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ISYE 6414 - Unit 4, ISYE 6414 -
Logistic regression, we model the__________________, not the response variable, given the predicting variables. correct answers probability of a success
g link function correct answers link the probability of success to the predicting variables
3 assumptions of the logistic regression model c...
ISYE 6414 - Unit 4, ISYE 6414 - Unit 5 || Already Passed.
Logistic regression, we model the__________________, not the response variable, given the
predicting variables. correct answers probability of a success
g link function correct answers link the probability of success to the predicting variables
3 assumptions of the logistic regression model correct answers Linearity, Independence, Logit
link function
Logistic Model: Linearity assumption correct answers 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 correct answers 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 correct answers 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 correct answers 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 correct answers to the odds of
success
Estimate the model parameters method correct answers 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. correct answers D
Logistic regression models the probability of a success given a set of predicting variables. correct
answers True
Logistic regression: Using the R statistical software to fit correct answers 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 correct answers
maximum likelihood estimation
, MLE: Using MLE, can we derive estimated coefficients/parameters in exact form? correct
answers No, they are approximate estimated parameters
MLE : The sampling distribution of MLEs can be approximated by a correct answers normal
distribution
Betaj: What can we use to test if Betaj is = 0? correct answers z test (wald test)
Z test: When would we reject the null hypothesis for a z test? correct answers 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? correct answers Large, if it was a small then the statistical inference is not reliable
Deviance correct answers 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? correct answers 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? correct answers 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? correct answers No
Logistic model: When we are testing for overall regression for a Logistic model, what is the H0
and HA? correct answers H0: all regression coefficients except intercept are 0
HA: at least one is not 0.
Null hypothesis: If we reject the null hypothesis for overall regression, what does that mean
correct answers Meaning that the overall regression has statistically significant power in
explaining the response variable.
Null-deviance correct answers Test statistic for Overall Regression, shows how well the response
variable is predicted by a model that includes only the intercept.
Distribution: What is the distribution and DOF of overall regression test statistic? correct
answers chi-squared with p degrees of freedom where p is the number of predicting variables.
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