ISYE6501 INTRODUCTION ANALYTICS
MODELING ACTUAL EXAM PAPER 2026
SOLVED QUESTIONS WITH FULL SOLUTION
GRADED A+
◉ Columns Answer: The 'answer' for each data point
(response/outcome)
◉ Structured Data Answer: Quantitative, Categorical, Binary, Unrelated,
Time Series
◉ Unstructured Data Answer: Text
◉ Support Vector Model Answer: Supervised machine learning
algorithm used for both classification and regression challenges.
Mostly used in classification problems by plotting each data item as a
point in n-dimensional space (n is the number of features you have) with
the value of each feature being the value of a particular coordinate.
Then you classify by finding a hyperplane that differentiates the 2
classes very well. Support vectors are simply the coordinates of
individual observation -- it best segregates the two classes (hyperplane /
line).
◉ What do you want to find with a SVM model? Answer: Find values
of a0, a1,...,up to am that classifies the points correctly and has the
maximum gap or margin between the parallel lines.
,◉ What should the sum of the green points in a SVM model be?
Answer: The sum of green points should be greater than or equal to 1
◉ What should the sum of the red points in a SVM model be? Answer:
The sum of red points should be less than or equal to -1
◉ What should the total sum of green and red points be? Answer: The
total sum of all green and red points should be equal to or greater than 1
because yj is 1 for green and -1 for red.
◉ First principal component Answer: PCA -- a linear combination of
original predictor variables which captures the maximum variance in the
data set. It determines the direction of highest variability in the data.
Larger the variability captured in first component, larger the information
captured by component. No other component can have variability higher
than first principal component.
it minimizes the sum of squared distance between a data point and the
line.
◉ Second principal component Answer: PCA -- also a linear
combination of original predictors which captures the remaining
variance in the data set and is uncorrelated with Z¹. In other words, the
correlation between first and second component should is zero.
◉ What if it's not possible to separate green and red points in a SVM
model? Answer: Utilize a soft classifier -- In a soft classification
, context, we might add an extra multiplier for each type of error with a
larger penalty, the less we want to accept mis-classifying that type of
point.
◉ Soft Classifier Answer: Account for errors in SVM classification.
Trading off minimizing errors we make and maximizing the margin.
To trade off between them, we pick a lambda value and minimize a
combination of error and margin. As lambda gets large, this term gets
large.
The importance of a large margin outweighs avoiding mistakes and
classifying known data points.
◉ Should you scale your data in a SVM model? Answer: Yes, so the
orders of magnitude are approximately the same.
Data must be in bounded range.
Common scaling: data between 0 and 1
a. Scale factor by factor
b. Linearly
◉ How should you find which coefficients to hold value in a SVM
model? Answer: If there is a coefficient who's value is very close to 0,
means the corresponding attribute is probably not relevant for
classification.
◉ Does SVM work the same for multiple dimensions? Answer: Yes
MODELING ACTUAL EXAM PAPER 2026
SOLVED QUESTIONS WITH FULL SOLUTION
GRADED A+
◉ Columns Answer: The 'answer' for each data point
(response/outcome)
◉ Structured Data Answer: Quantitative, Categorical, Binary, Unrelated,
Time Series
◉ Unstructured Data Answer: Text
◉ Support Vector Model Answer: Supervised machine learning
algorithm used for both classification and regression challenges.
Mostly used in classification problems by plotting each data item as a
point in n-dimensional space (n is the number of features you have) with
the value of each feature being the value of a particular coordinate.
Then you classify by finding a hyperplane that differentiates the 2
classes very well. Support vectors are simply the coordinates of
individual observation -- it best segregates the two classes (hyperplane /
line).
◉ What do you want to find with a SVM model? Answer: Find values
of a0, a1,...,up to am that classifies the points correctly and has the
maximum gap or margin between the parallel lines.
,◉ What should the sum of the green points in a SVM model be?
Answer: The sum of green points should be greater than or equal to 1
◉ What should the sum of the red points in a SVM model be? Answer:
The sum of red points should be less than or equal to -1
◉ What should the total sum of green and red points be? Answer: The
total sum of all green and red points should be equal to or greater than 1
because yj is 1 for green and -1 for red.
◉ First principal component Answer: PCA -- a linear combination of
original predictor variables which captures the maximum variance in the
data set. It determines the direction of highest variability in the data.
Larger the variability captured in first component, larger the information
captured by component. No other component can have variability higher
than first principal component.
it minimizes the sum of squared distance between a data point and the
line.
◉ Second principal component Answer: PCA -- also a linear
combination of original predictors which captures the remaining
variance in the data set and is uncorrelated with Z¹. In other words, the
correlation between first and second component should is zero.
◉ What if it's not possible to separate green and red points in a SVM
model? Answer: Utilize a soft classifier -- In a soft classification
, context, we might add an extra multiplier for each type of error with a
larger penalty, the less we want to accept mis-classifying that type of
point.
◉ Soft Classifier Answer: Account for errors in SVM classification.
Trading off minimizing errors we make and maximizing the margin.
To trade off between them, we pick a lambda value and minimize a
combination of error and margin. As lambda gets large, this term gets
large.
The importance of a large margin outweighs avoiding mistakes and
classifying known data points.
◉ Should you scale your data in a SVM model? Answer: Yes, so the
orders of magnitude are approximately the same.
Data must be in bounded range.
Common scaling: data between 0 and 1
a. Scale factor by factor
b. Linearly
◉ How should you find which coefficients to hold value in a SVM
model? Answer: If there is a coefficient who's value is very close to 0,
means the corresponding attribute is probably not relevant for
classification.
◉ Does SVM work the same for multiple dimensions? Answer: Yes
