Biometrija_2011
.pdf
81
'=LgA B'=LgB
(5.1 - 5.2). -
' '; Lg Y (X) X .
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Y (x) A X m . |
5.3( ) |
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Lg Y ( x) Lg ( A) m Lg X
LgA, -
- m, LgX. -
Lg Y (X) Lg X.
5.4
a) Y/X X/Y
, ,
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X Y. -
Y/X X/Y.
TB :
TB(Y/X)=BY/X / SY/X TB(X/Y)=BX/Y / SX/Y. |
(5.4) |
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SY/X SX/Y BY/X BX/Y : |
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(1 r 2 ) (Yi |
Y )2 |
(1 r 2 ) ( Xi X )2 |
(5.5) |
SY / X |
; SX /Y |
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(n 2) ( Xi X )2 |
(n 2) (Yi Y )2 |
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i 1 n.
T t ,
2 k=n-2,
. BY/X BX/Y , -
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T (y/x) > tk,p T (x/y) > tk,p
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. ,
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, . YX X Y ,
( . YX X Y ).
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Y / X Y / X ; X / Y X / Y ; |
(5.6) |
- ,
p ( , p=0.95 =1.96). Y/X X/Y
Y (X) X (Y), -
Yi Xi:
Y / X |
(Yi |
Y ( X ))2 |
( X i |
X (Y )) 2 |
(5.7) |
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n 2 |
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i 1 n.
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Y: Y (x) ( AY / X BY / X X ) Y / X ;
Y: Y (x) ( AY / X BY / X X ) Y / X ;
(5.8)
X: X ( x) ( AX / Y BX / Y Y ) X / Y ;
X: X (x) ( AX / Y BX / Y Y ) X / Y ;
, -
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( . 4.2,5.1,5.2) , , -
Y X.
, " " X Y
p * 100 0/0
5.5
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1., -
Y, - X.
, Y,X -
X ( . X).
4.2 - 4.3.
2.X: YX YX = (Y1 + Y2 + .... Yk )/K, - Y X;
, ( . . 4.1); .
3., -
YX , - X.
. , .
5.5.1 - 5.3 .
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6.5.4 - 5.5 ,
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7.X -
Y (x) . .
8.5.6 - 5.8 .
9.-
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X,Y .
-
- -- . 4.1.
, 4,
( -
r = 0.564). , .
1.X - ,
Y - . X -
( . . 4.2).
2.Xi YX . : Xi =
11,3 YX =(0.7 + 0.75)/2 =0.725 0.73. ( . .4.2) .
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3.. ( . 5.1)
Y =
+*X.
4.5.1 - 5.2 X/Y , X/Y, Y/X BY/X
B Y / X |
0 ,564 |
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(Y i |
0 ,703 ) |
( X i |
11 ,87 ) |
2 |
0 ,0756 0 ,024 ; |
0 ,564 |
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40 ,388 |
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AY/X = 0,703 - 0,0235 * 11,87 = 0,424.
B X / Y |
0,564 |
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( X i 11,87) 2 |
0564 |
40,388 |
13,036. |
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(Yi 0,703) |
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0,0756 |
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AX/Y = 11.87 - 13.036 * 0.703 = 2,7.
X ( y) :
X ( y) = 2.7 + 13.036 Y.
Y (x) :
Y (x) = 0.42 + 0.024 * X ;
5. 5.4 - 5.5 BY/X BX/Y:
SX / Y |
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(1 0,5642 ) 0,0756 4,5 |
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(20 2) 40,388 |
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SX / Y |
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(1 0,5642 ) 40,388 4,5 ; |
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(20 2) 0,0756 |
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Tb (y/x) = |
0,024 |
= 3,0 ; Tb(x/y) = |
13,036 |
= 2,9. |
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0,008 |
4,5 |
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2. k = 20 - 2 = 18, -
= 0,05, tk,p = 2,1. Tb > tk,p B
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6.( .4) Y(X) X(Y)
( . 4.2 4.3 ).
7.5.6 - 5.7 -
Y/X = 658; Y/X = 1,96 * 0,0658 = 0.129
p = 0.95. Y(X) :
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Y ( x ) = 0,42 + 0,024 * X ± 0,129
X(Y)
X/Y = 1,21 ; X/Y = 1,96 * 1,21 = 2,37
X(Y) :
X ( y) = 2.7 + 13.036 * Y ± 2.37.
9.
. . 5.1 - 5.2. , -
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( . . 4.2 ). -
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0.05. -
X Y -
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5.1. , -
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(r = 0,975; , , )
5.2. ,
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1.26 |
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Y (x) = 0,958 + 0,018 * X ;
Y (x) = 0,958 + 0,018 * X ± 0.1)
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, , -
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Y (x) = 7.07+1.83 * X)
5.4.
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4.6 |
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6.4 |
6.1 |
7.5 |
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,
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VI.
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( -
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= 0,1; = 0,05 = 0,01, -
0,9, 0,95 0,99 .
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III. -
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6.1
III - V
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( . 2.13). -
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95% [4]. -
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6.2
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1.– -
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20 – 50.
5. – .
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6.3
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1.Q – . [6]
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1 2. -
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2. .
S1,
S2 , -
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Q = S1 + S2
. Q,
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11, -
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2. – [1]
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