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ISYE 6414 - Unit 4 Study Guide | Verified and Updated

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ISYE 6414 - Unit 4 Study Guide | Verified and Updated In logistic regression, we model the__________________, not the response variable, given the predicting variables. - Answer-probability of a success g link function - Answer-link the probability of success to the predicting variables 3 assu...

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  • October 6, 2024
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ISYE 6414 - Unit 4 Study Guide | Verified
and Updated

In logistic regression, we model the__________________, not the response variable, given the

predicting variables. - Answer✔✔-probability of a success


g link function - Answer✔✔-link the probability of success to the predicting variables


3 assumptions of the logistic regression model - Answer✔✔-Linearity, Independence, Logit link function


Linearity assumption for a Logistic Model - Answer✔✔-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 - Answer✔✔-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 - Answer✔✔-The logit function which is the log of the ratio between the probability of

a success and the probability of a failure


What is the interpretation of coefficient Beta in terms of logistic regression? - Answer✔✔-the log of the

odds ratio for an increase of one unit in the predicting variable, holding all other variables constant


We interpret the beta in a logistic regression model in respect to? - Answer✔✔-to the odds of success


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What method do we use to estimate the model parameters? - Answer✔✔-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. - Answer✔✔-D


Which one is correct?


A) The logit link function is the only link function that can be used for modeling binary response data.


B) Logistic regression models the probability of a success given a set of predicting variables.


C) The interpretation of the regression coefficients in logistic regression is the same as for standard linear

regression assuming normality.


D) None of the above. - Answer✔✔-B


In logistic regression,


A) The estimation of the regression coefficients is based on maximum likelihood estimation.


B) We can derive exact (close form expression) estimates for the regression coefficients.


C) The estimations of the regression coefficients is based on minimizing the sum of least squares.


D) All of the above. - Answer✔✔-A



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Using the R statistical software to fit a logistic regression,


A) We can use the lm() command.


B) The input of the response variable is exactly the same if the binary response data are with or without

replications.


C) We can obtain both the estimates and the standard deviations of the estimates for the regression

coefficients.


D) None of the above. - Answer✔✔-C


Using MLE, can we derive estimated coefficients/parameters in exact form? - Answer✔✔-No, they are

approximate estimated parameters


The sampling distribution of MLEs can be approximated by a... - Answer✔✔-normal distribution


What can we use to test if Betaj is = 0? - Answer✔✔-z test (wald test)


When would we reject the null hypothesis for a z test? - Answer✔✔-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? - Answer✔✔-

Large, if it was a small then the statistical inference is not reliable


Deviance - Answer✔✔-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




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