2.4.1
(), , xi, yi , . , .
, . , , .
. () , . , .
.
2.4.2 ()
X Y , , , . .
, ( 5):
5
X | x1 | x2 | x3 | xn | |
Y | y1 | y2 | y3 | yn |
( ) , X Y (xi, yi), i = 1, , n ( 29).
29.
29 , a) , ) , ) - .
X Y, , (, ). () , (xi, yi) . . . , , , .
y = ax + b (2.57)
a b (2.57). , y = ax 2 + bx + c . .
2.4.3
(2.57) .
, , (. 29). , (, , ). , , (x 1, y 1)
|
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(x 2, y 2), , ( 30).
30.
(2.57), :
(2.58)
a b. (2.58), (2.57). , , .
. x (. 30) ( :
, (2.58), a b (2.57).
( 30 *) . , .
(2.57), , .
2.13
:
6
1,0 | 1,4 | 3,0 | 4,0 | 6,0 | 8,0 | 10 | |
4,5 | 7,0 | 10,4 | 15 | 24 | 25 | 35 |
: () , 1- 4 (x, y), 2- - 3 . :
= 2,35; = 8,0;
= 9,23; = 28.
(2.58), : = 3,32; = 1,43.
, () :
, . , .
2.4.4
( 5) X Y, . , .
( ) () () , () . (, ) , () (). . , , . , , X Y.
|
|
2.4.5
, , Y = y; () , , , (, ).
, , . , .
. , .
2.4.6
. .
, .
, : . ( ). ( ) , () ().
2.4.7 ()
. x y :
= f ̃(x) = x + ; (2.67)
x ̃(y) = g (y) = y + . (2.68)
, .
.
, , , , , , 2.4.3.
. () ( ) Y :
= - - - , i = 1, , n, - () ,
( 2.67) .
a1 a0 , - :
T = = - - = min. (2.69)
(2.69) ( - ). :
= ;
=
(), , , . , :
= - ; = ; (2.70)
= , = = , = - ( .
r = , (2.71)
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,
, , (2.71),
= - . (2.72)
, , , y, , , = g (y) [ (2.68)]:
. (2.73)
(2.72) (2.73) .
[. (2.67) (2.68)] . , ( ).
2.14 ( )
( Excel) . 6 2.13. () . r.
2.4.8
. : .
, ( 29). 29, . 29, 29, , .
r. .
1) X Y , r = 0. .
2) (2.71) , X Y, r , , = .
3) X Y , Y = αX + b,
r =
| r | , . | r | < 0,5, . , , ( )
= + (2.76)
, . , .
2.4.9
, , . ( ) , . . , , .
, , () , . = α + β + γ, α , β , γ , , α, β γ .
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D ( ) = D (α + β + γ). (. . 1.2.4.2) D = + + , , - , - , . . .
, () , . .
2.4.10
2.4.10.1
. - . , . , ?
m ( m ). ( ) n . N = m n.
, , α, : . .
F = , (2.77)
- , ; , ( ). , F F () = m 1 = N m = m (n - 1), .
(. . 2.3.6),
(F > ) = α,
- () ( F - ).
[. (2.77)] , , . (F < ) , .
F
Q = (2.78)
= , m , n - .
():
- ; (2.79)
= (2.80)
, Q = + . = , j = 1, 2, , m ( - ). , () , ( Q 1); Q 2 . , .
:
= , = , = , (2.81)
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F (. 2.77).
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Q , :
= Q - . (2.82)
2.4.10.2
, ( . 2.4.10.2). (2.78) (2.80) . , (2.78) (2.79).
N = m n, = = ,
Q = - ( ; (2.83)
. (2.84)
() ( ).
2.4.10.3
.
j j = 1, 2, , m.
N = ,
(2.84)
= , (2.85)
= = . [. (2.81)] :
, = , = . (2.86)
, , .