eksperimentalni gr
TRANSCRIPT
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UNIVERZITET U TUZLI
MAINSKI FAKULTETOdsjek: Proizvodno mainstvo
Tuzla: 08.06.2016.god.
SEMINARSKI RAD
Predmet: Teorija eksperimentalnog istraivanja
Studenti: Asistenti:Edin Jusufovi II - 476/12 Mr.sc. Jasmin Hlilovi, v.as.Mirhada atovi II - 111/09 Mr.sc. Demal Kovaevi, v.as.
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Zadatak 1. Primjenom viestruke linearne regresije prikazati matematski model zavisnosti faktora ugla u
ravni smicanja pri obradi elika rezanjem (zavisno promjenjiva) od pokazatelja mehanikih osobina
obraivanih elika. Podaci za posmatrane pokazatelje (nezavisno promjenjive), kai i ugla u ravni smicanja
prikazani su u donjoj tabeli. Metodom izbora iz svih jednaina izabrati regresijonu jednainu koja najbolje
opisuje date uslove.
Tabela 1
HB HVmax/HVmin Rm A5 144 1,661691542 525 33,2 13,1307 1,18115942 891 28 31,7
257 1,617370892 795 8,4 30,1
329 1,306483301 1001 14,8 30,1
231 1,309734513 828 27,4 12,4
260 1,416356877 929 26 20
189 1,767195767 619 33,6 16,5
116 1,533678756 453 24,4 8,8
352 1,472636816 1223 34 23,1263 1,629268293 856 29,2 11,7
170 1,403409091 598 15,6 9,88
207 2,118811881 721 14,8 10,1
189 1,380577428 629 14,6 8,94
345 2,018867925 1052 20 23,1
197 1,472440945 718 21,6 8,94
HB - Tvrdoa po Brinell-u [MPa]
Hvmax/Hvmin - Odnos max i min izmerene tvrdoe po Vickers-u [MPa]
Rm - Zatezna vrstoa [MPa]A5 - Relatvino izduenje[%] - Ugao u ravni smicanja []
Zadatak 2: Ispituje se prosjena trajnost automobilskih baterija istih osbina etri razliita proizvoaa. Na
temelju ispitivanja pomou sluajnih uzoraka, dobiveni su ovi rezultati o trajnosti baterija navedenih
proizvoaa (u hiljadama sati).
Tabela 2
Ponavljanja Vremena trajnosti baterije [h x 103]
Proizvoa A Proizvoa B Proizvoa C Proizvoa D
1 53 48 65 60
2 61 52 72 53
3 63 56 58 68
4 59 50 59 55
5 62 51 71
6 68
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Zdatak 3:Primjenom regresijone analize prikazati matematski model zavisnosti faktra ugla u ravni smicanja
(zavisno promjenljiva) od mehnike karakteristike (nezavisno pronljiva) pri obradi devet elika grubim
struganjem prema podacima prikazanih u donjoj tabeli.
Tabela 3
n 1,44 13,1
1,327 18,11,193 27,4
0,96 24,1
1,625 15,8
1,078 9,71
1,635 11,7
1,707 9,71
1,658 12,7
Potrebno je odrediti:
- Nacrtati dijagram rasipanja, odrediti koeficijente korekcije, te procijeniti parametre regresije
Gaussovom metodom najmanjih kvadrata.
- Izraunati vrijednost procjene standardne devijacije, koeficijent varijacije i koeficijent determinacije,
te napisati jednainu sa izraunatim koeficijentima.
- Pomou Fisherovog F-testa sprovesti skupni test o znaajnosti regresije ako je prag znaajnosti 5%.
- U nekom od statistikih programskih paketa sprovesti regresijonu analizu i grafiki prikazati analizu
reziduala, dijagram rasturanja reziduala, itd.
