What is the meaning of ~ in aggregate?

Question

x <- iris[,1:4]
names(x) <- c(\"x1\",\"x2\",\"x3\",\"x4\")
aggregate(x1+x2+x3+x4~x1,FUN=sum,data=x)

Here is the output ,i wonder
1. What

Answer 1

Regarding your second question, in the Iris data set there is only one row where the first column is 4.3. That row is:

(x[x[,1]==4.3,])

#     x1 x2  x3  x4
# 14 4.3  3 1.1 0.1

# and 4.3 + 3.0 + 1.1 + 0.1 = 8.5.

sum(x[x[,1]==4.3,])

# [1] 8.5


# There are four rows where x1 = 6.9.  Those rows are:

x[x[,1]==6.9,]

#      x1  x2  x3  x4
# 53  6.9 3.1 4.9 1.5
# 121 6.9 3.2 5.7 2.3
# 140 6.9 3.1 5.4 2.1
# 142 6.9 3.1 5.1 2.3

# and

# 6.9 + 3.1 + 4.9 + 1.5 +
# 6.9 + 3.2 + 5.7 + 2.3 +
# 6.9 + 3.1 + 5.4 + 2.1 +
# 6.9 + 3.1 + 5.1 + 2.3 = 69.4

sum(x[x[,1]==6.9,])

# [1] 69.4

Regarding your new question, I think

transform(x,x1=sort(x1))

is only sorting the first column and the other columns remain unchanged, in which case you are changing the data set.

4.3+3.5+1.4+0.2=9.4

#      x1  x2  x3  x4
# 1   4.3 3.5 1.4 0.2
# 2   4.4 3.0 1.4 0.2
# 3   4.4 3.2 1.3 0.2
# 4   4.4 3.1 1.5 0.2
# 5   4.5 3.6 1.4 0.2

If you want to order the data set by increasing values of the first column without changing the data set use:

x[order(x$x1),]

#      x1  x2  x3  x4
# 14  4.3 3.0 1.1 0.1
# 9   4.4 2.9 1.4 0.2
# 39  4.4 3.0 1.3 0.2
# 43  4.4 3.2 1.3 0.2
# 42  4.5 2.3 1.3 0.3