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1
2 II
3 Excel, Mathematica Mathematica Osaka Electro-Communication University (2007 Apr)
4 II
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13 y y = a x + b (x 2, y 2 ) (x 1, y 1 ) y 1 = ax 1 + b y 2 = a x 2 + b x
14 y 1 = a x 1 + b y 2 = a x 2 + b x 1 1 a y 1 = x 2 1 b y 2 a x y 1 b = x 2 1 y 2
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21 100 (Kg) (cm)
22 100 (Kg) Kg 70.5 Kg cm (cm)
23
24 ?
25 y x
26 y x
27 y x
28 y x
29 y x
30 y y = a x + b a b x
31 y i ax i +b y d i y = ax a x b d i = y i (a x i + b) x i i (x( i, y i ) x Σ d 2 = Σ{ ( +b)} ab i y i (a x i 2 a,
32 y = a x b n n Σ d i 2 = Σ{ y i (a x i + b)} 2 a, b i=1 1 i=1 1 n i (x i, y i )
33 n f (a,b)= Σ{ y ( i (a x i + b)} 2 a, b i=1 f (a,b) ab a, a f (a,b) = 0 b f (a,b) = 0 a, b 0
34 y y = b y i b d i d i = y i b x i i (x( i, y i ) Σ d 2 = Σ{ i y i b} 2 b x
35 y = b n n Σ d i 2 = Σ{ y i b} 2 b i=1 1 i=1 1 n i (x i, y i )
36 n f (b)= Σ{ y i b} 2 b i=1 f (b) b f (b) d db f (b) = 0 b 0 b
37 f(x) = ax 2 + bx + c f (x) f (x) = 2ax + b = 0 b x x = b 2a b 2a
38 n f (b) = Σ{ y 2 i b} i=1 f (b) = Σ{ y 2 2 i 2y i b + b } = Σy 2 2 i 2bΣy + i nb 1 Σ nσy i b d =2nb =2(nb )=0 db f (b) 2Σy Σy i i b = 1 Σ n Σy i b y i
39 y b = 1 n Σy i y = b = n Σy i y i d i x i n 1 d i = y i b i (x( i, y i ) Σ d i 2 = Σ{ y i b} 2 b x 1 n Σy i
40 n f (a,b)= Σ{ y ( i (a x i + b)} 2 a, b i=1 f (a,b) ab a, a f (a,b) = 0 b f (a,b) = 0 a, b 0
41 g(x,y) = ax 2 + bxy + cy 2 + dx + ey + f g(x,y) y g (x,y) = g (x,y) x =0 x x x g (x,y) = g (x,y) y =0 y y y x
42 g(x,y) = ax 2 + bxy + cy 2 + dx + ey + f g(y) = cy 2 + (bx + e)y + (ax 2 + dx + f) y y y y g (x,y) = g y (x,y) =0 x g (x,y) = g x (x,y) =0 x y g(x) = ax 2 +(by + d)x + (cy 2 + ey + f) x x x
43 g(x,y) = ax 2 + bxy + cy 2 + dx + ey + f g(y) = cy 2 + (bx + e)y + (ax 2 + dx + f) g (y) = 2cy + (bx + e) y y y g (x,y) = g y (x,y) =0 x g (x,y) = g x (x,y) =0 x g(x) = ax 2 +(by + d)x + (cy 2 + ey + f) g (x) ) = 2ax +(b (by + d) x
44 g(x,y) = ax 2 + bxy + cy 2 + dx + ey + f g x (x,y) = 2ax + by + d = 0 y g y (x,y) = 2cy + bx + e = 0 2ae bd x y = b2 4ac 2bd ae x = b2 4ac
45 x, y f(x, y) = 3x 2 + 5xy + 2y 2 5x 8y +6 f(x, y) = 3x 2 a 2 + 5xya y 2cx 2b 2 y +6
46 n f (a,b)= Σ{ y ( i (a x i + b)} 2 a, b i=1 f (a,b) ab a, a f (a,b) = 0 b f (a,b) = 0 a, b 0
47 A. B. n f (a,b)= Σ{ y i (a x i + b)} 2 a, b i=1 f (a,b) a, b f a (a,b), f b (a,b) f (a,b) f a (a,b) = 0 f b (a,b), = 0 a, b
