In the expression Pr(Y = 1 | = ?(?₀ + ?₁X), A)(?₀ + ?₁X)plays the role of z in the cumulative standard normal distribution function. B)?₁cannot be negative since probabilities have to lie between 0 and 1. C)?₀cannot be negative since probabilities have to lie between 0 and 1. D)min (?₀ + ?₁X) 0 since probabilities have to lie between 0 and 1.

Question

In the expression Pr(Y = 1 | = ?(?₀ + ?₁X), A)(?₀ + ?₁X)plays the role of z in the cumulative standard normal distribution function. B)?₁cannot be negative since probabilities have to lie between 0 and 1. C)?₀cannot be negative since probabilities have to lie between 0 and 1. D)min (?₀ + ?₁X)> 0 since probabilities have to lie between 0 and 1.

Quizplus · Accepted Answer

The expression inside the conditional probability Pr(Y = 1 | ...) is a function of variables and parameters, which can be interpreted as the argument $z$ in the cumulative standard normal distribution function, $\Phi(z)$. This is a common form in statistics and econometrics, especially in models like probit or logistic regression, where the probability of an event (e.g., $Y=1$) is modeled as a function of predictors ($X$) through a link function (e.g., the cumulative distribution function of a standard normal distribution). Choices B, C, and D make incorrect assumptions about the nature of the parameters and the expression, as they do not necessarily relate to the direct interpretation of probabilities within the expression's context.

In the Expression Pr(Y = 1 | = ?(?0

In the Expression Pr(Y = 1 | = ?(?₀