I am trying to understand the difference between logistic regression probabilities and linear regression prediction intervals.
For example, let's say we have a database of student test scores in the range of 1 to 100 and some predictors. The goal of this study is to build a model to predict if other students will reach at least a score of 60 with an 80% confidence. To simplify, we are assuming that all the linear modeling requirements in the data are verified.
The first method would be to run a linear regression on the observed data, then calculate the 80% prediction intervals and finally determine whether a student will reach a score of 60 or higher based on the lower end of the prediction interval. The other approach is to categorize our data and run a logistic regression on each student score < 60 (0) or >= 60 (1) observation.
Is there any benefit in using the logistic regression approach in this case? Or does linear regression will result in the same level of accuracy when using prediction intervals?