NA coefficient in linear regression R -


i have run simulation r.

basically have create set of variables (x) in matrix nxp first variable has value 1, , other 23 variables has random values randomly extracted n(0,1). vector beta of length 24 has first 2 values 1 , rest 0. vector epsilon of length 24 extracted n(0,1). after create variable y is: y=x %*% beta + epsilon. select variable of x has max(cor(abs(xj,y))) j goes (3,24) , have run model y ~ x1 + x2 + xj , see results.

> set.seed(123) >  > n=25 p=24 b=seq(1,1000) >  > x <- cbind(matrix(1,nrow=25,ncol=1),matrix(rnorm(25*23),nrow=25, > ncol=23)) beta <- t(t(c(1,1,rep(0,22)))) eps <- t(t(rnorm(25))) >  > y <- x %*% beta + eps >  > j<-seq(3,24) m <- which.max(abs(cor(x[,j],y))) >  > newx <- as.data.frame(cbind(y,x[,1], x[,2], x[,m+2])) anyna(newx[,2]) > mod <- lm(v1 ~ . , data=newx) > summary(mod)  call: lm(formula = v1 ~ ., data = newx)  residuals:      min       1q   median       3q      max  -1.42575 -0.90957  0.06547  0.38879  2.39707   coefficients: (1 not defined because of singularities)             estimate std. error t value pr(>|t|)     (intercept)   1.1235     0.2421   4.641 0.000126 *** v2                na         na      na       na     v3            0.6803     0.2775   2.452 0.022612 *   v4           -0.5943     0.3036  -1.957 0.063101 .   --- signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1  residual standard error: 1.085 on 22 degrees of freedom multiple r-squared:  0.3958,     adjusted r-squared:  0.3408  f-statistic: 7.205 on 2 , 22 df,  p-value: 0.003919

everything works fine, can see estimated coefficient v2, coefficient variable x1, composed 1, na. don't understand why have na result, values in variable listed numeric , there's no missing value.

if can me understand, thanks!


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