ISYE6414 | ISYE 6414 Final Exam | Real Exam Questions & Verified Correct Answers | A+ Graded | Latest update ( 2025/2026)

Prepare with confidence using this ISYE 6414 Final Exam (2022–2023) complete exam guide featuring real questions and 100% verified correct answers. Covers key topics from the ISYE 6414 course: • Probability and statistical inference • Hypothesis testing • Regression analysis • Maximum likelihood estimation • ANOVA and experimental design Answers are clearly explained for deep understanding Graded A+ — trusted by top-performing students Fully aligned with course material from Georgia Tech or similar programs Instant access – study anytime, anywhere This is the most reliable and updated resource for students in Industrial Engineering, Data Science, or Statistics tracks. ISYE 6414 final exam 2022 questions and answers ISYE6414 final real exam with solutions ISYE 6414 Georgia Tech final test bank ISYE 6414 statistics exam verified answers ISYE 6414 final exam prep guide A+ graded ISYE 6414 final exam questions with explanations Final exam ISYE real questions PDF ISYE6414 statistical methods exam review ISYE 6414 real final questions updated version Georgia Tech ISYE 6414 final exam ISYE6414 | ISYE 6414 Final Exam | Real Exam Questions & Verified Correct Answers | A+ Graded | Latest Edition 1. We should always use mean squared error to determine the best value of lambda in lasso regression. a. True b. False Sol: False. The criterion used is a choice we make. Explanation: While Mean Squared Error (MSE) is commonly used to evaluate model performance and help choose the best λ (lambda) in lasso regression, it is not the only option, nor is it always the best. Other criteria or methods may also be used depending on the context: • Cross-validation (often k-fold CV) to minimize validation error (e.g., using mean absolute error (MAE) or deviance depending on the type of regression). • Information criteria, such as AIC or BIC, particularly in generalized linear models. • Domain-specific performance metrics may be more appropriate in certain applications (e.g., classification accuracy, ROC-AUC for classification tasks). 2. Standard linear regression is an example of a generalized linear model where the response is normally distributed and the link is the identity function. a. True b. False Sol: True. See Unit 4.4.1. ________________________________________ Explanation: Generalized Linear Models (GLMs) extend linear regression by allowing: • Different distributions for the response variable (not just normal). • Different link functions connecting predictors to the expected response. However, standard linear regression is actually a special case of a GLM: • Response distribution: Normal (Gaussian) • Link function: Identity (i.e., the mean of the response is directly modeled as a linear combination of predictors) This fits the definition of a GLM. 3. Goodness-of-fit assessment for logistic regression involves checking for the independence, constant variance, and normality of the deviance residuals. a. True b. False Sol: False. We don’t have constant variance in binomial regression. ________________________________________ Explanation: In logistic regression, the standard assumptions for assessing model goodness-of-fit differ from those in linear regression. Specifically: • The response is binary, not continuous. • Variance is not constant—it depends on the mean (since it's a binomial distribution). • Normality of residuals is not assumed. Instead of checking for independence, constant variance, and normality (as in linear regression), we typically assess logistic regression fit using: • Deviance and deviance residuals • Hosmer–Lemeshow test • Area under the ROC curve (AUC) • Classification accuracy or confusion matrices ________________________________________ 4. You are interested in understanding the relationship between stress level and exercise, with stress as the response. In your model, the number of hours a person spends exercising per week would be considered an explanatory variable while the person’s age would be a controlling variable. a. True b. False Sol: True. Time spent exercising is part of the relationship you are trying to understand while age could act as a confounding variable that you need to control. ________________________________________ Explanation: In statistical modeling: • The response variable (also called the dependent variable) is the main outcome you are trying to explain or predict — in this case, stress level. • The explanatory variable (also called the independent or predictor variable) is the main variable you're studying the effect of — here, it's hours of exercise per week. • A controlling variable (or control variable) is a factor that might influence the response and is held constant or adjusted for to isolate the effect of the explanatory variable — in this case, age. ________________________________________ Application to the scenario: • Stress level = Response variable • Hours of exercise = Explanatory variable (primary predictor of interest) • Age = Controlling variable (adjusted for to prevent confounding) ________________________________________ 5. The hypothesis test for goodness-of-fit using Pearson residuals and the test using deviance residuals will always reach the same conclusion. a. True b. False Sol: False. One test may conclude plausibly good fit while the other rejects it. ________________________________________ Explanation: While Pearson residuals and deviance residuals both serve to assess goodness-of-fit in generalized linear models (GLMs), they are not guaranteed to always lead to the same conclusion in hypothesis testing. Key Differences: • Pearson residuals are based on the standardized difference between observed and expected counts. • Deviance residuals come from the log-likelihood function and are more closely tied to the overall model likelihood. Both tests are asymptotically equivalent (i.e., they behave similarly in large samples), but: • In small or moderate samples, the tests may yield different p-values or test statistics, especially if the data deviate from model assumptions (like dispersion or overdispersion). • The distributional assumptions and robustness of the two tests can vary. ________________________________________ 6. A logistic regression model with high goodness of fit can have low predictive power. a. True b. False Sol: True. See Unit 4.2.3. ________________________________________ Explanation: A logistic regression model can fit the training data very well (i.e., have high goodness of fit) but still perform poorly when predicting new or unseen data. This situation typically arises due to: ________________________________________ Reasons Why This Is True: 1. Overfitting: • The model captures the noise in the training data rather than the underlying pattern. • As a result, the model fits the current data well but fails to generalize to new data. 2. Lack of Relevant Predictors: • The model may fit well statistically due to the structure of the data, but it might lack key predictors that actually determine the outcome in real-world scenarios. 