t | s | |||||||||||||||||
A | B | C | ||||||||||||||||
x^3 | lnx | x | y | y=Ax^3+Blnx+Cx+D | Dolne 95% | Górne 95% | Dolne 70,0% | Górne 70,0% | C | B | A | D | ||||||
12 | 81 | 64 | 1.38629436111989 | 4 | 6 | 12.0835840788883 | -16.9792124999777 | 41.1463806577542 | -2.60114816157517 | 26.7683163193517 | 0.76519620386902 | -1.99502004952187 | 2.33788458894409E-05 | 11.7869880622486 | ||||
98 | 57 | 64 | 1.38629436111989 | 4 | 16 | 12.0835840788883 | -16.9792124999777 | 41.1463806577542 | -2.60114816157517 | 26.7683163193517 | 0.222933084343403 | 4.11384703476294 | 1.30755025062738E-05 | 7.11390669023145 | ||||
43 | 89 | 2197 | 2.56494935746154 | 13 | 19 | 16.6687766428209 | -26.9855276403076 | 60.3230809259495 | -5.38869355974113 | 38.726246845383 | r^2 | 0.977391582717519 | 4.07339286069054 | #N/A | #N/A | |||
67 | 70 | 2744 | 2.63905732961526 | 14 | 20 | 17.2989141851154 | -27.4894424308165 | 62.0872708010473 | -5.33156539074286 | 39.9293937609737 | ||||||||
69 | 31 | 13824 | 3.17805383034795 | 24 | 25 | 24.1346050106768 | -30.3874166398007 | 78.6566266611543 | -3.41406144244179 | 51.6832714637954 | ||||||||
63 | 89 | 29791 | 3.43398720448515 | 31 | 33 | 29.3536762573311 | -31.1510973403024 | 89.8584498549647 | -1.21793088790875 | 59.925283402571 | ||||||||
74 | 62 | 79507 | 3.76120011569356 | 43 | 34 | 39.0455370876756 | -31.3620826881879 | 109.453156863539 | 3.4702599015577 | 74.6208142737935 | ||||||||
88 | 13 | 97336 | 3.8286413964891 | 46 | 39 | 41.623400435293 | -31.284362497659 | 114.531163368245 | 4.78486103264879 | 78.4619398379372 | ||||||||
97 | 16 | 110592 | 3.87120101090789 | 48 | 40 | 43.378795540076 | -31.2127631626843 | 117.970354242836 | 5.68947462505525 | 81.0681164550968 | ||||||||
34 | 72 | 125000 | 3.91202300542815 | 50 | 44 | 45.1645896618598 | -31.1275431750822 | 121.456722498802 | 6.61600953041261 | 83.7131697933069 | ||||||||
17 | 46 | 195112 | 4.06044301054642 | 58 | 47 | 52.6291960498513 | -30.6815011953871 | 135.93989329509 | 10.5343040977713 | 94.7240880019313 | ||||||||
83 | 77 | 250047 | 4.14313472639153 | 63 | 55 | 57.5745223370925 | -30.3430454291581 | 145.492090103343 | 13.1518894918067 | 101.997155182378 | ||||||||
73 | 50 | 274625 | 4.17438726989564 | 65 | 61 | 59.617170568212 | -30.1994169438468 | 149.433758080271 | 14.2350087109513 | 104.999332425473 | ||||||||
87 | 71 | 314432 | 4.21950770517611 | 68 | 64 | 62.7533847251123 | -29.9778909845458 | 155.48466043477 | 15.8985010108879 | 109.608268439337 | ||||||||
1 | 38 | 328509 | 4.23410650459726 | 69 | 67 | 63.8185600450228 | -29.9028262486445 | 157.53994633869 | 16.4633972618118 | 111.173722828234 | ||||||||
37 | 73 | 389017 | 4.29045944114839 | 73 | 70 | 68.1815268293083 | -29.5989103831927 | 165.961964041809 | 18.7754232244963 | 117.58763043412 | ||||||||
75 | 64 | 421875 | 4.31748811353631 | 75 | 70 | 70.4261786119557 | -29.4459539961366 | 170.298311220048 | 19.96319162259 | 120.889165601321 | ||||||||
75 | 44 | 474552 | 4.35670882668959 | 78 | 80 | 73.8750485793835 | -29.2170622516132 | 176.96715941038 | 21.7850840245533 | 125.965013134214 | ||||||||
28 | 26 | 512000 | 4.38202663467388 | 80 | 81 | 76.2304224734507 | -29.0656927780501 | 181.526537724952 | 23.0268274844648 | 129.434017462437 | ||||||||
