ISYE 6414 - Module 4 Questions and answers latest update

ISYE 6414 - Module 4

True/False: Logistic regression answers "Yes/No" type binary Questions.
True

Ex: Yes/No
True/False
Weak/Strong etc.,

In Logistic regression modeling, we model the __________
probability of yes.

What are the assumptions of a Linear Regression?
The assumptions are that the error terms are normally distributed with mean zero,
and constant variance, and that they are independent. The normality assumption
also implies that the response variable is normally distributed

Why can't we use Linear Regression to answer yes/no type questions?
Refer to the assumptions in the previous question above. The assumption is that
the response variable is normally distributed.

But for the Yes/No type questions, the response variable is a binary variable and it is not
normally distributed. So, we do not have a normality assumption. Thus we cannot apply
the Linear Regression models.

Logistic regression model is
One common model used to model s-shaped patterns for explaining binary
response data

,True/False: In logistic regression, (given the predicting variables) we model the
expectation of the response variable.
False.

Logistic regression does not model the expectation of the response variable. It models
the probability of a success.

In Logistic Regression, how the probability of success and the predicting variables are
linked?

using the g-link function.

In one way, the g-link function of the probability of success in logistic regression is a
________
linear model of the predicting variables.

What error terms the logistic regression model has?
The logistic regression. model does not have any error terms.

True/False: In logistic regression, the error terms are assumed to follow a normal
distribution.
False.

Logistic regression. model does not have any error terms.

True/False: The g function is the s-shape function that models the probability of a
success with respect to the predicting variables
True

What are the Logistic regression model's assumptions?
Linearity assumption - linearity of the g function of the probability of success
i.e., we write the g function as a linear combination of predicting variables.

Independence assumption - that the response variables are random variables and
independent of each other

, Third assumption (specific to logistic regression): The logistic regression model
assumes that the link function is the so-called logit function

How the "Linearity assumption" of logistic regression differs from that of Linear
Regression?
The linearity assumption in logistic regression refers to the linearity of the log-
odds of the dependent variable (also known as the logit) with respect to the
independent variables.

The g-link function is a non-linear transformation of the probability of success or
the expectation of the response variable.

True/False: Logit function is the only function that yields s-shaped curves.
False.

There are other s-shaped functions too that yield s-shaped curves. They are used in
modeling binary responses but they are under a more general framework called the
binomial model.

Logit link function formula
g(p) = ln (p/1-p)

the link function g is the log of (p divided by one minus p). where p = probability of
success.

The objective of the logistic regression model is to estimate the probability of a success
given the predicting variables.
True

The logit function g(p) = ln(p/1+p) can be rewritten as
the ration between the exponential of the linear combination of the predicting variables
over 1 plus the same exponential. This means,

p(x1,..,xp) =