When Using Logistic Regression, Where P Being the Probability That $\frac{p}{1+k_{k}-\beta 0+\beta_{1} X_{1}+\beta_{2} X_{2}+\ldots+\beta_{k} X_{k}}$

question 11

Multiple Choice

When using logistic regression, where p being the probability that the dependent variable Y = 1, X₁, X₂ ..., Xk are the independent variables, and β₀, β₁, β₂ ..., βk are unknown regression coefficients, ________ is called the odds of belonging to category 1(Y = 1) .

• A)p(β₀ + β₁X₁ ₊ β₂X₂ + ...+ βkXk)
• B) \(\frac{p}{1+k_{k}-\beta 0+\beta_{1} X_{1}+\beta_{2} X_{2}+\ldots+\beta_{k} X_{k}}\)
• C) \(\frac{p}{1-p}\)
• D) \({ \frac { \sum _ { i = 1 } ^ { n } B_{i} X _ { i } } { p } }\)

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Definitions:

Probability

A measure of the likelihood of a given event happening, often expressed as a number between 0 and 1.

Von Neuman-Morgenstern

Refers to the theory of expected utility, formulated by John von Neumann and Oskar Morgenstern, which addresses choices made under conditions of risk.

Expected Utility Function

A mathematical expression that represents a consumer's preference for uncertain outcomes, weighting each outcome by its probability of occurrence.

Von Neuman-Morgenstern Utility Function

A utility function that accounts for the existence of risk and uncertainty, allowing for the calculation of expected utility.