3. Data Separation or Imbalance: • In cases where the classes are imbalanced, a model may appear to fit well based on certain metrics but fail to predict the minority class accurately. 4. Goodness-of-Fit ≠ Predictive Accuracy: • Goodness-of-fit measures how well the model fits the training data. • Predictive power (assessed by metrics like accuracy, AUC, precision-recall) measures how well the model performs on unseen data. ________________________________________   7. If we apply a Poisson regression model using a small sample size, the estimators of the regression coefficient may not follow an approximate Normal distribution, affecting the reliability of the statistical inference on the coefficients. a. True b. False Sol: True. See Unit 4.2.1. ________________________________________ Explanation: Poisson regression is used for modeling count data and assumes that the mean equals the variance (equidispersion). The maximum likelihood estimators (MLEs) for the regression coefficients in Poisson regression are asymptotically normally distributed, meaning that they approach a normal distribution as the sample size becomes large. ________________________________________ Why the Statement Is True: 1. Small Sample Size: • In small samples, the asymptotic normality of the estimators does not hold well. • The sampling distribution of the coefficient estimates may deviate significantly from normality. 2. Impact on Statistical Inference: • If the estimators are not approximately normally distributed, then confidence intervals and p-values (based on the normal approximation) may be inaccurate or misleading. • This affects the reliability of hypothesis tests and model interpretation. 3. Solution: • Use bootstrap methods or exact inference for small samples to get more accurate estimates of variability and significance. • Ensure larger sample sizes where possible to rely on normal approximation. ________________________________________ 8. You fit a regression model using three predictors. You notice the estimated coefficient for predictor X1 is an order of magnitude larger than the estimated coefficient for predictor X2. It is correct to conclude that X1 has a greater effect on the response than X2. a. True b. False Sol: False. We do not know that the variables are on the same scale in order to directly compare them. We can only conclude that a 1-unit change in X1 is associated with a greater change in the response than a 1-unit change in X2 holding other variables constant. ________________________________________ Explanation: The magnitude of regression coefficients cannot be directly compared to determine which predictor has a greater effect on the response unless the variables are on the same scale. ________________________________________ Key Points: 1. Coefficient Size Depends on Unit of Measurement: o If X1 is measured in dollars and X2 in cents, or one is in kilograms and the other in grams, the coefficient magnitudes will differ simply due to the units, not their true impact. 2. Standardization Is Required for Fair Comparison: o To compare the effects of predictors, you should standardize them (e.g., convert to z-scores). o After standardization, the coefficients reflect the change in the response per 1 standard deviation increase in the predictor. 3. Interpretation Without Standardization Is Misleading: o A large coefficient might just reflect a small range or large scale of the variable rather than a strong effect. ________________________________________ Correct Practice: To assess which predictor has a greater impact, use: • Standardized coefficients (also called beta coefficients) • Partial R² values • Variable importance measures (in more complex models) ________________________________________ 9. Regularized regression with a lambda value equal to 0 is equivalent to regression model estimation without penalization. a. True b. False Sol: True. See Unit 5.2.2. ________________________________________ Explanation: In regularized regression (e.g., Lasso, Ridge, or Elastic Net), the lambda (λ) parameter controls the strength of the penalty applied to the coefficients: • λ = 0 means no penalty is applied. • Therefore, the model behaves like ordinary least squares (OLS) regression. ________________________________________ Details: • Ridge Regression (L2 penalty): Minimizes: RSS+λ∑βj2text{RSS} + lambda sum beta_j^2RSS+λ∑βj2 • Lasso Regression (L1 penalty): Minimizes: RSS+λ∑∣βj∣text{RSS} + lambda sum |beta_j|RSS+λ∑∣βj∣ • When λ = 0, both reduce to minimizing the Residual Sum of Squares (RSS) only — which is what standard linear regression does. ________________________________________ Conclusion: Regularized regression with λ = 0 is equivalent to performing unpenalized regression, so the statement is true. 10. In a Poisson regression model, the difference between the null deviance and residual deviance follows a normal distribution. a. True b. False Sol: False. It follows a Chi-square distribution (this is used to check the overall regression significance). ________________________________________ Explanation: In a Poisson regression model, the difference between the null deviance and the residual deviance follows a chi-squared distribution, not a normal distribution. ________________________________________ Details: • Null deviance: Deviance of a model with only the intercept (no predictors). • Residual deviance: Deviance of the fitted model with predictors. • Difference (Δ deviance): Measures the improvement in fit by including the predictors. ΔD=Null Deviance−Residual DevianceDelta D = text{Null Deviance} - text{Residual Deviance}ΔD=Null Deviance−Residual Deviance • Under the null hypothesis (that the predictors have no effect), this difference follows a chi-squared distribution with degrees of freedom equal to the number of predictors added. ________________________________________ Conclusion: The statement is false because the difference in deviance does not follow a normal distribution — it follows a chi-squared distribution. 