Chapter 9 PCA Exam Questions and Answers
with Verified Solutions | Latest Updated 2026
PCA provides low-dimensional T
linear surfaces that are closest
to the observations
The first principal component T
is the line in the p-dimensional
space that is closest to the
observations
PCA finds a low dimension T
representation of a dataset
that contains as much variation
as possible.
PCA serves as a tool for data T
visualization.
Use all possible principal F. use the least amount of PCs. If using all
components to provide the PC's, then it is identical to using all of the
best understanding of data original features.
If all principal components are used, PCR
is equivalent to performing ordinary least
squares using the original predictors.
, For a given principal T.
component, the sum of the
squares of the loadings across
the four variables is one.
There are four variables. The T. since p=4, four PCs capture all the
four principal components variations.
explain 100% of the variance.
PCA is a suitable technique F. It is a suitable technique when IT IS
when the variables in the data STRONGLY LINEARLY RELATED
are strongly non-linearly
related.
Distinct principal components T
are uncorrelated with each
other.
If the number of principal T.
components is equal to the
number of original variables,
then the approximation of the
data by the principal
component scores and
loadings is exact.
Neither the score or loading F. Both the score and loading vectors are
vectors are unique up to a unique up to a sign flip.
sign flip
with Verified Solutions | Latest Updated 2026
PCA provides low-dimensional T
linear surfaces that are closest
to the observations
The first principal component T
is the line in the p-dimensional
space that is closest to the
observations
PCA finds a low dimension T
representation of a dataset
that contains as much variation
as possible.
PCA serves as a tool for data T
visualization.
Use all possible principal F. use the least amount of PCs. If using all
components to provide the PC's, then it is identical to using all of the
best understanding of data original features.
If all principal components are used, PCR
is equivalent to performing ordinary least
squares using the original predictors.
, For a given principal T.
component, the sum of the
squares of the loadings across
the four variables is one.
There are four variables. The T. since p=4, four PCs capture all the
four principal components variations.
explain 100% of the variance.
PCA is a suitable technique F. It is a suitable technique when IT IS
when the variables in the data STRONGLY LINEARLY RELATED
are strongly non-linearly
related.
Distinct principal components T
are uncorrelated with each
other.
If the number of principal T.
components is equal to the
number of original variables,
then the approximation of the
data by the principal
component scores and
loadings is exact.
Neither the score or loading F. Both the score and loading vectors are
vectors are unique up to a unique up to a sign flip.
sign flip
