1
ISYE 6501 - MIDTERM EXAM 2 LATEST
2026/2027 | 60 VERIFIED Q&A | DETAILED
RATIONALES | NGN-ALIGNED | PASS
GUARANTEED – A+ GRADED
SECTION I: ADVANCED REGRESSION AND REGULARIZATION - Questions 1-10
Q1: Multiple linear regression assumptions
The student is reviewing multiple linear regression. Which of the following is NOT an assumption of
multiple linear regression?
A. Linearity between dependent and independent variables
B. Independence of errors
C. Homoscedasticity of errors
D. Multicollinearity among independent variables
Correct Answer: D
Rationale: Multiple linear regression assumes linearity, independence of errors, homoscedasticity
(constant variance of errors), and normality of errors. Multicollinearity (high correlation among
independent variables) is not an assumption; it is a problem that can violate the stability of
coefficient estimates. [100% CORRECT]
Q2: Adjusted R-squared
The student is reviewing model fit. How does adjusted R-squared differ from R-squared?
A. Adjusted R-squared always increases when a new variable is added
B. Adjusted R-squared penalizes for the number of predictors in the model
C. Adjusted R-squared is always higher than R-squared
D. Adjusted R-squared can be negative
Correct Answer: B
Rationale: Adjusted R-squared penalizes for the number of predictors in the model, so it only
increases if a new variable improves the model more than would be expected by chance. R-squared
always increases with additional variables, even if they are not useful. [100% CORRECT]
Q3: AIC and BIC
The student is reviewing model selection. What is the purpose of AIC and BIC?
A. To measure the goodness of fit only
B. To compare models by balancing goodness of fit and model complexity
C. To test the null hypothesis
D. To calculate p-values
,2
Correct Answer: B
Rationale: AIC (Akaike Information Criterion) and BIC (Bayesian Information Criterion) are used for
model selection. They balance goodness of fit with model complexity, penalizing models with more
parameters. Lower AIC/BIC indicates a better model. [100% CORRECT]
Q4: Lasso regression
The student is reviewing Lasso regression. What is a key advantage of Lasso regression over Ridge
regression?
A. Lasso performs feature selection by shrinking coefficients to zero
B. Lasso always has lower bias
C. Lasso is computationally simpler
D. Lasso does not require tuning
Correct Answer: A
Rationale: Lasso (L1 regularization) can shrink some coefficients exactly to zero, effectively
performing feature selection. Ridge (L2) shrinks coefficients but does not eliminate them. [100%
CORRECT]
Q5: Elastic net
The student is reviewing Elastic Net. What is Elastic Net?
A. A combination of Lasso and Ridge regularization
B. A type of decision tree
C. A clustering algorithm
D. A time series model
Correct Answer: A
Rationale: Elastic Net combines L1 (Lasso) and L2 (Ridge) penalties. It is useful when there are
multiple correlated features, as it can select groups of correlated variables. [100% CORRECT]
Q6: Polynomial regression
The student is reviewing polynomial regression. When is polynomial regression appropriate?
A. When the relationship between variables is non-linear
B. When the relationship is strictly linear
C. When there is no relationship
D. When the data is categorical
Correct Answer: A
Rationale: Polynomial regression is used when the relationship between the independent and
dependent variables is non-linear. It adds polynomial terms (e.g., x², x³) to capture curvature. [100%
CORRECT]
Q7: Interaction terms
The student is reviewing interaction terms. What is an interaction term in regression?
A. A term that represents the product of two independent variables
B. A term that represents the sum of two independent variables
, 3
C. A term that represents the square of an independent variable
D. A term that represents the intercept
Correct Answer: A
Rationale: An interaction term is the product of two independent variables (e.g., x1 * x2). It models
the effect of one variable on the dependent variable that depends on the value of another variable.
[100% CORRECT]
Q8: Heteroscedasticity
The student is reviewing heteroscedasticity. What is heteroscedasticity?
A. Constant variance of errors
B. Non-constant variance of errors
C. Normality of errors
D. Independence of errors
Correct Answer: B
Rationale: Heteroscedasticity occurs when the variance of the errors is not constant across all levels
of the independent variables. It violates the homoscedasticity assumption and can lead to inefficient
estimates. [100% CORRECT]
Q9: Weighted least squares
The student is reviewing weighted least squares. When is weighted least squares used?
A. When there is heteroscedasticity
B. When there is multicollinearity
C. When there is non-linearity
D. When there is autocorrelation
Correct Answer: A
Rationale: Weighted least squares (WLS) is used when the errors have non-constant variance
(heteroscedasticity). It assigns weights to observations inversely proportional to the variance of their
errors. [100% CORRECT]
Q10: Stepwise regression
The student is reviewing stepwise regression. What is stepwise regression?
