PCA Exam Questions and Answers with
Verified Solutions | Latest Updated 2026
Why does prediction accuracy Accuracy decays when the number of
often decay in traditional variables (p) is approximately equal to
statistical models when p is the number of observations (n).
large?
How does PCA handle It seeks a low-dimensional representation
redundant or uninformative that captures most of the data's variation
features? while minimizing redundancy and noise.
In PCA, how is a new variable As a linear combination (a weighted sum)
(a principal component) of the original variables: Z = w1X1 + w2X2
mathematically represented? +... + wpXp.
What is the core criterion for To find the direction (linear combination)
choosing weights in PCA? that captures the maximum empirical
variance in the data.
What does it mean for a PCA It is the direction that accounts for the
direction to be the 'most greatest amount of sample variability.
interesting'?
What constraint is applied It must maximize variance while being
when finding the second uncorrelated (orthogonal) to the first
principal component (Z2)? principal component (Z1).
, What does the condition It implies that the directions of the
Cor(Z1, Z2) = 0 imply principal components are perpendicular
geometrically? or orthogonal to each other.
How does PCA simplify high- By reducing the data to a few principal
dimensional data components, it allows for 2D or 3D
visualization? scatterplots that represent the most
significant information.
What is a 'noise feature' in the A feature that is uninformative for the
context of high-dimensional specific problem under study.
data?
True or False: PCA is the only False; PCA is the most common form, but
method for dimension far from the only one.
reduction.
What is the relationship When p > 3, it becomes difficult to draw
between p and n that makes standard 2D or 3D scatterplots.
data visualization difficult?
How is the weight vector for As w1,..., wp.
PCA denoted?
What is the result of applying A set of derived predictors (principal
PCA to a dataset with p components) that represent the data in a
variables? lower-dimensional space.
What does the term The presence of correlation among
'redundancy' refer to in high- features.
dimensional data?
Verified Solutions | Latest Updated 2026
Why does prediction accuracy Accuracy decays when the number of
often decay in traditional variables (p) is approximately equal to
statistical models when p is the number of observations (n).
large?
How does PCA handle It seeks a low-dimensional representation
redundant or uninformative that captures most of the data's variation
features? while minimizing redundancy and noise.
In PCA, how is a new variable As a linear combination (a weighted sum)
(a principal component) of the original variables: Z = w1X1 + w2X2
mathematically represented? +... + wpXp.
What is the core criterion for To find the direction (linear combination)
choosing weights in PCA? that captures the maximum empirical
variance in the data.
What does it mean for a PCA It is the direction that accounts for the
direction to be the 'most greatest amount of sample variability.
interesting'?
What constraint is applied It must maximize variance while being
when finding the second uncorrelated (orthogonal) to the first
principal component (Z2)? principal component (Z1).
, What does the condition It implies that the directions of the
Cor(Z1, Z2) = 0 imply principal components are perpendicular
geometrically? or orthogonal to each other.
How does PCA simplify high- By reducing the data to a few principal
dimensional data components, it allows for 2D or 3D
visualization? scatterplots that represent the most
significant information.
What is a 'noise feature' in the A feature that is uninformative for the
context of high-dimensional specific problem under study.
data?
True or False: PCA is the only False; PCA is the most common form, but
method for dimension far from the only one.
reduction.
What is the relationship When p > 3, it becomes difficult to draw
between p and n that makes standard 2D or 3D scatterplots.
data visualization difficult?
How is the weight vector for As w1,..., wp.
PCA denoted?
What is the result of applying A set of derived predictors (principal
PCA to a dataset with p components) that represent the data in a
variables? lower-dimensional space.
What does the term The presence of correlation among
'redundancy' refer to in high- features.
dimensional data?
