%
%  �}�N���i�������v�w�@�����{�̕��j�@�@�@1994-07-02
% JUSE Multinomial Regretion             1994-07-08
%
%
% �܂̈�i��d�ہj----------------------------
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% �܂̈�i��d�ہF�������[�h�j----------------
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%
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%
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%a -- �������v�w�@�����{�̕��@1994-07-02 ----------------------------------
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%
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%
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%
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%
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%
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%
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%
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%
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%
%
%b -- JUSE Multinomial Regretion ------------------------------------------
% beta_0 hat
\newcommand{\betazh}
{\ovy-\hat{\beta_1} \ovx_1- \cdots - \hat{\beta_p} \ovx_p}
\newcommand{\betazhb}
{\ovy-\hat{\beta_1} \ovx_1 - \hat{\beta_2} \ovx_2}
\newcommand{\betazha}
{\ovy-\hat{\beta_1} \ovx}
% seki-wa
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{\beta_0 + \beta_1 x_{{#1} 1} + \cdots + \beta_p x_{{#1} p}}
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{\beta_0 + \beta_1 x}
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{\hat{\beta_0} + \hat{\beta_1} x_{{#1} 1} + \cdots + \hat{\beta_p} x_{{#1} p}}
\newcommand{\betahxa}
{\hat{\beta_0} + \hat{\beta_1} x}
%
\newcommand{\betahwa}[4]
{\hat{\beta_0} \sum{#1} + \hat{\beta_1} \sum{#2} + \cdots + \hat{\beta_p} \sum{#3} = \sum{#4}}
\newcommand{\betahwaa}[3]
{\hat{\beta_0} \sum{#1} + \hat{\beta_1} \sum{#2} = \sum{#3}}
\newcommand{\betahsf}[1]
{\hat{\beta_1} S_{{#1} 1} + \cdots + \hat{\beta_p} S_{{#1} p} = S_{{#1} y}}
\newcommand{\betahs}[2]
{\hat{\beta_1} S_{#1} + \cdots + \hat{\beta_p} S_{#2}}
\newcommand{\betahsr}
{S_R = \hat{\beta_1} S_{1y} + \cdots + \hat{\beta_p} S_{py}}
\newcommand{\betahsra}
{S_R = \hat{\beta_1} S_{xy}}
% beta_j hat
\newcommand{\betajh}
{\hat{\beta_j} = S^{j1} S_{1y} + \cdots + S^{jp} S_{py}}
\newcommand{\betajha}
{\hat{\beta_1} = S_{xy} / S_{xx}}
% zansa no jyo-ken
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{\dsum{i=1}{n} e_i =0}
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{\dsum{i=1}{n} (x_{ij} - \ovx_j) e_i =0}
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{\dsum{i=1}{n} (x_{i} - \ovx) e_i =0}
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{\dsum{i=1}{n} (\hat{y_i} - \ovy) e_i =0}
%
% hensa no siki
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{(x_{0 {#1}}-\ovx_{#1})}
%b -- JUSE ST -------------------------------------------------------------
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%c-- test (by Prof. Kouno) ------------------------------------------------
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%
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%
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