, [2]. . 7.1. ; , .
.
1. . , , .7.2.
yt = a0 + a1 t (7.2.)
a0 a1 :
a0 = (7.3.)
a1 = (7.4.)
, (7.3.),(7.4) .
. 7.2. , a0 = 45,2, a1 = -3,0. ,
yt = 45,2 3,0t
7.1.
1- | 2- | 3- | ||||||
j | . | j | . | j | . | |||
* * | ||||||||
: * - |
(7.5)
. 7.2. (7.5), σt
σt =
yi σt c
;
;
.
(7.2). yt = 0,
(7.6)
σt , (7.5);
tβ , β.
tβ , ( ) , b.
yt.
. 7.2. , yt σ.
. 7.3. b tb .
, , , .. (7.6).
7.2.
(7.2) N = 5
|
|
ti, | yi, . | ti2 | yiti | (yt - yi)2 | |
*: |
b=0,9 . 7.3 tb = 1,643 (7.5)
yc = 1,8×1,643 = 2,96.
yc = 3,0.
. 7.2. b=0,9.
, =15. , , , , .
. 7.2. (N = 5)
1- ; 2- ; 3, 3- ; 4- .
, . , , (7.2), . ,
yc* = |a1|t+tbst (7.7)
t - , .
7.3.
b tb
b | tb | b | tb |
0,80 0,82 0,84 0,86 0,88 0,90 0,91 | 1,282 1,340 1,404 1,475 1,554 1,643 1,694 | 0,92 0,94 0,95 0,96 0,98 0,99 0,999 | 1,750 1,880 1,960 2,053 2,325 2,576 3,290 |
=15 , .. 16 . (7.7)
yc* = |-3,0|1,0+1,643×1,8=6,0 .
, t=2 (17 ) yc* =9,0 .
, () . , ,
(y) = 1 - F(y) = 1 - , (7.8)
yt , (7.2)
s - , (7.5).
7.4.
*
(x), (x) x
x | (x) | (x) | x | (x) | (x) |
0,00 -0,125 -0,253 -0,385 -0,525 -0,675 -0,842 -1,037 | 0,50 0,45 0,40 0,35 0,30 0,25 0,20 0,15 | 0,50 0,55 0,60 0,65 0,70 0,75 0,80 0,85 | -1,280 -1,405 -1,555 -1,645 -1,75 -2,05 -2,30 -3,10 | 0,10 0,08 0,06 0,05 0,04 0,02 0,01 0,001 | 0,90 0,92 0,94 0,95 0,96 0,98 0,99 0,999 |
* |
(7.9)
F(x) = , (7.10)
(7.10) , . mx =0 sx =1.
|
|
(x) = (7.11)
, F(y) = ().
. 7.4. (x) (x).
b x, b (x)
2(x) 1 = b (7.12)
. 7.3 .
, , . . y = 0.
, :
(7.9) x= ;
. 7.4 x (x).
13, 14 15 . , t=13
,
x = .
. 7.4 (= 13 ) >0,999, .. .
, =14 ; x = -1,78, =14 @ 0,95.
, =15, @ 0,5.
, , . , .
) )
. 7.3. :
) ; ) .
, . 7.1.
D = ×100% (7.13)
, , .
(7.13),
D = ×100%=50%
, , : t () t =- t :
(7.14)
(7.14), t = 5
= (7.15)
, @7 t=2 .
2. [2] , =10 . , (7.15) t=7,5 .
N=7 , (. 7.5),
y*t=47-3,9t
, st*=2,1.
= ,
, (7.13)
D = ×100%=20%
7.5
(7.2) N=7
ti | yi | ti2 | yiti | ( -yi)2 | |
43,1 | 4,41 | ||||
39,2 | 0,04 | ||||
35,3 | 7,29 | ||||
31,4 | 12,96 | ||||
27,6 | 0,25 | ||||
23,6 | 0,36 | ||||
19,7 | 0,49 | ||||
12, 13 14 (7.7). b=0,95, . . tb=1,96.
yc(t = 0)=|-3,9|×0+1,96×2,1=4,11 4,0
yc(t = 1)=|-3,9|×1+4,0 8,0
yc(t = 2)=|-3,9|×2+4,0 12,0
.
(7.9) = ; . (7.4) =101,0, .. . =11 0,98, =12 0,6.
. 7.4. (N = 7)
1- ; 2- ; 3, 3- ; 4- .
3. . , 7 .
|
|
:
, (7.16)
(7.17)
, 1
.
. 7.6.
m(t)
m(t)=b0+b1t (7.18)
, b0 b1. .
= .
D(t) s(t) , , .
s(t)=c0+c1t+c2t2 (7.19)
s,
(7.20)
. 7.6
s=
.
(7.6). , b=0,95
yc=1,96×4,81=9,429
7.6.