1
ISYE 6501 - FINAL EXAM 2026/2027 |
COMPREHENSIVE REVIEW | 100 VERIFIED
Q&A | DETAILED RATIONALES | NGN-
ALIGNED | PASS GUARANTEED – A+ GRADED
SECTION I: ADVANCED REGRESSION AND MODEL SELECTION - Questions 1-15
Q1: Multiple linear regression assumptions
The student is reviewing multiple linear regression. Which of the following is NOT an assumption?
A. Linearity
B. Independence of errors
C. Homoscedasticity
D. Multicollinearity
Correct Answer: D
Rationale: Multiple linear regression assumes linearity, independence of errors, homoscedasticity
(constant variance), and normality of errors. Multicollinearity (high correlation among predictors) is
a problem, not an assumption. [100% CORRECT]
Q2: Adjusted R-squared
The student is reviewing model fit. How does adjusted R-squared differ from R-squared?
A. It always increases with new variables
B. It penalizes for the number of predictors
C. It is always higher than R-squared
D. It can be negative
Correct Answer: B
Rationale: Adjusted R-squared penalizes for the number of predictors, so it only increases if a new
variable improves the model more than expected by chance. [100% CORRECT]
Q3: AIC and BIC
The student is reviewing model selection. What is the purpose of AIC and BIC?
A. Measure goodness of fit only
B. Compare models by balancing fit and complexity
C. Test the null hypothesis
D. Calculate p-values
Correct Answer: B
Rationale: AIC and BIC are used for model selection. They balance goodness of fit with model
complexity, penalizing models with more parameters. Lower values indicate better models. [100%
CORRECT]
,2
Q4: Lasso regression
The student is reviewing Lasso regression. What is a key advantage of Lasso over Ridge?
A. Performs feature selection by shrinking coefficients to zero
B. Always has lower bias
C. Computationally simpler
D. Does not require tuning
Correct Answer: A
Rationale: Lasso (L1) 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. Combination of Lasso and Ridge
B. A decision tree
C. A clustering algorithm
D. A time series model
Correct Answer: A
Rationale: Elastic Net combines L1 and L2 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 it appropriate?
A. When the relationship is non-linear
B. When the relationship is strictly linear
C. When there is no relationship
D. When data is categorical
Correct Answer: A
Rationale: Polynomial regression is used when the relationship between 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?
A. Product of two independent variables
B. Sum of two independent variables
C. Square of an independent variable
D. 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 that depends on the value of another. [100% CORRECT]
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Q8: Heteroscedasticity
The student is reviewing heteroscedasticity. What is it?
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 errors is not constant across all levels of
independent variables. It violates the homoscedasticity assumption. [100% CORRECT]
Q9: Weighted least squares
The student is reviewing weighted least squares. When is it 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 errors have non-constant variance. It assigns
weights inversely proportional to the variance of errors. [100% CORRECT]
Q10: Stepwise regression
The student is reviewing stepwise regression. What is it?
A. Automatic variable selection based on statistical criteria
B. A clustering method
C. A time series model
D. A dimensionality reduction technique
Correct Answer: A
Rationale: Stepwise regression automatically adds or removes predictors based on statistical criteria
(e.g., p-values, AIC). It can be forward, backward, or mixed. [100% CORRECT]
Q11: Regularization parameter
The student is reviewing regularization. What does the tuning parameter λ control?
A. The strength of the penalty
B. The number of predictors
C. The intercept
D. The error variance
Correct Answer: A
Rationale: In regularization, λ controls the strength of the penalty. A larger λ increases
regularization, shrinking coefficients more toward zero. [100% CORRECT]
ISYE 6501 - FINAL EXAM 2026/2027 |
COMPREHENSIVE REVIEW | 100 VERIFIED
Q&A | DETAILED RATIONALES | NGN-
ALIGNED | PASS GUARANTEED – A+ GRADED
SECTION I: ADVANCED REGRESSION AND MODEL SELECTION - Questions 1-15
Q1: Multiple linear regression assumptions
The student is reviewing multiple linear regression. Which of the following is NOT an assumption?
A. Linearity
B. Independence of errors
C. Homoscedasticity
D. Multicollinearity
Correct Answer: D
Rationale: Multiple linear regression assumes linearity, independence of errors, homoscedasticity
(constant variance), and normality of errors. Multicollinearity (high correlation among predictors) is
a problem, not an assumption. [100% CORRECT]
Q2: Adjusted R-squared
The student is reviewing model fit. How does adjusted R-squared differ from R-squared?
A. It always increases with new variables
B. It penalizes for the number of predictors
C. It is always higher than R-squared
D. It can be negative
Correct Answer: B
Rationale: Adjusted R-squared penalizes for the number of predictors, so it only increases if a new
variable improves the model more than expected by chance. [100% CORRECT]
Q3: AIC and BIC
The student is reviewing model selection. What is the purpose of AIC and BIC?
A. Measure goodness of fit only
B. Compare models by balancing fit and complexity
C. Test the null hypothesis
D. Calculate p-values
Correct Answer: B
Rationale: AIC and BIC are used for model selection. They balance goodness of fit with model
complexity, penalizing models with more parameters. Lower values indicate better models. [100%
CORRECT]
,2
Q4: Lasso regression
The student is reviewing Lasso regression. What is a key advantage of Lasso over Ridge?
A. Performs feature selection by shrinking coefficients to zero
B. Always has lower bias
C. Computationally simpler
D. Does not require tuning
Correct Answer: A
Rationale: Lasso (L1) 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. Combination of Lasso and Ridge
B. A decision tree
C. A clustering algorithm
D. A time series model
Correct Answer: A
Rationale: Elastic Net combines L1 and L2 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 it appropriate?
A. When the relationship is non-linear
B. When the relationship is strictly linear
C. When there is no relationship
D. When data is categorical
Correct Answer: A
Rationale: Polynomial regression is used when the relationship between 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?
A. Product of two independent variables
B. Sum of two independent variables
C. Square of an independent variable
D. 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 that depends on the value of another. [100% CORRECT]
, 3
Q8: Heteroscedasticity
The student is reviewing heteroscedasticity. What is it?
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 errors is not constant across all levels of
independent variables. It violates the homoscedasticity assumption. [100% CORRECT]
Q9: Weighted least squares
The student is reviewing weighted least squares. When is it 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 errors have non-constant variance. It assigns
weights inversely proportional to the variance of errors. [100% CORRECT]
Q10: Stepwise regression
The student is reviewing stepwise regression. What is it?
A. Automatic variable selection based on statistical criteria
B. A clustering method
C. A time series model
D. A dimensionality reduction technique
Correct Answer: A
Rationale: Stepwise regression automatically adds or removes predictors based on statistical criteria
(e.g., p-values, AIC). It can be forward, backward, or mixed. [100% CORRECT]
Q11: Regularization parameter
The student is reviewing regularization. What does the tuning parameter λ control?
A. The strength of the penalty
B. The number of predictors
C. The intercept
D. The error variance
Correct Answer: A
Rationale: In regularization, λ controls the strength of the penalty. A larger λ increases
regularization, shrinking coefficients more toward zero. [100% CORRECT]
