1
ISYE 6501 MIDTERM 2 STUDY GUIDE | 2026
UPDATE | PRACTICE QUESTIONS AND
ANSWERS | EXAM REVIEW | 100% CORRECT
ANSWERS | VERIFIED SOLUTIONS | GEORGIA
TECH COMPLETE REVIEW
This practice examination is designed for students preparing for ISYE 6501
Midterm 2 at Georgia Tech. It serves as a comprehensive study guide and exam
review, reflecting the latest update for 2026. The questions are crafted to mirror
the difficulty, quantitative rigor, and scope of the midterm examination, covering
all essential topics including regression modeling, variable selection,
regularization, optimization, simulation, clustering, principal component analysis,
model validation, and data exploration. By engaging with these practice questions
and answers, students can assess their readiness, identify knowledge gaps, and
reinforce their understanding of critical analytics modeling concepts. The detailed
rationales provide verified solutions, ensuring a deep comprehension of the
material and enhancing the effectiveness of your preparation for this rigorous
graduate-level examination.
Table of Contents
1. Linear and Multiple Regression
2. Variable Selection and Regularization
3. Optimization and Linear Programming
4. Simulation and Queueing
5. Clustering and PCA
6. Model Validation and Performance Metrics
7. Time Series and Change Detection
8. Data Exploration and Analytics Process
, 2
Question 1: In simple linear regression, what does the slope coefficient represent?
A) The predicted value when the predictor equals zero
B) The change in the mean response for a one-unit increase in the predictor
C) The proportion of variance explained by the model
D) The correlation between the response and predictor
Correct Answer: B
The slope coefficient measures the expected change in the response for a one-unit
increase in the predictor, holding other factors constant. Option A describes the
intercept. Option C describes R². Option D describes the correlation coefficient.
Question 2: Which assumption is NOT required for ordinary least squares
regression?
A) Linearity between predictors and response
B) Independence of errors
C) Constant variance of errors
D) Normality of the predictor variables
Correct Answer: D
OLS requires linearity, independent errors, and homoscedasticity. Normality of
predictors is not required; normality is assumed for errors in inference. Options A,
B, and C are standard assumptions.
Question 3: If R² = 0.85 in a regression model, what does this indicate?
A) 85% of the variability in the response is explained by the model
B) The correlation between response and predictor is 0.85
C) The model predicts 85% of future observations correctly
D) The slope is statistically significant at 0.85
Correct Answer: A
R² measures the proportion of total variability in the response explained by the
model. Option B is incorrect because R² = r² in simple regression, so r ≈ 0.92.
Option C confuses explanatory power with prediction accuracy. Option D is
unrelated.
, 3
Question 4: A residual plot shows a funnel shape with increasing spread as fitted
values increase. Which assumption is violated?
A) Linearity
B) Independence
C) Homoscedasticity
D) Normality
Correct Answer: C
A funnel pattern indicates heteroscedasticity, or non-constant error variance.
Option A would show a curved pattern. Option B would show correlation over
time. Option D is assessed with a Q-Q plot.
Question 5: In multiple regression, why is adjusted R² preferred over R² for model
comparison?
A) It always increases when predictors are added
B) It penalizes additional predictors that do not improve the model
C) It measures correlation rather than variance
D) It is always lower than R²
Correct Answer: B
Adjusted R² includes a penalty for the number of predictors, making it more
suitable for comparing models of different complexity. Option A is true of R², not
adjusted R². Option C is incorrect. Option D is not always true.
Question 6: A VIF value of 12 for a predictor indicates:
A) No multicollinearity
B) Moderate multicollinearity
C) Severe multicollinearity
D) The predictor is insignificant
Correct Answer: C
VIF greater than 10 is generally considered severe multicollinearity. Option A
would be near 1. Option B would be between 5 and 10. Option D is determined by
the p-value, not VIF alone.
, 4
Question 7: Which variable selection method starts with no predictors and adds
one at a time?
A) Backward elimination
B) Forward selection
C) Stepwise selection
D) LASSO
Correct Answer: B
Forward selection begins with an empty model and adds predictors one by one.
Option A starts with all predictors and removes them. Option C combines forward
and backward. Option D is a regularization method.
Question 8: What does the Akaike Information Criterion (AIC) penalize?
A) Only model fit
B) The number of parameters
C) The sample size only
D) The R² value
Correct Answer: B
AIC = -2 log-likelihood + 2k, where k is the number of parameters. The penalty
term 2k penalizes complexity. Options A, C, and D are incomplete or incorrect.
Question 9: How does BIC differ from AIC?
A) BIC penalizes additional parameters more heavily, especially for large samples
B) BIC has no penalty term
C) BIC always selects larger models
D) BIC is only for linear regression
Correct Answer: A
BIC = -2 log-likelihood + k log(n). The penalty grows with sample size, so BIC
favors more parsimonious models than AIC. Option B is false. Option C is false.
Option D is false.
Question 10: What is a key advantage of LASSO regression?
