Обработка экспериментальных данных
.pdf, & Independent Variables (.0 , . 0) . #1, #2, #3
#4. ' ,6 . &.
!0 7 . . 9 5 5 5
& ( . 3.8) 9 0 0 1 , &6+ . &:-44 . R-squarted (63,3437%), 0
-44 . R-squarted (adjusted for d.f.) (47,0521%),
7 Standard Error of Est. (15,9144) &3
7 Mean absolute error (10,0556).
. 3.8. . 9 5 5 5 &.
' + 5 -44 .
, &/ 6 & . & 0. & + . , . 01,
7 - & 5 , & 01
&3.
&6+ . &/ . & 638 :
Y = 2,02497 + 0,883885 X1 + 0,126044 X2 - 0,0637985 X3 + 0,104146 X4
& 6 &/ , + , &6+ . & 0 . 5 4 Observed versus Predicted (&3 - ,) ( . 3.9).
, + + . & 9 , & 5 3 + &3 & ,, . + 6 . &/.
31
. 3.9. 4 + 9 . 9 5 5 5 &.
3.5. 2# '-0. 1 6 2 + % 5 + # 2# +.
7 5 0 . 9 0 5 0 & , &/ 6 &
. . & + .01 , . 01 1 8 1
& 6 .63 . &/. ! , Statgraphics Plus for Windows & 0
& + , . .0 , 6 0: , & &/ 6 & + , & &/ 6. /7 5 6,,0 .01
, . 01. $1 0 0 & , , 7 5 . 9
5 , 0 & 1 3.4 3.5.
= &/3 5 & & 1 9 & + 5
0 9 :
Y= a0 + … + an (Xn/Zn)
!& 6 1 01 01 + &3.4 3.5.
,6 . & & 5 / 63
.63 , . 63 Ri = Xi/Zi. & -5 & 6, 9 5 & & , .07, 0 & / ,6 & 0 / & 5 Modify Column ( . 3.10).
32
& 3.4.
< |
Y |
X1 |
X2 |
X3 |
X4 |
#5 |
#6 |
#7 |
#8 |
#9 |
#10 |
#11 |
#12 |
,/, |
|
|
|
|
|
|
|
|
|
|
|
|
|
1 |
0 |
80 |
107 |
44 |
87 |
85 |
214 |
47 |
91 |
69 |
77 |
54 |
86 |
2 |
15 |
94 |
93 |
72 |
106 |
130 |
254 |
75 |
97 |
130 |
69 |
99 |
76 |
3 |
6 |
95 |
115 |
81 |
186 |
73 |
79 |
95 |
111 |
96 |
129 |
114 |
110 |
4 |
15 |
99 |
126 |
87 |
74 |
69 |
107 |
61 |
121 |
65 |
176 |
85 |
78 |
5 |
6 |
117 |
53 |
94 |
122 |
139 |
113 |
101 |
144 |
108 |
59 |
127 |
148 |
6 |
9 |
78 |
80 |
58 |
112 |
66 |
195 |
96 |
94 |
86 |
79 |
144 |
142 |
7 |
6 |
91 |
95 |
120 |
82 |
131 |
142 |
62 |
140 |
106 |
50 |
76 |
116 |
8 |
9 |
104 |
52 |
45 |
113 |
136 |
385 |
65 |
53 |
114 |
180 |
82 |
84 |
9 |
3 |
55 |
54 |
65 |
140 |
77 |
173 |
117 |
117 |
82 |
100 |
90 |
107 |
10 |
12 |
130 |
109 |
51 |
34 |
129 |
302 |
37 |
126 |
123 |
126 |
60 |
62 |
11 |
21 |
64 |
66 |
70 |
186 |
61 |
204 |
157 |
129 |
66 |
86 |
99 |
69 |
12 |
3 |
81 |
82 |
94 |
167 |
78 |
112 |
153 |
130 |
85 |
75 |
138 |
149 |
13 |
12 |
58 |
144 |
49 |
53 |
53 |
289 |
55 |
115 |
82 |
135 |
105 |
81 |
14 |
12 |
91 |
144 |
49 |
49 |
82 |
293 |
64 |
88 |
113 |
124 |
90 |
60 |
& 3.5.
