A data scientist applies the elbow method to choose k for PROC HPCLUS. The within-cluster sum of squares (WCSS) values are: k=2: 1200, k=3: 700, k=4: 500, k=5: 480, k=6: 465. Which k value does the elbow method suggest?
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Short Explanation and Infographic
Here's the deal — c is correct because the largest drop in WCSS occurs from k=2 to k=3 (500 units), and the second largest from k=3 to k=4 (200 units). After k=4 the WCSS decreases by only 20 and 15 units — diminishing returns indicate the 'elbow' is at k=4, where additional clusters provide minimal improvement.
Full explanation below image
Full Explanation
C is correct because the largest drop in WCSS occurs from k=2 to k=3 (500 units), and the second largest from k=3 to k=4 (200 units). After k=4 the WCSS decreases by only 20 and 15 units — diminishing returns indicate the 'elbow' is at k=4, where additional clusters provide minimal improvement. A and B are before the elbow. D over-clusters with minimal WCSS gain.