ISYE 6414 - UNIT 4, ISYE 6414 - UNIT 5 EXAM 2024 WITH 100 PERCENT ACCURATE SOLUTIONS
Logistic regression, we model the__________________, not the response variable, given the predicting variables. - Precise Answer ✔✔probability of a success
g link function - Precise Answer ✔✔link the probability of success to the predicting variables
3 assumptions of the logistic regression model - Precise Answer ✔✔Linearity, Independence, Logit link function
Logistic Model: Linearity assumption - Precise 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 - Precise 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 - Precise Answer ✔✔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 - Precise Answer ✔✔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 - Precise Answer ✔✔to the odds of success
Estimate the model parameters method - Precise 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. - Precise Answer ✔✔D
Logistic regression models the probability of a success given a set of predicting variables. - Precise Answer ✔✔True Logistic regression: Using the R statistical software to fit - Precise Answer ✔✔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 - Precise Answer ✔✔maximum likelihood estimation
MLE: Using MLE, can we derive estimated coefficients/parameters in exact form? - Precise Answer ✔✔No, they are approximate estimated parameters
MLE : The sampling distribution of MLEs can be approximated by a - Precise Answer ✔✔normal distribution
Betaj: What can we use to test if Betaj is = 0? - Precise Answer ✔✔z test (wald test)
Z test: When would we reject the null hypothesis for a z test? - Precise 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.
Logistic regression: Does the statistical inference for logistic regression rely on a small or large sample size? - Precise Answer ✔✔Large, if it was
a small then the statistical inference is not reliable Deviance - Precise 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
Deviance: Under testing a subset of coefficients, what is the distribution
and degrees of freedom for the deviance? - Precise 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.
Subset: What is the purpose of testing a subset of coefficients? - Precise
Answer ✔✔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? - Precise Answer ✔✔No
Logistic model: When we are testing for overall regression for a Logistic model, what is the H0 and HA? - Precise Answer ✔✔H0: all regression coefficients except intercept are 0 HA: at least one is not 0.
Logistic regression, we model the__________________, not the response variable, given the predicting variables. - Precise Answer ✔✔probability of a success
g link function - Precise Answer ✔✔link the probability of success to the predicting variables
3 assumptions of the logistic regression model - Precise Answer ✔✔Linearity, Independence, Logit link function
Logistic Model: Linearity assumption - Precise 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 - Precise 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 - Precise Answer ✔✔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 - Precise Answer ✔✔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 - Precise Answer ✔✔to the odds of success
Estimate the model parameters method - Precise 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. - Precise Answer ✔✔D
Logistic regression models the probability of a success given a set of predicting variables. - Precise Answer ✔✔True Logistic regression: Using the R statistical software to fit - Precise Answer ✔✔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 - Precise Answer ✔✔maximum likelihood estimation
MLE: Using MLE, can we derive estimated coefficients/parameters in exact form? - Precise Answer ✔✔No, they are approximate estimated parameters
MLE : The sampling distribution of MLEs can be approximated by a - Precise Answer ✔✔normal distribution
Betaj: What can we use to test if Betaj is = 0? - Precise Answer ✔✔z test (wald test)
Z test: When would we reject the null hypothesis for a z test? - Precise 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.
Logistic regression: Does the statistical inference for logistic regression rely on a small or large sample size? - Precise Answer ✔✔Large, if it was
a small then the statistical inference is not reliable Deviance - Precise 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
Deviance: Under testing a subset of coefficients, what is the distribution
and degrees of freedom for the deviance? - Precise 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.
Subset: What is the purpose of testing a subset of coefficients? - Precise
Answer ✔✔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? - Precise Answer ✔✔No
Logistic model: When we are testing for overall regression for a Logistic model, what is the H0 and HA? - Precise Answer ✔✔H0: all regression coefficients except intercept are 0 HA: at least one is not 0.
