Usuari:Lixiaoxu

Xiaoxu LI szpku.lixiaoxu@gmail.com Shenzhen Graduate School of Peking University, Guangdong, China

Regression of Inputted Data

<Rform name="owndata"> Enter your own data for a scatterplot:
You can use <a href="https://spreadsheets.google.com/ccc?key=0Aic4pmEZm32xclhJZm9hNWFyZlZOV1RSV19xWXRlbmc&hl=en">the free online spreadsheet </a> of Google Docs to edit your data before pasting. Just click the link, need NO login.
<textarea name="mydata" rows="8"> 1.262954285 3.8739569 -0.326233361 1.0400041 1.329799263 2.0161824 1.272429321 2.8284819 0.414641434 2.1324980 -1.539950042 0.4565291 -0.928567035 1.6093698 -0.294720447 0.9723025 -0.005767173 2.5310696 2.404653389 2.7861843 </textarea> <input type="submit" value=" Submit "> </Rform>

<R output="display" name="owndata" iframe="height:500px;"> if (exists("mydata")) {

 main <- "Data from user"
 x <- readdataSK(mydata, format="txt") 

} else {

 main <- "Default data"
 set.seed(0);
 x<-matrix(rnorm(20),10,2);
 x[,2]=2.1+x[,1]*.8+x[,2];
 colnames(x)<-c('V1','V2');

}

pdf(rpdf, width=6, height=6) lm.m<-lm(x[,2]~x[,1]); main<-paste(main,'\nV2 =',round(lm.m$coefficients[1],3),'+',round(lm.m$coefficients[2],3),'*V1 + ',round(summary(lm.m)$sigma,3),'*e') plot(x, cex=2, main=main) abline(lm.m)

</R>

回归分析课件

输入参数

<Rform name="Tri"> 向量${\vec {Y}}$与${\vec {X}}_{1}$、${\vec {X}}_{2}$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${\vec {X}}_{1}$与${\vec {X}}_{2}$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$N$个分量代表$N$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${\vec {X}}_{2}$加入前后，回归方程

${\vec {Y}}=\beta _{1}{\vec {X}}_{1}+{\vec {\epsilon }}$

与

${\vec {Y}}=\beta _{1}{\vec {X}}_{1}+\beta _{2}{\vec {X}}_{2}+{\vec {\epsilon }}$

的$R^{2}$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($R^{2}$)可以相加

第三个角度为90

($R_{1}^{2}+R_{2}^{2}-R_{12}^{2}$)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: 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>

R 代码

cy1 <- 89; ## \angle YX_1
cy2 <- 89; ## \angle YX_2
c12 <- 177.9; ## \angle X_1X_2
N <- 100;
rawdata=TRUE;

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);

require(MASS);## install.packages('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');

R2<-matrix(rep(NA,3),nrow=3);
colnames(R2)<-c('R^2');
rownames(R2)<-c('Y = b_1*X_1 + e','Y =b_2*X_2 + e','Y =b_1*X_1 + b_2*X_2 + e');
lm1 <- lm(Y~0+X_1);
lm2 <- lm(Y~0+X_2);
lm12 <- lm(Y~0+X_1+X_2);
R2[,1] <- c( summary(lm1)$r.squared, summary(lm2)$r.squared, summary(lm12)$r.squared);

R2
R2[1,1]+R2[2,1]-R2[3,1]
summary(lm1)
summary(lm2)
summary(lm12)
cat('\ncorr')
S
cat('\nraw data')
if (rawdata) (x);