ISYE 6501 MIDTERM EXAM– QUESTIONS AND ANSWERS |
VERIFIED AND WELL DETAILED ANSWERS PLUS RATIONALES |
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1. A manufacturing plant manager wants to forecast monthly electricity consumption
based on historical data that exhibits a clear upward trend and strong seasonal variations.
Which modeling approach is most appropriate for capturing both components effectively?
A. Simple exponential smoothing
B. Holt-Winters additive or multiplicative smoothing
C. Basic moving average model
D. Single linear regression without time indices
ANSWER: B. Holt-Winters additive or multiplicative smoothing
Holt-Winters exponential smoothing specifically extends basic smoothing methods to capture
both trend and seasonality, making it ideal for this type of time series data. Simple smoothing
handles neither, a moving average handles neither adequately without lagging, and basic
linear regression fails to capture periodic seasonal cycles.
2. An analyst is building a classification model to detect fraudulent transactions, which
account for less than 0.1 percent of the total dataset. After training, the model achieves an
accuracy of 99.9 percent by simply predicting every transaction as legitimate. What
primary metric failure does this scenario illustrate?
A. High variance due to overfitting
B. Multicollinearity among predictor variables
C. The accuracy paradox driven by severe class imbalance
D. Excessive regularization suppressing true signal
ANSWER: C. The accuracy paradox driven by severe class imbalance
When classes are heavily skewed, overall accuracy becomes a misleading metric because a
naive model predicting the majority class still achieves near-perfect score. Metrics like
precision, recall, F1-score, or AUC-ROC must be used instead.
,3. In regularized regression techniques such as Ridge and Lasso, what is the fundamental
mathematical difference between their penalty terms?
A. Ridge uses the L1 norm of the coefficients, while Lasso uses the L2 norm.
B. Ridge uses the L2 norm (squared coefficients), while Lasso uses the L1 norm (absolute
coefficients).
C. Ridge penalizes intercept terms, whereas Lasso penalizes error residuals.
D. Ridge applies non-linear transformations, while Lasso applies linear scaling.
ANSWER: B. Ridge uses the L2 norm (squared coefficients), while Lasso uses the L1 norm
(absolute coefficients).
Ridge regression adds a penalty proportional to the sum of squared coefficients (L2),
shrinking them toward zero uniformly. Lasso adds a penalty proportional to the sum of
absolute values (L1), which can drive coefficients completely to zero, performing effective
feature selection.
4. A retail chain wants to group its store locations into distinct clusters based on customer
demographics, average basket size, and local foot traffic. Which unsupervised machine
learning algorithm is best suited for this partitioning task when the number of target
clusters is known in advance?
A. K-Means clustering
B. Apriori association rule mining
C. Logistic regression
D. Decision tree classification
ANSWER: A. K-Means clustering
K-Means is a classic unsupervised partitioning algorithm designed to group observations into
a pre-specified number of clusters (k) based on feature proximity. Apriori is for association
rules, while logistic regression and decision trees are supervised methods requiring labeled
target outputs.
5. During exploratory data analysis for a predictive maintenance model, an analyst
observes that several continuous predictor variables are on drastically different scales—
one ranges from 0 to 1, while another ranges from 0 to 100,000. Why is feature scaling
essential before applying distance-based algorithms like K-Nearest Neighbors (KNN)?
A. Unscaled features will prevent the algorithm from computing categorical interactions.
, B. Features with larger numerical ranges will disproportionately dominate the distance
calculation, skewing results.
C. Scaling eliminates the need to check for missing values in the dataset.
D. Distance-based algorithms require all inputs to be transformed into binary indicators.
ANSWER: B. Features with larger numerical ranges will disproportionately dominate the
distance calculation, skewing results.
Distance metrics like Euclidean distance calculate straight-line separation across dimensions.
If one variable has massive numeric values, variations in that variable dictate the distance
score, rendering smaller-scale variables virtually meaningless without normalization.
6. A data science team is evaluating a logistic regression model on a validation dataset. By
lowering the classification threshold from 0.5 to 0.2, what direct impact will this change
have on the model's performance metrics?
A. Specificity will increase while sensitivity decreases.
B. Sensitivity (recall) will increase, while false positives will likely increase.
C. Overall accuracy will automatically reach 100 percent.
D. The area under the ROC curve will shift downward.
ANSWER: B. Sensitivity (recall) will increase, while false positives will likely increase.
