Module 3 ISYE-6414 Revision
Assignment Questions Fully
Answered Rated A+.
Logistic regression use - Answer 3.1) Modeling binary response data
What are some examples of a binary response? - Answer 3.1) Zero or one, yes or no, winter or
summer, small or big, leave or not leave.
Are binary variables normally distributed? - Answer 3.1) No. This is unlike linear regression
where the assumption is that the error terms are normally distributed with mean zero.
Why can't we apply the linear regression model to logistic regression? - Answer 3.1) Because
logistic regression does not have the normality assumption.
What are we modeling in logistic regression? - Answer 3.1) The probability of success, given
the predicting variables.
What model is used to model s-shaped probability curves? - Answer 3.1) Logistic regression is
commonly used to model s-shaped patterns for explaining binary response data.
What is the g function? - Answer 3.1) The g function is the s-shape function that models the
probability of a success with respect to the predicting variables.
What is the g link function? - Answer 3.1) We link the probability of success to the predicting
variables using the g link function, in a way that this g function of the probability of success is a
linear model of the predicting variables.
In a logistic regression model do we have an error term? - Answer 3.1) No, we do not have an
error term in logistic regression.
What are the logistic regression model assumptions? - Answer 3.1) Assumption 1 is the
linearity of the link function of the probability of a success in the predicted variables, that is we
write the g function of the probability of a success as a linear combination of the predicting
,Assumption 2, the response data are independent random variables (Independence)
Assumption 3 assumes that the link function is the so-called logit function. This is an
assumption since the logit function is not the only function that yields s-shaped curves.
g(p) = ln[p/(1-p)]
What kind of transformation is the g link function? - Answer 3.1) It is a non-linear
transformation of the probability of success or of the expectation of the response variable.
What is the equation for the logit link function? - Answer 3.1) g(p) = ln[p/(1-p)] where p is the
probability of success.
Are there other functions that are s-shaped and used in modeling binary responses? - Answer
3.1) Yes. And this is done under a more general framework called binomial model.
What is the probability of success given predictors model for logistic regression? - Answer 3.2)
p(X1,...,Xp) = e^(B0+B1X1+...+BpXp)/(1+e^(B0+B1X1+...+BpXp)
OR by linking p = Pr(Y = 1 | X1,...,Xp) to the logit link function g(p)=ln[p/(1-p)] = B0 + B1X1 + ... +
BpXp
What is the model that generalizes linear regression when the response variable y is binary or
binomial? - Answer 3.2) Logistic regression
What is the objective of the model where Yi takes 0 or one values (thus binary) and we want to
relate OR regress Y onto some predicting variables? - Answer 3.2) The objective of the model
is to estimate the probability of a success given the predicting variables.
True or False: The probability of success using the logit link function is not the same as the
probability of success equal to the ratio between the exponential of the linear combination of
the predicting variables over 1 plus the same exponential. - Answer 3.2) False.
g(p) = ln[p/(1-p) and
, What is the probability of success given one predicting variable X = x? - Answer 3.2) p = p(x) =
Pr(Y = 1 | x)
What is the logit function given one predicting variable X = x? - Answer 3.2) It is the log odds
function, ln[p/(1-p)] = B0 + B1x
What is the exponential of the logit function given one predicting variable X = x? - Answer 3.2)
p(X) / [1-p(X)] = e^(B0 + B1x) and is the ODDS of Y = 1 at X = x.
What is the odds ratio (or X = a vs. X = b)? - Answer 3.2) e^(B0 + B1a)/e^(B0 + B1b) = e^[B1(a-
b)]
What is the log odds function? - Answer 3.2) It is the log of the ratio between probability of a
success and the probability of a failure (so, the ratio between the log of P over 1 - p).
What is the odds ratio? - Answer 3.2) Comparing odds for two different values of the
predicting variable. Can also be worded as the ratio of the odds of the response given A vs. the
odds of the response given B.
What is the interpretation of the odds ratio at X = b + 1 vs. X = b? - Answer 3.2)
e^[B0+B1(b+1)]/e^(B0+B1b) = e^B1
The regression coefficient B1 can be interpreted as the log of the odds ratio for an increase of
one unit in the predicting variable.
If X is a dummy variable of a categorical factor, interpret as the log of odds ratio of one category
vs. the baseline
Interpret B with respect to the odds of success, not directly with respect to the response
variable.
What does the odds ratio of e^B1 say? - Answer 3.2) The odds ratio is equal to exponential of
the coefficient beta, or that the log of the odds ratio is equal to the coefficients. Thus, we
interpret the regression coefficient beta as the log of the odds ratio for an increase of one unit
in the predicting variable.