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RIJEENJE:
Zadatka 1:
Tabela 4
X1 X2 X3 X4 Y
HB HVmax/HVmin Rm A5
144 1,661691542 525 33,2 13,1
307 1,18115942 891 28 31,7
257 1,617370892 795 8,4 30,1
329 1,306483301 1001 14,8 30,1
231 1,309734513 828 27,4 12,4
260 1,416356877 929 26 20
189 1,767195767 619 33,6 16,5
116 1,533678756 453 24,4 8,8
352 1,472636816 1223 34 23,1
263 1,629268293 856 29,2 11,7170 1,403409091 598 15,6 9,88
207 2,118811881 721 14,8 10,1
189 1,380577428 629 14,6 8,94
345 2,018867925 1052 20 23,1
197 1,472440945 718 21,6 8,94
Tabela 5
HB HVmax/HVmin Rm A5 HB 1
HVmax/HVmin -0,073473139 1
Rm 0,967084976 -0,079327982 1
A5 0,002727218 -0,091233505 0,089092535 1
0,760944257 -0,206667055 0,643092977 -0,092860044 1
Broj moguih jednaina (4 varijable i 12 promjenjivih):
()=
!! !=
= 4, 4 jednaine sa po 1varijablom
()= !! != = 6, 6 jednaine sa po 2 varijablom()= !! != = 4, 4 jednaine sa po 3 varijablom()= !! != = 1, 1 jednaine sa po 4 varijablom4 + 6 + 4 + 1 = 15 -jednaina
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Tabela 5.1
SUMMARY OUTPUT
Regression Statistics
Multiple R 0,76094
R Square 0,57904
Adjusted R Square 0,54665
Standard Error 5,69651
Observations 15
ANOVA
df SS MS F
Significance
F
Regression 1 580,260 580,260 17,882 0,001
Residual 13 421,854 32,450Total 14 1002,113
Coefficients
Standard
Error t Stat P-value Lower 95%
Upper
95%
Lower
95,0%
Upper
95,0%
Intercept -3,652018999 5,15276 -0,70875 0,49099 -14,78388 7,47984 -14,78388 7,47984
HB 0,088087819 0,02083 4,22865 0,00099 0,04308 0,13309 0,04308 0,13309
Slika 1: Rezultati obrade podataka za regresiju = f(HB)
X1 X2 X3 X4 Y
HB Rm Hvmax/HVmin A5
144 525 1,661691542 33,2 13,1
307 891 1,18115942 28 31,7
257 795 1,617370892 8,4 30,1
329 1001 1,306483301 14,8 30,1231 828 1,309734513 27,4 12,4
260 929 1,416356877 26 20
189 619 1,767195767 33,6 16,5
116 453 1,533678756 24,4 8,8
352 1223 1,472636816 34 23,1
263 856 1,629268293 29,2 11,7
170 598 1,403409091 15,6 9,88
207 721 2,118811881 14,8 10,1
189 629 1,380577428 14,6 8,94345 1052 2,018867925 20 23,1
197 718 1,472440945 21,6 8,94
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SUMMARY_OUTPUT
Regression Statistics
Multiple R 0,64309
R Square 0,41357
Adjusted R Square 0,36846
Standard Error 6,72350Observations 15
ANOVA
df SS MS F
Significance
F
Regression 1 414,443 414,443 9,168 0,010
Residual 13 587,671 45,205
Total 14 1002,113
Coefficients
Standard
Error t Stat P-value Lower 95%
Upper
95%
Lower
95,0%
Upper
95,0%
Intercept -3,144875153 6,94965 -0,45252 0,65835 -18,15869 11,86894 -18,15869 11,86894
Rm 0,02581797 0,00853 3,02787 0,00970 0,00740 0,04424 0,00740 0,04424
Slika 2: Rezultati obrade podataka za regresiju = f(Rm)
SUMMARY OUTPUT
Regression Statistics
Multiple R 0,20667
R Square 0,04271
Adjusted R Square -0,03093
Standard Error 8,59030
Observations 15
ANOVA
df SS MS F
Significance
F
Regression 1 42,8015 42,8015 0,5800 0,4599
