Does the Best-Fitting Curve Always Exist?

Table 2

Percentage (%) of randomly generated samples of n points for which the best-fitting ellipse exists.

Distribution	𝑛=5	𝑛=6	𝑛=8	𝑛=10	𝑛=20	𝑛=50
Normal 𝐕1	22	23	23	24	27	27
Normal 𝐕2	22	22	24	26	27	33
Square [0,1]×[0,1]	28	32	40	46	52	60
Rectangle [0,2]×[0,1]	28	29	28	30	31	32