"out the window" vs. "out of the window"

Question

What is the difference between the expression "out the window" and "out of the window"?

I googled it but found conjectures of foreign speakers, only. One of the conjectures was that "out the window" is a shortened form of "out of the window", mainly used in Northern American English. Is that true?

In the Cambridge Dictionary the following example sentence can be found:

He leaned out the window.

On the other hand, I found this sentence in a book:

Graham took off his gloves, leaned out of the window, and felt the stone below the sash.

Answer 1

As a native U.S. speaker, I see no difference. I would call these 100% the same.

I feel this is simply evidence of an American, if not human, tendency to leave out what is not required while still bringing forth the meaning. My ear would not react to either of these differently. When speaking, I would regard "of" (in this case, not all cases) an unnecessary syllable, especially if speaking quickly.

My own example:

"Well, that idea is out the window." -- sounds more natural for me to say
"Well, that idea is out of the window." -- this sounds noticeably more stilted for me to say, like Sean Astin pronouncing po-ta-toes to Gollum in the Lord of the Rings movies.

But, for some reason, hearing another say either one doesn't sound much different, and certainly doesn't turn my head at all.