Residual 13 959,3120 73,7932
Total 14 1002,1135
Coefficients
Standard
Error t Stat
P-
value Lower 95%
Upper
95%
Lower
95,0%
Upper
95,0%
Intercept 27,66811902 13,8831 1,9929 0,0677 -2,3246 57,6608 -2,3246 57,6608
HVmax/HVmin -6,72236640 8,8267 -0,7616 0,4599 -25,7914 12,3467 -25,7914 12,3467
Slika 3: Rezultati obrade podataka za regresiju = f(HVmax/HVmin)
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SUMMARY OUTPUT
Regression Statistics
Multiple R 0,09286
R Square 0,00862
Adjusted R Square -0,06764
Standard Error 8,74191Observations 15
ANOVA
df SS MS F
Significance
F
Regression 1 8,64121 8,64121 0,11307 0,74204
Residual 13 993,4722 76,42094
Total 14 1002,113
Coefficients
Standard
Error t Stat P-value Lower 95%
Upper
95%
Lower
95,0%
Upper
95,0%
Intercept 19,46962482 7,03050 2,76931 0,01594 4,28114 34,65811 4,28114 34,65811
A5 -0,097177003 0,28899 -0,33626 0,74204 -0,72150 0,52715 -0,72150 0,52715
Slika 4: Rezultati obrade podataka za regresiju = f(A5)
SUMMARY OUTPUT
Regression Statistics
Multiple R 0,8438353
R Square 0,7120581
Adjusted R Square 0,6640678
Standard Error 4,9036586
Observations 15
ANOVA
df SS MS F
Significance
F
Regression 2 713,563 356,782 14,838 0,001
Residual 12 288,550 24,046
Total 14 1002,113
Coefficients
Standard
Error t Stat P-value Lower 95%
Upper
95%
Lower
95,0%
Upper
95,0%
Intercept 3,7209086 5,42956 0,68531 0,50617 -8,10909 15,55091 -8,10909 15,55091
HB 0,2485529 0,07047 3,52698 0,00417 0,09501 0,40210 0,09501 0,40210
Rm -0,0575441 0,02444 -2,35451 0,03641 -0,11079 -0,00429 -0,11079 -0,00429
Slika 5: Rezultati obrade podataka za regresiju = f(HB, Rm)
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SUMMARY OUTPUT
Regression Statistics
Multiple R 0,775814
R Square 0,601888
Adjusted R Square 0,535535
Standard Error 5,765948Observations 15
ANOVA
df SS MS F
Significance
F
Regression 2 603,160 301,580 9,071 0,004
Residual 12 398,954 33,246
Total 14 1002,11
Coefficients
Standard
Error t Stat P-value Lower 95%
Upper
95%
Lower
95,0%
Upper
95,0%
Intercept 4,308777 10,9183 0,394637 0,70003 -19,4802 28,0977 -19,4802 28,0977
HB 0,086799 0,02114 4,105462 0,00145 0,04073 0,13286 0,04073 0,13286
HVmax/HVmin -4,9304 5,94071 -0,82993 0,42278 -17,8741 8,0133 -17,8741 8,0133
Slika 6: Rezultati obrade podataka za regresiju = f(HB, HVmax/Hvmin)
SUMMARY OUTPUT
Regression StatisticsMultiple R 0,766843
R Square 0,588049
Adjusted R Square 0,51939
Standard Error 5,865306
Observations 15
ANOVA
df SS MS F
Significance
F
Regression 2 589,292 294,646 8,565 0,005
Residual 12 412,822 34,402
Total 14 1002,113
Coefficients
Standard
Error t Stat P-value Lower 95%
Upper
95%
Lower
95,0%
Upper
95,0%
Intercept -1,37011 6,92685 -0,19780 0,84651 -16,4624 13,7222 -16,4624 13,72220
HB 0,088118 0,02145 4,10834 0,00145 0,04139 0,13485 0,04139 0,13485
A5 -0,09935 0,19390 -0,51239 0,61768 -0,52181 0,32311 -0,52181 0,32311
Slika 7: Rezultati obrade podataka za regresiju = f(HB, A5)
