ISYE6414 REGRESSION MIDTERM 2
EXAM 2022-2024 / ISYE6414 MIDTERM 2
REAL EXAM QUESTIONS AND 100%
CORRECT ANSWERS/ GRADED A
In logistic regression, the relationship between the probability of success and the
predicting variables is nonlinear. --CORRECT ANSWER--> TRUE: The equation
that links the predictors to the probability is:
????(????1,...,????????)=
????????????(????0+????1????1+...+????????????????) / 1+????????????(????0+????1????1+...+????????????????)
This relationship is not linear.
In logistic regression, the error terms are assumed to follow a normal distribution. -
-CORRECT 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. --CORRECT
ANSWER--> TRUE: ????(????)=ln(p/1−????)
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. --CORRECT 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. --
CORRECT 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 ???????? represents
the estimated expected change in the response variable associated with one unit
increase in the corresponding predicting variable, ???????? , holding all else in the model
fixed. --CORRECT ANSWER--> 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. --CORRECT
ANSWER--> FALSE: The coefficient estimator follows an approximate normal
distribution
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 in
the reduced model. --CORRECT ANSWER--> 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 ????????|????????,1,⋯,????????,???? is Binomial. --CORRECT 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 ????, then it is plausible that the model is a good
fit. --CORRECT ANSWER--> 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. --CORRECT 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.
Category | Exams and Certifications |
Comments | 0 |
Rating | |
Sales | 0 |