how can I change my x and y values to suit properly - r

Question

Heres my code
so the problem right now the code works but only if in the line
lyst[[elementname]] <- rgamma(10000,i,j) 10000 is set to 100
and in the line
plot(y=sample_mean_q4[,j],x=1:7000,xlab="n value",ylab="Values", main=paste("Alpha-Lambda:",colnames(lyst[,j]),type="l")) the value of x=1:1000 is set to x=1:700
otherwise I get the error "Error in xy.coords(x, y, xlabel, ylabel, log) :
'x' and 'y' lengths differ"
I need the values to be 10000 and x=1=1:1000
#Question 1
set.seed(10000)
v <- c(0.1,0.5,1,2,5,10,100)
lyst <- list()
for(i in v)
{
for(j in v)
{
elementname <- paste0(as.character(i),"-",as.character(j))
print(elementname)
lyst[[elementname]] <- rgamma(10000,i,j)
}
}
#Question 2
pdf("Question2.pdf",width = 20, height = 10)
par(mfcol=c(7,7))
for(x in names(lyst))
{
hist(lyst[[x]],
xlab = "Value",
main = paste("Alpha-Lambda:",x))
}
dev.off()
#Question 3
theoretical_mean <- matrix(ncol=7,nrow=7,dimnames=list(as.character(v), as.character(v)))
theoretical_var <- matrix(ncol=7,nrow=7,dimnames=list(as.character(v), as.character(v)))
for (i in 1:7)
{
for (j in 1:7)
{
theoretical_mean[j,i] <- as.character(v[i]/v[j])
theoretical_var[j,i] <- as.character(v[i]/(v[j]^2))
}
}
sample_mean <-lapply(lyst, mean)
sample_mean <- as.data.frame(matrix(unlist(sample_mean),nrow = 7, ncol = 7, byrow = T))
sample_mean <- round(sample_mean,digits = 3)
sample_mean <- data.matrix(sample_mean, rownames.force = NA)
sample_var <-lapply(lyst, var)
sample_var <- as.data.frame(matrix(unlist(sample_var),nrow = 7, ncol = 7, byrow = T))
sample_var <- round(sample_var,digits = 3)
sample_var <- data.matrix(sample_var, rownames.force = NA)
theor_sample_mean <- matrix(paste(theoretical_mean, sample_mean, sep=" - "),nrow=7,dimnames = dimnames(theoretical_var))
theor_sample_var <- matrix(paste(theoretical_var, sample_var, sep=" - "),nrow=7,dimnames= dimnames(theoretical_var))
sink("Q3.txt")
cat("Theoretical Mean vs. Sample Mean:\n")
print(as.table(theor_sample_mean))
cat("\n")
cat("Theoretical Variance vs. Sample Variance:\n")
print(as.table(theor_sample_var))
sink()
lyst = matrix(unlist(lyst), ncol = 7, byrow = F)
colnames(lyst) = c("100-0.1","100-0.5","100-1","100-2","100-5","100-10","100-100")
#Question 4
q4mean <- function(x)
{
m <- matrix(nrow=nrow(x))
for (j in 1:ncol(x))
{
v <- c()
for(i in 1:nrow(x))
{
v <- c(v,mean(x[1:i,j]))
}
m <- cbind(m,v)
}
m <- m[,-1]
colnames(m) <- colnames(x)
rownames(m) <- NULL
return(m)
}
sample_mean_q4 <- q4mean(lyst)
pdf("Question4.pdf",width=15,height=10)
for (i in 1:7)
{
for (j in 1:7)
{
plot(y=sample_mean_q4[,j],x=1:1000,xlab="n value",ylab="Values", main=paste("Alpha-Lambda:",colnames(lyst[,j]),type="l"))
}
}
dev.off()

Answer 1

Please do not add many questions in one post. Identify the problem and add one per post. The error in your code is related to Question-4.
# Select names of the column to be included in the plot
selected_cols <- c("100-0.1","100-0.5","100-1","100-2","100-5","100-10","100-100")
# this is equivalent to: `lyst = matrix(unlist(lyst), ncol = 7, byrow = F) `
# I used abc as name instead of lyst
abc <- sapply(selected_cols, function(x) lyst[[x]])
sample_mean_q4 <- q4mean(abc)
# draw plot
for(x in selected_cols){
pdf(paste0("Question4", "_", x, ".pdf"),width=15,height=10)
plot( x=1:1000, y = sample_mean_q4[1:1000, x],
xlab="n value", ylab="Values", main=bquote(alpha - lambda == .(x) ), type="l")
dev.off()
}
Data:
q4mean <- function(x)
{
m <- matrix(nrow=nrow(x))
for (j in 1:ncol(x)) {
v <- c()
for(i in 1:nrow(x)){
v <- c(v,mean(x[1:i,j]))
}
m <- cbind(m,v)
}
m <- m[,-1]
colnames(m) <- colnames(x)
rownames(m) <- NULL
return(m)
}
set.seed(10000)
v <- c(0.1,0.5,1,2,5,10,100)
lyst <- list()
for(i in v){
for(j in v){
elementname <- paste0(as.character(i),"-",as.character(j))
print(elementname)
lyst[[elementname]] <- rgamma(10000,i,j)
}
}

Answer 2

are you aware of R's recycling functionality? Have you tried breaking the problem into smaller chunks?