Ćwiczenie 1 aproksymacja Ewa10 12 2015


Overview

Model 1
Model 2
Model 3
Model 4
Zestawienie
wsp do Surfera
Arkusz1


Sheet 1: Model 1

Zestaw 51

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Nr X [m] Y [m] ∆z [mm]








1 0.7 0.7 1.6








2 0.3 10.2 26.6








3 0.2 20.3 43.0








4 0.7 30.2 74.4











5 10.5 0.7 -10.2











6 10.1 10.4 7.6











7 10.2 20.0 21.6











8 10.8 30.3 81.4











9 20.1 0.2 -39.1











10 20.6 10.2 -40.0











11 20.6 20.3 -9.2











12 20.8 30.1 33.4











13 30.1 0.6 -121.7











14 30.0 10.4 -103.7











15 30.1 20.4 -59.4











16 30.5 30.1 -23.0



























Model 1:




































A
L
Lśr
L' L'L'





1 0.7 0.7
1.6
-7.294
8.894 79.099





1 0.3 10.2
26.6


33.894 1148.786





1 0.2 20.3
43.0


50.294 2529.461





1 0.7 30.2
74.4


81.694 6673.869





1 10.5 0.7
-10.2


-2.906 8.446





1 10.1 10.4
7.6


14.894 221.824





1 10.2 20.0
21.6


28.894 834.849





1 10.8 30.3
81.4


88.694 7866.581





1 20.1 0.2
-39.1


-31.806 1011.638





1 20.6 10.2
-40.0


-32.706 1069.699





1 20.6 20.3
-9.2


-1.906 3.634





1 20.8 30.1
33.4


40.694 1655.981





1 30.1 0.6
-121.7


-114.406 13088.790





1 30.0 10.4
-103.7


-96.406 9294.165





1 30.1 20.4
-59.4


-52.106 2715.061





1 30.5 30.1
-23.0


-15.706 246.686












suma 0.000 48448.569





















A^T
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
0.7 0.3 0.2 0.7 10.5 10.1 10.2 10.8 20.1 20.6 20.6 20.8 30.1 30 30.1 30.5
0.7 10.2 20.3 30.2 0.7 10.4 20 30.3 0.2 10.2 20.3 30.1 0.6 10.4 20.4 30.1
















A^T*A
(A^T*A)^-1








16 246.3 245.1
0.300474911367237 -0.007734767580419 -0.00776224123549








246.3 5761.69 3792.93
-0.007734767580419 0.000507612608963 -5.1762721371326E-06








245.1 3792.93 5708.27
-0.00776224123549 -5.17627213713277E-06 0.000511916669095
























((A^T*A)^-1)*A^T
0.2896270051961 0.218979620491109 0.141354460770698 0.060640888749134 0.213826282907998 0.141626449955909 0.06633545733716 -0.018256487936643 0.143453634753726 0.061963838608612 -0.016434797869841 -0.09405171549373 0.063001062455344 -0.01229542489442 -0.090691314007366 -0.16907896102379
-0.007383062144641 -0.007635281773529 -0.00773832338301 -0.007535762172686 -0.002408458576806 -0.002661713460122 -0.002660644411742 -0.002409392449377 0.002467210605304 0.002669254188414 0.002616973839829 0.002667768894678 0.007541266186076 0.007439777458236 0.007438775997761 0.007591611201616
-0.00740752295762 -0.002542244092361 0.002628631892714 0.007694018780687 -0.007458250424564 -0.002490588225486 0.002423294170614 0.007692930099012 -0.007763900971628 -0.002647322416745 0.002523035941116 0.007538784043821 -0.007610897025361 -0.002593596041015 0.002525053022723 0.007488574204091
















X
V VV
m0^2
cov (X)





7.53 a0 5.26 27.69
346.86
104.223791738401 -2.68290887175341 -2.69243848103583





-3.80 a1 8.88 78.91


-2.68290887175341 0.176072307000874 -0.001795460082664





2.85 a2 21.68 469.84
m0
-2.69243848103582 -0.001795460082664 0.177565228539099







16.62 276.12
18.62











-20.19 407.76




0.9 i 0.95







-8.80 77.46
błędy prametrów a0 10.209 0.737 nieistotny







4.20 17.68
a1 0.420 9.060 istotny







-28.49 811.87
a2 0.421 6.770 istotny







-29.21 853.46













-1.69 2.85













-3.68 13.51













-19.08 364.02













16.51 272.64













26.85 720.83













10.70 114.39













0.45 0.20












suma 0.00 4509.2260



























R^2














0.906927571006411














































delta Z -6.70619529293978





























1 15 15












15














15






























23.5935814465622 -0.068756167980245 -0.055891954189291




























V(delta Z) 4.66089













t= 1.7709 alfa=0.1
alfa=0.05 2.16









1-alfa/2=0.9 1.35 alfa=0.2













Sheet 2: Model 2

Nr X [m] Y [m] ∆z [mm]











1 0.7 0.7 1.6











2 0.3 10.2 26.6











3 0.2 20.3 43











4 0.7 30.2 74.4











5 10.5 0.7 -10.2











6 10.1 10.4 7.6











7 10.2 20 21.6











8 10.8 30.3 81.4











9 20.1 0.2 -39.1











10 20.6 10.2 -40











11 20.6 20.3 -9.2











12 20.8 30.1 33.4











13 30.1 0.6 -121.7











14 30 10.4 -103.7











15 30.1 20.4 -59.4











16 30.5 30.1 -23











a0 a1 a2 a3 a4 a5









A
L
Lśr
L' L'L'


