ISYE 6414 CERTIFICATION SCRIPT 2026
QUESTIONS WITH SOLUTIONS GRADED A+
◍ True.
Answer: in Poisson regression, we model the log of the expected response
variable, not the expected log response variable.
◍ T/F: An approximate test can be used to test for the overall regression in
Poisson regression..
Answer: T
◍ True.
Answer: Logistic regression models the probability of a success given a set
of predicting variables.
◍ Cross validation.
Answer: Split the data into two parts, first part called the training data and
testing/validation data. The training data will be used to fit the model and
thus get the estimated regression coefficients. The testing or validation data
will be used to predict or classify the responses for this portion of the data,
then compare to the observed response to estimate the classification error,
one can repeat the process several times.
◍ Goodness of fit.
Answer: means that the model assumptions hold and fits the data well.
◍ In logistic regression, how do we define residuals for evaluating g-o-f?.
Answer: binary data with replications.
◍ T/F: When a Poisson regression does not fit well the data, it may that there
may be more variability in the estimators than provided by the model..
Answer: T
◍ True - the test for regression coefficients in Poisson regression follows a
, chi-square distribution with q degrees of freedom..
Answer: We use a chi-square testing procedure to test whether a subset of
regression coefficients are zero in Poisson regression.
◍ True.
Answer: An overdispersion parameter of 1 indicates that the variability of
the response is close to the variability estimated by the model.
◍ False - the shrinkage penalty is applied to all b1...BP, but not the intercept
B0..
Answer: In regularized regression, the penalization is generally applied to all
regression coefficients, where p = number of predictors.
◍ In logistic regression,A) The hypothesis test for subsets of coefficients is a
goodness of fit test.B) The hypothesis test for subsets of coefficients is
approximate; it relies on large sample size.C) We can use the partial F test
for testing whether a subset of coefficients are all zero.D) None of the
above..
Answer: B
◍ T/F: The estimated regression coefficients in Poisson regression are
approximate..
Answer: T
◍ False - there is no closed form solution, we we use a numerical
approximation..
Answer: We can derive exact estimates for the logistic regression
coefficients.
◍ we estimate the Poisson model parameters using....
Answer: MLE
◍ Under testing a subset of coefficients, what is the distribution and degrees of
freedom for the deviance?.
Answer: 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.
◍ Another GOF test is hypotheses testing, what is the H0 and HA?.
Answer: H0: is that the model fits well. HA: the alternative is that the model
does not fit well.
◍ What method do we use to estimate the model parameters?.
Answer: Maximum Likelihood Estimation approach
◍ Log odds function.
Answer: The logit function which is the log of the ratio between the
probability of a success and the probability of a failure
◍ True - we predict if a response will be a success or failure.
Answer: In logistic regression, prediction is a classification of a future
binary response.
◍ distribution of pearson residuals?.
Answer: From the binomial approximation with a normal distribution using
the central limit theorem
◍ Using MLE, can we derive estimated coefficients/parameters in exact form?.
Answer: No, they are approximate estimated parameters
◍ Under the null hypothesis of good fit, the test statistic's (sum of squared
deviances) distribution and DOF is...?.
Answer: Chi square with n-p-1 DF
◍ False - The coefficient estimator follows an approximate normal
distribution..
Answer: Under logistic regression, the sampling distribution used for a
coefficient estimator is a chi-square distribution when the sample size is
large.
◍ Which one is correct?A) The estimated regression coefficients and their
standard deviations are approximate not exact in Poisson regression.B) We
use the glm() R command to fit a Poisson linearregression.C) The
QUESTIONS WITH SOLUTIONS GRADED A+
◍ True.
Answer: in Poisson regression, we model the log of the expected response
variable, not the expected log response variable.
◍ T/F: An approximate test can be used to test for the overall regression in
Poisson regression..
Answer: T
◍ True.
Answer: Logistic regression models the probability of a success given a set
of predicting variables.
◍ Cross validation.
Answer: Split the data into two parts, first part called the training data and
testing/validation data. The training data will be used to fit the model and
thus get the estimated regression coefficients. The testing or validation data
will be used to predict or classify the responses for this portion of the data,
then compare to the observed response to estimate the classification error,
one can repeat the process several times.
◍ Goodness of fit.
Answer: means that the model assumptions hold and fits the data well.
◍ In logistic regression, how do we define residuals for evaluating g-o-f?.
Answer: binary data with replications.
◍ T/F: When a Poisson regression does not fit well the data, it may that there
may be more variability in the estimators than provided by the model..
Answer: T
◍ True - the test for regression coefficients in Poisson regression follows a
, chi-square distribution with q degrees of freedom..
Answer: We use a chi-square testing procedure to test whether a subset of
regression coefficients are zero in Poisson regression.
◍ True.
Answer: An overdispersion parameter of 1 indicates that the variability of
the response is close to the variability estimated by the model.
◍ False - the shrinkage penalty is applied to all b1...BP, but not the intercept
B0..
Answer: In regularized regression, the penalization is generally applied to all
regression coefficients, where p = number of predictors.
◍ In logistic regression,A) The hypothesis test for subsets of coefficients is a
goodness of fit test.B) The hypothesis test for subsets of coefficients is
approximate; it relies on large sample size.C) We can use the partial F test
for testing whether a subset of coefficients are all zero.D) None of the
above..
Answer: B
◍ T/F: The estimated regression coefficients in Poisson regression are
approximate..
Answer: T
◍ False - there is no closed form solution, we we use a numerical
approximation..
Answer: We can derive exact estimates for the logistic regression
coefficients.
◍ we estimate the Poisson model parameters using....
Answer: MLE
◍ Under testing a subset of coefficients, what is the distribution and degrees of
freedom for the deviance?.
Answer: 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.
◍ Another GOF test is hypotheses testing, what is the H0 and HA?.
Answer: H0: is that the model fits well. HA: the alternative is that the model
does not fit well.
◍ What method do we use to estimate the model parameters?.
Answer: Maximum Likelihood Estimation approach
◍ Log odds function.
Answer: The logit function which is the log of the ratio between the
probability of a success and the probability of a failure
◍ True - we predict if a response will be a success or failure.
Answer: In logistic regression, prediction is a classification of a future
binary response.
◍ distribution of pearson residuals?.
Answer: From the binomial approximation with a normal distribution using
the central limit theorem
◍ Using MLE, can we derive estimated coefficients/parameters in exact form?.
Answer: No, they are approximate estimated parameters
◍ Under the null hypothesis of good fit, the test statistic's (sum of squared
deviances) distribution and DOF is...?.
Answer: Chi square with n-p-1 DF
◍ False - The coefficient estimator follows an approximate normal
distribution..
Answer: Under logistic regression, the sampling distribution used for a
coefficient estimator is a chi-square distribution when the sample size is
large.
◍ Which one is correct?A) The estimated regression coefficients and their
standard deviations are approximate not exact in Poisson regression.B) We
use the glm() R command to fit a Poisson linearregression.C) The
