ISYE 6414 CORRECT TEST PAPER QUESTIONS AND
ANSWERS SURE A+
✔✔When would we reject the null hypothesis for a z test? - ✔✔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? - ✔✔Large, if it was a small then the statistical inference is not reliable
✔✔Deviance - ✔✔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? - ✔✔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? - ✔✔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? - ✔✔No
✔✔When we are testing for overall regression for a Logistic model, what is the H0 and
HA? - ✔✔H0: all regression coefficients except intercept are 0
HA: at least one is not 0.
, ✔✔If we reject the null hypothesis for overall regression, what does that mean -
✔✔Meaning that the overall regression has statistically significant power in explaining
the response variable.
✔✔Null-deviance - ✔✔Test statistic for Overall Regression, shows how well the
response variable is predicted by a model that includes only the intercept.
✔✔What is the distribution and DOF of overall regression test statistic? - ✔✔chi-
squared with p degrees of freedom where p is the number of predicting variables.
✔✔When do we reject the null hypothesis for the overall regression test in regards to
the p value? - ✔✔when the P-value is small, indicating that the overall regression has
explanatory power.
✔✔Logistic regression is different from standard linear regression in that:
A) The sampling distribution of the regression coefficient is approximate.
B) A large sample data is requirded for making accurate statistical inferences.
C) A normal sampling distribution is used instead of a t-distribution for statistical
inference.
D) All of the above. - ✔✔D
✔✔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. - ✔✔B
✔✔In logistic regression, how do we define residuals for evaluating g-o-f? - ✔✔binary
data with replications.
✔✔What is the distribution of binary data WITHOUT replications? - ✔✔a binomial
distribution with one trial where ni = 1
✔✔What is the distribution of binary data WITH replications? - ✔✔binomial distribution
with more than one trial or ni greater than 1
✔✔Pearson Residuals - ✔✔as the standardized difference between the ith observed
response and estimated expected response, which is ni times the probability of
success.
✔✔Deviance residuals - ✔✔the signed square root of the log-likelihood evaluated at the
saturated model when we assume that the estimate expected response is the observed
response versus the fitted model.
ANSWERS SURE A+
✔✔When would we reject the null hypothesis for a z test? - ✔✔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? - ✔✔Large, if it was a small then the statistical inference is not reliable
✔✔Deviance - ✔✔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? - ✔✔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? - ✔✔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? - ✔✔No
✔✔When we are testing for overall regression for a Logistic model, what is the H0 and
HA? - ✔✔H0: all regression coefficients except intercept are 0
HA: at least one is not 0.
, ✔✔If we reject the null hypothesis for overall regression, what does that mean -
✔✔Meaning that the overall regression has statistically significant power in explaining
the response variable.
✔✔Null-deviance - ✔✔Test statistic for Overall Regression, shows how well the
response variable is predicted by a model that includes only the intercept.
✔✔What is the distribution and DOF of overall regression test statistic? - ✔✔chi-
squared with p degrees of freedom where p is the number of predicting variables.
✔✔When do we reject the null hypothesis for the overall regression test in regards to
the p value? - ✔✔when the P-value is small, indicating that the overall regression has
explanatory power.
✔✔Logistic regression is different from standard linear regression in that:
A) The sampling distribution of the regression coefficient is approximate.
B) A large sample data is requirded for making accurate statistical inferences.
C) A normal sampling distribution is used instead of a t-distribution for statistical
inference.
D) All of the above. - ✔✔D
✔✔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. - ✔✔B
✔✔In logistic regression, how do we define residuals for evaluating g-o-f? - ✔✔binary
data with replications.
✔✔What is the distribution of binary data WITHOUT replications? - ✔✔a binomial
distribution with one trial where ni = 1
✔✔What is the distribution of binary data WITH replications? - ✔✔binomial distribution
with more than one trial or ni greater than 1
✔✔Pearson Residuals - ✔✔as the standardized difference between the ith observed
response and estimated expected response, which is ni times the probability of
success.
✔✔Deviance residuals - ✔✔the signed square root of the log-likelihood evaluated at the
saturated model when we assume that the estimate expected response is the observed
response versus the fitted model.
