I am currently writing up a statistical part of a report. In the field where I am from a "parameter" would refer to what is known as the "independent variable" or "predictor" in statistics (that is $x_{1}$ below).

To avoid confusion I was wondering if the "parameter" in statistics ($\beta$ right ??) had another name I could use ? I was thinking of "coefficient" but I want to make sure it doesn't have another specific meaning in statistics.

At the start of the section I will add a paragraph explaining the correspondence in terminology. I hope this will keep the report rigorous whilst still understandable for people with no background in statistics.

$y = \beta_{0} + \beta_{1}x_{1}$

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    $\begingroup$ To describe the "betas" you can also use the term "coefficient". $\endgroup$ – Alecos Papadopoulos Dec 6 '17 at 10:40
  • $\begingroup$ Thanks I had just thought of that and edited the question with that suggestion :) It doesn't have another meaning which could lead to confusion right ? $\endgroup$ – Sorade Dec 6 '17 at 10:41
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    $\begingroup$ It is not much of an answer, but I'd recommend to use the terminology that is common in your field. If at some point you are looking to publish this manuscript, editors might even require you to do so. Secondly, I'd say that between the suggestions put forward (parameter, predictor, coefficient, independent variable), I'd be okay with any of them, as long as you use the one you chose consistently. $\endgroup$ – IWS Dec 6 '17 at 10:53
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    $\begingroup$ I am with Alecos Papadopoulos and IWS. Coefficient is a very common term for what you want to say in statistics and if you call it "the linear regression coefficients" in the first place and than stick to coefficient, that should be without any problem. $\endgroup$ – Bernhard Dec 6 '17 at 11:47
  • $\begingroup$ Statistical people can almost be defined by their preferring to use the word parameters for whatever unknown constants are being estimated. Scientists often use parameters as meaning just variables. Politicians and pundits and some others seem to have picked up the word as meaning "limits" or as just meaning not much precisely. Perhaps originally there was some confusion with "perimeter", as in "within the parameters of government policy" or "expanding the parameters of our ongoing personal relationship". Bayesians can and should speak for whatever else they want to say. $\endgroup$ – Nick Cox Dec 6 '17 at 13:46

In usual terminology, if we have a regression model

$$ Y = \beta_0 + \beta_1 X_1 + \beta_2 X_2 + \beta_3 X_1 X_2 + \varepsilon $$

then $Y$ is called the dependent, target, or predicted variable, while $X_1,X_2$ are independent variables, features, predictors, or just "variables". $X_1 X_2$ is the interaction term and sometimes we talk about "terms" in regression models. $\beta_0, \beta_1, \beta_2, \beta_3$ are regression parameters, or coefficients, where $\beta_0$ is called the intercept, or bias term, and $\varepsilon$ is the noise, or error term.

Calling the variables "parameters" would be very confusing for most of the statistical audience. Even if your variables describe things like parameters of some machine that are fixed before the experiment, or parameters of the experiment that are manipulated by the researcher, then using descriptive names for them rather than calling them "parameters" would seem more appropriate to me. The main reason is that in most statistical/machine learning problems we talk about estimating parameters of models: sometimes we could have parameters that are known in advance and the ones to be estimated, but "estimating the parameters" is a big part of statistics.


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