Lowering the decision threshold makes the model more sensitive, classifying more instances as
the positive class. This captures more true positives (increasing sensitivity) but also catches
more negative instances incorrectly (increasing false positives and reducing specificity).
7. When performing linear regression, what assumption about the residuals (error terms)
must hold true to ensure that hypothesis testing and confidence intervals for the
coefficients are valid?
A. Residuals must be perfectly correlated with the predictor variables.
B. Residuals must be identically distributed, independent, and normally distributed with a mean
of zero.
C. Residuals must exhibit a strong upward trend over time.
D. Residuals must follow a binomial distribution with varying variance.
, ANSWER: B. Residuals must be identically distributed, independent, and normally
distributed with a mean of zero.
Valid statistical inference in linear regression relies on the Gauss-Markov theorem and error
assumptions: residuals should be independent, homoscedastic (constant variance), and
normally distributed around a mean of zero.
8. A logistics company is analyzing delivery time delays. They apply a time series
decomposition method and discover that the data contains a repeating seasonal pattern
that grows larger in magnitude as the overall trend increases over the years. Which
decomposition model should they select?
A. Additive decomposition model
B. Multiplicative decomposition model
C. Static mean-reverting model
D. Pure white noise model
ANSWER: B. Multiplicative decomposition model
When seasonal fluctuations increase or decrease proportionally with the level of the trend, a
multiplicative model is appropriate because components are multiplied rather than added. An
additive model assumes seasonal variations remain constant regardless of trend level.
9. In the context of variable selection and model building, what is the primary danger of
performing feature selection on the entire dataset before splitting it into training and
validation sets?
A. It guarantees that the model will underfit the training data.
B. It leads to data leakage, causing optimistic performance estimates on unseen data.
C. It removes all categorical variables automatically.
D. It makes the computation of decision boundaries impossible.
ANSWER: B. It leads to data leakage, causing optimistic performance estimates on unseen
data.
Using the entire dataset to select features means information from the validation or test
portion leaks into the training phase. This results in overly optimistic performance metrics
that fail to generalize to genuinely new data.
VERIFIED AND WELL DETAILED ANSWERS PLUS RATIONALES |
GUARANTEED PASS | LATEST EXAM UPDATE | EXAM PREP |
STUDY GUIDE | PRACTICE TEST| DOWNLOAD INSTANT PDF
1. A manufacturing plant manager wants to forecast monthly electricity consumption
based on historical data that exhibits a clear upward trend and strong seasonal variations.
Which modeling approach is most appropriate for capturing both components effectively?
A. Simple exponential smoothing
B. Holt-Winters additive or multiplicative smoothing
C. Basic moving average model
D. Single linear regression without time indices
ANSWER: B. Holt-Winters additive or multiplicative smoothing
Holt-Winters exponential smoothing specifically extends basic smoothing methods to capture
both trend and seasonality, making it ideal for this type of time series data. Simple smoothing
handles neither, a moving average handles neither adequately without lagging, and basic
linear regression fails to capture periodic seasonal cycles.
2. An analyst is building a classification model to detect fraudulent transactions, which
account for less than 0.1 percent of the total dataset. After training, the model achieves an
accuracy of 99.9 percent by simply predicting every transaction as legitimate. What
primary metric failure does this scenario illustrate?
A. High variance due to overfitting
B. Multicollinearity among predictor variables
C. The accuracy paradox driven by severe class imbalance
D. Excessive regularization suppressing true signal
ANSWER: C. The accuracy paradox driven by severe class imbalance
When classes are heavily skewed, overall accuracy becomes a misleading metric because a
naive model predicting the majority class still achieves near-perfect score. Metrics like
precision, recall, F1-score, or AUC-ROC must be used instead.
,3. In regularized regression techniques such as Ridge and Lasso, what is the fundamental
mathematical difference between their penalty terms?
A. Ridge uses the L1 norm of the coefficients, while Lasso uses the L2 norm.
B. Ridge uses the L2 norm (squared coefficients), while Lasso uses the L1 norm (absolute
coefficients).
C. Ridge penalizes intercept terms, whereas Lasso penalizes error residuals.
D. Ridge applies non-linear transformations, while Lasso applies linear scaling.
ANSWER: B. Ridge uses the L2 norm (squared coefficients), while Lasso uses the L1 norm
(absolute coefficients).