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SUMMARY OUTPUT
Regression Statistics
Multiple R 0,661778
R Square 0,437949
Adjusted R Square 0,344274
Standard Error 6,851024Observations 15
ANOVA
df SS MS F
Significance
F
Regression 2 438,8751 219,4375 4,675197 0,031525
Residual 12 563,2384 46,93653
Total 14 1002,113
Coefficients
Standard
Error t Stat P-value Lower 95%
Upper
95%
Lower
95,0%
Upper
95,0%
Intercept 5,159592 13,5142 0,3818 0,7093 -24,2852 34,6044 -24,2852 34,6044
Rm 0,025319 0,0087 2,9049 0,0132 0,0063 0,0443 0,0063 0,0443
HVmax/HVmin -5,09503 7,0619 -0,7215 0,4844 -20,4815 10,2914 -20,4815 10,2914
Slika 8: Rezultati obrade podataka za regresiju = f(Rm, HVmax/Hvmin)
SUMMARY OUTPUT
Regression StatisticsMultiple R 0,660527
R Square 0,436295
Adjusted R Square 0,342345
Standard Error 6,861098
Observations 15
ANOVA
df SS MS F
Significance
F
Regression 2 437,218 218,609 4,644 0,032
Residual 12 564,896 47,075
Total 14 1002,113
Coefficients
Standard
Error t Stat P-value Lower 95%
Upper
95%
Lower
95,0%
Upper
95,0%
Intercept 0,077245 8,47077 0,0091 0,99287 -18,3789 18,5334 -18,3789 18,5334
Rm 0,026359 0,00874 3,0173 0,01072 0,00733 0,04539 0,00733 0,04539
A5 -0,15839 0,22772 -0,6955 0,49995 -0,65455 0,33777 -0,65455 0,33777
Slika 9: Rezultati obrade podataka za regresiju = f(Rm, A5)
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SUMMARY OUTPUT
Regression Statistics
Multiple R 0,235152
R Square 0,055296
Adjusted R Square -0,10215
Standard Error 8,8821
Observations 15
ANOVA
df SS MS F
Significance
F
Regression 2 55,4131 27,7066 0,3512 0,7108
Residual 12 946,7004 78,8917
Total 14 1002,113
Coefficients
Standard
Error t Stat P-value Lower 95%
Upper
95%
Lower
95,0%
Upper
95,0%
Intercept 30,90336 16,4783 1,8754 0,0853 -4,9997 66,8064 -4,9997 66,8064
HVmax/HVmin -7,05667 9,1648 -0,7700 0,4562 -27,0251 12,9117 -27,0251 12,9117
A5 -0,11789 0,2949 -0,3998 0,6963 -0,7603 0,5245 -0,7603 0,5245
Slika 10: Rezultati obrade podataka za regresiju = f(HVmax/Hvmin, A5)
SUMMARY OUTPUT
Regression Statistics
Multiple R 0,859461
R Square 0,738674
Adjusted R Square 0,667403
Standard Error 4,879253
Observations 15
ANOVA
df SS MS F
Significance
F
Regression 3 740,23528 246,745 10,3643 0,00155
Residual 11 261,87821 23,8071
Total 14 1002,113
Coefficients
Standard
Error t Stat P-value Lower 95%
Upper
95%
Lower
95,0%
Upper
95,0%
Intercept 12,42460 9,83892 1,2628 0,23277 -9,23071 34,0799 -9,23071 34,0799
HB 0,249502 0,07013 3,5578 0,00449 0,09515 0,40385 0,09515 0,40385
Rm -0,058383 0,02433 -2,39953 0,03526 -0,11194 -0,00483 -0,11194 -0,0048
HVmax/HVmin -5,323879 5,02982 -1,05846 0,31253 -16,39443 5,74667 -16,39443 5,74667
Slika 11: Rezultati obrade podataka za regresiju = f(HB, Rm, HVmax/HVmin)
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SUMMARY OUTPUT
Regression Statistics
Multiple R 0,8443980
R Square 0,7130079
Adjusted R Square 0,6347374
Standard Error 5,1132502Observations 15
ANOVA
