I have noticed that Logistic Regression (https://en.wikipedia.org/wiki/Logistic_regression) is a model that used significantly for both Regression problems and Classification problems.

When used for Regression, the main purpose of Logistic Regression appears to be to estimate the effect of a predictor variable on the response variable. For example, here are some examples in which Logistic Regression is used for Regression problems:

• Modelling of binary logistic regression for obesity among secondary students in a rural area of Kedah : https://aip.scitation.org/doi/pdf/10.1063/1.4887702
• A logit model for the estimation of the educational level influence on unemployment in Romania : https://mpra.ub.uni-muenchen.de/81719/1/MPRA_paper_81719.pdf
• A logistic regression investigation of the relationship between the Learning Assistant model and failure rates in introductory STEM courses : https://stemeducationjournal.springeropen.com/articles/10.1186/s40594-018-0152-1

When used for Classification, the main purpose of Logistic Regression appears to be to estimate the relationship between a set of predictor variables and the response variable - specifically, the probability of the response variable assuming a certain value given an observed set of predictor variables. For example, here are some examples in which Logistic Regression is used for Classification problems:

• Using logistic regression to develop a diagnostic model for COVID‑19: A single‑center study : https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9277749/pdf/JEHP-11-153.pdf
• Logistic regression technique for prediction of cardiovascular disease : https://www.sciencedirect.com/science/article/pii/S2666285X22000449
• A Study of Logistic Regression for Fatigue Classification Based on Data of Tongue and Pulse : https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8917949/pdf/ECAM2022-2454678.pdf

Based on surveying such articles, I noticed the following patterns:

• When Logistic Regression is being used for Regression problems, the performance of the Regression Model seems to be primarily measured using metrics that correspond to the overall "Goodness of Fit" and "Likelihood" of the model
• When Logistic Regression is being used for Classification problems, the performance of the Regression Model seems to be primarily using metrics that correspond to the ability of the model to accurately classify individual subjects such as "AUC/ROC" and "F-Score".

Based on these observations, I have the following question:

My Question: Suppose if I am using Logistic Regression in a regression problem (e.g. estimating the effect of predictors such as age on income) and the model seems to be performing well (e.g. statistically significant model coefficients, statistically significant overall model fit, etc.), am I obliged to also measure the ability of the model to successfully classify individual observations based on metrics such as ROC/AUC? Or am I not obliged to this since I not working on a classification problem?

I feel that it might be possible to encounter a situation/dataset in which the goal was to build a Logistic Regression model for a Regression problem - and the resulting model might have good performance metrics used in regression problems, but might have poor ROC/AUC values. In such a case, is this a good Logistic Regression model as it performs well for the regression problem as intended - or is it a questionable model as it is unable to perform classification at a satisfactory level?

Thanks!