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I am reviewing a friend's paper, and they are throwing out variables that are below a certain correlation coefficient value before doing a multiple linear regression model.
Is this a wise thing to do? They are investigating transformations of variables as well, and I feel like a variable that is not linearly correlated could become very informative after a transformation.

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    $\begingroup$ for example x and x^2 $\endgroup$
    – rep_ho
    Commented Aug 8, 2022 at 13:56

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Yes, you can have zero correlation when you have a nonlinear dependency. For example, $y=x^2$ will have a correlation coefficient of zero, and the linear regression will fit a horizontal line. but regression to $y=ax^2+bx+c$ will show the dependency.

enter image description here

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    $\begingroup$ Thanks! This is a really great visualization for this question. $\endgroup$
    – Ryan Folks
    Commented Aug 8, 2022 at 14:28
  • $\begingroup$ You could also consider y=mod(x,2) - nonlinear functions can be very nonlinear indeed $\endgroup$ Commented Aug 9, 2022 at 14:55

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