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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. 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? 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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