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A model is linear if it is linear in the parameters. Therefore, a linear model can describe a curve, if a function (such as raising to a power, but not necessarily) is performed on one of the variables.

The name "linear model" is very unintuitive; intuitively the term conjures a line, not a curve.

  1. Is there a term that would fit the definition of a linear model, but be more intuitive to understand?

  2. Is there a way to make the term "Linear model" more intuitive to myself? ( This part of the question is a one on studying skills).

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    $\begingroup$ "linearly parameterized models"? $\endgroup$ – doubllle Sep 14 '20 at 13:07
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    $\begingroup$ What does "intuitive" mean any way? I translate it as "familiar to me and should be easy for you too". It is sometimes advertising, as in "this software has an intuitive interface" (so, the more you use it, the easier it gets), and sometimes an implied put-down if you don't work on the same level as the writer ("the result is intuitive given Fubini's theorem" or the Cauchy-Schwarz inequality, or whatever). It's a subtlety that has to be learned that "linear in parameters" is deeper and wider than "linear in variables" and thinking up different language for that won't make it easier. $\endgroup$ – Nick Cox Sep 14 '20 at 13:32
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    $\begingroup$ If you are familiary with linear algebra, then 'linear model' is very intuitive :) A way to make the term 'linear model' more intuitive to you could be Bapat, Linear Algebra and Linear Models, Springer, 2012. $\endgroup$ – Sergio Sep 14 '20 at 14:01
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    $\begingroup$ I don't have another / better term. For your own understanding, here are two threads that may help: Why is polynomial regression considered a special case of multiple linear regression?; & How to tell the difference between linear and non-linear regression models? $\endgroup$ – gung - Reinstate Monica Sep 14 '20 at 14:30
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    $\begingroup$ I don't see a problem with the term linear model. It's as intuitive as anything else. As Underminer noted, regression is a possible substitute with the obvious caveat that its use would be limited to a nontechnical audience. Anyone with even a moderate degree of statistical sophistication would demand more specificity. That said, my suggestion is to use the words classic regression. This phrase can be tracked back to how OLS or linear regression is taught in Stats 101 and, therefore, should be recognizable to all. $\endgroup$ – user234562 Sep 15 '20 at 11:11
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  1. For an alternative name, I think referring to the model as a Regression Model or simply as a Regression may be more intuitive to others. Regression models are most commonly linear models (but also include non-parametric and non-linear models). Since you are looking for something more intuitive, I think this would be easy to understand by others since most people intuit regression as a type of "line-fitting" and don't care if it's a straight line or a curved line.

  2. Since you already understand that a linear model is linear in the parameters, I don't think there is a more intuitive way to think of it by yourself. You understand the technical reason why linear models are named the way they are, and now have the responsibility to explain that reason to others, or you can dumb-it-down to layman's terms.

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