谁能用一元线性回归模型、多元线性回归模型和灰色系统（1,1）模型预测未来十年的人口值，最好详细点。谢谢 一元线性回归模型的基本假设条件有哪些
\u4e00\u5143\u7ebf\u6027\u56de\u5f52\u6a21\u578b\u662f\u5e72\u4ec0\u4e48\u7528\u7684\u3000\u3000\u4e00\u5143\u7ebf\u6027\u56de\u5f52\u6a21\u578b\u6709\u5f88\u591a\u5b9e\u9645\u7528\u9014\u3002\u5206\u4e3a\u4ee5\u4e0b\u4e24\u5927\u7c7b\uff1a
\u3000\u30001.\u5982\u679c\u76ee\u6807\u662f\u9884\u6d4b\u6216\u8005\u6620\u5c04\uff0c\u7ebf\u6027\u56de\u5f52\u53ef\u4ee5\u7528\u6765\u5bf9\u89c2\u6d4b\u6570\u636e\u96c6\u7684\u548cX\u7684\u503c\u62df\u5408\u51fa\u4e00\u4e2a\u9884\u6d4b\u6a21\u578b\u3002\u5f53\u5b8c\u6210\u8fd9\u6837\u4e00\u4e2a\u6a21\u578b\u4ee5\u540e\uff0c\u5bf9\u4e8e\u4e00\u4e2a\u65b0\u589e\u7684X\u503c\uff0c\u5728\u6ca1\u6709\u7ed9\u5b9a\u4e0e\u5b83\u76f8\u914d\u5bf9\u7684y\u7684\u60c5\u51b5\u4e0b\uff0c\u53ef\u4ee5\u7528\u8fd9\u4e2a\u62df\u5408\u8fc7\u7684\u6a21\u578b\u9884\u6d4b\u51fa\u4e00\u4e2ay\u503c\u3002
\u3000\u30002.\u7ed9\u5b9a\u4e00\u4e2a\u53d8\u91cfy\u548c\u4e00\u4e9b\u53d8\u91cfX1,...,Xp\uff0c\u8fd9\u4e9b\u53d8\u91cf\u6709\u53ef\u80fd\u4e0ey\u76f8\u5173\uff0c\u7ebf\u6027\u56de\u5f52\u5206\u6790\u53ef\u4ee5\u7528\u6765\u91cf\u5316y\u4e0eXj\u4e4b\u95f4\u76f8\u5173\u6027\u7684\u5f3a\u5ea6\uff0c\u8bc4\u4f30\u51fa\u4e0ey\u4e0d\u76f8\u5173\u7684Xj\uff0c\u5e76\u8bc6\u522b\u51fa\u54ea\u4e9bXj\u7684\u5b50\u96c6\u5305\u542b\u4e86\u5173\u4e8ey\u7684\u5197\u4f59\u4fe1\u606f\u3002
\u3000\u3000\u4e00\u5143\u7ebf\u6027\u56de\u5f52\u6a21\u578b\u8868\u793a\u5982\u4e0b\uff1a
\u3000\u3000yt = b0 + b1 xt +ut \uff081\uff09 \u4e0a\u5f0f\u8868\u793a\u53d8\u91cfyt \u548cxt\u4e4b\u95f4\u7684\u771f\u5b9e\u5173\u7cfb\u3002\u5176\u4e2dyt \u79f0\u4f5c\u88ab\u89e3\u91ca\u53d8\u91cf\uff08\u6216\u76f8\u4f9d\u53d8\u91cf\u3001\u56e0\u53d8\u91cf\uff09\uff0cxt\u79f0\u4f5c\u89e3\u91ca\u53d8\u91cf\uff08\u6216\u72ec\u7acb\u53d8\u91cf\u3001\u81ea\u53d8\u91cf\uff09\uff0cut\u79f0\u4f5c\u968f\u673a\u8bef\u5dee\u9879\uff0cb0\u79f0\u4f5c\u5e38\u6570\u9879\uff08\u622a\u8ddd\u9879\uff09\uff0cb1\u79f0\u4f5c\u56de\u5f52\u7cfb\u6570\u3002
