ISYE 6414 - Unit 4 Questions And Answers With Verified Solutions

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 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 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 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. What is the purpose of testing a subset of coefficients? - Answer-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? - Answer-No When we are testing for overall regression for a Logistic model, what is the H0 and HA? - Answer-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 - Answer-Meaning that the overall regression has statistically significant power in explaining the response variable. Null-deviance - Answer-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? - Answer-chi-squared with p degrees of freedom where p is the number of predicting variables