df SS MS F
Significance
F
Regression 3 714,515 238,172 9,110 0,003
Residual 11 287,599 26,145
Total 14 1002,113
CoefficientsStandard
Error t Stat P-value Lower 95%Upper95%
Lower95,0%
Upper95,0%
Intercept 3,1583474 6,38336 0,49478 0,63049 -10,8913 17,2080 -10,8913 17,2080
HB 0,2534410 0,07782 3,25669 0,00764 0,08216 0,42473 0,08216 0,42473
Rm -0,0593008 0,02710 -2,18849 0,05110 -0,11894 0,00034 -0,11894 0,00034
A5 0,0342918 0,17973 0,19080 0,85216 -0,36128 0,42987 -0,36128 0,42987
Slika 12: Rezultati obrade podataka za regresiju = f(HB, Rm, A5)
SUMMARY OUTPUT
Regression Statistics
Multiple R 0,783460263
R Square 0,613809983
Adjusted R Square 0,508485433
Standard Error 5,931474036
Observations 15
ANOVA
df SS MS F
Significance
FRegression 3 615,1073 205,0358 5,8278 0,0124
Residual 11 387,0062 35,1824
Total 14 1002,113
Coefficients
Standard
Error t Stat P-value Lower 95%
Upper
95%
Lower
95,0%
Upper
95,0%
Intercept 7,47138904 12,4742 0,5989 0,5613 -19,9842 34,9270 -19,9842 34,9270
HB 0,08674787 0,0217 3,9885 0,0021 0,0389 0,1346 0,0389 0,1346
HVmax/HVmin -5,2568418 6,1369 -0,8566 0,4099 -18,7640 8,2503 -18,7640 8,2503
A5 -0,1147456 0,1969 -0,5827 0,5718 -0,5481 0,3186 -0,5481 0,3186
Slika 13: Rezultati obrade podataka za regresiju = f(HB, HVmax/HVmin, A5)
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SUMMARY OUTPUT
Regression Statistics
Multiple R 0,681936225
R Square 0,465037015
Adjusted R Square 0,319138019
Standard Error 6,981101928Observations 15
ANOVA
df SS MS F Significance F
Regression 3 466,020 155,340 3,187 0,067
Residual 11 536,094 48,736
Total 14 1002,113
CoefficientsStandard
Error t Stat P-value Lower 95%Upper95%
Lower95,0%
Upper95,0%
Intercept 9,434671973 14,9147 0,6326 0,5399 -23,3923 42,2616 -23,3923 42,2616
Rm 0,025867544 0,0089 2,9026 0,0144 0,0063 0,0455 0,0063 0,0455
HVmax/HVmin -5,55191757 7,2219 -0,7688 0,4582 -21,4473 10,3434 -21,4473 10,3434
A5 -0,17354648 0,2325 -0,7463 0,4711 -0,6854 0,3383 -0,6854 0,3383
Slika 14: Rezultati obrade podataka za regresiju = f(Rm, HVmax/HVmin, A5)
Tabela 6: Regresijone jednaine
Najveikoefivcijent determinacije je R2= 0,738961772 kod jednaine sa 4 varijable
y = 12,03638077 + 0,252193718 HB0,059346605 Rm5,276482446 HVmaxHVmin+ 0,01894138 A5Ima jo jedan sa neznatno manjim koeficijentom korekcije R2= 0,738674096 kod jednaine sa 3 varijable
y = 12,42460385 + 0,249502194
HB0,058383797
Rm5,323879878
pa zbog toga sto ima jednu varijablu manje uzimamo tu jednainu.
Redni broj Varijable Regresijska jednaina Koef.Determinacije
a b1 X1 b3 X2 b2 X3 b4 X4 R^2
1 X1 -3,652018999+ 0,088087819 * HB + 0 * Rm + 0 * HVmax/HVmin + 0 * A5 = 0,579036163
2 X2 27,66811902 + 0 * HB + 0 * Rm + -6,722366395 * HVmax/HVmin + 0 * A5 = 0,042711271
3 X3 -3,144875153+ 0 * HB + 0,02581797 * Rm + 0 * HVmax/HVmin + 0 * A5 = 0,413568577
4 X4 19,46962482 + 0 * HB + 0 * Rm + 0 * HVmax/HVmin + -0,097177003 * A5 = 0,008622988
