124.         elseif nu == 1
     
125.             ser = sqrt(1-hatdiag) .* rmse;
     
126.             ser(~ok) = Inf;
     
127.         else % if nu == 0
     
128.             ser = rmse*ones(length(y),1); % == Inf
     
129.         end
     
130. 
     
131.         % Create confidence intervals for residuals.
     
132.         rint = [(r-tval*ser) (r+tval*ser)];
     
133.     end
     
134. 
     
135.     % Calculate R-squared and the other statistics.
     
136.     if nargout == 5
     
137.         % There are several ways to compute R^2, all equivalent for a
     
138.         % linear model where X includes a constant term, but not equivalent
     
139.         % otherwise.  R^2 can be negative for models without an intercept.
     
140.         % This indicates that the model is inappropriate.
     
141.         SSE = normr.^2;              % Error sum of squares.
     
142.         RSS = norm(yhat-mean(y))^2;  % Regression sum of squares.
     
143.         TSS = norm(y-mean(y))^2;     % Total sum of squares.
     
144.         r2 = 1 - SSE/TSS;            % R-square statistic.
     
145.         if p > 1
     
146.             F = (RSS/(p-1))/s2;      % F statistic for regression
     
147.         else
     
148.             F = NaN;
     
149.         end
     
150.         prob = fpval(F,p-1,nu); % Significance probability for regression
     
151.         stats = [r2 F prob s2];
     
152. 
     
153.         % All that requires a constant.  Do we have one?
     
154.         if ~any(all(X==1,1))
     
155.             % Apparently not, but look for an implied constant.
     
156.             b0 = R\(Q'*ones(n,1));
     
157.             if (sum(abs(1-X(:,perm)*b0))>n*sqrt(eps(class(X))))
     
158.                 warning(message('stats:regress:NoConst'));
     
159.             end
     
160.         end
     
161.     end
     
162. 
     
163.     % Restore NaN so inputs and outputs conform
     
164.     if havenans
     
165.         if nargout >= 3
     
166.             tmp = NaN(length(wasnan),1);
     
167.             tmp(~wasnan) = r;
     
168.             r = tmp;
     
169.             if nargout >= 4
     
170.                 tmp = NaN(length(wasnan),2);
     
171.                 tmp(~wasnan,:) = rint;
     
172.                 rint = tmp;
     
173.             end
     
174.         end
     
175.     end
     
176. 
     
