ISYE 6414 PRACTICE EXAMINATION 2026
QUESTIONS WITH ANSWERS GRADED A+
◍ Multicolinearity in multiple linear regression means that the columns in the
design matrix are (nearly) linearly dependent..
Answer: True. See Unit 3.3.3
◍ In the GLMs the link function cannot be a non linear regression..
Answer: False - It can be linear, non linear, or parametric
◍ For the testing procedure for subsets of coefficients, we compare the
likelihood of a reduced model versus a full model. This is a goodness of fit
test.
Answer: False - it provides inference of the predictive power of the model
◍ For logistic regression we can define residuals for evaluating model
goodness of fit for models with and without replication..
Answer: False - can only be with replication under the assumption that Yi is
binary and n1 is greater than 1
◍ AIC looks just like the Mallow's Cp except that the variance is the true
variance and not its estimate..
Answer: True
◍ The estimators of the variance parameter and of the regression coefficients
in a regression model are random variables..
Answer: True
◍ The log odds function, also called the logit function, which is the log of the
ratio between the probability of a success and the probability of a failure.
Answer: True
◍ When dealing with a multiple linear regression model, an adjusted
R-squared canbe greater than the corresponding unadjusted R-Squared
, value..
Answer: False - the adjusted rsquared value take the number and types of
predictors into account. It is lower than the r squared value.
◍ The R-squared and adjusted R-squared are not appropriate model
comparisons for non linear regression but are for linear regression models..
Answer: TRUE - The underlying assumption of R-squared calculations is
that you are fitting a linear model.
◍ The F-test can be used to evaluate the relationship between two qualitative
variables..
Answer: False
◍ We can use residual analysis to conclusively determine the assumption
ofindependence.
Answer: False - we can only determine uncorrelated errors.
◍ The statistical inference for linear regression under normality relies on large
size of sample data..
Answer: False. As we are already assuming normality, we do not need to
rely on a large sample size.
◍ Let Y^ be the predicted response at x^ . The variance of Y^ given x^
depends on both the value of x^ and the design matrix..
Answer: True (but the wording was confusing, so everyone got credit no
matter what on this question)
◍ The regression coefficient is used to measure the linear dependence between
two variables..
Answer: False
◍ The Mallow's CP complexity penalty is two times the size of the model (the
number of variables in the submodel) times the estimated variance divided
by n..
Answer: True
◍ L2 does not perform variable selection.
, Answer: True - is equal to the sum of the squared regression coefficients to
be penalized and does not do variable selection
◍ If a predicting variable is a categorical variable with 5 categories in a linear
regression model without intercept, we will include 5 dummy variables..
Answer: True
◍ We can do a partial F test to determine if variable selection is necessary..
Answer: True
◍ If the normality assumption does not hold for a regression, we may use a
transformation on the response variable..
Answer: True
◍ The larger the coefficient of determination or R-squared, the higher the
variability explained by the simple linear regression model..
Answer: True. R-squared is the proportion of variability explained by the
model.
◍ In testing for a subset of coefficients in logistic regression the null
hypothesis is that the coefficient is equal to zero.
Answer: True
◍ Maximum Likelihood Estimation is not applicable for simple linear
regression and multiple linear regression..
Answer: False - In SLR and MLR, the SLE and MLE are the same with
normal idd data.
◍ The smaller the coefficient of determination or R-squared, the higher the
variability explained bythe simple linear regression..
Answer: False (Explanation: The larger the R-squared)
◍ The backward elimination requires a pre-set probability of type II error.
Answer: False - Type I error
◍ When selecting variables for a model, one needs also to consider the
research hypothesis, as well as any potential confounding variables to
control for.
QUESTIONS WITH ANSWERS GRADED A+
◍ Multicolinearity in multiple linear regression means that the columns in the
design matrix are (nearly) linearly dependent..
Answer: True. See Unit 3.3.3
◍ In the GLMs the link function cannot be a non linear regression..
Answer: False - It can be linear, non linear, or parametric
◍ For the testing procedure for subsets of coefficients, we compare the
likelihood of a reduced model versus a full model. This is a goodness of fit
test.
Answer: False - it provides inference of the predictive power of the model
◍ For logistic regression we can define residuals for evaluating model
goodness of fit for models with and without replication..
Answer: False - can only be with replication under the assumption that Yi is
binary and n1 is greater than 1
◍ AIC looks just like the Mallow's Cp except that the variance is the true
variance and not its estimate..
Answer: True
◍ The estimators of the variance parameter and of the regression coefficients
in a regression model are random variables..
Answer: True
◍ The log odds function, also called the logit function, which is the log of the
ratio between the probability of a success and the probability of a failure.
Answer: True
◍ When dealing with a multiple linear regression model, an adjusted
R-squared canbe greater than the corresponding unadjusted R-Squared
, value..
Answer: False - the adjusted rsquared value take the number and types of
predictors into account. It is lower than the r squared value.
◍ The R-squared and adjusted R-squared are not appropriate model
comparisons for non linear regression but are for linear regression models..
Answer: TRUE - The underlying assumption of R-squared calculations is
that you are fitting a linear model.
◍ The F-test can be used to evaluate the relationship between two qualitative
variables..
Answer: False
◍ We can use residual analysis to conclusively determine the assumption
ofindependence.
Answer: False - we can only determine uncorrelated errors.
◍ The statistical inference for linear regression under normality relies on large
size of sample data..
Answer: False. As we are already assuming normality, we do not need to
rely on a large sample size.
◍ Let Y^ be the predicted response at x^ . The variance of Y^ given x^
depends on both the value of x^ and the design matrix..
Answer: True (but the wording was confusing, so everyone got credit no
matter what on this question)
◍ The regression coefficient is used to measure the linear dependence between
two variables..
Answer: False
◍ The Mallow's CP complexity penalty is two times the size of the model (the
number of variables in the submodel) times the estimated variance divided
by n..
Answer: True
◍ L2 does not perform variable selection.
, Answer: True - is equal to the sum of the squared regression coefficients to
be penalized and does not do variable selection
◍ If a predicting variable is a categorical variable with 5 categories in a linear
regression model without intercept, we will include 5 dummy variables..
Answer: True
◍ We can do a partial F test to determine if variable selection is necessary..
Answer: True
◍ If the normality assumption does not hold for a regression, we may use a
transformation on the response variable..
Answer: True
◍ The larger the coefficient of determination or R-squared, the higher the
variability explained by the simple linear regression model..
Answer: True. R-squared is the proportion of variability explained by the
model.
◍ In testing for a subset of coefficients in logistic regression the null
hypothesis is that the coefficient is equal to zero.
Answer: True
◍ Maximum Likelihood Estimation is not applicable for simple linear
regression and multiple linear regression..
Answer: False - In SLR and MLR, the SLE and MLE are the same with
normal idd data.
◍ The smaller the coefficient of determination or R-squared, the higher the
variability explained bythe simple linear regression..
Answer: False (Explanation: The larger the R-squared)
◍ The backward elimination requires a pre-set probability of type II error.
Answer: False - Type I error
◍ When selecting variables for a model, one needs also to consider the
research hypothesis, as well as any potential confounding variables to
control for.