48 A f (a,b)= Σ{ y i (a x i + b)} 2 = Σ{ y 2 i 2y i (ax i + b) + (a x i + b) 2 } = Σ{ y 2 i 2ax i y i 2by i + a 2 x i2 + 2abx i + b 2 } = Σy i 2 Σ2ax i y i Σ2by i + Σa 2 x i2 + Σ2abx i + Σb 2 x i y i Σ n= Σ 1 = Σy i 2 2aΣx i y i 2bΣy i + a 2 Σx i2 + 2abΣx i + nb 2 = a 2 Σx i2 + 2abΣx i + nb 2 2aΣx i y i 2bΣy i + Σy i 2
49 A 1 f (a,b)=(, ) Σ{ { y (a( x + b)} 2 i i = a 2 Σx i2 + 2abΣx i + nb 2 2aΣx i y i 2bΣy i + Σy i 2 i i iy i y i y i = a 2 Σx i2 + 2abΣx i 2aΣx i y i + nb 2 2bΣy i + Σy i 2 = a 2 Σx i2 + 2a(bΣx i Σx i y i )+ nb 2 2bΣy i + Σy i 2 f Σ Σ Σ a (a,b) = 2aΣx i2 + 2(bΣx i Σx i y i )
50 A f (a,b)= Σ{ y + 2 i (a x i b)} = a 2 Σx i2 + 2abΣx i + nb 2 2aΣx i y i 2bΣy i + Σy i 2 i i iy i y i y i = nb 2 + 2abΣx i 2bΣy i + a 2 Σx i2 2aΣx i y i + Σy i 2 i i i i i i = nb 2 + 2b(aΣx i Σy i ) + a 2 Σx i2 2aΣx i y i + Σy i 2 f b (a,b) = 2nb + 2(aΣx i Σy i )
51 B f = i2 a (a,b) 2aΣx + 2bΣx i 2Σx i y i = 0 f (a,b) = 2aΣx + 2nb b, 2Σyy i i = 0 Σx 2 Σ Σ i Σx a i Σx i y i = Σx i n b Σy i a 2 1 Σx i Σx i Σx i y = i b Σx i n Σy i
52 a b e f a+e b+f c d g h c+g d+h ( ) +( ) = ( ) a b e ae+bf c d f ce+df ( ) ( ) = ( ) a 1=a a 1 0 a a 0 1 b b 1 1 a a = a a = 1 a b 1 a b 1 0 c d c d 0 1 ( ) ( ) = ( ) ( ) ( ) = ( ) a b 1 0 a b c d 0 1 c d ( ) ( ) = ( )
53 1 1 a a = a a = 1 a b 1 a b 1 0 c d c d 0 1 ( ) ( ) = ( ) a b x e c d y f ( ) ( ) = ( ) 1 1 a b a b x a b e c d c d y c d f 1 0 x a b 1 e 0 1 y c d f ( ) ( ) ( ) = ( ) ( ) ( ) ( ) = ( ) ( ) x a b 1 e y c d f ( ) = ( ) ( )
54
55 : y y = a x + b (x 2, y 2 ) (x 1, y 1 ) y 1 = ax 1 + b y 2 = a x 2 + b x
56 y 1 = a x 1 + b y 2 = a x 2 + b x 1 1 a y 1 = x 2 1 b y 2 a x y 1 b = x 2 1 y 2
57 n y y = a x + b (x i, y i ) (x 1, y 1 ) (x 2, y 2 ) y 1 = a x 1 + b y 2 = ax 2 +b y 3 = a x 3 + b y i = a x i + b y n = a x n + b x
58 y 1 = ax 1 + b a x 1 + b = y 1 x 1 1 y 1 y 2 = a x 2 + b a x 2 + b = y 2 x 2 1 y 2 y 3 = a x 3 +b a x 3 +b = y 3 x 3 1 y 3 a y +b ax + = = i = a x i i b y i x i 1 b y i y n =ax n +b ax n + b = y n x n 1 y n
59 x 1 1 y 1 x 2 1 a = y 2 b x n 1 y n x 1 x 2 x n x 1 1 x 2 1 a = x 1 x 2 x n b y 1 y 2 x n 1 y n
60 x 1 1 y 1 x 1 x 2 x n x 1 x 1 x 2 x 2 a = n y b x n 1 y n Σx 2 i Σx a i Σx i y = i Σx n b i Σyy i
61 Σx i 2 Σx i a Σx i y i = Σx i n b Σy i a 2 1 Σx i Σx i Σx i y = i b Σx i n Σy i
62 a
63 Excel
64 2004
65 R R 2 R x = (x1, x 2,, x n ) R = cosθ = 1 < R < 1 = = x y x y θ y = (y 1, y 2,, y n ) x y = Σ x y =xy +xy + + x y = x y cosθ x 2 = Σ x i2 = x 12 + x x 2 n R R = 11 x y = Σ x iy i = x 1 y 1 + x 2 y x n y n R = 0 R = 1 R 2 0 = < R 2 = < 1 R = 0 R = 1