1.00 0.70 0.70 0.49 0.49 0.49
1.60
-7.29375
8.894 79.099


1.00 0.30 10.20 0.09 104.04 3.06
26.60


33.894 1148.786


1.00 0.20 20.30 0.04 412.09 4.06
43.00


50.294 2529.461


1.00 0.70 30.20 0.49 912.04 21.14
74.40


81.694 6673.869


1.00 10.50 0.70 110.25 0.49 7.35
-10.20


-2.906 8.446


1.00 10.10 10.40 102.01 108.16 105.04
7.60


14.894 221.824


1.00 10.20 20.00 104.04 400.00 204.00
21.60


28.894 834.849


1.00 10.80 30.30 116.64 918.09 327.24
81.40


88.694 7866.581


1.00 20.10 0.20 404.01 0.04 4.02
-39.10


-31.806 1011.638


1.00 20.60 10.20 424.36 104.04 210.12
-40.00


-32.706 1069.699


1.00 20.60 20.30 424.36 412.09 418.18
-9.20


-1.906 3.634


1.00 20.80 30.10 432.64 906.01 626.08
33.40


40.694 1655.981


1.00 30.10 0.60 906.01 0.36 18.06
-121.70


-114.406 13088.790


1.00 30.00 10.40 900.00 108.16 312.00
-103.70


-96.406 9294.165


1.00 30.10 20.40 906.01 416.16 614.04
-59.40


-52.106 2715.061


1.00 30.50 30.10 930.25 906.01 918.05
-23.00


-15.706 246.686












suma = 0.000 48448.569


A^T*A









16.000 246.300 245.100 5761.690 5708.270 3792.930









246.300 5761.690 3792.930 149027.139 88738.781 89202.923









245.100 3792.930 5708.270 89202.923 147497.109 88738.781









5761.690 149027.139 89202.923 4074628.375 2088810.770 2317551.631









5708.270 88738.781 147497.109 2088810.770 4034286.358 2297150.084









3792.930 89202.923 88738.781 2317551.631 2297150.084 2088810.770

























(A^T*A)^-1









0.718120683484766 -0.046287437125051 -0.047894208533559 0.000747180486243 0.000793637575669 0.001005611872582









-0.046287437125051 0.00761139170633 0.001195438756202 -0.000200139833774 -6.17160929528221E-06 -6.29370780281028E-05









-0.047894208533559 0.001195438756202 0.007804866249632 -4.50886454331783E-06 -0.000203438657926 -6.6924641179569E-05









0.000747180486243 -0.000200139833774 -4.5088645433174E-06 6.5756072143961E-06 1.50599349518706E-07 -7.95153355892865E-08









0.000793637575669 -6.17160929528256E-06 -0.000203438657926 1.50599349518709E-07 6.59458589672468E-06 4.5689641944153E-08









0.001005611872582 -6.29370780281034E-05 -6.69246411795684E-05 -7.95153355892675E-08 4.56896419441357E-08 4.22158484644084E-06

























((A^T*A)^-1)*A^T
0.653441 0.301428 0.067774 -0.015232 0.288733 0.020207 -0.111559 -0.088120 0.084107 -0.112979 -0.143003 -0.014376 -0.008468 -0.096549 -0.027454 0.202048
-0.040255 -0.032663 -0.023305 -0.011915 0.011938 0.015325 0.019127 0.022531 0.025829 0.023903 0.020981 0.016429 0.001065 -0.005943 -0.015341 -0.027708
-0.041729 0.010703 0.026677 0.001688 -0.030967 0.015857 0.024899 -0.007697 -0.024404 0.019200 0.021436 -0.016271 -0.012596 0.022197 0.017465 -0.026459
0.000607 0.000657 0.000678 0.000610 -0.000633 -0.000642 -0.000656 -0.000672 -0.000620 -0.000632 -0.000648 -0.000620 0.000676 0.000606 0.000602 0.000688
0.000650 -0.000597 -0.000620 0.000661 0.000607 -0.000651 -0.000675 0.000650 0.000690 -0.000649 -0.000663 0.000610 0.000625 -0.000644 -0.000633 0.000639
0.000917 0.000322 -0.000330 -0.000929 0.000320 0.000114 -0.000104 -0.000288 -0.000288 -0.000115 0.000101 0.000332 -0.000925 -0.000328 0.000285 0.000915
















X
V VV
m0^2
cov (X)


8.5627 a0 6.90 47.61
55.60
39.9291230718764 -2.57368547676308 -2.66302557626745 0.041544913380478 0.044128031906252 0.055914278959386


-0.1550 a1 -9.43 88.83


-2.57368547676307 0.423210475870895 0.066469080085066 -0.011128224319569 -0.000343155339722 -0.003499442910032


0.0860 a2 -2.13 4.52
m0
-2.66302557626746 0.066469080085067 0.433968095068372 -0.000250702996592 -0.011311646352387 -0.003721160378271


-0.1362 a3 4.72 22.27
7.46
0.041544913380478 -0.011128224319569 -0.000250702996592 0.000365618531501 8.37366211525436E-06 -4.42123126914994E-06


0.0739 a4 2.46 6.03


0.044128031906253 -0.000343155339722 -0.011311646352387 8.37366211525452E-06 0.000366673788869 2.54044672191474E-06


0.0333 a5 -2.11 4.46


0.055914278959386 -0.003499442910032 -0.003721160378271 -4.42123126914888E-06 2.54044672191378E-06 0.000234729600147




9.30 86.43





0.9 0.95





-9.02 81.30
błędy prametrów a0 6.32 ok 1.355 nieistotny nieistotny





-10.34 107.00
a1 0.65 błąd większy 0.238 nieistotny nieistotny





3.12 9.75
a2 0.66 błąd większy 0.130 nieistotny nieistotny





2.90 8.40
a3 0.02 ok 7.125 istotny istotny





3.43 11.74
a4 0.02 ok 3.861 istotny istotny





2.84 8.05
a5 0.02 ok 2.175 istotny nieistotny





4.28 18.29













-7.16 51.29





A (15,15)


0.25 0.06
R^2
x 15.00
1 15 15 225 225 225

suma = 0.00 556.02
0.98852
y 15.00













delta Z 1.00











-6.76441726820539 1.40307278447856 1.40474236240287 -0.045985529833919 -0.045736716491556 -3.78685514011712E-06







V (delta Z) 3.84
























alfa=0.1 1 - alfa = 0.9 t = 1.8125












1 - alfa = 0.7 t = 1.0931












1 - alfa = 0.8 t = 1.3722











alfa=0.05 1 - alfa = 0.95 t = 2.2281











alfa=0.2 1-alfa/2=0.90 t= 1.372










Sheet 3: Model 3

A
L
Lśr
L' L'L'




