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=>m
三維數據(1.3),(2,3),(2,9),(3,5),試利用最小平方法求出y對x的最適
y=mx+k
[ 3-(m +k)] + [3-(2m+k)] + [9-12m+k])] + [5-(3m+k)]²
=9-6m-6k+m²+2 mk + k² + 9-12m-6k+4m²+4mk+k² +84-36m-10
+4m² +4mk +k² +25-30m tok + 9m² + Omk+k"
= 18m+4k²-84m-40k +16mk +124

Answer 1

✨ 最佳解答 ✨

qn

18m²+4k²-84m-40k+16mk+124
=18m²+(16k-84)m+(4k²-40k+124)
=18[m²+(8/9 k - 14/3)m]+(4k²-40k+124)
=18[m²+2(4/9 k - 7/3)m]+(4k²-40k+124)
=18[m²+2(4/9 k - 7/3)m+(4/9 k - 7/3)²] - 18(4/9 k -7/3)² + (4k²-40k+124)
=18(m+4/9 k - 7/3)² - 18(16/81 k² - 56/27 k + 49/9) + (4k²-40k+124)
=2(3m+4/3 k -7)² - 32/9 k² + 112/3 k - 98 +4k²-40k+124
=2(3m+4/3 k -7)² + 4/9 k² - 8/3 k + 26
=2(3m+4/3 k -7)² + 4/9 (k²-6k) +26
=2(3m+4/3 k -7)² + 4/9 (k²-6k+9) -4 +26
=2(3m+4/3 k -7)² + 4/9 (k-3)² +22
≥22

最小值發生時，3m+4/3 k -7=0 且 k-3=0
解得 k=3, m=1