66 R R 2 R = 0.8, R 2 =
67 R R 2 R = 0.95, R 2 =
68 R R 2 R = 0.8, R 2 =
69 R R 2 R = 0.5, R 2 =
70 R R 2 R = 0.5, R 2 =
71 R R 2 R = 0, R 2 = 0
72 R R 2 R = 0, R 2 = 0
73 R R 2 R = 0, R 2 = 0
74 R R 2 R = , R 2 =
75
76 2004 R 2 R 2 R 2
77 2004 R 2 R 2
78 A. B. R 2 C. ( D. E. ( F.
79 Y = 45.4 X +221 Y = 400 = X X = = 179 X = 179/45.4 = = x 700 = x 700 = 8
80 x, y x, y y = ax + b d i = y i (a x i + b) i i i y = ax 2 + bx +c d = i y (a( i x i2 + b x + c) ) i
81 y = ax 2 + bx +c n n Σ d i 2 = Σ{y i (a x i2 + b x i + c)} 2 i=1 1 i=1 1 a, b, c n i (x i, y i )
82 n f (a,b,c)= b Σ{y ( 2 i (a x i2 + b x i + c)} 2 i=1 abc a, b, f (a,b,c) b a, b,c b b b a f (a,b,c) = 0 b f (a,b,c) = 0 c f (a,b,c) = 0 a, b, c 0
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I A A441 : April 15, 2013 Version : 1.1 I Kawahira, Tomoki TA (Shigehiro, Yoshida )
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Microsoft Word - 倫理 第40,43,45,46講 テキスト.docx
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Microsoft Word - 計算力学2007有限要素法.doc
95 2 x y yz = zx = yz = zx = { } T = { x y z xy } () {} T { } T = { x y z xy } = u u x y u z u x x y z y + u y (2) x u x u y x y x y z xy E( ) = ( + )( 2) 2 2( ) x y z xy (3) E x y z z = z = (3) z x y
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http://www.ss.u-tokai.ac.jp/~mahoro/2016autumn/alg_intro/ 1 1 2016.9.26, http://www.ss.u-tokai.ac.jp/~mahoro/2016autumn/alg_intro/ 1.1 1 214 132 = 28258 2 + 1 + 4 1 + 3 + 2 = 7 6 = 42, 4 + 2 = 6 2 + 8
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x, y x 3 y xy 3 x 2 y + xy 2 x 3 + y 3 = x 3 y xy 3 x 2 y + xy 2 x 3 + y 3 = 15 xy (x y) (x + y) xy (x y) (x y) ( x 2 + xy + y 2) = 15 (x y)
x, y x 3 y xy 3 x 2 y + xy 2 x 3 + y 3 = 15 1 1977 x 3 y xy 3 x 2 y + xy 2 x 3 + y 3 = 15 xy (x y) (x + y) xy (x y) (x y) ( x 2 + xy + y 2) = 15 (x y) ( x 2 y + xy 2 x 2 2xy y 2) = 15 (x y) (x + y) (xy
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2005 II 3 I 18, 19 1. A, B AB BA 0 1 0 0 0 0 (1) A = 0 0 1,B= 1 0 0 0 0 0 0 1 0 (2) A = 3 1 1 2 6 4 1 2 5,B= 12 11 12 22 46 46 12 23 34 5 25 2. 3 A AB = BA 3 B 2 0 1 A = 0 3 0 1 0 2 3. 2 A (1) A 2 = O,
solutionJIS.dvi
May 0, 006 6 morimune@econ.kyoto-u.ac.jp /9/005 (7 0/5/006 1 1.1 (a) (b) (c) c + c + + c = nc (x 1 x)+(x x)+ +(x n x) =(x 1 + x + + x n ) nx = nx nx =0 c(x 1 x)+c(x x)+ + c(x n x) =c (x i x) =0 y i (x
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zz + 3i(z z) + 5 = 0 + i z + i = z 2i z z z y zz + 3i (z z) + 5 = 0 (z 3i) (z + 3i) = 9 5 = 4 z 3i = 2 (3i) zz i (z z) + 1 = a 2 {
04 zz + iz z) + 5 = 0 + i z + i = z i z z z 970 0 y zz + i z z) + 5 = 0 z i) z + i) = 9 5 = 4 z i = i) zz i z z) + = a {zz + i z z) + 4} a ) zz + a + ) z z) + 4a = 0 4a a = 5 a = x i) i) : c Darumafactory
Microsoft Word - 表紙.docx
黒住英司 [ 著 ] サピエンティア 計量経済学 訂正および練習問題解答 (206/2/2 版 ) 訂正 練習問題解答 3 .69, 3.8 4 (X i X)U i i i (X i μ x )U i ( X μx ) U i. i E [ ] (X i μ x )U i i E[(X i μ x )]E[U i ]0. i V [ ] (X i μ x )U i i 2 i j E [(X i
5.. z = f(x, y) y y = b f x x g(x) f(x, b) g x ( ) A = lim h 0 g(a + h) g(a) h g(x) a A = g (a) = f x (a, b)
5 partial differentiation (total) differentiation 5. z = f(x, y) (a, b) A = lim h 0 f(a + h, b) f(a, b) h............................................................... ( ) f(x, y) (a, b) x A (a, b) x
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