The probability of an outcome in logistic regression is modeled by which function?

The probability of an outcome in logistic regression is modeled by which function?

• A. Linear function
• B. Exponential function
• C. Logistic function
• D. Quadratic function

Answer: (C)

In logistic regression, the probability of an outcome is modeled using the logistic function. This function is specifically designed to take any input value and map it to a value between 0 and 1, which is ideal for representing probabilities. The logistic function is an S-shaped curve that allows for capturing the relationship between independent variables and the probability of a binary dependent variable effectively. The logistic function is mathematically defined as: \[ P(Y=1 | X) = \frac{1}{1 + e^{-(\beta_0 + \beta_1X_1 + \beta_2X_2 + ... + \beta_kX_k)}} \] where \( P(Y=1 | X) \) is the probability of the outcome occurring, \( e \) is the base of the natural logarithm, and \( \beta \) values represent the coefficients estimated from the data. Using a linear function would not be suitable here since it can produce probabilities outside the [0,1] range, which is not meaningful in the context of probability. The exponential function does appear in the formula for logistic regression, but it is part of the composite logistic function rather than a model on its own. A quadratic function typically indicates a parabolic relationship

In logistic regression, the probability of an outcome is modeled using the logistic function. This function is specifically designed to take any input value and map it to a value between 0 and 1, which is ideal for representing probabilities. The logistic function is an S-shaped curve that allows for capturing the relationship between independent variables and the probability of a binary dependent variable effectively.

The logistic function is mathematically defined as:

[ P(Y=1 | X) = \frac{1}{1 + e^{-(\beta_0 + \beta_1X_1 + \beta_2X_2 + ... + \beta_kX_k)}} ]

where ( P(Y=1 | X) ) is the probability of the outcome occurring, ( e ) is the base of the natural logarithm, and ( \beta ) values represent the coefficients estimated from the data.

Using a linear function would not be suitable here since it can produce probabilities outside the [0,1] range, which is not meaningful in the context of probability. The exponential function does appear in the formula for logistic regression, but it is part of the composite logistic function rather than a model on its own. A quadratic function typically indicates a parabolic relationship