I have a dataset where I'm trying to predict a student's percentage score on a school exam from some other collected IVs. I'm wondering how to correctly run this analysis in
A few related questions:
First, I've seen a number of questions on this topic (e.g. What are the issues with using percentage outcome in linear regression?) where the usual recommendation is to use logistic regression. I'm a bit confused about how logistic regression fits into this. I've never formally taken a class on logistic regression, and my understanding (from the machine learning world) is that the evaluation of the linear input through a logistic function is interpreted as the probability that this data point belongs to the majority (1) class. However, I don't have classes per se, so I'm confused about how a logistic model actually works in this case as I essentially have a continuous variable that is bounded by 0 and 100.
I've also seen Poisson regression being recommended in some places. However, that appears to predict integer values, and is likely not a good model for this?
Finally, what are the steps for running this in
R? Would I convert my percentage DV to a logit, run the regular
lm() function and interpret the coefficients (and their p values) like normal? Is the interpretation of the significance the same as linear regression (i.e. the IV is a significant predictor of the percentage DV when holding all other IVs constant)?
In the comments, it has been suggested that the answer can be found here: How to do logistic regression in R when outcome is fractional (a ratio of two counts)?
The solution there, as proposed by Greg, is to use 2 columns, one specifying a proportion and another to specify the weight (number of total points). This won't work in my case.
In the dataset I only have access to the final percentage/proportion. The data comes from different classes and I have no way of knowing the number of points the individual received on the exam, nor the total number of points available for that exam (as it would likely be different for individuals in different classes)
Option #1 in Greg's post is also not possible because I don't have a binary/categorical response.