ISYE 6414 Final Exam questions and
answers
In Logistic Regression, the relationship between the probability of success and the predicting variables
is non-linear. - ANSWER-True - The relationship that links the predictors is highly non-linear.
In Logistic Regression, the error terms follow a normal distribution. - ANSWER-False - In logistic
regression, there are no error terms.
The logit function is the log of the ratio of the probability of success to the probability of failure and is
also known as the log-odds function. - ANSWER-True - the logit function is also known as the log-odds
function, which is the ln(P/1-p).
The number of parameters that need to be estimated in a logistic regression model with 6 predicting
variables and an intercept is the same as the number of parameters that need to be estimated in a
standard linear regression model with an intercept and same predicting variables. - ANSWER-False -
As there is no error term in logistic regression, there is no additional parameter for the variance of the
error terms.
The log-likelihood function is a linear function with a closed form solution. - ANSWER-False - log-
likelihood is a non-linear function, and a numerical algorithm is needed in order to maximize it.
In Logistic Regression, the estimated value for a regression coefficient B represents the estimated
expected change in the response variable associated with a one unit increase in the predicting
variable, holding all else fixed. - ANSWER-False - We interpret logistic regression coefficients with
respect to the odds of success.
Under logistic regression, the sampling distribution used for a coefficient estimator is a chi-square
distribution when the sample size is large. - ANSWER-False - The coefficient estimator follows an
approximate normal distribution.
When testing a subset of coefficients, deviance follows a chi-square distribution with q degrees of
freedom, where q is the number of regression coefficients in the reduced model. - ANSWER-False -
when testing a subset of coefficients, deviance follows 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.
Logistic regression deals with the case where the dependent variable is binary and the conditional
distribution is binomial. - ANSWER-True - logistic regression is the generalization of the standard
regression model that is used when the response variable y is binary or binomial.
It is good practice to perform a goodness-of-fit test on logistic regression models without replications.
- ANSWER-False - The residuals can only be defined for logistic regression with replications.
In Logistic regression, if the p-value of the deviance test for GOF is smaller than the significance level
alpha, then is is plausible that the model is a good fit. - ANSWER-False - for logistic regression, if the p-
value of the deviance test for GOD is large, then the model is a good fit.
If a logistic regression model provides accurate classification, then we can conclude that it is a good fir
for the data. - ANSWER-False - GOF is no guarantee for good prediction and vice-versa.
, For both logistic regression and Poisson regression, the deviance residuals should follow an
approximate standard normal distribution if the model is a good fit for the data. - ANSWER-True - the
deviance residuals are approximately N(0,1) if the model is a good fit to the data.
The logit link function is the best link function to model binary response data because it always fits
the data better than other link functions. - ANSWER-False
Although there are no error terms in logistic regression model using binary data with replications, we
can still perform residual analysis. - ANSWER-True - we can use the Pearson or deviance residuals, but
only if the model has replications.
For a classification model, the training error tends to underestimate the true classification error rate
of the model. - ANSWER-True - The error rate is biased downwards, since the model sees the data 2
times, once for training and once for testing.
The estimated regression coefficients in Poisson regression are approximate. - ANSWER-True - the
parameters and their standard errors are approximate.
A t-test is used for testing the statistical significance of a coefficient given all predicting variables in a
Poisson regression model. - ANSWER-False - we use a z-test, since the the distributions are
approximately normal with large N.
An overdispersion parameter of 1 indicates that the variability of the response is close to the
variability estimated by the model. - ANSWER-True
In Poisson regression, we assume a non linear relationship between the log rate and the predicting
variables. - ANSWER-False - we assume that the log rate is a linear combination of the predicting
variables, hence Poisson regression is a generalized linear model (GLM)
Logistic regression models the probability of a success given a set of predicting variables. - ANSWER-
True
The estimation of logistic regression coefficients is based on maximum likelihood. - ANSWER-True
What are the differences between logistic regression and standard regression. - ANSWER-1) no error
term
2) the response variable is not normally distributes (binomial)
3) it models probability, not expectation of response
The logit link function is the only link function that can be used for modeling binary response data. -
ANSWER-False - Come back and name other link functions
The interpretation of the regression coefficients is the same in logistic regression as standard
regression. - ANSWER-False - logistic regression coefficients are interpreted with respect to odds
We can derive exact estimates for the logistic regression coefficients. - ANSWER-False - there is no
closed form solution, we we use a numerical approximation.
The estimations of the regression coefficients is based on minimizing the sum of least squares in
logistic regression. - ANSWER-False - fill in later
Differences between logistic regression and linear regression - statistical inference. - ANSWER-1) The
sampling distribution of the regression coefficients is approximate
2) a large sample size is required for making accurate statistical inferences
3) a normal sampling distribution is used instead of a t-distribution for statistical inference
answers
In Logistic Regression, the relationship between the probability of success and the predicting variables
is non-linear. - ANSWER-True - The relationship that links the predictors is highly non-linear.