1.00 0.70 0.49 0.49
1.6
-7.29375
8.89375 79.0987890625




1.00 10.20 0.09 3.06
26.6


33.89375 1148.7862890625




1.00 20.30 0.04 4.06
43


50.29375 2529.4612890625




1.00 30.20 0.49 21.14
74.4


81.69375 6673.8687890625




1.00 0.70 110.25 7.35
-10.2


-2.90625 8.44628906250001




1.00 10.40 102.01 105.04
7.6


14.89375 221.8237890625




1.00 20.00 104.04 204.00
21.6


28.89375 834.8487890625




1.00 30.30 116.64 327.24
81.4


88.69375 7866.5812890625




1.00 0.20 404.01 4.02
-39.1


-31.80625 1011.6375390625




1.00 10.20 424.36 210.12
-40


-32.70625 1069.6987890625




1.00 20.30 424.36 418.18
-9.2


-1.90625 3.63378906250001




1.00 30.10 432.64 626.08
33.4


40.69375 1655.9812890625




1.00 0.60 906.01 18.06
-121.7


-114.40625 13088.7900390625




1.00 10.40 900.00 312.00
-103.7


-96.40625 9294.1650390625




1.00 20.40 906.01 614.04
-59.4


-52.10625 2715.0612890625




1.00 30.10 930.25 918.05
-23


-15.70625 246.6862890625












suma = 0 48448.569375




A^T*A











16 245.1 5761.69 3792.93











245.1 5708.27 89202.923 88738.781











5761.69 89202.923 4074628.3753 2317551.6309











3792.93 88738.781 2317551.6309 2088810.7699



























(A^T*A)^-1











0.3499 -0.0174 -0.0005 0.0006











-0.0174 0.0014 0.0000 -0.0001











-0.0005 0.0000 0.0000 0.0000











0.0006 -0.0001 0.0000 0.0000



























((A^T*A)^-1)*A^T
0.337774760764342 0.174336021047833 -0.000681082447777 -0.162428377982118 0.290618663062203 0.186680956333837 0.080461831148993 -0.02774692297071 0.15958368434304 0.104622871463799 0.058680784506345 0.013976701171698 -0.073855232294247 -0.058218565534783 -0.046642714079485 -0.037163378532968
-0.016430216628727 -0.003324868424927 0.010717250507888 0.023573592295912 -0.013906751511253 -0.0061716985506 0.001623927818303 0.009288718033985 -0.006610286341831 -0.003898359186311 -0.001699559437752 0.000309528196148 0.006481143878697 0.00318877651629 3.16013853962974E-05 -0.003172798551218
-0.000450207203123 -0.000202812900814 6.37036080218516E-05 0.000297673580921 -0.000317995575562 -0.000240561676808 -0.000154503074818 -7.80825736578736E-05 6.01906481505102E-05 -4.89904419895742E-06 -9.74502666850817E-05 -0.000186822514678 0.00070556868912 0.00044820300604 0.000197883263751 -3.98879656603194E-05
0.000584404210895 5.11725701958444E-05 -0.00052279931916 -0.001026682885914 0.000419421954577 0.00024040249123 5.39911926923887E-05 -0.00010093158555 -7.38103847548176E-05 8.16647465454803E-05 0.000273969646987 0.000468482369823 -0.000915417028097 -0.000377670785767 0.000157766134305 0.000686036671991
















X
V VV
m0^2
cov (X)




-0.85 a0 -0.84 0.70
115.492
40.4076 -2.0087 -0.0541 0.0720




2.38 a3 -3.11 9.65


-2.0087 0.1612 0.0031 -0.0066




-0.14 a4 4.55 20.72
m0
-0.0541 0.0031 0.0002 -0.0002




0.03 a5 -2.82 7.95
10.75
0.0720 -0.0066 -0.0002 0.0004






-4.20 17.68













5.35 28.67



a/ma
0.9 0.95





17.08 291.59
błędy prametrów a0 6.36 -0.134 błąd większy nieistotny nieistotny





-16.04 257.28
a3 0.40 5.922 ok istotny istotny





-17.78 316.24
a4 0.01 -11.385 ok istotny istotny





10.66 113.65
a5 0.02 1.552 ok nieistotny nieistotny





10.56 111.47













-3.22 10.39
R^2
x 15.00
A (15,15)



-4.16 17.28
0.97139
y 15.00
1 15 225 225



11.43 130.55













-0.24 0.06


delta Z 10.50





-7.21 52.03





14.3020653524284 -0.386257744619789 -0.019049421539694 0.024015122687354


suma = 0.00 1385.905


















V (delta Z) 3.10








alfa=0.05 1-alfa=0.95 t= 2.179











alfa=0.1 1 - alfa = 0.9 t = 1.7823











alfa=0.2 1-alfa/2=0.9 t= 1.358

estymacja przedzialowa







Sheet 4: Model 4

A
L
Lśr
L' L'L'