\u3000\u3000\u5728\u6a21\u578b (1) \u4e2d\uff0cxt\u662f\u5f71\u54cdyt\u53d8\u5316\u7684\u91cd\u8981\u89e3\u91ca\u53d8\u91cf\u3002b0\u548cb1\u4e5f\u79f0\u4f5c\u56de\u5f52\u53c2\u6570\u3002\u8fd9\u4e24\u4e2a\u91cf\u901a\u5e38\u662f\u672a\u77e5\u7684\uff0c\u9700\u8981\u4f30\u8ba1\u3002t\u8868\u793a\u5e8f\u6570\u3002\u5f53t\u8868\u793a\u65f6\u95f4\u5e8f\u6570\u65f6\uff0cxt\u548cyt\u79f0\u4e3a\u65f6\u95f4\u5e8f\u5217\u6570\u636e\u3002\u5f53t\u8868\u793a\u975e\u65f6\u95f4\u5e8f\u6570\u65f6\uff0cxt\u548cyt\u79f0\u4e3a\u622a\u9762\u6570\u636e\u3002ut\u5219\u5305\u62ec\u4e86\u9664xt\u4ee5\u5916\u7684\u5f71\u54cdyt\u53d8\u5316\u7684\u4f17\u591a\u5fae\u5c0f\u56e0\u7d20\u3002ut\u7684\u53d8\u5316\u662f\u4e0d\u53ef\u63a7\u7684\u3002\u4e0a\u8ff0\u6a21\u578b\u53ef\u4ee5\u5206\u4e3a\u4e24\u90e8\u5206\u3002\uff081\uff09b0 +b1 xt\u662f\u975e\u968f\u673a\u90e8\u5206\uff1b\uff082\uff09ut\u662f\u968f\u673a\u90e8\u5206\u3002
\u4e00\u5143\u7ebf\u6027\u56de\u5f52\u7684\u57fa\u672c\u5047\u8bbe\u6709\u54ea\u4e9b\uff0c\u6570\u5b66\u8868\u8fbe\u5f0f\u5982\u4f55
1\u56de\u5f52\u6a21\u578b\u662f\u6b63\u786e\u8bbe\u5b9a\u7684
2\u89e3\u91ca\u53d8\u91cfX\u662f\u786e\u5b9a\u6027\u53d8\u91cf\uff0c\u4e0d\u662f\u968f\u673a\u53d8\u91cf\uff0c\u5728\u91cd\u590d\u62bd\u6837\u4e2d\u53d6\u56fa\u5b9a\u503c
E(i)=0 i=1,2, \u2026,n
Var (i)=2 i=1,2, \u2026,n
Cov(i, j)=0 i\u2260j i,j= 1,2, \u2026,n
3\u89e3\u91ca\u53d8\u91cfX\u5728\u6240\u62bd\u53d6\u7684\u6837\u672c\u4e2d\u5177\u6709\u53d8\u5f02\u6027\uff0c\u800c\u4e14\u968f\u7740\u6837\u672c\u5bb9\u91cf\u7684\u65e0\u9650\u589e\u52a0\uff0c\u89e3\u91ca\u53d8\u91cfX \u7684\u6837\u672c\u65b9\u5dee\u8d8b\u4e8e\u4e00\u4e2a\u975e\u96f6\u7684\u6709\u9650\u5e38\u6570Cov(Xi, i)=0 i=1,2, \u2026,n
4\u968f\u673a\u8bef\u5dee\u9879\u03bc\u5177\u6709\u7ed9\u5b9aX\u6761\u4ef6\u4e0b\u7684\u96f6\u5747\u503c\uff0c\u540c\u65b9\u5dee\u4ee5\u53ca\u4e0d\u5e8f\u5217\u76f8\u5173\u6027
i~N(0, 2 ) i=1,2, \u2026,n
5\u968f\u673a\u8bef\u5dee\u9879\u4e0e\u89e3\u91ca\u53d8\u91cf\u4e4b\u95f4\u4e0d\u76f8\u5173
6\u968f\u673a\u8bef\u5dee\u9879\u670d\u4ece\u96f6\u5747\u503c\uff0c\u540c\u65b9\u5dee\u7684\u6b63\u6001\u5206\u5e03
\u56de\u5f52\u5206\u6790\u4e3b\u8981\u5185\u5bb9\uff1a
1\u6839\u636e\u6837\u672c\u89c2\u5bdf\u503c\u5bf9\u8ba1\u91cf\u7ecf\u6d4e\u5b66\u6a21\u578b\u53c2\u6570\u8fdb\u884c\u4f30\u8ba1\uff0c\u6c42\u5f97\u56de\u5f52\u65b9\u7a0b
