# Methodology: breaking multi-regression apart

I have to perform a multiple regression where my independent variable is store visits, while the dependents include hour of day, day of week, and others.

I need to do this in Excel. Excel limits variables in a multiple regression to 16, and unfortunately, I have about 50 (due to dummy variables such as hour of day (12) and day of week (7).

It seems like I could run several multiple regressions; one for hour of day, one for day of week, etc. Such as:

1) Store visits = B0 + xMonday + xTuesday + ... + xSunday

2) Store visits = B0 + x1:00 + x2:00 + ... + x12:00


Would this be a statistical mistake? I think this would reveal the most important day of week and hour to explain store visits.

• Number of store visits is presumably the dependent (outcome, response) variable here and the other variables predictors (explanatory variables, covariates). The fact that dependent and independent are so often confused is one of several strong arguments against this terminology, long past its sell by date. – Nick Cox Feb 9 '16 at 21:36
• That's interesting @NickCox, but what's the alternative terminology? – MonkeySeeMonkeyDo Feb 10 '16 at 7:54
• Already answered: outcome and response are some good alternatives for dependent variable and I suggested three alternatives for independent variables. There are others yet. – Nick Cox Feb 10 '16 at 8:50

Would this be a statistical mistake?

No, creating multiple models is not a statistical mistake, but it's probably not what you want to do. There is nothing wrong with building multiple models, and you can conceivably derive useful information from each model. However, it would be a mistake to make many inferences about store visits from your models and try to combine them. For example, suppose you create the following model and find it to be a good predictor of the number of store visits:

storeVisits = b0 + b1*Monday + ... + b7*Sunday


If you find this to be a good model and Sunday (for example) has the largest regression coefficient, you might conclude that on average more store visits occur on Sunday than any other day of the week.

Now, suppose you create the following model and, again, find it to be a good predictor of number of store visits:

storeVisits = b0 + b1*1oclock + b2*2oclock + ...


If the regression coefficient for 2oclock is the largest, you might conclude that on any given day, on average the most store visits happen between 2:00 and 3:00.

This so far is completely fine. Where you would be mistaken, however, is to assume that you can combine these conclusions and make a reliable prediction about the number of visits during a certain period on a certain day. For example, despite what you found about the busiest day (Sunday) and busiest hour (2:00 - 3:00), concluding that on average the most store visits happen between 2:00 and 3:00 on Sunday is not a sound conclusion.

• That was very clearly explained @BenF! Such powers of articulation you have :) – MonkeySeeMonkeyDo Feb 10 '16 at 8:02
• Thank you @BenF, I was under a big time crunch last week and your clear answer helped resolve this question I was struggling to understand in the statistics books. I remember wishing during school years for stats books that took smaller steps while explaining concepts. But I guess that's what a community like this is all about - facilitating the learning platform. Thanks again man! – MonkeySeeMonkeyDo Feb 14 '16 at 7:40