Explanation

In logistic regression, the linear combination $y_i = \alpha + \beta_1 x_{1i} + \beta_2 x_{2i} + \beta_3 x_{3i}$ represents the log-odds of the probability, not the probability itself.

The actual probability that $y_i = 0$ (or equivalently, the probability of the negative class) is given by the logistic function:

$P(y_i = 0) = \frac{1}{1 + e^{y_i}} = \frac{1}{1 + e^{\alpha + \beta_1 x_{1i} + \beta_2 x_{2i} + \beta_3 x_{3i}}}$

And the probability that $y_i = 1$ is:

P(y_i = 1) = \frac{e^{y_i}}{1 + e^{y_i}} = \frac{e^{\alpha + \beta_1 x_{1i} + \beta_2 x_{2i} + \beta_3 x_{3i}}}{1 + e^{\alpha + \beta_1 x_{1i} + \beta_2 x_{2i} + \beta_3 x_{3i}}}}

Therefore, the correct answer is A. 1 / (1 + e^(y_i)) which represents the sigmoid function applied to the negative of the linear combination, transforming the real-valued output into a probability between 0 and 1.