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Must the graph of a linear model always be a straight line of the form $y=mx+b$?

I think that yes, but am checking, whether there might be some exceptions.

mavavilj
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  • in the definition of "linear" models: yes. But could you explain more the context of your question? Did you want to use a regression model on a specific data base and want to know if the regression model must be linear? – Metariat Oct 03 '16 at 17:05
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    No, a linear model remains linear even if you fit a polynomial. Check [this answer](http://stats.stackexchange.com/a/92087/67822). Also, if you're doing multiple regression, you will be generating a hyperplane. – Antoni Parellada Oct 03 '16 at 17:06
  • @Metariat Well I'm plotting a linear regression model that has multiple parameters and I'm plotting it by changing the parameters. Since the model is fairly complex I was confused about the simplicity of the plot, which is a straight line. – mavavilj Oct 03 '16 at 17:07
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    The term linear refers to linear *in the parameters* only. Polynomials and splines are easy ways of introducing nonlinearity in the relationship between x and y while maintaining linearity in the parameters. – Maarten Buis Oct 03 '16 at 17:09
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    This question really seems to be asking "what exactly does 'linear' in 'linear model' refer to?" If that is so, please visit [How to tell the difference between linear and non-linear regression models?](http://stats.stackexchange.com/questions/148638) A closely related thread is at http://stats.stackexchange.com/questions/33876. – whuber Oct 03 '16 at 17:23
  • It may be hard to provide more specific answers w/o more information. Can you say more about your situation, your data & your model? Can you paste in some sample data, or your code, or a figure you want help interpreting? – gung - Reinstate Monica Oct 03 '16 at 17:26
  • @gung No I'm just asking whether linear **models** always exhibit a straight line plot. Since "linear" tends to mean such line. – mavavilj Oct 03 '16 at 17:34
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    @mavavilj, if that is your only question, it has been answered many times on the site, including in the links already provided. – gung - Reinstate Monica Oct 03 '16 at 19:08
  • There is a wonderful vagueness to this question: in the expression "$y=mx+b$", which is supposed to be the variable(s)? Probably $x$ was intended, but this describes part of a "linear model" in the sense that it is expresses $y$ as a linear function of both $m$ and $b$--the linearity with respect to $x$ is irrelevant! – whuber Oct 03 '16 at 21:29

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