< |
Z1 |
Z2 |
Z3 |
Z4 |
Z5 |
Z6 |
Z7 |
Z8 |
Z9 |
Z10 |
Z11 |
Z12 |
,/, |
|
|
|
|
|
|
|
|
|
|
|
|
1 |
113 |
115 |
67 |
163 |
88 |
293 |
96 |
98 |
94 |
93 |
79 |
58 |
2 |
124 |
75 |
76 |
152 |
86 |
125 |
108 |
139 |
133 |
60 |
101 |
62 |
3 |
122 |
107 |
77 |
191 |
91 |
101 |
96 |
142 |
99 |
123 |
116 |
147 |
4 |
124 |
78 |
75 |
105 |
82 |
121 |
89 |
83 |
78 |
171 |
82 |
97 |
5 |
112 |
84 |
92 |
131 |
124 |
154 |
91 |
139 |
97 |
100 |
116 |
120 |
6 |
87 |
58 |
90 |
221 |
60 |
137 |
127 |
227 |
109 |
79 |
159 |
119 |
7 |
97 |
74 |
88 |
94 |
113 |
191 |
61 |
125 |
111 |
95 |
85 |
75 |
8 |
111 |
43 |
84 |
116 |
88 |
284 |
91 |
70 |
108 |
147 |
124 |
71 |
9 |
70 |
100 |
63 |
132 |
99 |
209 |
104 |
141 |
91 |
130 |
79 |
97 |
10 |
123 |
74 |
67 |
74 |
66 |
194 |
61 |
115 |
118 |
106 |
100 |
81 |
11 |
76 |
76 |
42 |
231 |
62 |
156 |
140 |
130 |
72 |
79 |
117 |
66 |
12 |
75 |
59 |
96 |
170 |
86 |
94 |
119 |
119 |
89 |
63 |
126 |
116 |
13 |
69 |
115 |
77 |
72 |
48 |
274 |
89 |
100 |
67 |
146 |
99 |
74 |
14 |
80 |
83 |
66 |
56 |
70 |
235 |
70 |
88 |
117 |
107 |
89 |
71 |
& , & Name 6 / . , . R1 , & Formula X1/Z1. & 5 + 1 . 5 / &/ 0
11 , . 01 (R2-R12).
& + & & 1 . 0, & / . 6 Relate/Multiple Regression. ! 0 7 . + . (Y)
.01 (Z1-Z12) , . 01 ,6 / &.
! , 7 ( . 3.11) & 6 / .
+ 6 + . p-Value (0,4028) & Analysis of Variance (& ,), 5 , &6+ . &/ &..
33
. 3.10. . , ..
. 3.11. 6&/ . 9 5 5 5 &.
34
2 &/ 6 + / + + .
. &. & &/, & , 07 + & 6 6. /7 / & + .01 , . 01.
. 3.12. & 5 , . , 6 0 , 7 5 5.
. 3.13. 5 5 & , 7 5 0. & . , . 01.
35
& -5 1 . 0 / , , .07
. 3 Analysis Options ( . 3.12). ! 5 6,, Fit & 5 5 & 6 6 / . , & 9 Forward Selection (&5 . , & &/ 5 6 & + 5 6,,0 , . 01). &/ 0 ,
& . .. & 9 , , &6+ . 63 6
5 5 & ( . 3.13) , + ,
. &/ & & 0 . 6 . + . p-Value (0,0092).
. 3.14. 5 5 & , & &/ 0. 6. /7 . 5 6,,0 , . 01.
&, ,6 . , 6 6 , & &/ 0. 6. /7 . 5 6,,0 , . 01. & 0 5 . 3 Analysis Options, 5 6,, Fit & 5 5 & 6 6 / . , & 9
Backward Selection / . Constant in Model (6+ 0 /
6 . &). $ 5 5 & ( 3.14) , + /
, 5 . &/ & &6+7 . ., + . , 0 68. - . .9 6 / , & 0 .6 6 3
+ . p-Value (0,0000), -44 6 . R-squarted (91,2995%) .6 -44 6 . R-squarted (adjusted for d.f.) (89,7176%).
36
! 5, 1 . &/ , + &/ . & & 638 :
Y = 26,4285 + 40,057 R1 - 23,9856 R10 - 29,6389 R11 - 13,5816 R12 - 2,53363 R2 + +15,0752 R3 + 15,5018 R4 - 35,0928 R5 + 31,8532 R6 - 34,3913 R7 + 3,45723 R8 + +20,4982 R9
& , 6 , 7 5 . 9 5 . &/ , & & 638 :
Y = 8,27119 R12 + 8,68307 R3 + 8,99869 R6
. ., , . , 01 07 , 6 , &
. 6, 8 . , &6+ .01 . . + 1 .&
, 0 / 1 /.
