*y=-
Z y ,
---------
va
h'
A , formulalar bo‘yicha regressiya
tenglamasining ikkinchi tartibli koeffitsiyentlari va koeffitsiyent-
laming xatoliklarini hisoblaymiz
60 =61.54
6 44
= -5-34
fcl2-2.18
6U
-
0.2
614
=
1.2
623 = 0.56
624 = 0.79
6
,, =4.5
b22 =1-3
633 = 4.09
^ = ^ =
0 . 5 4 5
\ = K = 0-6'
\ - K = ° - S6i
6, =17.37
634 =l-9
62
= 6.4
63
= 4.7
64 = -4.37
Styudent mezoni bo‘yicha koeffitsiyentlaming ahamiyatliligini
?I
2
~
I
34
-
?I3 -
^14 -
^23 =
{24 —
2.18
0.61
1.9
0.61
0.2
0.61
1.2
0.61
0.56
0.61
0.76
0.61
= 3.57
= 0.318
= 3.18
= 1.97
= 0.91
= 1.25
4 0 7
www.ziyouz.com kutubxonasi
h =
h ~
u =
1 7 .3 7
0 . 5 4 5
6 . 4
0 . 5 4 5
4 . 7 0
0 . 5 4 5
4 . 3 7
0 . 5 4 5
= 3 1 . 9
= 1 1 .7
= 8 .6 4
= 8 . 6 4
_____ A5
0 . 8 6 4
= 5 .2
1 .3
. _
t 21
= — — = 1 . 5
0 . 8 6 4
t e k s h i r a m i z .
^33 —
'
4 . 0 9
0 . 8 6 4
5 . 3 4
0 . 8 6 4
4 . 7 3
6.22
A h a m i y a t l i l i k s a t h i
r
= 0 . 0 5 v a e r k i n l i k d a r a j a s i s o n i
/ = 3
u c h u n S t y u d e n t m e z o n i n i n g j a d v a l q i y m a t i r ^ / / ) = 3 . 1 8 .
A h a m i y a t s i z
k o e f f i t s i y e n t l a m i
t a s h l a b
y u b o r g a n d a n
s o ‘ n g
o ‘ l c h a m s i z k o ‘r i n i s h d a g i r e g r e s s i y a t e n g l a m a s i n i o l a m i z :
y
=
6 1 . 5 4 + 1 7 . 3 7
jc
, + 6 . 4
x
2
+ A . l x l
- 4 . 3 7 x 4
+
+ 2 . 1 8 x , x 2 + 1 . 9
x
2
x
3 + 4 . 5 (
x
12 - 0 . 8 ) + 4 . 0 9 (
x
3 - 0 . 8 ) -
- 5 . 3 4 (
x
4 - 0 . 8 ) = 5 8 . 9 + 1
1 3 1 x x
+ 6 . 4
x
2 + 4 . 7 x 3 -
- 4 . 3 7
x
4 + 2 . 1 8
x
^ 2 + 1 . 9
x
3
x
4 + 4 . 5
x
2 + 4 . 0 9
x
3 - 5 . 3 4
x
4
O l i n g a n
t e n g l a m a n i
m o n a n d l i k k a
t e k s h i r i s h
u c h u n
q o l d i q
d i s p e r s i y a n i h i s o b l a y m i z :
Z(.y,-j>,)2
£•»2
_ ________
^miq
N _ L
396.2
2 5 - 1 0
2 6 . 4
4 0 8
www.ziyouz.com kutubxonasi
F - nisbat:
F =
26,4
5,95
= 4,4
Ahamiyatlilik sathi
r = 0.05 va erkinlik darajalari sonlari
/ i = 1 5 ,/, =3 uchun Fisher mezonining jadval qiymati
8 , 6
ga teng
va
F{FP( f }, f 2) , demak, olingan tenglama tajribaga monand.
2 - Z °
Regressiya tenglamasi natural masshtabda [x = —---- ga
Az;
qarang quyidagi ko‘rinishni qabul qiladi:
y = 90.64 - 0.242z, - 0.07z3 + 0.35z
4
+ 0.00388z,z2 + 0.00506z3z4 +
+ 0.0072z,2 + 0.0102z
3
- 0.015z2
j> =
1 0 0
% ga mos keluvchi shartni regressiya tenglamasi
bo‘yicha Gauss - Zeydel usuli bilan aniqlaymiz:
z, = 90° C ,z
2
=50 daq, z
3
=90%, z
4
=32.5.
