> But the line you cited was about "response" being a matrix, which is not our 
> case.
Yes, you're right; I picked the wrong thing to cite.
The only documentation I found about lm accepting a matrix in the predictors is 
a one-line statement in "Introduction to R" which says "term_i
    is either

        a vector or matrix expression, or 1,
        a factor, or
        a formula expression consisting of factors, vectors or matrices 
connected by formula operators. "

Not the most informative documentation. But Peter Dalgaard is a most 
authoritative source!

>And also I have checked:
>
>Any more thoughts?

Data frames are odd things; a column need not contain only a vector if the 
number of rows is OK. I am half surprised that including a matrix in one works. 
But the gods of R are powerful and their magic is strong. Here, names(tmp) is 
showing that the data frame has one element called X (in effect, the whole 
matrix is regarded as one element of the data frame), but on display the magic 
has expanded X to show all the columns of X.

This is the main reason I generally keep to simple things in data frames; 
complicated things make it less easy to predict behaviour.



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