5 X1X2 4,308776638 + 0,086798611 * HB + 0 * Rm + -4,930402365 * HVmax/HVmin + 0 * A5 = 0,535535444
6 X1X3 3,720908601 + 0,248552964 * HB + -0,057544177 * Rm + 0 * HVmax/HVmin + 0 * A5 = 0,712058145
7 X1X4 -1,370112321+ 0,088117791 * HB + 0 * Rm + 0 * HVmax/HVmin + -0,09934948 * A5 = 0,588048942
8 X2X3 5,159591859 + 0 * HB + 0,025319119 * Rm + -5,09502899 * HVmax/HVmin + 0 * A5 = 0,437949483
9 X2X4 30,9033612 + 0 * HB + 0 * Rm + -7,056674412 * HVmax/HVmin + -0,117889771 * A5 = 0,055296265
10 X3X4 0,077245259 + 0 * HB + 0,026359335 * Rm + 0 * HVmax/HVmin + -0,158392595 * A5 = 0,436295443
11 X1X2X3 12,42460385 + 0,249502194 * HB + -0,058383797 * Rm + -5,323879878 * HVmax/HVmin + 0 * A5 = 0,738674096
12 X1X2X4 7,471389047 + 0,08674787 * HB + 0 * Rm + -5,2568418 * HVmax/HVmin + -0,1147456 * A5 = 0,613809983
13 X1X3X4 3,158347393 + 0,253441042 * HB + -0,059300794 * Rm + 0 * HVmax/HVmin + 0,034291782 * A5 = 0,71300794814 X2X3X4 9,434671973 + 0 * HB + 0,025867544 * Rm + -5,551917579 * HVmax/HVmin + -0,173546488 * A5 = 0,465037015
15 X1X2X3X4 12,03638077 + 0,252193718 * HB + -0,059346605 * Rm + -5,276482446 * HVmax/HVmin + 0,01894138 * A5 = 0,738961772
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Zadata 2:
Tabela 2
Ponavljanja Vremena trajnosti baterije [h x 103]
Proizvoa A Proizvoa B Proizvoa C Proizvoa D
1 53 48 65 60
2 61 52 72 53
3 63 56 58 68
4 59 50 59 555 62 51 71
6 68
Prosjena trajnost se rauna kao:
XA= =
+++++ = = 61 103[h] NA= 6XB=
=++++ = = 51,4 103[h] NB= 5
XC= = ++++ = = 65 103[h] NC= 5XD=
=+++ = = 59 103[h] ND= 4
X =+,++ = , = 59,1 103[h]
Tabela 7
Suma kvadrata izmeu uzoraka:
SST= = = 953,2 103[h]
Yi(PA, PB, PC, PD) Yi - Ysr (Yi - Ysr)**2
53 -6,2 38,44
61 1,8 3,24
63 3,8 14,44
59 -0,2 0,04
62 2,8 7,84
68 8,8 77,44
48 -11,2 125,44
52 -7,2 51,84
56 -3,2 10,24
50 -9,2 84,64
51 -8,2 67,24
65 5,8 33,6472 12,8 163,84
58 -1,2 1,44
59 -0,2 0,04
71 11,8 139,24
60 0,8 0,64
53 -6,2 38,44
68 8,8 77,44
55 -4,2 17,64
Srednja vrijednost 59,2
SUMA = SST 953,2
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Tabela 8
Ukupna suma kvadrata:
SSW= 122 + 35,2 + 170 + 134 = 461,2 103[h]Suma kvadrata unutar uzorka
SSB= SSTSSW= 492 103
[h]
F =
=
,= 5,689
dfB= n - 1 = 4 - 1 = 3
dfw= N - n = 20 - 4 = 16
Ft(3;16;0,05)= 3,24
F > Ft vrijednost se NE MOE prihvatiti
Anova: Single Factor
SUMMARY
Groups Count Sum Average Variance
Proizvoa A 6 366 61 24,4
Proizvoa B 5 257 51,4 8,8
Proizvoa C 5 325 65 42,5
Proizvoa D 4 236 59 44,66667
ANOVA
Source of Variation SS df MS F P-value F crit
Between Groups 492 3 164 5,689505 0,007563 3,238872
Within Groups 461,2 16 28,825
Total 953,2 19
Vremena trajnos ti ba terij e [h x 10**3]
Proizvoa A Proizvoa B Proizvoa C Proizvoa D PA - PAsr PB - PBsr PC - PCsr PD - PDsr A - Pasr)**(PB - PBsr)**2 (PC - PCsr)**2 (PD - PDsr)**2
53 48 65 60 -8 -3,4 0 1 64 11,56 0 1
61 52 72 53 0 0,6 7 -6 0 0,36 49 36
63 56 58 68 2 4,6 -7 9 4 21,16 49 81
59 50 59 55 -2 -1,4 -6 -4 4 1,96 36 16
62 51 71 1 -0,4 6 1 0,16 36 0
