Error in Y$x : $ operator is invalid for atomic vectors

This error message typically occurs when you try to use the $ operator on an object that is not a data frame or list. The $ operator is used to extract a specific variable from a data frame or list by referring to its column name.

To avoid this error, you should first check that the object you are trying to access with the $ operator is actually a data frame or list. If it is not, you may need to use a different method to extract the desired information from the object.

For example, if Y is a vector, you can access its elements using square brackets, like this:

Y[1]

If Y is a list, you can access its elements using double square brackets, like this:

Y[[1]]