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I am new to machine learning and it's hard to find an instructor to help you with theory based questions. If this question does not fit to this site feel free to remove it.

I am comparing the 3 types of linear regression: Single, Multiple, and polynomial.

Can we say the following:

  1. Single linear regression: is when there is a single independent variable related linearly to a single dependent variable. And to train and predict values, the LinearRegression() class is used.

  2. Multiple linear regression: is when there is a multiple independent variables related linearly to a single dependent variable and we should avoid multicollinearity and dummy variable trap while coding and analyzing.

    To code it using the backward elimination method:

    a. So we check p-values and remove the higher than the significance level and keep the other;

    b. A new field is added to the beginning of the set to calculate b0 intercept;

    c. Avoid dummy variable trap;

    d. Afterwards, we user the same LinearRegression() class to train and predict on the final data set after removing the interdependent features.

  3. Polynomial linear regression: is when a single or multiple independent feature is/are related linearly with a parabola to a single dependent variable. We figure out that by adding a new field to the data set with a second degree (or even more for better precision) and then run the LinearRegression() class on the new data set.

Is all of the above true ?

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  • $\begingroup$ The concept of linear regression is far broader in scope than the limited characterizations here. See stats.stackexchange.com/questions/148638 for a general account of what it encompasses. $\endgroup$ – whuber Aug 26 at 14:24
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No, it isn't true. 1. seems fine. 2. seems OK up to the "but" (and the bullet points are not really part of the definition). 3. isn't true. You can have polynomial regression with more than one independent variable and part of what you have is a method for doing things rather than a definition.

In addition, there are other types of linear regression.

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  • $\begingroup$ I've edited my question to fit your answer. Can you check it again please ? The sub points of point 2 are coding steps not in the definition. $\endgroup$ – alim1990 Aug 27 at 5:03
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    $\begingroup$ Backward elimination is a terrible method. Not all polynomials are parabolas. If you want definitions, look in a dictionary of statistics. $\endgroup$ – Peter Flom - Reinstate Monica Aug 27 at 9:32
  • $\begingroup$ What is better then backward elimination method ? $\endgroup$ – alim1990 Aug 27 at 12:58
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    $\begingroup$ The best method is to have all your models prescribed a priori, based on substantive knowledge. Next best is to have several possible models based on substantive knowledge and statistics (and NOT jut p values). If you MUST use an automated method (i.e. you want the computer to do your thinking) then LASSO is pretty good. $\endgroup$ – Peter Flom - Reinstate Monica Aug 28 at 12:34

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