11. You want to examine the relationship between study time and score on exams. You create five exams and recruit 50 participants. For each participant in your study, you record their time studying for and grade on each of those five exams. If you were to use all the data you recorded to build a simple linear regression model, you would violate the independence assumption. a. True b. False Sol: True. Because you are collecting 5 observations from each person, the observations coming from the same person would be correlated. Similarly, all observations from the same test may be correlated. Explanation: In this scenario: • You have repeated measures: each of the 50 participants has five data points (one for each exam). • You are using all the data (i.e., 50 participants × 5 exams = 250 observations) to build a simple linear regression model. ________________________________________ The Issue: Simple linear regression assumes independence of observations. However, in your data: • Each participant contributes multiple observations. • These within-subject measurements are not independent — performance across exams may be correlated within each participant. ________________________________________ What this means: Using standard linear regression on such clustered or longitudinal data violates the independence assumption, because: • The residuals from the same participant are likely correlated. • This can lead to underestimated standard errors and inflated Type I error rates. ________________________________________ Recommended alternatives: • Use mixed-effects models (e.g., random intercept models). • Use generalized estimating equations (GEE). ________________________________________ 12. Maximum likelihood estimation produces unbiased coefficient estimates for logistic and Poisson regression. a. True b. False   Sol: True. Coefficient estimators follow an approximate normal distribution with the true coefficient as the mean. ________________________________________ Explanation: Maximum Likelihood Estimation (MLE) is a widely used method for estimating the coefficients in logistic and Poisson regression models. However, MLE does not always produce unbiased estimates, particularly in small samples. ________________________________________ Key Points: • MLE estimates are asymptotically unbiased, meaning they become unbiased only as sample size approaches infinity. • In small samples, MLE can produce biased estimates of regression coefficients, especially in logistic regression where separation or sparse data can lead to inflated coefficient estimates. • In Poisson regression, bias is also possible when event counts are low or the model is misspecified. ________________________________________ Summary: • In large samples: MLE ≈ unbiased and efficient. • In small samples: MLE may be biased. ________________________________________ 13. If considering only BIC for the model selection criterion, a model with lower BIC is preferred over a model with higher BIC. a. True b. False Sol: True. A lower BIC corresponds to a lower penalized prediction risk, and the statement specified that is the only thing we are considering. 14. If we do not penalize the training risk, our variable selection method would always prefer more complex models. a. True b. False Sol: True. See Unit 5.1.3. 15. One goal of variable selection is to balance the bias-variance tradeoff when making predictions. a. True b. False Sol: True. See Unit 5.1.4. 16. Forward stepwise selection is computationally more expensive than backward stepwise selection because it takes more iterations to terminate. a. True b. False Sol: False. Backwards is more expensive because it fits larger models. 17. When testing for the significance of a subset of predictors, the null hypothesis is that all coefficients for variables in that subset are 0 and the alternative is that all those coefficients are not 0. a. True b. False Sol: False. The alternative is that at least one variable is significantly nonzero. 18. Classification error estimated from leave-one-out cross validation tends to have higher bias but lower variability than classification error estimated from 2-fold cross validation. a. True b. False Sol: False. It has lower bias but higher variability. 19. One reasonable method for variable selection is to fit the full model and then drop all variables with a high p-value in that full model. a. True b. False   Sol: False. Significance should be interpreted conditionally. Correlations between predictors may cause multiple predictors to have high p-values despite at least one being useful to the model. By dropping them all at once, you cannot evaluate how one performs without the others. 20. The logit link is the only link function that yields s-shaped curves. a. True b. False Sol: False. Other link functions, such as probit and cloglog, yield s-shaped curves. 21. Which of the following is TRUE about adjusted R-squared? a. The adjusted R2 can be used to compare models, and its value will always be less than or equal to that of R2. b. The adjusted R2 cannot be used to compare models, and its value will always be less than or equal to that of R2. c. The adjusted R2 can be used to compare models, and its value will always be greater than or equal to that of R2. d. The adjusted R2 cannot be used to compare models, and its value will always be greater than or equal to that of R2. Sol: a. Negative values can occur with a sufficiently small R-square value and large number of predictors. It cannot be greater than R-squared (you can either recall this from previous 2)