1.0 0.7 0.5 0.5
1.60
-7.29
8.89 79.10







1.0 10.2 0.1 3.1
26.60


33.89 1148.79






1.0 20.3 0.0 4.1
43.00


50.29 2529.46













1.0 30.2 0.5 21.1
74.40


81.69 6673.87













1.0 0.7 110.3 7.4
-10.20


-2.91 8.45













1.0 10.4 102.0 105.0
7.60


14.89 221.82













1.0 20.0 104.0 204.0
21.60


28.89 834.85













1.0 30.3 116.6 327.2
81.40


88.69 7866.58













1.0 0.2 404.0 4.0
-39.10


-31.81 1011.64













1.0 10.2 424.4 210.1
-40.00


-32.71 1069.70













1.0 20.3 424.4 418.2
-9.20


-1.91 3.63













1.0 30.1 432.6 626.1
33.40


40.69 1655.98













1.0 0.6 906.0 18.1
-121.70


-114.41 13088.79













1.0 10.4 900.0 312.0
-103.70


-96.41 9294.17













1.0 20.4 906.0 614.0
-59.40


-52.11 2715.06













1.0 30.1 930.3 918.1
-23.00


-15.71 246.69





















suma = 0.00 48448.57






































a0 a1 a2 a3 a4 a5 a6 a7
















A
AT
1.00 0.70 0.70 0.49 0.49 0.49 0.34 0.34
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1.00 0.30 10.20 0.09 104.04 3.06 0.03 1061.21
0.7 0.3 0.2 0.7 10.5 10.1 10.2 10.8 20.1 20.6 20.6 20.8 30.1 30 30.1 30.5
1.00 0.20 20.30 0.04 412.09 4.06 0.01 8365.43
0.7 10.2 20.3 30.2 0.7 10.4 20 30.3 0.2 10.2 20.3 30.1 0.6 10.4 20.4 30.1
1.00 0.70 30.20 0.49 912.04 21.14 0.34 27543.61
0.49 0.09 0.04 0.49 110.25 102.01 104.04 116.64 404.01 424.36 424.36 432.64 906.01 900 906.01 930.25
1.00 10.50 0.70 110.25 0.49 7.35 1157.63 0.34
0.49 104.04 412.09 912.04 0.49 108.16 400 918.09 0.04 104.04 412.09 906.01 0.36 108.16 416.16 906.01
1.00 10.10 10.40 102.01 108.16 105.04 1030.30 1124.86
0.49 3.06 4.06 21.14 7.35 105.04 204 327.24 4.02 210.12 418.18 626.08 18.06 312 614.04 918.05
1.00 10.20 20.00 104.04 400.00 204.00 1061.21 8000.00
0.343 0.027 0.008 0.343 1157.625 1030.301 1061.208 1259.712 8120.601 8741.816 8741.816 8998.912 27270.901 27000 27270.901 28372.625
1.00 10.80 30.30 116.64 918.09 327.24 1259.71 27818.13
0.343 1061.208 8365.427 27543.608 0.343 1124.864 8000 27818.127 0.008 1061.208 8365.427 27270.901 0.216 1124.864 8489.664 27270.901
1.00 20.10 0.20 404.01 0.04 4.02 8120.60 0.01
















1.00 20.60 10.20 424.36 104.04 210.12 8741.82 1061.21
















1.00 20.60 20.30 424.36 412.09 418.18 8741.82 8365.43
















1.00 20.80 30.10 432.64 906.01 626.08 8998.91 27270.90
















1.00 30.10 0.60 906.01 0.36 18.06 27270.90 0.22
















1.00 30.00 10.40 900.00 108.16 312.00 27000.00 1124.86
















1.00 30.10 20.40 906.01 416.16 614.04 27270.90 8489.66
















1.00 30.50 30.10 930.25 906.01 918.05 28372.63 27270.90









































A^T*A
















16.00 246.30 245.10 5761.69 5708.27 3792.93 149027.14 147497.11
















246.30 5761.69 3792.93 149027.14 88738.78 89202.92 4074628.38 2297150.08
















245.10 3792.93 5708.27 89202.92 147497.11 88738.78 2317551.63 4034286.36
















5761.69 149027.14 89202.92 4074628.38 2088810.77 2317551.63 115192570.20 54077560.29
















5708.27 88738.78 147497.11 2088810.77 4034286.36 2297150.08 54343756.12 114167657.84
















3792.93 89202.92 88738.78 2317551.63 2297150.08 2088810.77 63614045.02 62867851.52
















149027.14 4074628.38 2317551.63 115192570.20 54343756.12 63614045.02 3326287856.60 1408160845.48
















147497.109 2297150.0841 4034286.3575 54077560.29083 114167657.83821 62867851.51901 1408160845.48077 3300720709.92449









































(A^T*A)^-1
















0.81750018157172 -0.087356619322787 -0.092547652714117 0.004437874875875 0.004782690202926 0.001027407542038 -8.01467877425598E-05 -8.61306549070089E-05
















-0.087356619322797 0.044297415987979 0.000772481530975 -0.003524358480605 8.25404122408563E-05 -7.66695845842814E-05 7.22807023960495E-05 -2.35915628908849E-06
















-0.092547652714115 0.000772481530967 0.045942851457766 5.97533446807626E-05 -0.003659205670965 -7.21933968268281E-05 -1.4838606909387E-06 7.5040935690543E-05
















0.004437874875876 -0.003524358480605 5.9753344680012E-05 0.000307809579108 -1.02376407969933E-05 1.16113243602455E-06 -6.54998997125933E-06 2.64791405545624E-07
















0.004782690202926 8.25404122415426E-05 -0.003659205670966 -1.02376407970591E-05 0.000319798475569 5.04159440548782E-07 2.33720925142795E-07 -6.801722267155E-06
















0.001027407542038 -7.6669584584282E-05 -7.21933968268154E-05 1.16113243602463E-06 5.04159440547621E-07 4.22749764927742E-06 -2.69639118541114E-08 -9.79281432064461E-09
















-8.0146787742579E-05 7.22807023960494E-05 -1.48386069092224E-06 -6.54998997125933E-06 2.33720925141352E-07 -2.69639118541094E-08 1.42422275765133E-07 -5.92782212246737E-09
















-8.61306549070085E-05 -2.35915628910299E-06 7.5040935690544E-05 2.64791405547021E-07 -6.80172226715502E-06 -9.79281432066987E-09 -5.92782212249805E-09 1.47715358528896E-07









































(A^T*A)^-1*AT








0.69653166456727 0.257036798625 0.17603875568918 -0.025066323005796 0.241833522506049 -0.128835573722336 -0.114204319553485 -0.182317933445937 0.189549143435828 -0.121336701859098 0.001884969882036 0.041110350921626 -0.012120604916047 -0.194608214637585 0.025191088586112 0.149313376927142








-0.057507766919159 -0.060653983561266 -0.048988706891047 -0.026041942745683 0.072896525411916 0.081252629274065 0.088459577008725 0.079496221687057 -0.034042316236063 -0.040708566637416 -0.040663597143106 -0.054604617804512 0.023159495347471 0.011608931005522 0.0070534594099 -0.000715341206417








-0.061620795949601 0.075015885831924 -0.040216594160715 0.023525976614031 -0.049704441804323 0.078674648756865 -0.039251494612967 0.01735751759956 -0.056177080830936 0.088128850645726 -0.041971786466898 0.00485650360083 -0.030664255889631 0.088253041836027 -0.04846321423795 -0.00774276093195








0.002156874662286 0.003237005134452 0.00295923403498 0.001904674099317 -0.006168879170188 -0.006573000604078 -0.006981761937232 -0.005815967743375 0.004782773394449 0.005268691907534 0.004894175071351 0.00583040417042 -0.001337692977315 -0.00093972837363 -0.001471443218592 -0.001745358450379








0.002428703544523 -0.006462026552044 0.005405405113342 -0.001336791312166 0.002387855684059 -0.006251581937422 0.005231851971748 -0.001541912819537 0.003486520721 -0.006982449778266 0.004997119740762 -0.001401372379229 0.002292771880163 -0.006604559799684 0.005370307182594 -0.001019841259843








