# One multiple linear regression, or many simple linear regressions for prediction?

I would like to create a model which predicts the amount of energy used in an area, dependent on the number of properties in 5 categories (detached, semi, flats, bungalow and terrace). I have daily data, giving the total daily energy consumption, with the number of properties in each of the 5 categories.

My question, would it be better to build a multiple linear regression model using total energy consumption as the dependent variable, with property type as the explanatory variables (a coefficient for each of the 5 groups). Or, would it be better to create 5 simple regression models, using energy as the dependent, and each property type as different explanatory variables.

To be clear, I have some daily data which only contains readings from areas with one property type (daily energy readings for an area with only detached properties, for example), and some data which is from areas with a combination of properties (for example, daily energy readings for an area with semi-detached and flats).

What would be the difference between the methods, and are there any benefits/caveats to doing either way?

• What is your aim? You want good predictability or good interpretability or both? This CV thread looks related.
– Krrr
Aug 29, 2017 at 8:52
• Both, I guess. One problem i am facing with MLR modelling is some negative coefficients, which in the context of the problem doesn't make sense (negative energy usage for flats - but they don't produce energy!). So, was thinking that a model for each category may solve this. Aug 29, 2017 at 9:19
• Aha! Perhaps add that to your question so we get a better handle of the question. Also this document provides several reasons and justifications.
– Krrr
Aug 29, 2017 at 9:23
• Aug 29, 2017 at 9:57
• See also en.wikipedia.org/wiki/Simpson%27s_paradox (particularly the illustration, which succinctly demonstrates why leaving out predictors that are related to the response can be a problem (above and beyond the impact on standard errors) Aug 29, 2017 at 10:00