ISYE 6414 - Final Exam Questions and Answers 100% Graded A+!!
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ISYE 6414
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ISYE 6414
ISYE 6414 - Final Exam Questions and Answers 100% Graded A+!!
Logistic Regression - ANS Commonly used for modeling binary response data. The response variable is a binary variable, and thus, not normally distributed.
In logistic regression, we model the probability of a success, not the res...
ISYE 6414 - Final Exam Questions
and Answers 100% Graded A+!!
Logistic Regression - ANS Commonly used for modeling binary response data. The
response variable is a binary variable, and thus, not normally distributed.
In logistic regression, we model the probability of a success, not the response variable.
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In this model, we do not have an error term
g-function - ANS We link the probability of success to the predicting variables using
the g link function. The g function is the s-shape function that models the probability of
success with respect to the predicting variables
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The link function g is the log of the ratio of p over one minus p, where p again is the
probability of success
Logit function (log odds function) of the probability of success is a linear model in the
predicting variables
The probability of success is equal to the ratio between the exponential of the linear
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combination of the predicting variables over 1 plus this same exponential
Odds of a success - ANS This is the exponential of the Logit function
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Logistic Regression Assumptions - ANS Linearity: The relationship between the g of
the probability of success and the predicted variable, is a linear function.
Independence: The response binary variables are independently observed
Logit: The logistic regression model assumes that the link function g is a logit function
Linearity Assumption - ANS The Logit transformation of the probability of success is a
linear combination of the predicting variables. The relationship may not be linear,
however, and transformation may improve the fit
,The linearity assumption can be evaluated by plotting the logit of the success rate
versus the predicting variables.
If there's a curvature or some non-linear pattern, it may be an indication that the lack of
fit may be due to the non-linearity with respect to some of the predicting variables
Logistic Regression Coefficient - ANS We interpret the regression coefficient beta as
the log of the odds ratio for an increase of one unit in the predicting variable
We do not interpret beta with respect to the response variable but with respect to the
odds of success
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The estimators for the regression coefficients in logistic regression are unbiased and
thus the mean of the approximate normal distribution is beta. The variance of the
estimator does not have a closed form expression
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Model parameters - ANS The model parameters are the regression coefficients.
There is no additional parameter to model the variance since there's no error term.
For P predictors, we have P + 1 regression coefficients for a model with intercept (beta
0).
We estimate the model parameters using the maximum likelihood estimation approach
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Response variable - ANS The response data are Bernoulli or binomial with one trial
with probability of success
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MLE - ANS The resulting log-likelihood function to be maximized, is very complicated
and it is non-linear in the regression coefficients beta 0, beta 1, and beta p
MLE has good statistical properties under the assumption of a large sample size i.e.
large N
For large N, the sampling distribution of MLEs can be approximated by a normal
distribution
The least square estimation for the standard regression model is equivalent with MLE,
under the assumption of normality.
, MLE is the most applied estimation approach
Parameter estimation - ANS Maximizing the log likelihood function with respect to
beta0, beta1 etc in closed (exact) form expression is not possible because the log
likelihood function is a non-linear function in the model parameters i.e. we cannot derive
the estimated regression coefficients in an exact form
Use numerical algorithm to estimate betas (maximize the log likelihood function). The
estimated parameters and their standard errors are approximate estimates
Binomial Data - ANS This is binary data with repititions
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Marginal Relationship - ANS Capturing the association of a predicting variable to the
response variable without consideration of other factors
Conditional Relationship - ANS Capturing the association oof a predicting variable to
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the response variable conditional of other predicting variables in the model
Simpson's paradox - ANS This is when the addition of a predictive variable reverses
the sign on the coefficients of an existing parameter
It refers to reversal of an association when looking at a marginal relationship versus a
partial or conditional one. This is a situation where the marginal relationship adds a
wrong sign
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This happens when the 2 variables are correlated
Normal Distribution - ANS Normal distribution relies on a large sample of data. Using
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this approximate normal distribution we can further derive confidence intervals.
Since the distribution is normal, the confidence interval is the z-interval
**Applies for Logistic & Poisson Regression
Hypothesis Testing (coefficient == 0) - ANS To perform hypothesis testing, we can use
the approximate normal sampling distribution.
The resulting hypothesis test is also called the Wald test since it relies on the large
sample normal approximation of MLEs
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