83 | 55 | 970299 | 4.59511985013459 | 99 | 96 | 101.058526801986 | -27.7788212379183 | 229.89587484189 | 35.9601129792368 | 166.156940624735 | ||||||||
PODSUMOWANIE - WYJŚCIE | ||||||||||||||||||
Statystyki regresji | ||||||||||||||||||
Wielokrotność R | 0.988631166167403 | |||||||||||||||||
R kwadrat | 0.977391582717519 | |||||||||||||||||
Dopasowany R kwadrat | 0.973152504477054 | |||||||||||||||||
Błąd standardowy | 4.07339286069054 | |||||||||||||||||
Obserwacje | 20 | |||||||||||||||||
ANALIZA WARIANCJI | ||||||||||||||||||
df | SS | MS | F | Istotność F | ||||||||||||||
Regresja | 3 | 11477.0695296396 | 3825.6898432132 | 230.567007088379 | 2.2557980579198E-13 | |||||||||||||
Resztkowy | 16 | 265.480470360395 | 16.5925293975247 | |||||||||||||||
Razem | 19 | 11742.55 | ||||||||||||||||
Współczynniki | Błąd standardowy | t Stat | Wartość-p | Dolne 95% | Górne 95% | Dolne 70,0% | Górne 70,0% | |||||||||||
Przecięcie | 11.7869880622485 | 7.11390669023143 | 1.65689382437838 | 0.117016508515195 | -3.29382032852653 | 26.8677964530236 | 4.16701822943116 | 19.4069578950659 | D | |||||||||
x^3 | 2.3378845889441E-05 | 1.30755025062738E-05 | 1.78798832994935 | 0.092730182640763 | -4.3399809797654E-06 | 5.10976727586474E-05 | 9.37318922493213E-06 | 3.73845025539499E-05 | A | |||||||||
lnx | -1.99502004952184 | 4.11384703476293 | -0.484952413802329 | 0.634282800393535 | -10.7159861208662 | 6.72594602182251 | -6.40151449297073 | 2.41147439392705 | B | |||||||||
x | 0.765196203869019 | 0.222933084343403 | 3.43240307342773 | 0.003418224571632 | 0.292599180131844 | 1.23779322760619 | 0.526404292278962 | 1.00398811545908 | C |
x^2 | sinx | x | y | y=Kx^2+Gsinx+E | Dolne 95% | Górne 95% | Dolne 75,0% | Górne 75,0% | ||||||
16 | -0.756802495307928 | 4 | 6 | 17.4851801706649 | 16.202680880639 | 18.7676794606908 | 16.7611751440913 | 18.2091851972385 | ||||||
16 | -0.756802495307928 | 4 | 16 | 17.4851801706649 | 16.202680880639 | 18.7676794606908 | 16.7611751440913 | 18.2091851972385 | ||||||
169 | 0.420167036826641 | 13 | 19 | 20.8802781049319 | 15.3954923636401 | 26.3650638462237 | 17.7839703897873 | 23.9765858200766 | ||||||
196 | 0.99060735569487 | 14 | 20 | 22.088671488604 | 14.6118002251156 | 29.5655427520924 | 17.8677784090451 | 26.309564568163 | ||||||
576 | -0.905578362006624 | 24 | 25 | 22.4263047259513 | 21.1266571470119 | 23.7259523048908 | 21.6926190333008 | 23.1599904186018 | ||||||
961 | -0.404037645323065 | 31 | 33 | 26.837511963183 | 23.4444577591237 | 30.2305661672423 | 24.9220424434095 | 28.7529814829565 | ||||||
1849 | -0.831774742628598 | 43 | 34 | 34.3505407207872 | 31.5915762799043 | 37.10950516167 | 32.7930317701999 | 35.9080496713744 | ||||||
2116 | 0.901788347648809 | 46 | 39 | 39.7372352856323 | 30.7492890658266 | 48.7251815054379 | 34.6633001245598 | 44.8111704467047 | ||||||
2304 | -0.768254661323667 | 48 | 40 | 38.674923793875 | 35.2663260442187 | 42.0835215435313 | 36.7506795283917 | 40.5991680593583 | ||||||
2500 | -0.262374853703929 | 50 | 44 | 41.3414535152062 | 36.0033779904654 | 46.679529039947 | 38.3279676269886 | 44.3549394034237 | ||||||
3364 | 0.992872648084537 | 58 | 47 | 51.4587544809056 | 40.9755805071381 | 61.9419284546731 | 45.5407234063618 | 57.3767855554494 | ||||||
