Chapter 13 Multiple choice questions

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. Download the data file for the multiple-choice questions for Chapter 13, and open it in R. Conduct k-means clustering with 3 clusters on the data stored in clusterdata. How many observations are in the largest cluster?

8 correct incorrect

11 correct incorrect

13 correct incorrect

15 correct incorrect

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. What percentage of the variance is explained by the three-cluster solution?

78% correct incorrect

64% correct incorrect

55% correct incorrect

12% correct incorrect

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. Try running clustering solutions with 2, 4, 5 and 6 clusters. Which one explains the greatest proportion of the variance?

2 clusters correct incorrect

4 clusters correct incorrect

5 clusters correct incorrect

6 clusters correct incorrect

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. Consider the following cluster solutions, with between 2 and 6 clusters. The values are residual sums of squares:
Clusters (k): 2   3   4   5   6
RSS: 138   120   99   86   85
Calculate the AIC score for each solution using the expression:
AIC <- 2*k + n*log(RSS)
Where k is the number of clusters, and n is the sample size of 20 data points.
Which solution has the lowest AIC score?

2 clusters correct incorrect

3 clusters correct incorrect

5 clusters correct incorrect

6 clusters correct incorrect

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. Calculate the distance matrix for the data in clusterdata. What is the largest distance between any two points?

3.01 correct incorrect

9.09 correct incorrect

0.17 correct incorrect

3.94 correct incorrect

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. The dataset swiss is part of the datasets package and contains demographic information for 47 Swiss provinces. Load it into the environment with data(swiss). The fifth column contains information about the percentage of Catholics in each province. How many provinces had more than 50% Catholic citizens?

10 correct incorrect

18 correct incorrect

24 correct incorrect

29 correct incorrect

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. Calculate a distance matrix on a subset of the swiss data that excludes column 5. What is the smallest distance in the matrix?

117.84 correct incorrect

35.98 correct incorrect

4.99 correct incorrect

3.75 correct incorrect

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. Conduct metric multidimensional scaling on the distance matrix you calculated in Question 7, to reduce it to two dimensions. Plot the data, representing the data for majority Catholic provinces in a different colour from majority non-Catholic provinces. Which of the following best describes the results?

The Catholic data points cluster in the lower right corner, apart from two outliers correct incorrect

The Catholic data points cluster in the upper left corner, apart from two outliers correct incorrect

The data points are not well segregated, and there is no clear structure to the results correct incorrect

The Catholic data points cluster in the centre of the plot, with non-Catholic data points at more extreme locations correct incorrect

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. Now conduct k-means clustering on the subset of Swiss data excluding the religion column, to find two clusters. Plot the scaled data again, but this time colour code according to cluster. What do you notice?

There is very little correspondence between the k-means clusters and the religion categories correct incorrect

The clusters map exactly onto the religious groupings correct incorrect

The clusters reveal similar groupings to the religion data, but the correspondence is not perfect correct incorrect

All of the Catholic provinces fall within one cluster correct incorrect

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. Use the isoMDS function in the MASS package to conduct non-metric multidimensional scaling on the same data. Plot the results. How do they compare to the metric scaling?

The results are identical correct incorrect

The results are completely different correct incorrect

The results are substantially different, but the overall structure is similar correct incorrect

The results are very similar, with only slight differences in the point locations correct incorrect