Question 1

Simple Euclidean distance is a common measurement of similarity on a perceptual map.

Accepted Answer

Euclidean distance is a commonly used method of measuring the similarity between points on a perceptual map.

Question 2

It is always advisable to have as many factors as the number of input variables.

Accepted Answer

Having as many factors as the number of input variables can lead to an over-parameterized model, potentially leading to overfitting and decreased model generalization ability. It is important to carefully select only relevant and important factors to include in the model.

Question 3

In quick clustering, the first step is to identify the highest entry in each column of a matrix of inter-band inter-product, etc.) correlations. 38.Consider the following data:  The following is an accurate graphical representation of the data shown above:

Accepted Answer

The answer of In quick clustering, the first step is...

Question 4

If a clustering procedure starts with one cluster and subdivides until all objects are in their own single-object cluster, the procedure is termed top-down hierarchical clustering.

Accepted Answer

This is the definition of top-down hierarchical clustering or divisive clustering.

Question 5

The ABC Company is involved in trying to segment its market so that it can better design specific marketing programs directed at each segment.One method of segmenting that it might use is cluster analysis.

Accepted Answer

Cluster analysis is a commonly used technique in market segmentation to group together consumers that share similar characteristics, behaviors, or preferences. By using this method, the ABC Company can identify homogeneous groups of customers and tailor its marketing strategies accordingly to meet their specific needs and wants.

Question 6

Factor loadings and correlations are identical if each variable has its mean subtracted and is divided by its standard deviation.

Accepted Answer

Factor loadings and correlations are affected by the scale of the variables. By standardizing the variables, we remove the influence of differing scales and can ensure that factor loadings and correlations are comparable.

Question 7

While analyzing and interpreting consumer perception data using factor analysis, a researcher found the factor loading on Factor 1 to be high.However, he could not interpret the factor meaningfully. A probable cause for this situation is computation error or shortsightedness in his interpretation, since a high loading ensures meaningfulness.

Accepted Answer

A high loading on a factor does not ensure meaningfulness if the researcher has not carefully considered the items that loaded on the factor and their underlying conceptual similarities or differences. The researcher may need to conduct further analyses or qualitative research to better understand the factor's meaning.

Question 8

Varimax searches for a set of factor loadings such that each factor has some loadings close to 0 and some loadings close to -1 or +1. Factor Loadings

Accepted Answer

This statement accurately describes the objective of the Varimax rotation method for factor analysis.

Question 9

An attractive feature of varimax rotation is that it may retain the variance explained, while reducing the number of factors in the solution as compared to principal components analysis).

Accepted Answer

Varimax rotation, a method of orthogonal rotation, does not reduce the number of factors in the solution; it aims to make the loadings within each factor more interpretable by maximizing the variance of the squared loadings of a factor on all the variables. The number of factors is determined before applying the rotation, and the total variance explained remains the same before and after rotation.

Question 10

After performing a principal components analysis, a researcher finds that the cumulative variance explained by the solution is 0.56.He can increase the explained variance by performing a varimax rotation.

Accepted Answer

Varimax rotation, a method of orthogonal rotation, simplifies the interpretation of the principal components by redistributing the variance but does not increase the total explained variance.

Question 11

The basic task in cluster analysis is to uncover competing explanations for a causal phenomenon.

Accepted Answer

The basic task in cluster analysis is to group items or observations together based on their similarities, without necessarily inferring causality.

Question 12

A nonhierarchical clustering program is one in which objects are allowed to leave one cluster to join another as clusters are being formed if the clustering criterion will be improved by doing so.

Accepted Answer

In a nonhierarchical clustering program, objects are allowed to leave one cluster to join another if it improves the clustering criterion. This is known as the "relaxation principle" and is a defining feature of nonhierarchical clustering.

Question 13

The first factor accounts for more of the variation in the data than the second factor.

Accepted Answer

This statement means that the first principal component (factor) has a higher eigenvalue than the second principal component, indicating that it explains more of the variance in the data than the second.

Question 14

The percent of variance explained is a summary measurement indicating how much of the total original variance of all the respondents is represented by the factor.

Accepted Answer

The statement accurately defines the concept of percent of variance explained.

Question 15

In both principal components analysis and varimax rotation, the factors are constrained to be uncorrelated or geometrically perpendicular.

Accepted Answer

Both principal components analysis and varimax rotation aim to produce uncorrelated factors, which are represented as orthogonal axes in the factor space.

Question 16

The variation in variable 3 is shown to be completely explained by the two-factor solution.

Accepted Answer

The statement does not provide enough information to conclude that the variation in variable 3 is completely explained by the two-factor solution without additional statistical evidence or analysis details.

Question 17

All factor analysis methods constrain the factors to be uncorrelated.

Accepted Answer

Factor analysis methods can be divided into two main types: exploratory factor analysis (EFA) and confirmatory factor analysis (CFA). In EFA, factors can be either correlated or uncorrelated, depending on the rotation method used (orthogonal rotations assume uncorrelated factors, while oblique rotations allow for correlated factors). CFA, on the other hand, can explicitly model factors to be correlated if specified by the researcher.

Question 18

Rotation of factors changes the interpretation of the factors while retaining the principal component patterns of loadings.

Accepted Answer

Rotation of factors changes the interpretation of the factors by altering the loadings to achieve a simpler, more interpretable structure, but it does not retain the original principal component patterns of loadings.

Question 19

Communality is the percent of a variable's variance which contributes to the correlation with other variables or is common to other variables.

Accepted Answer

This is the correct definition of communality. It measures how much of a variable's variance can be explained by the other variables in the correlation matrix. A high communality suggests that the variable is a good measure of the underlying construct being studied.

Question 20

An attractive feature of principal components analysis is the easy interpretability of the factors.

Accepted Answer

Principal Components Analysis (PCA) often results in components that are linear combinations of the original variables, making the interpretation of these components less straightforward compared to the original variables.

Quiz 20: Iscriminant, Factor and Cluster Analysis