“I wonder if demonstrated interest can also include essays”
It can, but essays are also a separate category, and in fact the highest ranking non-academic category, that I wonder if interest is the traditional ways you show it.
“The earlier survey shows a strong correlation between demonstrated interest and yield. 64% of colleges with a yield of >60% said that demonstrated interest was “considerable importance”, the clear majority.”
And the best way to show interest is applying early, especially ED, and as the Harvard data shows, SCEA as well.
“We’ve got to know “grades and strength of curriculum” are important”
It’s the most important, there’s probably not even a close second. Even tippy tops say that, here’s Yale’s first statement about admissions:
“Yale is above all an academic institution. This means academic strength is our first consideration in evaluating any candidate. The single most important document in your application is your high school transcript, which tells us a great deal about your academic drive and performance over time. We look for students who have consistently taken a broad range of challenging courses in high school and have done well.”
Now if Yale or a similar type college is filling out the survey, what do you think they’re going to rank 1-4, all the academic factors. It starts with the transcript and for many appliacnts, it will end there.