Generally for a linear regression we write the estimator as $\hat{y}$ -- eg, $\hat{y} = f(\hat{\beta},x)$

What is the equivalent notation for a logistic regression?

Is it $\hat{p}(Y=1|X=x)$?


1 Answer 1


You could say $\hat{p}$ where

$$\hat{p} = Pr( Y=1 \vert X = x) = \dfrac{1}{1 + \exp({-x^T \hat{\beta}})}$$

We call $$f(x) = \dfrac{1}{1 + \exp({-x})} $$

the logistic function.

enter image description here

  • $\begingroup$ Ok so not $\hat{p}=\hat{P}(Y=1|X=x)$? $\endgroup$ Jan 31, 2019 at 2:43
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    $\begingroup$ Honestly, it doesn't matter so long as you are consistent and explain any non-standard notation. $\endgroup$ Jan 31, 2019 at 2:47
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    $\begingroup$ Disagree - shouldn't it be at least $$\hat{p} = Pr( Y=1 \vert X = x, \hat{\beta}) = \dfrac{1}{1 + \exp({-x^T\hat{\beta}})}$$ $\endgroup$ Jan 31, 2019 at 2:50
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    $\begingroup$ I think @DemetriPananos is missing a hat over the $\beta$ in the denominator above if you want to use standard notation. $\endgroup$ Jan 31, 2019 at 2:51
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    $\begingroup$ @user0 Again, it is all context dependent. You can suppress explicit dependence on the coefficient so long as you are consistent. $\endgroup$ Jan 31, 2019 at 2:54

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