Residuals or error

[Pita Fouta]

Good morning everyone,

To express a regression in a research paper, do we have to use the error term et or the residuals ut.

Thanks in advance

[Nick Cox]

In literature I look at, the error term is an unobserved disturbance in a model specification and a residual is what you can calculate after a model fit using data.

Is a "research paper" a paper for an academic journal or an assignment as part of a degree course? Either way, it is entirely possible that different terms could be used in your unstated field for different context within a report on your project.

Look at published papers in relevant journals or ask an advisor, supervisor, mentor for advice on what is expected.

[Krishanu Karmakar]

By the statement "To express a regression" I am guessing you mean "To write the population model". If that is the meaning that you had in mind then the notations should use the error term or the disturbance term. Now whether you use et (e with a subscript t) or ut (u with a suscript t) or epsilont(epsilon with a subscript t) that is your (author's choice). It is not as if only et or only ut can be used to denote disturbances - usage varies from author to author.

But, just as Prof. Cox has written above, the residual term (again what notation is used - et or ut or et with a hat or ut with a hat) should be used or stated only after the parameters have been estimated using the sample data. It should not be used when stating a population model (that is when you are saying that "this is the model whose parameters I am/we are going to estimate" at the beginning of the Methods section of a paper.)