# Correct "hat" notation for a prediction from a GLM

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

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.

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