In logistic regression, the relationship between the probability of success and the predicting variables is nonlinear. - ANS TRUE: The equation that links the predictors to the probability is:
ISYE 6414 - Unit 4, ISYE 6414 - Unit 5
Exam Questions And Answers
Logistic regression, we model the__________________, not the response variable, given the
predicting variables. - ANS probability of a success
g link function - ANS link the probability of success to the predicting variables
3 assumptions of the logistic regression model - ANS Linearity, Independence, Logit link
function
Logistic Model: Linearity assumption - ANS 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 - ANS 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 - ANS The logit function which is the log of the ratio between the
probability of a success and the probability of a failure
Logistic regression: interpretation of coefficient Beta in terms of - ANS the log of the odds
ratio for an increase of one unit in the predicting variable, holding all other variables constant
Logistic regression: We interpret the beta in a model in respect to - ANS to the odds of
success
Estimate the model parameters method - ANS 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. - ANS D
, Logistic regression models the probability of a success given a set of predicting variables. - ANS
True
Logistic regression: Using the R statistical software to fit - ANS We can obtain both the
estimates and the standard deviations of the estimates for the regression coefficients.
Logistic regression: The estimation of the regression coefficients is based on - ANS
maximum likelihood estimation
MLE: Using MLE, can we derive estimated coefficients/parameters in exact form? - ANS
No, they are approximate estimated parameters
MLE : The sampling distribution of MLEs can be approximated by a - ANS normal
distribution
Betaj: What can we use to test if Betaj is = 0? - ANS z test (wald test)
Z test: When would we reject the null hypothesis for a z test? - ANS 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.
Logistic regression: Does the statistical inference for logistic regression rely on a small or large
sample size? - ANS Large, if it was a small then the statistical inference is not reliable
Deviance - ANS 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
Deviance: Under testing a subset of coefficients, what is the distribution and degrees of freedom
for the deviance? - ANS 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.
Subset: What is the purpose of testing a subset of coefficients? - ANS It simply compares
two models and decides whether the larger model is statistically significantly better than the
reduced model.
Subset: Is testing a subset of coefficients a GOF test? - ANS No
Logistic model: When we are testing for overall regression for a Logistic model, what is the H0
and HA? - ANS H0: all regression coefficients except intercept are 0
HA: at least one is not 0.
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