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My question is about the validity of using a logistic regression model to predict the probability of X occurring when knowing only one or two input variables.

Consider the binary response variable that a person will either become obese (1) or they will not become obese (0). Say we have a sample of people and data for the independent variables currently at a healthy weight, these variables are: initial weight, age, daily exercise (time), calories consumed per day. And we have some numerical model which uses the above variables to calculate precisely what the outcome will eventually be for each person: whether or not they will grow to obesity.

We want to use this data to make a prediction on anyone in the total population given their age and calories consumed. Logistic regression seems to be the way to go, but please tell me if there is a more appropriate approach.

What if, when going to the total population we are only able to know a given person's age and calories consumed. For some reason the initial weight and daily exercise is not available. So then for our logistic regression, we would only be able to use age and calories consumed as predicting factors to whether someone will become obese. Is logistic regression still appropriate for this kind of problem?

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  • $\begingroup$ Logistic regression will still work under the conditions you describe. You wouldn't want to make strong causal inferences from a model that you knew to be poorly specified, but there's no problem (other than maybe reduced accuracy) with using an under-specified model to generate predictions. You just need only to use the variables you have for the total population when estimating the initial model. $\endgroup$ – ulfelder Jul 1 '17 at 10:46
  • $\begingroup$ Do you mean that you estimate the model with four independent variables (initial weight, age, exercise per day and calories per day) and the predict obese with only two of them ? That looks impossible, what do you use for values for the two other variables ? Or do you mean that you estimate the model with only two independent variables and then predict with two ? $\endgroup$ – user83346 Jul 1 '17 at 10:46

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