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Say I'm using multiple logistic regression to help caterers in a large city predict the probability invited adults will come to a wedding. Say I have a proprietary dataset of likely relevant predictor variables for each invited guest's traits, like age, gender, marital status, how far away they live from the event site, and whether the event is on a Saturday, and I have guests' attendance history to past weddings (1 = they attended; 0 = they didn't).

Say the results show all of the coefficients are significant (age: younger people are more likely to attend; gender: women are more likely to attend; marital status: single people are more likely to attend; how far away they live: the closer you live, the more likely you'll attend; Saturday: people are more likely to attend Saturday weddings).

Say I show those results to the caterers and teach them how to calculate the predicted probability of attendance given an invited guest's traits. However, the caterers unanimously proclaim they don't have access to all those data. They don't know the age, gender, or marital status of the guests but they do know how far away they live and whether the wedding is on a Saturday.

The caterers ask me if I can re-run the model using only those variables they have information on, so that they can feasibly employ the predicted probability calculations with their own data. What are the implications of this? Is there a better strategy?

Usually, omitted-variable bias is a concern because leaving out relevant variables "results in the model attributing the effect of the missing variables to the estimated effects of the included variables". But is that a bad thing here?

For instance, I assume some of the omitted variables correlate, like marital status and how fare they live away, with married folk being more likely to live in the suburbs, farther away from the event locations in the downtown area of the city. Would the caterers' ability to control for how far they live away capture the effects of marital status too, then, so that all in all the reduced model will still be effective at predicting attendance?

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