Take a simple linear regression $y = ax + b$. Here, $y$ is predicted. In my analysis I need to compare the predicted $y$s to the actual $y$s from my data set upon which the regression was built. What diacritical mark should I use to denote the predicted $y$? ŷ, ý, or maybe $y'$? Is there a standard mathematical symbol for a predicted value? Or should I use another letter?

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    $\begingroup$ A good approximation is y with a circumflex (U+0177): ŷ .... but in MathJax/ LaTeX markup it looks more mathematical (the way it tends to be written by hand): $\hat{y}$ $\endgroup$ – Glen_b Feb 4 '16 at 4:42

The predicted outcome is generally expressed as $\large \hat y$ - or "why - hat". You can think of the hat matrix, which "puts a hat on the $\large y$" as in $\large \hat y = H y$, the linear algebra equation that relates the observed values of the response variable, $\large y$, to the predicted values, $\large \hat y$, to make it easy to remember.

What you want to compare are the residuals: $e = \large y - \hat y = y - H y$.

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    $\begingroup$ Why hat? Because, good sir, it is predicted to rain. $\endgroup$ – Matthew Drury Feb 4 '16 at 4:50
  • $\begingroup$ Exactly, residuals! That is what I am calculating and I will make sure to use $e$ for notation. @MatthewDrury That's a nice one! $\endgroup$ – Arthur Tarasov Feb 4 '16 at 5:51

Yes, there is a standard symbol for predicted value. It is $\hat{y}$. You can see that in, e. g., Introduction to Statistical Learning


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