ISYE 6414 - Unit 4 || with Errorless Solutions 100%.
In logistic regression, we model the__________________, not the response variable, given the
predicting variables. correct answers probability of a success
g link function correct answers link the probability of success to the predicting variables
3 assumptions of the logistic regression model correct answers Linearity, Independence, Logit
link function
Linearity assumption for a Logistic Model correct answers Similar to the regression model we
have learned in the previous lectures, the relationship we assume now, between the link, the g of
the probability of success and the predicted variable, is a linear function.
Logit link function assumption correct answers The logistic regression model assumes that the
link function is a so-called logit function. This is an assumption since the logit function is not the
only function that yields s-shaped curves. And it would seem that there is no reason to prefer the
logit to other possible choices.
Log odds function correct answers The logit function which is the log of the ratio between the
probability of a success and the probability of a failure
What is the interpretation of coefficient Beta in terms of logistic regression? correct answers the
log of the odds ratio for an increase of one unit in the predicting variable, holding all other
variables constant
We interpret the beta in a logistic regression model in respect to? correct answers to the odds of
success
What method do we use to estimate the model parameters? correct answers Maximum
Likelihood Estimation approach
Logistic regression is different from standard linear regression in that:
A) It does not have an error term
B) The response variable is not normally distributed.
C) It models probability of a response and not the expectation of the response.
D) All of the above. correct answers D
Which one is correct?
A) The logit link function is the only link function that can be used for modeling binary response
data.
B) Logistic regression models the probability of a success given a set of predicting variables.
C) The interpretation of the regression coefficients in logistic regression is the same as for
standard linear regression assuming normality.
D) None of the above. correct answers B
, In logistic regression,
A) The estimation of the regression coefficients is based on maximum likelihood estimation.
B) We can derive exact (close form expression) estimates for the regression coefficients.
C) The estimations of the regression coefficients is based on minimizing the sum of least
squares.
D) All of the above. correct answers A
Using the R statistical software to fit a logistic regression,
A) We can use the lm() command.
B) The input of the response variable is exactly the same if the binary response data are with or
without replications.
C) We can obtain both the estimates and the standard deviations of the estimates for the
regression coefficients.
D) None of the above. correct answers C
Using MLE, can we derive estimated coefficients/parameters in exact form? correct answers No,
they are approximate estimated parameters
The sampling distribution of MLEs can be approximated by a... correct answers normal
distribution
What can we use to test if Betaj is = 0? correct answers z test (wald test)
When would we reject the null hypothesis for a z test? correct answers We reject the null
hypothesis that the regression coefficient is 0 if the z value is larger in absolute value than the z
critical point. Or the 1- alpha over 2 normal quanta. We interpret this that the coefficient is
statistically significant.
Does the statistical inference for logistic regression rely on a small or large sample size? correct
answers Large, if it was a small then the statistical inference is not reliable
Deviance correct answers the test statistic is the difference of the log likelihood under the
reduced model and the log likelihood under the full model for testing the subset of coefficients
Under testing a subset of coefficients, what is the distribution and degrees of freedom for the
deviance? correct answers For large sample size data, the distribution of this test statistic,
assuming the null hypothesis is true, is a chi square distribution. With Q degrees of freedom
where Q is the number of regression coefficients discarded from the full model to get the reduced
model or the number of Z predicting variables.
What is the purpose of testing a subset of coefficients? correct answers It simply compares two
models and decides whether the larger model is statistically significantly better than the reduced
model.
Is testing a subset of coefficients a GOF test? correct answers No
In logistic regression, we model the__________________, not the response variable, given the
predicting variables. correct answers probability of a success
g link function correct answers link the probability of success to the predicting variables
3 assumptions of the logistic regression model correct answers Linearity, Independence, Logit
link function
Linearity assumption for a Logistic Model correct answers Similar to the regression model we
have learned in the previous lectures, the relationship we assume now, between the link, the g of
the probability of success and the predicted variable, is a linear function.
Logit link function assumption correct answers The logistic regression model assumes that the
link function is a so-called logit function. This is an assumption since the logit function is not the
only function that yields s-shaped curves. And it would seem that there is no reason to prefer the
logit to other possible choices.
Log odds function correct answers The logit function which is the log of the ratio between the
probability of a success and the probability of a failure
What is the interpretation of coefficient Beta in terms of logistic regression? correct answers the
log of the odds ratio for an increase of one unit in the predicting variable, holding all other
variables constant
We interpret the beta in a logistic regression model in respect to? correct answers to the odds of
success
What method do we use to estimate the model parameters? correct answers Maximum
Likelihood Estimation approach
Logistic regression is different from standard linear regression in that:
A) It does not have an error term
B) The response variable is not normally distributed.
C) It models probability of a response and not the expectation of the response.
D) All of the above. correct answers D
Which one is correct?
A) The logit link function is the only link function that can be used for modeling binary response
data.
B) Logistic regression models the probability of a success given a set of predicting variables.
C) The interpretation of the regression coefficients in logistic regression is the same as for
standard linear regression assuming normality.
D) None of the above. correct answers B
, In logistic regression,
A) The estimation of the regression coefficients is based on maximum likelihood estimation.
B) We can derive exact (close form expression) estimates for the regression coefficients.
C) The estimations of the regression coefficients is based on minimizing the sum of least
squares.
D) All of the above. correct answers A
Using the R statistical software to fit a logistic regression,
A) We can use the lm() command.
B) The input of the response variable is exactly the same if the binary response data are with or
without replications.
C) We can obtain both the estimates and the standard deviations of the estimates for the
regression coefficients.
D) None of the above. correct answers C
Using MLE, can we derive estimated coefficients/parameters in exact form? correct answers No,
they are approximate estimated parameters
The sampling distribution of MLEs can be approximated by a... correct answers normal
distribution
What can we use to test if Betaj is = 0? correct answers z test (wald test)
When would we reject the null hypothesis for a z test? correct answers We reject the null
hypothesis that the regression coefficient is 0 if the z value is larger in absolute value than the z
critical point. Or the 1- alpha over 2 normal quanta. We interpret this that the coefficient is
statistically significant.
Does the statistical inference for logistic regression rely on a small or large sample size? correct
answers Large, if it was a small then the statistical inference is not reliable
Deviance correct answers the test statistic is the difference of the log likelihood under the
reduced model and the log likelihood under the full model for testing the subset of coefficients
Under testing a subset of coefficients, what is the distribution and degrees of freedom for the
deviance? correct answers For large sample size data, the distribution of this test statistic,
assuming the null hypothesis is true, is a chi square distribution. With Q degrees of freedom
where Q is the number of regression coefficients discarded from the full model to get the reduced
model or the number of Z predicting variables.
What is the purpose of testing a subset of coefficients? correct answers It simply compares two
models and decides whether the larger model is statistically significantly better than the reduced
model.
Is testing a subset of coefficients a GOF test? correct answers No