2\u5bf9\u56de\u5f52\u65b9\u7a0b\uff0c\u53c2\u6570\u4f30\u8ba1\u503c\u8fdb\u884c\u663e\u8457\u6027\u68c0\u9a8c
3\u5229\u7528\u56de\u5f52\u65b9\u7a0b\u8fdb\u884c\u5206\u6790\uff0c\u8bc4\u4ef7\u53ca\u9884\u6d4b
\u865a\u62df\u53d8\u91cf\u7684\u8bbe\u7f6e\u539f\u5219\uff0c\u5f15\u5165\u65b9\u6cd5\u548c\u6a21\u578b\u5177\u4f53\u5f62\u5f0f\u5199\u51fa
回归分析的：Y=443.57 -0.21295*x1+ 0.0019134*x2+ 0.043684*x3 -0.97484*x4+ 6.034*x5;
回归代码：[b,bint]=regress(Y,X)---X：是 自然增长率（x1） 人均GDP(x2) 农业人口(x3) 老年抚养比(x4) 妇女平均初婚年龄(x5) 历年数据；
GM（1,1）代码：
function [y,p,e]=gm_1_1(X,k)
%gray model: GM(1,1)
%Example [y,p]=gm_1_1([200 250 300 350],2)
if nargout>3,error('Too many output argument.');end
if nargin==1,k=1;x_orig=X;
elseif nargin==0|nargin>2
error('Wrong number of input arguments.');
end
x_orig=X;
predict=k;
%AGO process
x=cumsum(x_orig);
%compute the coefficient(a and u)------------------------
n=length(x_orig);
%first generate the matrix B
for i=1:(n-1);
B(i)=-(x(i)+x(i+1))/2;
end
B=[B' ones(n-1,1)];
%then generate the matrix Y
for i=1:(n-1);
y(i)=x_orig(i+1);
end
Y=y';
%get the coefficient. a=au(1) u=au(2)
au=(inv(B'*B))*(B'*Y);
%--------------------------------------------------------
%change the grey model to symbolic expression
coef1=au(2)/au(1);
coef2=x_orig(1)-coef1;
coef3=0-au(1);
costr1=num2str(coef1);
costr2=num2str(abs(coef2));
costr3=num2str(coef3);
eq=strcat(costr1,'+',costr2,'e^(',costr3,'*(t-1))');
%comparison of calculated and observed value
for t=1:n+predict
mcv(t)=coef1+coef2*exp(coef3*(t-1));
end
x_mcv0=diff(mcv);
x_mcve=[x_orig(1) x_mcv0];
x_mcv=diff(mcv(1:end-predict));
x_orig_n=x_orig(2:end);
x_c_error=x_orig_n-x_mcv;
x_error=mean(abs(x_c_error./x_orig_n));
if x_error>0.2
disp('model disqualification!');
elseif x_error>0.1
disp('model check out');
else
disp('model is perfect!');
end
%predicting model and plot gragh
plot(1:n,x_orig,'diamond',1:n+predict,x_mcve);
x_mcve
p=x_mcve(end-predict+1:end);
xlabel('CURVE OF GREY MODEL ANALYSIS');
title('GM(1,1)');
grid on
y=eq;
e=x_error;
p=x_mcve(end-predict+1:end);
woneng
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