ISYE6414 REGRESSION MIDTERM 2 EXAM 2022-2024 / ISYE6414 MIDTERM 2 REAL EXAM QUESTIONS AND 100% CORRECT ANSWERS/ GRADED A

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.