# If an OLS model is estimated without an intercept (no constant term) but the average residual is close to zero, are we OK?

Let's suppose an OLS model is estimated without an intercept (no constant term), but the mean residual is very close to zero (2.2E-11) does that mean the model is OK to have been estimated without a constant term?

P.S.: All the variables are standardized to have zero mean and 1 standard deviation.

The constant term can be omitted if there is a strong reason to expect that the dependent variable has conditional mean zero at the average value for all covariates. Having said that, having a zero mean for residuals per se is insufficient to assess whether the OLS regression is well specified or not. There are a battery of tests and analyses can be conducted for the assessment of an OLS regression.

Without going into the details of statistical inference on OLS, I refer to the introductory text of Isman and Kim (2020)

• Clarification should include if the average Y at the AVERAGE X (all of them) can be zero and is strongly implied by THEORY rather than the data. There is greater risk to omit the intercept when it is non-zero than to include it when it is zero. These decisions should not be based on the data.
– LSC
Oct 20 '20 at 9:27
• @LSC so if the residuals sum very close to zero (2e-11) without the intercept, is it ok not to include the intercept? Oct 20 '20 at 10:43
• @nyk I will accept your answer as long as someone does not post something contradictory to what you are saying. The variables are standardized to have mean zero and standard deviation 1, so I assume it is ok to estimate a model without intercept. Right? Oct 20 '20 at 10:44
• @adrCoder My answer was edited as I had failed to mention the covariates (i.e. Xs), which was pointed out rightly by LSC and sheb. If the dependent variable and the covariates (i.e. Y and Xs) are all standardized, it is OK to estimate the model without an intercept.
– nyk
Oct 20 '20 at 11:32
• Yes all the variables are standardized to have zero mean. Please take a look at wording it needs a bit editing I think. Oct 20 '20 at 11:41