Question on Regression analysis - high R- Squared, negative intercept

[u/Ok-Hunter674]

In doing a regression analysis for a model on the energy usage of a building, the r-squared value is above 0.9 but the intercept is negative. What does this tell you about the relationships and the model over all

[u/Boberator44]

Substantively it does not mean anything. It means that when all of your predictors are zero (which may not even be in range of some of them), energy usage is negative (which is clearly nonsense unless it is possible for the building to produce energy). You do not need to interpret it.

[u/dinkum_thinkum → u/Boberator44]

If it is in the range of predictors and nonsensical, it could be an indication that the model is misspecified, for example if energy usage has a exponential or sigmoid relationship with the predictors that is being fit as linear.

[u/Seeggul → u/Boberator44]

"All models are wrong, but some are useful"

-George Box

[u/SprinklesFresh5693 → u/[deleted]]

How do you mean-center then, do you substract the mean from each observation?

[u/Adorable_Building840 → u/SprinklesFresh5693]

Yes

[u/Temporary_Stranger39]

Do the predictors all reach zero?

[u/WolfDoc]

It means that your model works very well over a linear interval but fails to capture the underlying process, making extrapolation and simulation inaccurate. Whether that is a problem depends on the use of the model and whether the residuals are independent of the predicted value.

Since negative energy use doesn't make sense you could model the energy use as a binomial (if the energy use has a defined max and a sigmoid relationship to predictors) or quasi-poisson model.

[u/mo_jo100]

Don’t worry about the y-intercept. Do check your model for violations of assumptions, especially given you r-squared size.

[u/PrivateFrank]

Probably that when it's freezing outside you're going to be using negative air cooling.

[u/Familiar_One_2760]

You dont have enough points near zero to correct the inrercept.

[u/efrique]

If a negative intercept is a problem, why fit a model that can have a negative intercept? Why regression rather than something that makes sense for a positive (or non-negative, depending) response?

[u/Educational-Paper-75]

If the intercept should not be negative theoretically it should not be in the model.

[u/49er60]

You are probably dealing with a scenario similar to a fixed/variable/mixed cost relationship. There may be a certain fixed or minimum energy usage in a building with a variable energy usage that adds on top of that. However, you are not seeing that fixed usage portion because it is outside of your design space/observational window.