3969 | 0.167355700302807 | 63 | 55 | 55.6803581114691 | 47.4704339661622 | 63.890282256776 | 51.0456371449799 | 60.3150790779582 | ||||||
4225 | 0.826828679490103 | 65 | 61 | 59.1610427162771 | 48.4353556039101 | 69.8867298286441 | 53.1061065122555 | 65.2159789202987 | ||||||
4624 | -0.897927680689291 | 68 | 64 | 59.9627325282011 | 54.8053018803106 | 65.1201631760916 | 57.0512254869752 | 62.8742395694271 | ||||||
4761 | -0.114784813783187 | 69 | 67 | 62.5480439384302 | 54.5611448043795 | 70.5349430724809 | 58.039226534194 | 67.0568613426664 | ||||||
5329 | -0.676771956887308 | 73 | 70 | 66.8692953458387 | 60.2821763415124 | 73.4564143501651 | 63.1506911276058 | 70.5878995640717 | ||||||
5625 | -0.38778163540943 | 75 | 70 | 70.0985029416864 | 62.2349593696029 | 77.96204651377 | 65.6593230394859 | 74.5376828438869 | ||||||
6084 | 0.513978455987535 | 78 | 80 | 75.8678741038804 | 64.4611711207879 | 87.274577086973 | 69.4284862924261 | 82.3072619153347 | ||||||
6400 | -0.993888653923375 | 80 | 81 | 76.2644698400173 | 69.756880527224 | 82.7720591528106 | 72.5907622520434 | 79.9381774279912 | ||||||
9801 | -0.999206834186354 | 99 | 96 | 107.781646053793 | 98.0733640882042 | 117.489928019383 | 102.301062167982 | 113.262229939605 | ||||||
PODSUMOWANIE - WYJŚCIE | ||||||||||||||
Statystyki regresji | ||||||||||||||
Wielokrotność R | 0.980909365192373 | |||||||||||||
R kwadrat | 0.962183182722105 | |||||||||||||
Dopasowany R kwadrat | 0.957734145395294 | |||||||||||||
Błąd standardowy | 5.1109217985578 | |||||||||||||
Obserwacje | 20 | |||||||||||||
ANALIZA WARIANCJI | ||||||||||||||
df | SS | MS | F | Istotność F | ||||||||||
Regresja | 2 | 11298.4841322735 | 5649.24206613673 | 216.267725362453 | 8.13433939397901E-13 | |||||||||
Resztkowy | 17 | 444.065867726547 | 26.1215216309733 | |||||||||||
Razem | 19 | 11742.55 | ||||||||||||
Współczynniki | Błąd standardowy | t Stat | Wartość-p | Dolne 95% | Górne 95% | Dolne 75,0% | Górne 75,0% | |||||||
Przecięcie | 18.6079924904273 | 1.83729266286006 | 10.1279414361024 | 1.28463831680224E-08 | 14.731643844637 | 22.4843411362176 | 16.4196903789716 | 20.796294601883 | E | |||||
x^2 | 0.009269658523693 | 0.000448614625881 | 20.6628540152802 | 1.75530270268456E-13 | 0.008323164406197 | 0.010216152641188 | 0.008735337371222 | 0.009803979676163 | K | |||||
sinx | 1.67960183009735 | 1.63397689600397 | 1.02792263110021 | 0.318390737322384 | -1.76778804747277 | 5.12699170766747 | -0.266541625365653 | 3.62574528556036 | G |
x^2 | logx | x | y | y=Hx^2+Mlogx | Dolne 95% | Górne 95% | Dolne 80,0% | Górne 80,0% | ||||
16 | 0.602059991327962 | 4 | 6 | 9.4688473543303 | 8.06436126498808 | 10.8733334436725 | 8.57946852877244 | 10.3582261798882 | ||||
16 | 0.602059991327962 | 4 | 16 | 9.4688473543303 | 8.06436126498808 | 10.8733334436725 | 8.57946852877244 | 10.3582261798882 | ||||
169 | 1.11394335230684 | 13 | 19 | 18.5388826541653 | 15.8138009421546 | 21.2639643661761 | 16.8132479248727 | 20.2645173834579 | ||||
196 | 1.14612803567824 | 14 | 20 | 19.2362655793163 | 16.4123824868378 | 22.0601486717947 | 17.4480657193394 | 21.0244654392931 | ||||