177. end % nargout >= 2

function [b,bint,r,rint,stats] = regress(y,X,alpha)<br /> %REGRESS Multiple linear regression using least squares.<br /> %   B = REGRESS(Y,X) returns the vector B of regression coefficients in the<br /> %   linear model Y = X*B.  X is an n-by-p design matrix, with rows<br /> %   corresponding to observations and columns to predictor variables.  Y is<br /> %   an n-by-1 vector of response observations.<br /> %<br /> %   [B,BINT] = REGRESS(Y,X) returns a matrix BINT of 95% confidence<br /> %   intervals for B.<br /> %<br /> %   [B,BINT,R] = REGRESS(Y,X) returns a vector R of residuals.<br /> %<br /> %   [B,BINT,R,RINT] = REGRESS(Y,X) returns a matrix RINT of intervals that<br /> %   can be used to diagnose outliers.  If RINT(i,:) does not contain zero,<br /> %   then the i-th residual is larger than would be expected, at the 5%<br /> %   significance level.  This is evidence that the I-th observation is an<br /> %   outlier.<br /> %<br /> %   [B,BINT,R,RINT,STATS] = REGRESS(Y,X) returns a vector STATS containing, in<br /> %   the following order, the R-square statistic, the F statistic and p value<br /> %   for the full model, and an estimate of the error variance.<br /> %<br /> %   [...] = REGRESS(Y,X,ALPHA) uses a 100*(1-ALPHA)% confidence level to<br /> %   compute BINT, and a (100*ALPHA)% significance level to compute RINT.<br /> %<br /> %   X should include a column of ones so that the model contains a constant<br /> %   term.  The F statistic and p value are computed under the assumption<br /> %   that the model contains a constant term, and they are not correct for<br /> %   models without a constant.  The R-square value is one minus the ratio of<br /> %   the error sum of squares to the total sum of squares.  This value can<br /> %   be negative for models without a constant, which indicates that the<br /> %   model is not appropriate for the data.<br /> %<br /> %   If columns of X are linearly dependent, REGRESS sets the maximum<br /> %   possible number of elements of B to zero to obtain a "basic solution",<br /> %   and returns zeros in elements of BINT corresponding to the zero<br /> %   elements of B.<br /> %<br /> %   REGRESS treats NaNs in X or Y as missing values, and removes them.<br /> %<br /> %   See also LSCOV, POLYFIT, REGSTATS, ROBUSTFIT, STEPWISE.<br /> <br /> %   References:<br /> %      [1] Chatterjee, S. and A.S. Hadi (1986) "Influential Observations,<br /> %          High Leverage Points, and Outliers in Linear Regression",<br /> %          Statistical Science 1(3):379-416.<br /> %      [2] Draper N. and H. Smith (1981) Applied Regression Analysis, 2nd<br /> %          ed., Wiley.<br /> <br /> %   Copyright 1993-2009 The MathWorks, Inc.<br /> %   $Revision: 1.1.8.3 $  $Date: 2011/05/09 01:26:41 $<br /> <br /> if  nargin < 2<br />     error(message('stats:regress:TooFewInputs'));<br /> elseif nargin == 2<br />     alpha = 0.05;<br /> end<br /> <br /> % Check that matrix (X) and left hand side (y) have compatible dimensions<br /> [n,ncolX] = size(X);<br /> if ~isvector(y) || numel(y) ~= n<br />     error(message('stats:regress:InvalidData'));<br /> end<br /> <br /> % Remove missing values, if any<br /> wasnan = (isnan(y) | any(isnan(X),2));<br /> havenans = any(wasnan);<br /> if havenans<br />    y(wasnan) = [];<br />    X(wasnan,:) = [];<br />    n = length(y);<br /> end<br /> <br /> % Use the rank-revealing QR to remove dependent columns of X.<br /> [Q,R,perm] = qr(X,0);<br /> p = sum(abs(diag(R)) > max(n,ncolX)*eps(R(1)));<br /> if p < ncolX<br />     warning(message('stats:regress:RankDefDesignMat'));<br />     R = R(1:p,1:p);<br />     Q = Q(:,1:p);<br />     perm = perm(1:p);<br /> end<br /> <br /> % Compute the LS coefficients, filling in zeros in elements corresponding<br /> % to rows of X that were thrown out.<br /> b = zeros(ncolX,1);<br /> b(perm) = R \ (Q'*y);<br /> <br /> if nargout >= 2<br />     % Find a confidence interval for each component of x<br />     % Draper and Smith, equation 2.6.15, page 94<br />     RI = R\eye(p);<br />     nu = max(0,n-p);                % Residual degrees of freedom<br />     yhat = X*b;                     % Predicted responses at each data point.<br />     r = y-yhat;                     % Residuals.<br />     normr = norm(r);<br />     if nu ~= 0<br />         rmse = normr/sqrt(nu);      % Root mean square error.<br />         tval = tinv((1-alpha/2),nu);<br />     else<br />         rmse = NaN;<br />         tval = 0;<br />     end<br />     s2 = rmse^2;                    % Estimator of error variance.<br />     se = zeros(ncolX,1);<br />     se(perm,:) = rmse*sqrt(sum(abs(RI).^2,2));<br />     bint = [b-tval*se, b+tval*se];<br /> <br />     % Find the standard errors of the residuals.<br />     % Get the diagonal elements of the "Hat" matrix.<br />     % Calculate the variance estimate obtained by removing each case (i.e. sigmai)<br />     % see Chatterjee and Hadi p. 380 equation 14.<br />     if nargout >= 4<br />         hatdiag = sum(abs(Q).^2,2);<br />         ok = ((1-hatdiag) > sqrt(eps(class(hatdiag))));<br />         hatdiag(~ok) = 1;<br />         if nu > 1<br />             denom = (nu-1) .* (1-hatdiag);<br />             sigmai = zeros(length(denom),1);<br />             sigmai(ok) = sqrt(max(0,(nu*s2/(nu-1)) - (r(ok) .^2 ./ denom(ok))));<br />             ser = sqrt(1-hatdiag) .* sigmai;<br />             ser(~ok) = Inf;<br />         elseif nu == 1<br />             ser = sqrt(1-hatdiag) .* rmse;<br />             ser(~ok) = Inf;<br />         else % if nu == 0<br />             ser = rmse*ones(length(y),1); % == Inf<br />         end<br /> <br />         % Create confidence intervals for residuals.<br />         rint = [(r-tval*ser) (r+tval*ser)];<br />     end<br /> <br />     % Calculate R-squared and the other statistics.<br />     if nargout == 5<br />         % There are several ways to compute R^2, all equivalent for a<br />         % linear model where X includes a constant term, but not equivalent<br />         % otherwise.  R^2 can be negative for models without an intercept.<br />         % This indicates that the model is inappropriate.<br />         SSE = normr.^2;              % Error sum of squares.<br />         RSS = norm(yhat-mean(y))^2;  % Regression sum of squares.<br />         TSS = norm(y-mean(y))^2;     % Total sum of squares.<br />         r2 = 1 - SSE/TSS;            % R-square statistic.<br />         if p > 1<br />             F = (RSS/(p-1))/s2;      % F statistic for regression<br />         else<br />             F = NaN;<br />         end<br />         prob = fpval(F,p-1,nu); % Significance probability for regression<br />         stats = [r2 F prob s2];<br /> <br />         % All that requires a constant.  Do we have one?<br />         if ~any(all(X==1,1))<br />             % Apparently not, but look for an implied constant.<br />             b0 = R\(Q'*ones(n,1));<br />             if (sum(abs(1-X(:,perm)*b0))>n*sqrt(eps(class(X))))<br />                 warning(message('stats:regress:NoConst'));<br />             end<br />         end<br />     end<br /> <br />     % Restore NaN so inputs and outputs conform<br />     if havenans<br />         if nargout >= 3<br />             tmp = NaN(length(wasnan),1);<br />             tmp(~wasnan) = r;<br />             r = tmp;<br />             if nargout >= 4<br />                 tmp = NaN(length(wasnan),2);<br />                 tmp(~wasnan,:) = rint;<br />                 rint = tmp;<br />             end<br />         end<br />     end<br /> <br /> end % nargout >= 2

liwenhui

，程序中怎么会出现笑脸呢？

yangfuzhi

程序非常好。。。

darker50

liwenhui 发表于 2012-8-28 10:10
，程序中怎么会出现笑脸呢？

  您编辑完之后全部选中，之后点击编辑器上面的这个符号“<>”,之后所有代码就正常显示了。

darker50

liwenhui 发表于 2012-8-28 10:10
，程序中怎么会出现笑脸呢？

帮你编辑之后就会像上面的这样的显示了！

liwenhui

darker50 发表于 2012-8-28 14:14
帮你编辑之后就会像上面的这样的显示了！

原来如此，明白了。

小瑞儿

liwenhui 发表于 2012-8-28 10:09
多元线性回归的就是简单的矩阵计算，matlab中有现成regress函数可以调用，你要程序干什么？
根据最小二乘原 ...

非常感谢~