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?
Select an answer to reveal the explanation.
Short Explanation
You're looking for the point where the WCSS curve bends. The biggest drop happens from k=2 to k=3, then the next meaningful drop is from k=3 to k=4. After k=4, the gains are tiny, so the elbow is at k=4.
Full Explanation
The elbow method suggests k=4 because the largest WCSS drop is from k=2 to k=3 (500 units), and the second largest is from k=3 to k=4 (200 units). After k=4, WCSS falls by only 20 and 15 units, so diminishing returns put the elbow at k=4, where extra clusters give minimal improvement. The k=2 and k=3 choices are before the elbow, while the k=6 choice over-clusters with minimal WCSS gain.