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**Sex**and one response variable

**Survived**. Let's say the estimated coefficients are ##\hat{\beta_0}## and ##\hat{\beta_1}## for the intercept and the coefficient of Sex predictor, respectively. Mathematically this means that:

[tex]\hat{p}(X) = \frac{1}{1+e^{-(\hat{\beta_0}+\hat{\beta_1}X)}}[/tex]

where X is 1 for male, and 0 for female, and where ##\hat{p}## is the estimated probability. This model's estimates give ##\hat{p}(X=1)+\hat{p}(X=0)\neq 1##. Why? Is it because these are estimates, or because there is/are other reason(s) like Survived depends on other predictors?