0.000926078314361 0.000323134471025 -0.00031040446989 -0.000926488607471 0.000299958065649 8.04702390713615E-05 -0.000120569475478 -0.000312763852254 -0.000260929212974 -0.000100991602188 0.000133205706006 0.000355831758509 -0.000930467574732 -0.000344004182752 0.000286101124545 0.000901839298572








-3.36503651007968E-05 -5.62404465446453E-05 -4.94580601848485E-05 -2.82043265421719E-05 0.000120411382842 0.000128808463705 0.000137683019748 0.000111796303812 -0.000117407508519 -0.000128464096961 -0.000120361581425 -0.000140299640211 4.38352975643266E-05 3.34511255393546E-05 4.5242126709092E-05 5.28583055691263E-05








-3.84126708022174E-05 0.000127678382932 -0.000130520386759 4.35460423593549E-05 -3.93962383103943E-05 0.000120828299398 -0.000129080862423 4.69155360723174E-05 -6.00108659619847E-05 0.000138283089537 -0.000122166168974 4.451790479491E-05 -3.64636584286447E-05 0.000129211505859 -0.000130623716885 3.56938075913304E-05

































X
V VV
m0^2
cov (X)









8.42624790378179 a0 6.83224429072913 46.6795620479947
34.4345159477136
28.1502230395923 -3.00808290120887 -3.18683362330771 0.152816073187262 0.164689622065644 0.035378281391112 -0.002759815840679 -0.002965867409982









-0.408919875285653 a1 -8.63495221652376 74.5623997816486


-3.00808290120921 1.52536007728055 0.026600027597682 -0.121359578305842 0.002842239141639 -0.002640080033072 0.002488950999369 -8.12364048597666E-05









0.444346107668217 a2 -2.57423901620719 6.62670651256338
m0
-3.18683362330764 0.026600027597411 1.58201985120589 0.002057577500339 -0.126002976032825 -0.002485944674353 -5.10960246263139E-05 0.002583998296767









-0.112998904841607 a3 5.01908152359367 25.1911793404793
5.87
0.152816073187295 -0.121359578305842 0.002057577500313 0.010599273860643 -0.000352528205291 3.99830333856948E-05 -0.000225545734123 9.1179638770783E-06









0.041117621613045 a4 1.86505801347696 3.47844139363464


0.16468962206564 0.002842239141662 -0.126002976032826 -0.000352528205293 0.011012105707038 1.73604862957674E-05 8.04806692414397E-06 -0.00023421401388









0.033363392419592 a5 -1.97457861656462 3.89896071299424


0.035378281391111 -0.002640080033072 -0.002485944674353 3.99830333856977E-05 1.73604862957274E-05 0.000145571835223 -9.28489252753144E-07 -3.37210820897235E-07









-0.000506259127884 a6 8.22620918502512 67.6705175557917


-0.00275981584068 0.002488950999369 -5.10960246257474E-05 -0.000225545734123 8.04806692409429E-06 -9.28489252753074E-07 4.90424212614416E-06 -2.04121685411313E-07









0.00071556168166 a7 -9.17123314731819 84.1115174424679


-0.002965867409982 -8.1236404860266E-05 0.002583998296767 9.11796387712641E-06 -0.00023421401388 -3.37210820898105E-07 -2.04121685412369E-07 5.08650686898552E-06











-10.2322170262567 104.698265272417






















4.20454251713979 17.6781777784362



a/ma
0.9 0.95














2.72692820016301 7.43613740884426
Błędy parametrów a0 5.31 1.588 ok nieistotny nieistotny














4.10704567059761 16.8678241403745
a1 1.24 -0.331 błąd większy nieistotny nieistotny














2.5175867620591 6.33824310449521
a2 1.26 0.353 błąd większy nieistotny nieistotny














4.77341031869433 22.7854460706175
a3 0.10 -1.098 ok nieistotny nieistotny














-7.92901493792966 62.8692778859117
a4 0.10 0.392 błąd większy nieistotny nieistotny














0.244128479579636 0.059598714541865
a5 0.01 2.765 ok istotny istotny














Suma: 550.952255163419
a6 0.00 -0.229 błąd większy nieistotny nieistotny

















a7 0.00 0.317 błąd większy nieistotny nieistotny










































1-alfa=0.95 t= 2.306





















1 - alfa = 0.9 t = 1.860

















Sheet 5: Zestawienie


Zestawienie wyników: APROKSYMACJA






























































Zestaw nr: 51 Zaawansowane metody opracowania wyników obserwacji



































Ewelina Barszczak Specjalność: GNiK Kierunek: GiK






























































Model 1:






































































Model 2:
































































Model 3:







































































Model 1 Model 2 Model 3

















Odchylenie standardowe (δ₀) 18.62 Odchylenie standardowe (δ₀) 7.46 Odchylenie standardowe (δ₀) 10.75



































Wsp. korelacji wielorakiej . 0.91 Wsp. korelacji wielorakiej 0.99 Wsp. Korelacji wielorakiej 0.97



































Parametry modelu Odchylenie standard. parametrów Wartość odchylenia standardowego na poziomie 1-α=0.90 Parametry modelu Odchylenie standard. parametrów Wartość odchylenia standardowego na poziomie 1-α=0.90 Parametry modelu Odchylenie standard. parametrów Wartość odchylenia standardowego na poziomie 1-α=0.90





























































































