In Logistic Regression, the error terms follow a normal distribution. - ANSWER-False - In logistic
regression, there are no error terms.
The logit function is the log of the ratio of the probability of success to the probability of failure and is
also known as the log-odds function. - ANSWER-True - the logit function is also known as the log-odds
function, which is the ln(P/1-p).
The number of parameters that need to be estimated in a logistic regression model with 6 predicting
variables and an intercept is the same as the number of parameters that need to be estimated in a
standard linear regression model with an intercept and same predicting variables. - ANSWER-False -
As there is no error term in logistic regression, there is no additional parameter for the variance of the
error terms.
The log-likelihood function is a linear function with a closed form solution. - ANSWER-False - log-
likelihood is a non-linear function, and a numerical algorithm is needed in order to maximize it.
In Logistic Regression, the estimated value for a regression coefficient B represents the estimated
expected change in the response variable associated with a one unit increase in the predicting
variable, holding all else fixed. - ANSWER-False - We interpret logistic regression coefficients with
respect to the odds of success.
Under logistic regression, the sampling distribution used for a coefficient estimator is a chi-square
distribution when the sample size is large. - ANSWER-False - The coefficient estimator follows an
approximate normal distribution.
When testing a subset of coefficients, deviance follows a chi-square distribution with q degrees of
freedom, where q is the number of regression coefficients in the reduced model. - ANSWER-False -
when testing a subset of coefficients, deviance follows 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.
Logistic regression deals with the case where the dependent variable is binary and the conditional
distribution is binomial. - ANSWER-True - logistic regression is the generalization of the standard
regression model that is used when the response variable y is binary or binomial.
It is good practice to perform a goodness-of-fit test on logistic regression models without replications.
- ANSWER-False - The residuals can only be defined for logistic regression with replications.
In Logistic regression, if the p-value of the deviance test for GOF is smaller than the significance level
alpha, then is is plausible that the model is a good fit. - ANSWER-False - for logistic regression, if the p-
value of the deviance test for GOD is large, then the model is a good fit.
If a logistic regression model provides accurate classification, then we can conclude that it is a good fir
for the data. - ANSWER-False - GOF is no guarantee for good prediction and vice-versa.
, For both logistic regression and Poisson regression, the deviance residuals should follow an
approximate standard normal distribution if the model is a good fit for the data. - ANSWER-True - the
deviance residuals are approximately N(0,1) if the model is a good fit to the data.
The logit link function is the best link function to model binary response data because it always fits
the data better than other link functions. - ANSWER-False
Although there are no error terms in logistic regression model using binary data with replications, we
can still perform residual analysis. - ANSWER-True - we can use the Pearson or deviance residuals, but
only if the model has replications.
For a classification model, the training error tends to underestimate the true classification error rate
of the model. - ANSWER-True - The error rate is biased downwards, since the model sees the data 2
times, once for training and once for testing.
The estimated regression coefficients in Poisson regression are approximate. - ANSWER-True - the
parameters and their standard errors are approximate.
A t-test is used for testing the statistical significance of a coefficient given all predicting variables in a
Poisson regression model. - ANSWER-False - we use a z-test, since the the distributions are
approximately normal with large N.
An overdispersion parameter of 1 indicates that the variability of the response is close to the
variability estimated by the model. - ANSWER-True
In Poisson regression, we assume a non linear relationship between the log rate and the predicting
variables. - ANSWER-False - we assume that the log rate is a linear combination of the predicting
variables, hence Poisson regression is a generalized linear model (GLM)
Logistic regression models the probability of a success given a set of predicting variables. - ANSWER-
True
The estimation of logistic regression coefficients is based on maximum likelihood. - ANSWER-True
What are the differences between logistic regression and standard regression. - ANSWER-1) no error
term
2) the response variable is not normally distributes (binomial)
3) it models probability, not expectation of response
The logit link function is the only link function that can be used for modeling binary response data. -
ANSWER-False - Come back and name other link functions
The interpretation of the regression coefficients is the same in logistic regression as standard
regression. - ANSWER-False - logistic regression coefficients are interpreted with respect to odds
We can derive exact estimates for the logistic regression coefficients. - ANSWER-False - there is no
closed form solution, we we use a numerical approximation.
The estimations of the regression coefficients is based on minimizing the sum of least squares in
logistic regression. - ANSWER-False - fill in later
Differences between logistic regression and linear regression - statistical inference. - ANSWER-1) The
sampling distribution of the regression coefficients is approximate
2) a large sample size is required for making accurate statistical inferences
3) a normal sampling distribution is used instead of a t-distribution for statistical inference