Ridge regression adds a penalty proportional to the sum of squared coefficients (L2),
shrinking them toward zero uniformly. Lasso adds a penalty proportional to the sum of
absolute values (L1), which can drive coefficients completely to zero, performing effective
feature selection.
4. A retail chain wants to group its store locations into distinct clusters based on customer
demographics, average basket size, and local foot traffic. Which unsupervised machine
learning algorithm is best suited for this partitioning task when the number of target
clusters is known in advance?
A. K-Means clustering
B. Apriori association rule mining
C. Logistic regression
D. Decision tree classification
ANSWER: A. K-Means clustering
K-Means is a classic unsupervised partitioning algorithm designed to group observations into
a pre-specified number of clusters (k) based on feature proximity. Apriori is for association
rules, while logistic regression and decision trees are supervised methods requiring labeled
target outputs.
5. During exploratory data analysis for a predictive maintenance model, an analyst
observes that several continuous predictor variables are on drastically different scales—
one ranges from 0 to 1, while another ranges from 0 to 100,000. Why is feature scaling
essential before applying distance-based algorithms like K-Nearest Neighbors (KNN)?
A. Unscaled features will prevent the algorithm from computing categorical interactions.
, B. Features with larger numerical ranges will disproportionately dominate the distance
calculation, skewing results.
C. Scaling eliminates the need to check for missing values in the dataset.
D. Distance-based algorithms require all inputs to be transformed into binary indicators.
ANSWER: B. Features with larger numerical ranges will disproportionately dominate the
distance calculation, skewing results.
Distance metrics like Euclidean distance calculate straight-line separation across dimensions.
If one variable has massive numeric values, variations in that variable dictate the distance
score, rendering smaller-scale variables virtually meaningless without normalization.
6. A data science team is evaluating a logistic regression model on a validation dataset. By
lowering the classification threshold from 0.5 to 0.2, what direct impact will this change
have on the model's performance metrics?
A. Specificity will increase while sensitivity decreases.
B. Sensitivity (recall) will increase, while false positives will likely increase.
C. Overall accuracy will automatically reach 100 percent.
D. The area under the ROC curve will shift downward.
ANSWER: B. Sensitivity (recall) will increase, while false positives will likely increase.
Lowering the decision threshold makes the model more sensitive, classifying more instances as
the positive class. This captures more true positives (increasing sensitivity) but also catches
more negative instances incorrectly (increasing false positives and reducing specificity).
7. When performing linear regression, what assumption about the residuals (error terms)
must hold true to ensure that hypothesis testing and confidence intervals for the
coefficients are valid?
A. Residuals must be perfectly correlated with the predictor variables.
B. Residuals must be identically distributed, independent, and normally distributed with a mean
of zero.
C. Residuals must exhibit a strong upward trend over time.
D. Residuals must follow a binomial distribution with varying variance.
, ANSWER: B. Residuals must be identically distributed, independent, and normally
distributed with a mean of zero.
Valid statistical inference in linear regression relies on the Gauss-Markov theorem and error
assumptions: residuals should be independent, homoscedastic (constant variance), and
normally distributed around a mean of zero.
8. A logistics company is analyzing delivery time delays. They apply a time series
decomposition method and discover that the data contains a repeating seasonal pattern
that grows larger in magnitude as the overall trend increases over the years. Which
decomposition model should they select?
A. Additive decomposition model
B. Multiplicative decomposition model
C. Static mean-reverting model
D. Pure white noise model
ANSWER: B. Multiplicative decomposition model
When seasonal fluctuations increase or decrease proportionally with the level of the trend, a
multiplicative model is appropriate because components are multiplied rather than added. An
additive model assumes seasonal variations remain constant regardless of trend level.
9. In the context of variable selection and model building, what is the primary danger of
performing feature selection on the entire dataset before splitting it into training and
validation sets?
A. It guarantees that the model will underfit the training data.
B. It leads to data leakage, causing optimistic performance estimates on unseen data.
C. It removes all categorical variables automatically.
D. It makes the computation of decision boundaries impossible.
ANSWER: B. It leads to data leakage, causing optimistic performance estimates on unseen
data.
Using the entire dataset to select features means information from the validation or test
portion leaks into the training phase. This results in overly optimistic performance metrics
that fail to generalize to genuinely new data.