3.6. ! # '-0.
! # + ( &. dispersio - ) . . +
, / . (&
5):
σ 2 = (x1 − x)2 + + (xn − x)2 n
! , ,, , 6. 3 4. +
& &3 01 + (x1, x2,...,xn) &6+ & + 0 1 5 4. + 5:
x = x1 + x2 + + xn n
' + , 5 & & 0 & & 0 & 5 (& 6 . 5) 4 6&/ 0
,. -. 4 0 . 3 & + 7 &,
6&/ 0 , 0 9 + & . &
+ & 0. ., ..
! , 5 & & 9 8
, 6&/ 5 , +, 6 & & 0 & . & 6 .01 4, + 63 , 3, : .63 & 6 .0. & &6+ 0. &/ .. !0 0 & + & & 6 .01 4 6&/
, ,6 . + 8 , , 6 &
37
0, & . &/ , & 6&/ 5
,.
68 638 . 0 , 5 & & 4 63 , . . + , & 6 .01 4 (. 0, &6+ 0 . 7 0) , + &6 & 6 .01 4 ( -
. 5 4 0 .&). & 3 . 9 / & /
& 6&/ &/ &/ 01 & 6 .01 4 (5& 0 &), 1 .. , 6 5 1 01 01 . & , 5 & 0 & 3:
∙, & 0 , & 0 m-4 0 ,& 0;
∙, & 0 , & 0 & + 0 ,& 0;
∙&6+ 0 & + 0 ,& 0.
! + , . . + &
9 &/8 . 63 , &/ / 6. $1 0.
0. (& 3.6) & 3 6&/ 0 & 60 + 1.
|
|
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& 3.6. |
9 |
|
! |
|
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25 35 & |
35 45 & |
45 55 & |
1 4 & |
19 20 20 20 22 |
19 20 20 23 25 |
18 19 20 21 23 |
4 7 & |
30 31 32 32 34 |
20 29 30 31 31 |
19 25 25 26 26 |
7 10 & |
35 35 39 40 41 |
36 40 41 42 45 |
24 24 24 25 25 |
07 10 & |
40 40 41 41 42 |
28 31 35 36 40 |
20 24 25 31 32 |
! -& 63 & 6 1 . +
6&/ 5 , output 0 + 5
& 6 .01 4 age ( ) record (9), -
. 2.15.
& ,6 & 1 . 0, & / . 6
Compare/Analysis of Variance/Multifactor ANOVA. ! , 7 .
& 5 . & 6 .63 , . 63 output 4 0 age record.
& ,6 & 9 . , , + . & 0 & 0 , 5 & 6 9 / , 6
& + 01 46 ( & 9 , & 6.) 6 / . , ANOVA Table.
! -6 & 6 ( . 3.16) 0 + 0 & 9 5 4 6..0 (Sum of Squares), , 0 (Df), 0
(Mean Square), F-7 6 / + . (p-Value).
& + 01 01 . 9 & / 0 ., + , &/ / 6 0 3 & , &/ 4
– + 5, 5 9 0. , / .6
&3+ 3 & 95%.
38
. 3.16. & 6&/ , 5 &.
39
. 3.17. & , 5 & 6+ . . 5 ,.
&, & 6 / . & -1 61 4. & -5 & 6 , , , .07 0 / . 3 0 / ,6 Analysis Option. ! 0 7 . & 5 . & 6
, . 4, . &6+ 2 9 / . ! 6&/ & 6 . 5 4 5 , 5 & 6 6
& 0 + + . . 5 &
9 + 1 1 , &/ / ( . 3.17).
. 3.18 4 + 9 6&/ , 5 &.
& 0 5 4 + 5 9 6&/ & ( . 3.18.) 1 . 9 / , 6 5 4 + 1 46 (/ &
9 , & 6.) 0 / 0 7 . & 5 .
,6 0 Means Plot (5 4 1) Interactions Plot (5 4
.).
! 1 , & , 5 4 . 1
+ , &/ 6 + + 0
&/ 0 &0 & -1 1. ! 9 , &
, 5 4 . 9. $ 5 & 6, + , , &/ 6 &3 6 . & 01 &3
5 6,,0 9 . 0 4 7 &.
40