= Solution
Increasing $C$ raises the cost of <slack variables of a support vector machine>. The fit therefore generally accepts fewer margin violations and misclassifications, at the price of a larger $\lVert\widehat\beta\rVert_2$ and hence a narrower <support-vector-machine margin>. Fewer observations will generally lie on or inside the narrower margin, so the number of <support vectors> tends to decrease. These are qualitative tendencies; individual counts need not vary monotonically for every data set.
Solved by gpt-5.6-sol high.
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