作者rpm (我永遠的旭仔..)
站內Statistics
標題[問題] 2階微分求極值的問題--有關regression
時間Mon Jun 5 12:20:20 2006
老師出了一題統計公課
因為實在遠離數學太久了~~
可以請高手幫我解答或提示我那本參考書可以找到答案嗎? 感激不盡 T T
題目是:
simple regression
sample:(x1,y1),(x2,y2),...(xn,yn)
Y=a+bx+ε
^ ^
E(Y)=a + b x
2
E~ N(0,σ )
n 2 n 2
L= Σ εi = Σ [yi-(a+b*xi)]
i=1 i=1
^ _ _ 2 _2
δL/δa=0 , δL/δb=0 證明:b =Σxiyi-nx y / Σxi - nx
^ _ ^ _
a = y- b * x
接下來還要證明下面四項,D式子我不太會微分 >"<
Let L be a function of two variables with continuous second-order partial
derivatives in some circle centered at a critical point(a,b)
2
and let D=Lxx(a,b)Lyy(a,b)-{Lxy(a,b)}
(I) if D > 0 , Lxx(a,b)>0 ,then L has a relative minimum at (a,b)
(II) if D > 0 , Lxx(a,b)<0 ,then L has a relative maximum at (a,b)
(III) if D < 0 , then L has a saddle point at (a,b)
(IV) if D = 0 , then no conclusion can be drown
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