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ISYE 6414 - Unit 4, ISYE 6414 - Unit 5 Exam Questions And Answers
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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...

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  • November 21, 2024
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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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