ISYE 6501 MIDTERM 2 STUDY GUIDE | 2026
UPDATE | PRACTICE QUESTIONS AND
ANSWERS | EXAM REVIEW | 100% CORRECT
ANSWERS | VERIFIED SOLUTIONS | GEORGIA
TECH COMPLETE REVIEW
This practice examination is designed for students preparing for ISYE 6501
Midterm 2 at Georgia Tech. It serves as a comprehensive study guide and exam
review, reflecting the latest update for 2026. The questions are crafted to mirror
the difficulty, quantitative rigor, and scope of the midterm examination, covering
all essential topics including regression modeling, variable selection,
regularization, optimization, simulation, clustering, principal component analysis,
model validation, and data exploration. By engaging with these practice questions
and answers, students can assess their readiness, identify knowledge gaps, and
reinforce their understanding of critical analytics modeling concepts. The detailed
rationales provide verified solutions, ensuring a deep comprehension of the
material and enhancing the effectiveness of your preparation for this rigorous
graduate-level examination.
Table of Contents
1. Linear and Multiple Regression
2. Variable Selection and Regularization
3. Optimization and Linear Programming
4. Simulation and Queueing
5. Clustering and PCA
6. Model Validation and Performance Metrics
7. Time Series and Change Detection
8. Data Exploration and Analytics Process
, 2
Question 1: In simple linear regression, what does the slope coefficient represent?
A) The predicted value when the predictor equals zero
B) The change in the mean response for a one-unit increase in the predictor
C) The proportion of variance explained by the model
D) The correlation between the response and predictor
Correct Answer: B
The slope coefficient measures the expected change in the response for a one-unit
increase in the predictor, holding other factors constant. Option A describes the
intercept. Option C describes R². Option D describes the correlation coefficient.
Question 2: Which assumption is NOT required for ordinary least squares
regression?
A) Linearity between predictors and response
B) Independence of errors
C) Constant variance of errors
D) Normality of the predictor variables
Correct Answer: D
OLS requires linearity, independent errors, and homoscedasticity. Normality of
predictors is not required; normality is assumed for errors in inference. Options A,
B, and C are standard assumptions.
Question 3: If R² = 0.85 in a regression model, what does this indicate?
A) 85% of the variability in the response is explained by the model
B) The correlation between response and predictor is 0.85
C) The model predicts 85% of future observations correctly
D) The slope is statistically significant at 0.85
Correct Answer: A
R² measures the proportion of total variability in the response explained by the
model. Option B is incorrect because R² = r² in simple regression, so r ≈ 0.92.
Option C confuses explanatory power with prediction accuracy. Option D is
unrelated.
, 3
Question 4: A residual plot shows a funnel shape with increasing spread as fitted
values increase. Which assumption is violated?
A) Linearity
B) Independence
C) Homoscedasticity
D) Normality
Correct Answer: C
A funnel pattern indicates heteroscedasticity, or non-constant error variance.
Option A would show a curved pattern. Option B would show correlation over
time. Option D is assessed with a Q-Q plot.
Question 5: In multiple regression, why is adjusted R² preferred over R² for model
comparison?
A) It always increases when predictors are added
B) It penalizes additional predictors that do not improve the model
C) It measures correlation rather than variance
D) It is always lower than R²
Correct Answer: B
Adjusted R² includes a penalty for the number of predictors, making it more
suitable for comparing models of different complexity. Option A is true of R², not
adjusted R². Option C is incorrect. Option D is not always true.
Question 6: A VIF value of 12 for a predictor indicates:
A) No multicollinearity
B) Moderate multicollinearity
C) Severe multicollinearity
D) The predictor is insignificant
Correct Answer: C
VIF greater than 10 is generally considered severe multicollinearity. Option A
would be near 1. Option B would be between 5 and 10. Option D is determined by
the p-value, not VIF alone.
, 4
Question 7: Which variable selection method starts with no predictors and adds
one at a time?
A) Backward elimination
B) Forward selection
C) Stepwise selection
D) LASSO
Correct Answer: B
Forward selection begins with an empty model and adds predictors one by one.
Option A starts with all predictors and removes them. Option C combines forward
and backward. Option D is a regularization method.
Question 8: What does the Akaike Information Criterion (AIC) penalize?
A) Only model fit
B) The number of parameters
C) The sample size only
D) The R² value
Correct Answer: B
AIC = -2 log-likelihood + 2k, where k is the number of parameters. The penalty
term 2k penalizes complexity. Options A, C, and D are incomplete or incorrect.
Question 9: How does BIC differ from AIC?
A) BIC penalizes additional parameters more heavily, especially for large samples
B) BIC has no penalty term
C) BIC always selects larger models
D) BIC is only for linear regression
Correct Answer: A
BIC = -2 log-likelihood + k log(n). The penalty grows with sample size, so BIC
favors more parsimonious models than AIC. Option B is false. Option C is false.
Option D is false.
Question 10: What is a key advantage of LASSO regression?
