ISYE 6414 FINAL EXAM WITH ACTUAL QUESTIONS AND 100% VERIFIED ANSWERS

ISYE 6414 FINAL EXAM WITH ACTUAL
QUESTIONS AND 100% VERIFIED ANSWERS
Logistic *Regression *- *CORRECT *ANSWER-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.
*In *this *model, *we *do *not *have *an *error *term



g-function *- *CORRECT *ANSWER-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



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
*combination *of *the *predicting *variables *over *1 *plus *this *same *exponential



Odds *of *a *success *- *CORRECT *ANSWER-This *is *the *exponential *of *the *Logit *function



Logistic *Regression *Assumptions *- *CORRECT *ANSWER-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 *- *CORRECT *ANSWER-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 *- *CORRECT *ANSWER-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



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



Model *parameters *- *CORRECT *ANSWER-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



Response *variable *- *CORRECT *ANSWER-The *response *data *are *Bernoulli *or *binomial *with
*one *trial *with *probability *of *success

,MLE *- *CORRECT *ANSWER-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 *- *CORRECT *ANSWER-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 *- *CORRECT *ANSWER-This *is *binary *data *with *repititions



Marginal *Relationship *- *CORRECT *ANSWER-Capturing *the *association *of *a *predicting *variable
*to *the *response *variable *without *consideration *of *other *factors



Conditional *Relationship *- *CORRECT *ANSWER-Capturing *the *association *oof *a *predicting
*variable *to *the *response *variable *conditional *of *other *predicting *variables *in *the *model

, Simpson's *paradox *- *CORRECT *ANSWER-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



This *happens *when *the *2 *variables *are *correlated



Normal *Distribution *- *CORRECT *ANSWER-Normal *distribution *relies *on *a *large *sample *of
*data. *Using *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) *- *CORRECT *ANSWER-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



To *test *whether *the *coefficient *betaj *= *0 *or *not, *we *can *use *the *z- *value



**Applies *for *Logistic *& *Poisson *Regression



Wald *Test *(Z-test) *- *CORRECT *ANSWER-The *z-test *value *is *the *ratio *between *the
*estimated *coefficient *minus *0, *(which *is *the *null *value) *divided *by *the *standard *error