How do I make a checkbox remain checked in html with php code?

If I have an html checkbox in a table, how do I edit the checked state via php? Basically I want to have a checkbox labeled "retain settings" and when that is set to true all my other checkboxes will either remain checked or un-checked when the page refreshes. The actual line of code I need to have change per user is the "checked".

<input type="checkbox" name="upper" value="true" checked/>