7.53 10.21 18.08 8.56 6.32 11.45 -0.85 6.36 11.33

















-3.80 0.42 0.74 -0.16 0.65 1.18


















2.85 0.42 0.75 0.09 0.66 1.19


















-0.14 0.02 0.03 2.38 0.40 0.72

















0.07 0.02 0.03 -0.14 0.01 0.02

















0.03 0.02 0.03 0.03 0.02 0.04

















∆z(15,15) -6.71 ∆z(15,15) 1.00 ∆z(15,15) 10.50

















σ∆z(15,15) 4.66 σ∆z(15,15) 3.84 σ∆z(15,15) 3.10

















































































































































































































































































































































































Model 1 Model 2 Model 3
-3.50 -0.86 -3.78















δ1 -5.26 -6.90 0.84
-5.31 7.69 7.37















δ2 -8.88 9.43 3.11
-16.91 4.25 4.34















δ3 -21.68 2.13 -4.55
-32.82 -2.20 -3.94















δ4 -16.62 -4.72 2.82
14.48 -5.63 -6.13















δ5 20.19 -2.46 4.20
4.40 -14.09 -12.31















δ6 8.80 2.11 -5.35
15.86 -0.24 1.68















δ7 -4.20 -9.30 -17.08
4.55 -6.83 -6.99















δ8 28.49 9.02 16.04
17.11 5.25 5.37















δ9 29.21 10.34 17.78
29.84 14.15 16.29















δ10 1.69 -3.12 -10.66
16.60 -3.25 -1.18















δ11 3.68 -2.90 -10.56
31.25 10.74 10.44















δ12 19.08 -3.43 3.22
-33.54 -3.31 -4.37















δ13 -16.51 -2.84 4.16
-15.26 5.63 6.39















δ14 -26.85 -4.28 -11.43
-25.62 -13.92 -13.52















δ15 -10.70 7.16 0.24
-1.13 2.60 0.33















δ16 -0.45 -0.25 7.21
0.00 0.00 0.00















∑δ 0.00 0.00 0.00




























-3.50221182534591 -5.30598586187734 -16.9061713210149 -32.822411704786 14.4837247359498 4.39592374924731 15.8648792165103 4.5547901315544 17.1103421218587 29.8360333383684 16.5976479012344 31.2456272159976 -33.5371638165851 -15.2620570505069 -25.6214798102266 -1.13148702037795 1.24344978758018E-13

Weryfikacja statystyczna hipotez o istotności parametrów modelu 2, dla:







-0.856539328783522 7.69250390197842 4.25075026022608 -2.20058483502746 -5.62828381888193 -14.0895061572556 -0.243300894140361 -6.82706791177495 5.25389784086261 14.1508241063638 -3.24625052122473 10.7352798253405 -3.31069040684932 5.63398115083918 -13.9163502799111 2.60133706824212 3.72502029222233E-12










-3.77985346920145 7.37332724377741 4.33871638124182 -3.93760807403988 -6.13394332007043 -12.3116996890335 1.67646461697463 -6.98924736258385 5.36662509623806 16.294243014022 -1.17763976292491 10.4390886668291 -4.36761996598801 6.39086790369868 -13.5156430106773 0.333921731738119 4.81392703477468E-13






























1 - α = 0.70 1 - α = 0.80 1 - α = 0.95



















t = 1.0931 1.3722 2.2281

















Wartość parametru Odch. stand. parametru
Weryfikacja Weryfikacja Weryfikacja



































8.56 6.32 istotny nieistotny nieistotny

















-0.16 0.65 -0.24 nieistotny nieistotny nieistotny

















0.09 0.66 0.13 nieistotny nieistotny nieistotny

















-0.14 0.02 -7.13 istotny istotny istotny

















0.07 0.02 3.86 istotny istotny istotny

















0.03 0.02 2.17 istotny istotny nieistotny












































1 - α = 0.80
1 - α = 0.95













































t = 1.3722


t = 2.2281


















Wartość parametru
Decyzja
Wartość parametru
Decyzja




































8.56 1.36 nieistotny
8.56 1.36 nieistotny

















-0.16 -0.24 nieistotny
-0.16 -0.24 nieistotny

















0.09 0.13 nieistotny
0.09 0.13 nieistotny

















-0.14 -7.13 istotny
-0.14 -7.13 istotny

















0.07 3.86 istotny
0.07 3.86 istotny

















0.03 2.17 istotny
0.03 2.17 nieistotny


















Sheet 6: wsp do Surfera

Model 1




Punkty pierwotne
Nr X [m] Y [m] ∆z [mm]
a0 7.53

Nr X [m] Y [m] ∆z [mm]
1 0.70 0.70 6.86
a1 -3.80

1 0.7 0.7 1.6
2 0.30 10.20 35.48
a2 2.85

2 0.3 10.2 26.6
3 0.20 20.30 64.68




3 0.2 20.3 43
4 0.70 30.20 91.02




4 0.7 30.2 74.4
5 10.50 0.70 -30.39




5 10.5 0.7 -10.2
6 10.10 10.40 -1.20
To co na zielono, trzeba zapisać w pliku tekstowym, każdy model oddzielnie. Trzeba pamiętać, żeby zamienić , na .
6 10.1 10.4 7.6
7 10.20 20.00 25.80

7 10.2 20 21.6
8 10.80 30.30 52.91

8 10.8 30.3 81.4
9 20.10 0.20 -68.31

9 20.1 0.2 -39.1
10 20.60 10.20 -41.69

10 20.6 10.2 -40
11 20.60 20.30 -12.88

11 20.6 20.3 -9.2
12 20.80 30.10 14.32

12 20.8 30.1 33.4
13 30.10 0.60 -105.19

13 30.1 0.6 -121.7
14 30.00 10.40 -76.85




14 30 10.4 -103.7
15 30.10 20.40 -48.70




15 30.1 20.4 -59.4
16 30.50 30.10 -22.55




16 30.5 30.1 -23













Model 2








Nr X [m] Y [m] ∆z [mm]
a0 8.56269





1 0.7 0.7 8.50
a1 -0.15505





2 0.3 10.2 17.17
a2 0.08596





3 0.2 20.3 40.87
a3 -0.13624





4 0.7 30.2 79.12
a4 0.07393





5 10.5 0.7 -7.74
a5 0.03332





6 10.1 10.4 5.49








7 10.2 20 30.90








8 10.8 30.3 72.38








9 20.1 0.2 -49.44








10 20.6 10.2 -36.88








11 20.6 20.3 -6.30








12 20.8 30.1 36.83








13 30.1 0.6 -118.86








14 30 10.4 -99.42








15 30.1 20.4 -66.56








16 30.5 30.1 -22.75





















Model 3
a0 -0.85





Nr X [m] Y [m] ∆z [mm]
a2 2.38





1 0.7 0.7 0.76
a3 -0.14





2 0.3 10.2 23.49
a5 0.03





3 0.2 20.3 47.55








4 0.7 30.2 71.58








5 10.5 0.7 -14.40








6 10.1 10.4 12.95








7 10.2 20.0 38.68








8 10.8 30.3 65.36








9 20.1 0.2 -56.88








10 20.6 10.2 -29.34








11 20.6 20.3 1.36








12 20.8 30.1 30.18








13 30.1 0.6 -125.86








14 30.0 10.4 -92.27








15 30.1 20.4 -59.64








16 30.5 30.1 -30.21









Sheet 7: Arkusz1

A
L
Lśr
L' L'L'













