# Applying logistic regression with response and expected response

I hope my title is phrased correctly, otherwise feel free to rephrase it.

This is my first time working with such a data set and i'm trying to understand if a method i'm using is correct. Here is a breakdown of what kind of data i'm working with.

Let's say an experiment is run and you obtain a value x.

Now we already know beforehand, of what to expect x to be under a certain condition. So we have three columns. x, our classification of x, expected value of x.

You can tell straight away, some values of x are misclassified E.G when x = 12, classification = 0 (as 12 <15) but the actual result (expected) = 1. And again, for x = 17 and x = 18. These can be considered as type 1 or type 2 errors.

Now I hope I have clearly explained the structure of my data. What I want to do is assess whether dividing the data into x < 15 and x > 15 is sensible. My current method is applying a logistic regression model with Classifcation ~ x and then comparing the logistic regressions output with my expected results. I'm not even sure what this achieves, if i'm honest. I'm not sure how to tackle this problem.

EDIT: (Context)

• The goal is to identify which blood samples have lymphoma, with a new technique.
• We already know which blood samples have lymphoma (Expected column) with an old technique.
• X is a metric we use to determine if the blood sample is positive or negative of lymphoma.
• It was found that splitting X into below and above 15, we are able to classify lymphoma.
• My goal is not to compare whether the new technique is better than the old one. It is to show these thresholds are good enough to classify lymphoma.
• What is the purpose of all this work? If you are forced to classify $x$ on a binary scale, some of it makes sense, but otherwise why lose all that information? – whuber Oct 17 at 11:24
• @whuber Thank you for your reply. I've added in context to my question. – Ali Oct 17 at 11:57
• The reason behind this classification is due to the variability of x. The variance is so high (due to either human or machine error), that the magnitudes of x has no particular meaning. – Ali Oct 17 at 12:04
• Thank you for the clarifications. It looks like you might be seeking information on sensitivity and specificity. – whuber Oct 17 at 12:05
• Would they be enough information to indicate this binary classification of x, and x itself, is a valid metric? – Ali Oct 17 at 12:24