How does the 'elbow method' help in determining the optimal number of clusters in K-means clustering?
- By calculating the average distance between all pairs of clusters
- By comparing the silhouette scores for different numbers of clusters
- By creating a dendrogram of clusters
- By finding the point in the plot of within-cluster sum of squares where the decrease rate sharply shifts
The elbow method involves plotting the explained variation as a function of the number of clusters and picking the elbow of the curve as the number of clusters to use. This 'elbow' is the point representing the optimal number of clusters at which the within-cluster sum of squares (WCSS) doesn't decrease significantly with each iteration.
The type of factor analysis in which the researcher assumes that all variance in the observed variables is common variance is known as _______ factor analysis.
- common factor
- confirmatory
- exploratory
- principal component
The type of factor analysis in which the researcher assumes that all variance in the observed variables is common variance is known as common factor analysis.
The Kruskal-Wallis Test is used to compare ________ independent samples.
- four
- three
- three or more
- two
The Kruskal-Wallis Test is used to compare three or more independent samples. It's an extension of the Mann-Whitney U Test for more than two groups.
In which situation is Spearman's Rank Correlation preferable to Pearson's correlation?
- When the data is normally distributed
- When the relationship between variables is non-linear and monotonic
- When the relationship is linear
- When there are no ties in the ranks
Spearman's Rank Correlation is preferable to Pearson's correlation when the relationship between variables is non-linear but monotonic. Pearson's correlation measures linear relationships, while Spearman's can capture non-linear relationships.
What is the z-value associated with a 95% confidence interval in a standard normal distribution?
- 1.64
- 1.96
- 2
- 2.33
The z-value associated with a 95% confidence interval in a standard normal distribution is approximately 1.96. This means that we are 95% confident that the true population parameter lies within 1.96 standard deviations of the sample mean.
How is the interquartile range different from the range in handling outliers?
- Both exclude outliers
- Both include outliers
- The interquartile range does not include outliers, the range does
- The interquartile range includes outliers, the range does not
The interquartile range, which is the difference between the upper quartile (Q3) and the lower quartile (Q1), represents the middle 50% of the data and is not affected by outliers. The range, on the other hand, is the difference between the maximum and minimum data values and is significantly affected by outliers.
How can 'outliers' impact the result of K-means clustering?
- Outliers can distort the shape and size of the clusters
- Outliers can lead to fewer clusters
- Outliers can lead to more clusters
- Outliers don't impact K-means clustering
Outliers can have a significant impact on the result of K-means clustering. They can distort the shape and size of the clusters, as they may pull the centroid towards them, creating less accurate and meaningful clusters.
A positive Pearson's Correlation Coefficient indicates a ________ relationship between two variables.
- inverse
- linear
- perfect
- positive
A positive Pearson's Correlation Coefficient indicates a positive relationship between two variables. This means that as one variable increases, the other variable also increases, and vice versa.
What are the assumptions made in simple linear regression?
- Homogeneity, normality, and symmetry
- Independence, homogeneity, and linearity
- Linearity, homoscedasticity, and normality
- Symmetry, linearity, and independence
The assumptions made in simple linear regression include linearity (the relationship between the independent and dependent variables is linear), homoscedasticity (the variance of the residuals is constant across all levels of the independent variable), and normality (the residuals are normally distributed).
Principal Component Analysis (PCA) is a dimensionality reduction technique that projects the data into a lower dimensional space called the _______.
- eigen space
- feature space
- subspace
- variance space
PCA is a technique that projects the data into a new, lower-dimensional subspace. This subspace consists of principal components which are orthogonal to each other and capture the maximum variance in the data.