Assignment Questions Fully
Answered Rated A+.
Logistic regression use - Answer 3.1) Modeling binary response data
What are some examples of a binary response? - Answer 3.1) Zero or one, yes or no, winter or
summer, small or big, leave or not leave.
Are binary variables normally distributed? - Answer 3.1) No. This is unlike linear regression
where the assumption is that the error terms are normally distributed with mean zero.
Why can't we apply the linear regression model to logistic regression? - Answer 3.1) Because
logistic regression does not have the normality assumption.
What are we modeling in logistic regression? - Answer 3.1) The probability of success, given
the predicting variables.
What model is used to model s-shaped probability curves? - Answer 3.1) Logistic regression is
commonly used to model s-shaped patterns for explaining binary response data.
What is the g function? - Answer 3.1) The g function is the s-shape function that models the
probability of a success with respect to the predicting variables.
What is the g link function? - Answer 3.1) We link the probability of success to the predicting
variables using the g link function, in a way that this g function of the probability of success is a
linear model of the predicting variables.
In a logistic regression model do we have an error term? - Answer 3.1) No, we do not have an
error term in logistic regression.
What are the logistic regression model assumptions? - Answer 3.1) Assumption 1 is the
linearity of the link function of the probability of a success in the predicted variables, that is we
write the g function of the probability of a success as a linear combination of the predicting
,Assumption 2, the response data are independent random variables (Independence)
Assumption 3 assumes that the link function is the so-called logit function. This is an
assumption since the logit function is not the only function that yields s-shaped curves.
g(p) = ln[p/(1-p)]
What kind of transformation is the g link function? - Answer 3.1) It is a non-linear
transformation of the probability of success or of the expectation of the response variable.
What is the equation for the logit link function? - Answer 3.1) g(p) = ln[p/(1-p)] where p is the
probability of success.
Are there other functions that are s-shaped and used in modeling binary responses? - Answer
3.1) Yes. And this is done under a more general framework called binomial model.
What is the probability of success given predictors model for logistic regression? - Answer 3.2)
p(X1,...,Xp) = e^(B0+B1X1+...+BpXp)/(1+e^(B0+B1X1+...+BpXp)
OR by linking p = Pr(Y = 1 | X1,...,Xp) to the logit link function g(p)=ln[p/(1-p)] = B0 + B1X1 + ... +
BpXp
What is the model that generalizes linear regression when the response variable y is binary or
binomial? - Answer 3.2) Logistic regression
What is the objective of the model where Yi takes 0 or one values (thus binary) and we want to
relate OR regress Y onto some predicting variables? - Answer 3.2) The objective of the model
is to estimate the probability of a success given the predicting variables.
True or False: The probability of success using the logit link function is not the same as the
probability of success equal to the ratio between the exponential of the linear combination of
the predicting variables over 1 plus the same exponential. - Answer 3.2) False.
g(p) = ln[p/(1-p) and
, What is the probability of success given one predicting variable X = x? - Answer 3.2) p = p(x) =
Pr(Y = 1 | x)
What is the logit function given one predicting variable X = x? - Answer 3.2) It is the log odds
function, ln[p/(1-p)] = B0 + B1x
What is the exponential of the logit function given one predicting variable X = x? - Answer 3.2)
p(X) / [1-p(X)] = e^(B0 + B1x) and is the ODDS of Y = 1 at X = x.
What is the odds ratio (or X = a vs. X = b)? - Answer 3.2) e^(B0 + B1a)/e^(B0 + B1b) = e^[B1(a-
b)]
What is the log odds function? - Answer 3.2) It is the log of the ratio between probability of a
success and the probability of a failure (so, the ratio between the log of P over 1 - p).
What is the odds ratio? - Answer 3.2) Comparing odds for two different values of the
predicting variable. Can also be worded as the ratio of the odds of the response given A vs. the
odds of the response given B.
What is the interpretation of the odds ratio at X = b + 1 vs. X = b? - Answer 3.2)
e^[B0+B1(b+1)]/e^(B0+B1b) = e^B1
The regression coefficient B1 can be interpreted as the log of the odds ratio for an increase of
one unit in the predicting variable.
If X is a dummy variable of a categorical factor, interpret as the log of odds ratio of one category
vs. the baseline
Interpret B with respect to the odds of success, not directly with respect to the response
variable.
What does the odds ratio of e^B1 say? - Answer 3.2) The odds ratio is equal to exponential of
the coefficient beta, or that the log of the odds ratio is equal to the coefficients. Thus, we
interpret the regression coefficient beta as the log of the odds ratio for an increase of one unit
in the predicting variable.