1.0 0.7 0.5 0.5
1.60
-7.29
8.89 79.10







1.0 10.2 0.1 3.1
26.60


33.89 1148.79






1.0 20.3 0.0 4.1
43.00


50.29 2529.46













1.0 30.2 0.5 21.1
74.40


81.69 6673.87













1.0 0.7 110.3 7.4
-10.20


-2.91 8.45













1.0 10.4 102.0 105.0
7.60


14.89 221.82













1.0 20.0 104.0 204.0
21.60


28.89 834.85













1.0 30.3 116.6 327.2
81.40


88.69 7866.58













1.0 0.2 404.0 4.0
-39.10


-31.81 1011.64













1.0 10.2 424.4 210.1
-40.00


-32.71 1069.70













1.0 20.3 424.4 418.2
-9.20


-1.91 3.63













1.0 30.1 432.6 626.1
33.40


40.69 1655.98













1.0 0.6 906.0 18.1
-121.70


-114.41 13088.79













1.0 10.4 900.0 312.0
-103.70


-96.41 9294.17













1.0 20.4 906.0 614.0
-59.40


-52.11 2715.06













1.0 30.1 930.3 918.1
-23.00


-15.71 246.69





















suma = 0.00 48448.57






































a0 a1 a2 a3 a4 a5 a6 a7
















A
AT
1 0.7 0.2 0.49 0.04 0.14 0.34 0.01
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 0.1 10.6 0.01 112.36 1.06 0 1191.02
0.7 0.1 0.4 0.8 10.4 10 10.6 10.8 20.2 20.8 20.2 20.2 30.3 30.7 30.8 30.7
1 0.4 20.4 0.16 416.16 8.16 0.06 8489.66
0.2 10.6 20.4 30.2 0.7 10.5 20.5 30 0.7 10.2 20.2 30 0.4 10.1 20 30.1
1 0.8 30.2 0.64 912.04 24.16 0.51 27543.61
0.49 0.01 0.16 0.64 108.16 100 112.36 116.64 408.04 432.64 408.04 408.04 918.09 942.49 948.64 942.49
1 10.4 0.7 108.16 0.49 7.28 1124.86 0.34
0.04 112.36 416.16 912.04 0.49 110.25 420.25 900 0.49 104.04 408.04 900 0.16 102.01 400 906.01
1 10 10.5 100 110.25 105 1000 1157.63
0.14 1.06 8.16 24.16 7.28 105 217.3 324 14.14 212.16 408.04 606 12.12 310.07 616 924.07
1 10.6 20.5 112.36 420.25 217.3 1191.02 8615.13
0.34 0 0.06 0.51 1124.86 1000 1191.02 1259.71 8242.41 8998.91 8242.41 8242.41 27818.13 28934.44 29218.11 28934.44
1 10.8 30 116.64 900 324 1259.71 27000
0.01 1191.02 8489.66 27543.61 0.34 1157.63 8615.13 27000 0.34 1061.21 8242.41 27000 0.06 1030.3 8000 27270.9
1 20.2 0.7 408.04 0.49 14.14 8242.41 0.34
















1 20.8 10.2 432.64 104.04 212.16 8998.91 1061.21
















1 20.2 20.2 408.04 408.04 408.04 8242.41 8242.41
















1 20.2 30 408.04 900 606 8242.41 27000
















1 30.3 0.4 918.09 0.16 12.12 27818.13 0.06
















1 30.7 10.1 942.49 102.01 310.07 28934.44 1030.3
















1 30.8 20 948.64 400 616 29218.11 8000
















1 30.7 30.1 942.49 906.01 924.07 28934.44 27270.9









































A^T*A
















16.00 247.70 244.80 5846.93 5692.34 3789.70 153207.76 146602.62
















247.70 5846.93 3789.70 153207.77 88057.01 89361.39 4253978.01 2269275.45
















244.80 3789.70 5692.34 89361.39 146602.61 88057.01 2343492.80 3994977.82
















5846.93 153207.77 89361.39 4253978.11 2072520.83 2343493.01 122283263.85 53354420.63
















5692.34 88057.01 146602.61 2072520.83 3994977.63 2269275.54 54325432.92 112622341.69
















3789.70 89361.39 88057.01 2343493.01 2269275.54 2072520.83 65208707.66 61875683.61
















153207.76 4253978.01 2343492.80 122283263.85 54325432.92 65208707.66 3592013002.23 1398106381.93
















146602.62 2269275.451 3994977.824 53354420.6301 112622341.6872 61875683.6088 1398106381.9335 3243530873.929









































(A^T*A)^-1
















0.768303304433505 -0.084758394078463 -0.081269352783398 0.004380750346934 0.004038248922802 0.000957355807438 -7.90060723017674E-05 -7.18147843145286E-05
















-0.084758394078464 0.044178609985751 0.001706508566632 -0.003497484177882 -4.64790843069883E-05 -7.16366916755271E-05 7.09599778467174E-05 7.45699800698145E-07
















-0.081269352783394 0.001706508566631 0.044878425619146 -9.03074944713464E-05 -0.003619927824869 -5.18478247972536E-05 1.91425221095213E-06 7.45447785489404E-05
















0.004380750346934 -0.003497484177882 -9.03074944714358E-05 0.000302873249467 6.26479999437888E-06 9.41245849714312E-07 -6.36401675118786E-06 -1.14242490976045E-07
















0.004038248922802 -4.64790843068971E-05 -0.003619927824869 6.26479999437149E-06 0.00032031925541 -9.70249665163881E-07 -1.33022264396784E-07 -6.84080367127087E-06
















0.000957355807438 -7.16366916755247E-05 -5.18478247972615E-05 9.41245849714138E-07 -9.70249665163186E-07 4.13859220738736E-06 -2.22857493970811E-08 1.95697891280578E-08
















-7.90060723017673E-05 7.0959977846717E-05 1.91425221095405E-06 -6.36401675118785E-06 -1.33022264396944E-07 -2.22857493970849E-08 1.36467029760195E-07 2.47279675883202E-09
















-7.18147843145227E-05 7.45699800696251E-07 7.454477854894E-05 -1.1424249097589E-07 -6.84080367127086E-06 1.95697891280726E-08 2.47279675882866E-09 1.49184904439559E-07









