576 | 1.38021124171161 | 24 | 25 | 25.6513079172548 | 21.9422275643961 | 29.3603882701134 | 23.3025644493361 | 28.0000513851734 | ||||
961 | 1.49136169383427 | 31 | 33 | 30.1933939002311 | 25.8783933314348 | 34.5083944690275 | 27.4609566284922 | 32.9258311719701 | ||||
1849 | 1.63346845557959 | 43 | 34 | 38.8948617850565 | 33.4461033844979 | 44.3436201856151 | 35.444482045584 | 42.345241524529 | ||||
2116 | 1.66275783168157 | 46 | 39 | 41.3024377937957 | 35.5438117040843 | 47.061063883507 | 37.6558369856004 | 44.9490386019909 | ||||
2304 | 1.68124123737559 | 48 | 40 | 42.9644218075376 | 36.9925519187189 | 48.9362916963562 | 39.1827861840837 | 46.7460574309914 | ||||
2500 | 1.69897000433602 | 50 | 44 | 44.6731895055273 | 38.4825596880945 | 50.8638193229601 | 40.7530260248976 | 48.593352986157 | ||||
3364 | 1.76342799356294 | 58 | 47 | 51.9930174418732 | 44.8696717396758 | 59.1163631440706 | 47.4822195900909 | 56.5038152936554 | ||||
3969 | 1.79934054945358 | 63 | 55 | 56.9753306158302 | 49.2201608296459 | 64.7305004020144 | 52.0644355569346 | 61.8862256747258 | ||||
4225 | 1.81291335664286 | 65 | 61 | 59.0583350444281 | 51.0395624806168 | 67.0771076082393 | 53.980515777056 | 64.1361543118002 | ||||
4624 | 1.83250891270624 | 68 | 64 | 62.2806776695625 | 53.8546545636135 | 70.7067007755115 | 56.9449704732014 | 67.6163848659236 | ||||
4761 | 1.83884909073726 | 69 | 67 | 63.3810673615527 | 54.8161074126683 | 71.9460273104371 | 57.9573795955483 | 68.8047551275572 | ||||
5329 | 1.86332286012046 | 73 | 70 | 67.9151130309821 | 58.7783074960171 | 77.0519185659471 | 62.129308929609 | 73.7009171323552 | ||||
5625 | 1.8750612633917 | 75 | 70 | 70.2621512257823 | 60.8296862027702 | 79.6946162487943 | 64.2891232777369 | 76.2351791738277 | ||||
6084 | 1.89209460269048 | 78 | 80 | 73.8834862933949 | 63.9952484220235 | 83.7717241647664 | 67.6218440801952 | 80.1451285065947 | ||||
6400 | 1.90308998699194 | 80 | 81 | 76.3652469667884 | 66.1649191177802 | 86.5655748157966 | 69.9059764396557 | 82.8245174939211 | ||||
9801 | 1.99563519459755 | 99 | 96 | 102.67492352373 | 89.1752290586002 | 116.174617988859 | 94.1263572546185 | 111.223489792841 | ||||
PODSUMOWANIE - WYJŚCIE | ||||||||||||
Statystyki regresji | ||||||||||||
Wielokrotność R | 0.997785420659679 | |||||||||||
R kwadrat | 0.995575745681014 | |||||||||||
Dopasowany R kwadrat | 0.939774398218848 | |||||||||||
Błąd standardowy | 3.79184508662811 | |||||||||||
Obserwacje | 20 | |||||||||||
ANALIZA WARIANCJI | ||||||||||||
df | SS | MS | F | Istotność F | ||||||||
Regresja | 2 | 58238.1943951023 | 29119.0971975511 | 2025.24110620794 | 6.01932373437626E-21 | |||||||
Resztkowy | 18 | 258.805604897743 | 14.3780891609857 | |||||||||
Razem | 20 | 58497 | ||||||||||
Współczynniki | Błąd standardowy | t Stat | Wartość-p | Dolne 95% | Górne 95% | Dolne 80,0% | Górne 80,0% | |||||
Przecięcie | 0 | #N/A | #N/A | #N/A | #N/A | #N/A | #N/A | #N/A | ||||
x^2 | 0.007313191984371 | 0.00043185537386 | 16.9343544784506 | 1.66652920289939E-12 | 0.006405897512691 | 0.00822048645605 | 0.006738655506024 | 0.007887728462717 | H | |||
logx | 15.5330638429454 | 1.09889330639559 | 14.1351883322453 | 3.46686487752833E-11 | 13.2243746793796 | 17.8417530065111 | 14.0711061400877 | 16.995021545803 | M |