Should you autosave when app is minimized?

I'm developing an Android app that allows users to fill out different types of forms (input types = text, numbers, and sliders for certain numbers).

The save button is in the top-right corner, in the action bar. When the user fills out the entire form (~15 input fields), the user might accidentally press the back button and lose all data that was inputted. Hence, we're autosaving on back button press.

Should I also auto save forms when the user presses the Android home button?

To clarify, autosave implies auto submit - the form is saved to the server (in contrast to just keeping data persistent on the phone until the user submits).

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I'm leaning towards not autosaving on home button press because it is possible the user simply wants to cancel the input process. In this case, autosaving would lead to incorrect behaviour.