(A^T*A)^-1*AT








0.695133105249427 0.267635734732749 0.155887923010311 -0.022938625296076 0.223802521327779 -0.110935523431239 -0.11162028413689 -0.168113818349058 0.151107464324975 -0.092257936016738 -0.002656593268547 0.03000656504602 0.003983082006078 -0.176984605508797 0.010217081069978 0.147733909239493








-0.055193587073015 -0.066696698544649 -0.046426068553933 -0.023663409697435 0.076881821442204 0.084374678576753 0.081380540417567 0.080100720591485 -0.03442359334254 -0.042268799820938 -0.042160809997177 -0.048496544719358 0.016629102967686 0.019418601729359 0.008781775243391 -0.008237729219392








-0.071294021850143 0.076605979612098 -0.039113618262054 0.025828178288313 -0.041847030191042 0.08165691234389 -0.041367916904308 0.013366928013369 -0.038935547934172 0.081631854708991 -0.045127408638839 0.00183806697134 -0.04247337511077 0.086124657133146 -0.044430008067262 -0.002463650112558








0.00206107527406 0.00364561677661 0.002832521493329 0.001635907972437 -0.006446274390245 -0.006961737449572 -0.006239617486692 -0.005932246938271 0.004814260235718 0.005208060907295 0.005035645463837 0.005276078245354 -0.000586883531308 -0.001775151254917 -0.001602986811789 -0.000964268505846








0.003297361050467 -0.006495062196521 0.005394170846924 -0.001616708960454 0.001696453456004 -0.006648124206162 0.005351449870891 -0.001227133285536 0.002166198121448 -0.006477794260228 0.005359154021058 -0.001040938930841 0.003272262328007 -0.006567501469519 0.005068116342113 -0.001531902727653








0.000897834980238 0.000319292273488 -0.000332712565178 -0.000911062300527 0.000282437722355 0.000118662297066 -0.000125492979948 -0.000293978389033 -0.000267570243731 -5.69954375548203E-05 0.000117458964054 0.000318384049992 -0.000939768880166 -0.0003188236642 0.000273576440153 0.000918757732993








-3.2031622952362E-05 -6.3707495374792E-05 -4.7128584252949E-05 -2.21813459806532E-05 0.000125265344725 0.000136615584397 0.000120444068404 0.000114224114699 -0.000116610188295 -0.000124730473324 -0.000121892886741 -0.000126602827462 2.50731543458738E-05 5.14421106645647E-05 4.78395723392875E-05 3.39814748084989E-05








-5.6708377341256E-05 0.000127503544217 -0.000131001202959 5.04392851660837E-05 -2.46118819314009E-05 0.000129968080145 -0.000130981423954 3.99816200606458E-05 -3.3828558754208E-05 0.000127630341867 -0.000130873948005 3.64864147788056E-05 -5.63468674221356E-05 0.000129799876094 -0.000124863451296 4.74065493328369E-05

































X
V VV
m0^2
cov (X)









6.67897533234281 a0 6.78794176821376 46.0761534482007
3040.6043881734
2336.10639890825 -257.716744969504 -247.107950697212 13.3201287283795 12.2787173952086 2.91094026914051 -0.240226210133098 -0.218360348322482









-0.049080399308674 a1 19.7332918448578 389.40280703433


-257.716744969508 134.329675386075 5.18881743615705 -10.6344657388336 -0.14132450770211 -0.217818839062832 0.215761220025416 0.002267378086263









1.07269124926534 a2 40.818878325452 1666.18082774806
m0
-247.107950697199 5.18881743615365 136.457537871889 -0.274589363974521 -11.0067684291668 -0.157648723595775 0.005820483672692 0.226661180771322









-0.154801173496432 a3 79.0400039481868 6247.32222412939
55.14
13.3201287283799 -10.6344657388336 -0.274589363974792 0.92091773138894 0.019048778353937 0.002861956260991 -0.019350457260071 -0.000347366219378









-0.000608502774423 a4 -8.84058417104128 78.1559284852657


12.2787173952075 -0.141324507701833 -11.0067684291667 0.019048778353915 0.973964133617444 -0.002950145389521 -0.00040446808085 -0.020800177661499









0.031565751559108 a5 7.56509980666032 57.230735084732


2.91094026914052 -0.217818839062825 -0.157648723595799 0.002861956260991 -0.002950145389519 0.012583821626642 -6.77621474104975E-05 5.95039866984006E-05









0.000669678640409 a6 30.6353082474785 938.522111418022


-0.240226210133098 0.215761220025415 0.005820483672698 -0.019350457260071 -0.00040446808085 -6.77621474105091E-05 0.00041494224953 7.51879667596561E-06









0.001448470216327 a7 69.9055833502529 4886.79058353916


-0.218360348322464 0.002267378086257 0.226661180771321 -0.000347366219377 -0.020800177661499 5.95039866984456E-05 7.51879667595539E-06 0.000453612275088











-50.7603357296403 2576.6116833858






















-36.1764358179101 1308.73450848737


cov(X)











-5.71870921966777 32.7036351391132


40.1645709 -4.4309225 -4.2485171 0.2290133 0.2111076 0.0500476 -0.0041302 -0.0037543











37.9128726219409 1437.38591044752


-4.4309225 2.3095233 0.0892104 -0.1828377 -0.0024297 -0.003745 0.0037096 3.9E-05











-117.488719708567 13803.5992587582
błędy prametrów
-4.2485171 0.0892104 2.3461139 -0.004721 -0.1892393 -0.0027104 0.0001001 0.003897











-99.297514795525 9859.99644456751

0.2290133 -0.1828377 -0.004721 0.0158333 0.0003275 4.92E-05 -0.0003327 -6E-06











-69.8738534453458 4882.35539530166

0.2111076 -0.0024297 -0.1892393 0.0003275 0.0167454 -5.07E-05 -7E-06 -0.0003576











-20.9428270250128 438.602003799605

0.0500476 -0.003745 -0.0027104 4.92E-05 -5.07E-05 0.0002164 -1.2E-06 1E-06











Suma: 48649.6702107685


-0.0041302 0.0037096 0.0001001 -0.0003327 -7E-06 -1.2E-06 7.1E-06 1E-07














R^2
-0.0037543 3.9E-05 0.003897 -6E-06 -0.0003576 1E-06 1E-07 7.8E-06














-0.00415



















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