68 7 49 0 0 0
Suma 366 257 325 236 122 35,2 170 134
Veli ina uzorka 6 5 5 4
Prosjena trajnost 61 51,4 65 59
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Zadatak 3:
Tabela 3
n 1,44 13,1
1,327 18,1
1,193 27,4
0,96 24,1
1,625 15,81,078 9,71
1,635 11,7
1,707 9,71
1,658 12,7
Slika 11: Dijagram rasipanja
Koeficijent korekcije:
rxy=
=,, ,= - 0,574
nsr= = 1,402 sr= = 15,813
y = -13,039x + 34,101
R = 0,3295
8
10
12
14
16
18
20
22
24
26
28
30
0,8 0,9 1 1,1 1,2 1,3 1,4 1,5 1,6 1,7 1,8
Ugaouravnismicanja
Mehanika karakteristika
n
ni-
i-
(ni-
)2 (
i-
)2 ni
2
ni
(ni-
)2
(
i-
)2
1,44 13,1 0,0374 -2,71333 0,00140 7,3621 2,0736 171,61 18,864 -0,101599259
1,327 18,1 -0,075 2,286667 0,00570 5,2288 1,7609 327,61 24,0187 -0,17277037
1,193 27,4 -0,209 11,58667 0,04391 134,25 1,4232 750,76 32,6882 -2,42805037
0,96 24,1 -0,442 8,286667 0,19585 68,668 0,921 580,81 23,136 -3,66731037
1,625 15,8 0,222 -0,01333 0,04948 0,0001 2,6406 249,64 25,675 -0,002965926
1,078 9,71 2,480 -6,10333 6,15315 37,250 1,1620 94,2841 10,46738 -15,13965741
1,635 11,7 0,232 -4,11333 0,05403 16,919 2,6732 136,89 19,1295 -0,956121481
1,707 9,71 0,304 -6,10333 0,09268 37,250 2,9138 94,2841 16,57497 -1,858125926
1,658 12,7 0,255 -3,11333 0,06525 9,6928 2,7489 161,29 21,0566 -0,795283704
Srednja
vrijednost
1,402 15,813
Suma 12,623 142,32 2,805 1,07E-14 6,66148 316,6246 18,318 2567,178 191,6104 -25,12188481
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Radi lakeg oznaavanja uvodimo da je n = X, = YParamerti regresije su:
b + a = b+ a= _______________________________________________________________________________________________________
12,623
b + 9
a = 142,32 /
(-12,623)
18,318 b + 12,623 a = 191,61 / (9)_______________________________________________________________________________________________________5,521 b + 0 = -72b = -13,041
12,623 (-13,041) + 9 a = 142,329a = 306,936
a = 34,104
m= 34,10413,041 nStandardna devijacija se rauna kao:
= 1 136,729 2 1 4,419Koeficijent varijacije:
100% 4,41915,813 100% 27,845 %Koeficijent determinacije:
R = rxy2= 0,3295
FISHER-ov F-test se rauna kao :
= = 1
103,120922,7867 4,525
FISHER-ov test tabelarno :
Fkrit Ftab{,k,(n-(k+1)} = Ftab{0.5, 2, 6} = 4,74 4,74 ; < to znai da se ne moe potvrditi hipoteza o znaajnosti deformacionog otvrdnjavanja od mehanikekarakteristike.
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F-Test Two-Sample for Variances
n
Mean 1,402555556 15,81333333
Variance 0,076708278 39,578075
Observations 9 9
df 8 8
F 4,534894357
P(F
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Slika 111: Radturanje reziduala
Slika 111: Dijagram vjerovatnoe normalne raspodjele reziduala
-15
-10
-5
0
5
10
0,5 0,7 0,9 1,1 1,3 1,5 1,7 1,9
Resid
uals
n
Rasturanje rezuiduala
y = 0,1947x + 6,0761
R = 0,8873
0
5
10
15
20
25
30
0 20 40 60 80 100
Sample Percentile
Normalna raspodjela reziduala
8
13
18
23
28
33
0,8 1 1,2 1,4 1,6 1,8
n
n Line Fit Plot
Predicted