Lixiaoxu

Usuari:Lixiaoxu (mostra el codi font)

Revisió del 15:08, 6 jul 2009

3.297 bytes afegits , 6 jul 2009

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@@ Línia 3: / Línia 3: @@
-# Regression
+== Regression of two columns of inputted data ==
 <Rform name="owndata">
@@ Línia 41: / Línia 41: @@
 abline(lm.m)
+</R>
+== 回归分析课件 ==
+=== 输入参数 ===
+<Rform name="Tri">
+向量<math>\vec{Y}</math>与<math>\vec{X}_1</math>、<math>\vec{X}_2</math>的夹角(90度为直角)分别是
+:<Input name="cy1" value="89" size="5"/>度
+和
+:<Input name="cy2" value="89" size="5"/>度。
+向量<math>\vec{X}_1</math>与<math>\vec{X}_2</math>的夹角是
+:<Input name="c12" value="177.9" size="5"/>度。
+这三个角度应当满足两两之和大于第三者。
+这些向量的<math>N</math>个分量代表<math>N</math>个标准化之后的样本。
+请设定样本量为
+:<Input name="N" value="100" size="5"/>，输出模拟数据<Input name="rawdata" type="checkbox"/>
+<input type="submit" />
+</Rform>
+=== 练习 ===
+请观察<latex>\vec{X}_2</latex>加入前后，回归方程
+:<math>\vec{Y}=\beta_1\vec{X}_1+\vec{\epsilon}</math>
+与
+:<math>\vec{Y}=\beta_1\vec{X}_1+\beta_2\vec{X}_2+\vec{\epsilon}</math>
+的<math>R^2</math>的变化。
+==== 两个与DV相关极小的IV却能极好地预测DV ====
+三个角度分别为 89,89,177.9
+==== 两个与DV高正相关的IV却出现负回归系数 ====
+三个角度分别为 5,2.6,2.6
+==== 两个不相关的DV对IV的预测能力(<math>R^2</math>)可以相加 ====
+第三个角度为90
+==== (<math>R^2_1+R^2_2-R^2_{12}</math>)从0变大再变小甚至变负的情形 ====
+零:三个角度分别为：60,45,90
+正:三个角度分别为：60,45,45
+负:三个角度分别为：60,45,15.1
+与Redundancy的关系: [http://books.google.com/books?id=fuq94a8C0ioC&pg=PA76&lpg=PA76&dq=Redundancy+regression+Cohen&source=bl&ots=9ZvmtpyAdY&sig=FmCV5PlLJ0NsqHUj4Y328AHB45A&hl=en&sa=X&oi=book_result&resnum=1&ct=result Cohen & Cohen (2003, p. 76)]
+=== 结果 ===
+<R output="html" name="Tri" iframe="height:400px;">
+cy1 <- ifelse(exists("cy1"),as.numeric(cy1),89);
+cy2 <- ifelse(exists("cy2"),as.numeric(cy2),89);
+c12 <- ifelse(exists("c12"),as.numeric(c12),177.9);
+N <- ifelse(exists("N"),as.integer(N),100);
+rawdata <- ifelse(exists("rawdata"),as.logical(N),FALSE);
+S <- matrix(rep(1,9),3);
+S[1,2]<-S[2,1]<-cos(cy1/180*pi);
+S[1,3]<-S[3,1]<-cos(cy2/180*pi);
+S[2,3]<-S[3,2]<-cos(c12/180*pi);
+if ((det(S)<= 0 )|(N<1)) outHTML(rhtml,NA,title='Please check your input!\n Sum of any two angles should be larger than the third one.');
+require(MASS);
+x<-mvrnorm(n=N,mu=c(0,0,0),Sigma=S,empirical= TRUE);
+Y<-x[,1];X_1<-x[,2];X_2<-x[,3];
+colnames(x)<-colnames(S)<-rownames(S)<-c('Y','X_1','X_2');
+lm1 <- lm(Y~0+ X_1);
+lm2 <- lm(Y~0+ X_2);
+lm12 <- lm(Y~0+ X_1+X_2);
+R2<-matrix(rep(NA,3),nrow=3);
+rownames(R2)<-c('Y ~ 0+ X_1','Y ~ 0+ X_2','Y ~ 0+ X_1 + X_2');
+R2[,1] <- c( summary(lm1)$r.squared, summary(lm2)$r.squared, summary(lm12)$r.squared);
+colnames(R2)[1]<-round( summary(lm1)$r.squared + summary(lm2)$r.squared - summary(lm12)$r.squared,4);
+outHTML(rhtml, t(R2), title="R^2_1+R^2_2-R^2_12", format="f", digits=4);
+outHTML(rhtml, summary(lm1)$coefficients, title=rownames(R2)[1], format="f", digits=4);
+outHTML(rhtml, summary(lm2)$coefficients, title=rownames(R2)[2], format="f", digits=4);
+outHTML(rhtml, summary(lm12)$coefficients, title=rownames(R2)[3], format="f", digits=4);
+outHTML(rhtml, S, title="correlation\n", format="f", digits=4);
+if (rawdata) outHTML(rhtml, x, title="Raw data\n", format="f", digits=4);
 </R>