ISYE6414 MIDTERM PRACTICE TEST BANK EXAMPREP FULL SOLUTION SET HIGHLY ACCURATE REVIEW

ISYE6414 MIDTERM PRACTICE TEST BANK
EXAMPREP FULL SOLUTION SET HIGHLY
ACCURATE REVIEW

●● In logistic regression, the error terms are assumed to follow a normal
distribution..
Answer: FALSE: There are no error terms in logistic regression


●● The logit function is the log of the ratio of the probability of success
to the probability of failure. It is also known as the log odds function..
Answer: TRUE: 𝑔(𝑝)=ln(p/1−𝑝)
The logit link function is also known as the log odds function.


●● The number of parameters that need to be estimated in a logistic
regression model with 6 predicting variables and an intercept is the same
as the number of parameters that need to be estimated in a standard
linear regression model with an intercept and same predicting variables..
Answer: FALSE: As there is no error term in a logistic regression model,
there is no additional parameter for the variance of the error terms. As a
result, the number of parameters that need to be estimated in a logistic
regression model with 6 predicting variables and an intercept is 7. The
number of parameters that need to be estimated in a standard linear
regression model with an intercept and same predicting variables is 8.

,●● The log-likelihood function is a linear function with a closed-form
solution..
Answer: FALSE: The log-likelihood function is a non-linear function. A
numerical algorithm is needed in order to maximize it.


●● In logistic regression, the estimated value for a regression coefficient
𝛽𝑖 represents the estimated expected change in the response variable
associated with one unit increase in the corresponding predicting
variable, 𝑥𝑖 , holding all else in the model fixed.. Answ
er: FALSE: We interpret logistic regression coefficients with respect to
the odds of success.


●● Under logistic regression, the sampling distribution used for a
coefficient estimator is a Chi-squared distribution when the sample size
is large..
Answer: FALSE: The coefficient estimator follows an approximate
normal distribution


●● When testing a subset of coefficients, deviance follows a chi-square
distribution with 𝑞q degrees of freedom, where 𝑞q is the number of
regression coefficients in the reduced model.. An
swer: FALSE: When testing a subset of coefficients, deviance follows 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.

, ●● Logistic regression deals with the case where the dependent variable
is binary, and the conditional distribution 𝑌𝑖|𝑿𝑖,1,⋯,𝑿𝑖,𝑝 is Binomial..
Answer:
TRUE: Logistic regression is the generalization of the standard
regression model that is used when the response variable y is binary or
binomial.


●● In logistic regression, if the p-value of the deviance test for
goodness-of-fit is smaller than the significance level 𝛼, then it is
plausible that the model is a good fit.. A
nswer: FALSE: For logistic regression, if the p-value of the deviance test
for goodness-of-fit is large, then it is an indication that the model is a
good fit.


●● If a logistic regression model provides accurate classification, then
we can conclude that it is a good fit for the data..
Answer: FALSE: 'Goodness of fit doesn't guarantee good prediction."
And conversely, good prediction doesn't guarantee that the model is a
good fit.


To evaluate whether the model is a good fit or equivalently whether the
assumptions hold, we can use the Pearson or deviance residuals to
evaluate whether they are normally distributed. We can evaluate that
using the histogram and the normality plots. If they're normally
distributed, then we conclude that the model is a good fit.