Olingan optimal shartlar nazorat sinovlarida o‘rnatilgan.
Boratlarning
parchalanish
darajasi
parchalanish
uchun
konsentratsiyasi 30,3% bo‘lgan fosforli kislota qo‘llanilganda
98,5% ni, konsentratsiyasi 29,0% bo‘lgan ekstratsiyali kislota
qo'llanganda esa 98,9% ni tashkil qiladi.
5-misol. Ekstraksiyali fosfor kislota tarkibidagi aralashma-
laming fosforit flotokonsentratining parchalanishi (u) ga ta’sirini
o ‘matish va parchalanishni maksimal darajasini olish shartini
aniqlash talab qilinadi. Parchalanish darajasiga ta’sir qiluvchi
faktorlar sifatida quyidagilarni tanlaymiz: z, - jarayonning
harorati,°C; z
2
- z 5- M g0,S03,A I20 3 va G
larga mos keluvchi
fosforli kislotaning konsentratsiyasi,% (massa).
Variatsiyalashning asosiy sathi, oralig‘i va tadqiqot sohasining
chegaralari
1
-jadvalda keltirilgan.
4 0 9
www.ziyouz.com kutubxonasi
1
-jadval
Z2
ZA
Z 5
z “ ...........
50
2.1
2.0
1.33
0.75
.......
20
0.9
1.0
0.37
0.25
+ 2.......
90
3.9
4.0
2.07
1.25
-2 .......
10
0.9
0.0
0.59
0.25
Mustaqil faktorlaming o ‘zgarish sohasi sanoat ekstraksiyali
kislotasi aralashmalari konsentratsiyalarining o‘zgarish diapazoniga
mos keladi. Shuning uchun ham zimax ni aniqlashda 1-jadvalda
ko‘rsatilgan chegaralar uchun ekstrapolatsiyalash mazmunga ega
emas.
Yechim. Regressiya tenglamasini aniqlash uchun ikkinchi
tartibli rotatabelli rejadan foydalanamiz (
1
-jadval).
/ = 5 uchun rejalashtirish matritsasining sinovlar soni
32 ga
teng. Reja yadrosi o ‘zidajc
5
=
bosh munosabatli 25- l
yarim replikani namoyon qiladi. Yulduzli yelka kattaligia = 2 va
n
0
=
6
ni aniqlaymiz.
2-jadval
X
,
x,
X,
X,
u
X,
X
3
Xt
V
1
+ 1
+ 1 +1
+1
+1
34,7
17
-2
0
0
0
0
25
2
- 1
+ I +1.
+1
-1
40,0
18
+2
0
0
0
0
33.3
3
+1
- 1
+ 1
+1
-I
39,0
19
0
-2
0
0
0
49,2
4
- 1
-1
+1
+1
+1
39,2
20
0
+2
0
0
0
42,0
5
+ 1 + 1
-1
+1
-1
26,6
21
0
0
-2
0
0
17,5
6
--1
+ 1
-1
+1
+1
29,5
22
0
0
+2
0
0
41,0
7
+ 1
-1
-1
+1
+1
30,0
23
0
0
0
-2
0
35,6
8
-1
-1
-1
+1
-1
34,5
24
0
0
0
+2
0
27,2
9
+ 1 + 1
+1
-1
-1
32,2
25
0
0
0
0
-2 39,0
10
-1
+ 1
+ 1
-I
+1
41,4
26
0
0
0
0
+2 33,0
11
+ 1
-1
+1
-1
+1
33,7
27
0
0
0
0
0
35,4
12
-1
-1
+1
-1
-1
40,9 2V
0
0
0
0
0
35,4
13
+ 1
-1
-1
-1
+1
23,9
29
0
0
0
0
0
33,2
14
- 1 + 1
-1
-1
-1
33 3
39
0
0
0
0
0
32,4
15
+ 1
-1
-1
-1
-1
27,7
31
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