A. A method for automatically selecting variables based on statistical criteria
B. A method for clustering data
C. A method for time series forecasting
D. A method for dimensionality reduction
Correct Answer: A
Rationale: Stepwise regression is an automated procedure that adds or removes predictors based on
statistical criteria (e.g., p-values, AIC). It can be forward selection, backward elimination, or a
combination. [100% CORRECT]
SECTION II: CLASSIFICATION METHODS - Questions 11-20
ISYE 6501 - MIDTERM EXAM 2 LATEST
2026/2027 | 60 VERIFIED Q&A | DETAILED
RATIONALES | NGN-ALIGNED | PASS
GUARANTEED – A+ GRADED
SECTION I: ADVANCED REGRESSION AND REGULARIZATION - Questions 1-10
Q1: Multiple linear regression assumptions
The student is reviewing multiple linear regression. Which of the following is NOT an assumption of
multiple linear regression?
A. Linearity between dependent and independent variables
B. Independence of errors
C. Homoscedasticity of errors
D. Multicollinearity among independent variables
Correct Answer: D
Rationale: Multiple linear regression assumes linearity, independence of errors, homoscedasticity
(constant variance of errors), and normality of errors. Multicollinearity (high correlation among
independent variables) is not an assumption; it is a problem that can violate the stability of
coefficient estimates. [100% CORRECT]
Q2: Adjusted R-squared
The student is reviewing model fit. How does adjusted R-squared differ from R-squared?
A. Adjusted R-squared always increases when a new variable is added
B. Adjusted R-squared penalizes for the number of predictors in the model
C. Adjusted R-squared is always higher than R-squared
D. Adjusted R-squared can be negative
Correct Answer: B
Rationale: Adjusted R-squared penalizes for the number of predictors in the model, so it only
increases if a new variable improves the model more than would be expected by chance. R-squared
always increases with additional variables, even if they are not useful. [100% CORRECT]
Q3: AIC and BIC
The student is reviewing model selection. What is the purpose of AIC and BIC?
A. To measure the goodness of fit only
B. To compare models by balancing goodness of fit and model complexity
C. To test the null hypothesis
D. To calculate p-values
,2
Correct Answer: B
Rationale: AIC (Akaike Information Criterion) and BIC (Bayesian Information Criterion) are used for
model selection. They balance goodness of fit with model complexity, penalizing models with more
parameters. Lower AIC/BIC indicates a better model. [100% CORRECT]
Q4: Lasso regression
The student is reviewing Lasso regression. What is a key advantage of Lasso regression over Ridge
regression?
A. Lasso performs feature selection by shrinking coefficients to zero
B. Lasso always has lower bias
C. Lasso is computationally simpler
D. Lasso does not require tuning
Correct Answer: A
Rationale: Lasso (L1 regularization) can shrink some coefficients exactly to zero, effectively
performing feature selection. Ridge (L2) shrinks coefficients but does not eliminate them. [100%
CORRECT]
Q5: Elastic net
The student is reviewing Elastic Net. What is Elastic Net?
A. A combination of Lasso and Ridge regularization
B. A type of decision tree
C. A clustering algorithm
D. A time series model
Correct Answer: A
Rationale: Elastic Net combines L1 (Lasso) and L2 (Ridge) penalties. It is useful when there are
multiple correlated features, as it can select groups of correlated variables. [100% CORRECT]
Q6: Polynomial regression
The student is reviewing polynomial regression. When is polynomial regression appropriate?
A. When the relationship between variables is non-linear
B. When the relationship is strictly linear
C. When there is no relationship
D. When the data is categorical
Correct Answer: A
Rationale: Polynomial regression is used when the relationship between the independent and
dependent variables is non-linear. It adds polynomial terms (e.g., x², x³) to capture curvature. [100%
CORRECT]
Q7: Interaction terms
The student is reviewing interaction terms. What is an interaction term in regression?
A. A term that represents the product of two independent variables
B. A term that represents the sum of two independent variables
, 3
C. A term that represents the square of an independent variable
D. A term that represents the intercept
Correct Answer: A
Rationale: An interaction term is the product of two independent variables (e.g., x1 * x2). It models
the effect of one variable on the dependent variable that depends on the value of another variable.
[100% CORRECT]
Q8: Heteroscedasticity
The student is reviewing heteroscedasticity. What is heteroscedasticity?
A. Constant variance of errors
B. Non-constant variance of errors
C. Normality of errors
D. Independence of errors
Correct Answer: B
Rationale: Heteroscedasticity occurs when the variance of the errors is not constant across all levels
of the independent variables. It violates the homoscedasticity assumption and can lead to inefficient
estimates. [100% CORRECT]
Q9: Weighted least squares
The student is reviewing weighted least squares. When is weighted least squares used?
A. When there is heteroscedasticity
B. When there is multicollinearity
C. When there is non-linearity
D. When there is autocorrelation
Correct Answer: A
Rationale: Weighted least squares (WLS) is used when the errors have non-constant variance
(heteroscedasticity). It assigns weights to observations inversely proportional to the variance of their
errors. [100% CORRECT]
Q10: Stepwise regression
The student is reviewing stepwise regression. What is stepwise regression?
A. A method for automatically selecting variables based on statistical criteria
B. A method for clustering data
C. A method for time series forecasting
D. A method for dimensionality reduction
Correct Answer: A
Rationale: Stepwise regression is an automated procedure that adds or removes predictors based on
statistical criteria (e.g., p-values, AIC). It can be forward selection, backward elimination, or a
combination. [100% CORRECT]
SECTION II: CLASSIFICATION METHODS - Questions 11-20
