i V(ýška) H(motnost) P(ohlaví) Vi-mV zVi Hi-mH zHi zVi x zHi 1 172 85 1 -0.7 -0.050012088 9.75 0.614080057 -0.030711426 2 170 59 0 -2.7 -0.192903769 -16.25 -1.023466761 0.197430595 3 149 86 0 -23.7 -1.693266414 10.75 0.677062627 -1.146447405 V(ýška) H(motnost) 4 176 79 1 3.3 0.235771273 3.75 0.236184637 0.055685553 V(ýška) 1 5 185 86 1 12.3 0.878783835 10.75 0.677062627 0.594991691 H(motnost) 0.586992629 1 6 162 57 0 -10.7 -0.76447049 -18.25 -1.149431901 0.878706769 7 182 73 1 9.3 0.664446314 -2.25 -0.141710782 -0.094159207 8 190 96 1 17.3 1.236013036 20.75 1.306888326 1.615331007 9 154 55 0 -18.7 -1.336037212 -20.25 -1.275397041 1.703977907 10 167 63 1 -5.7 -0.407241289 -12.25 -0.771536481 0.314201511 11 204 93 0 31.3 2.236254799 17.75 1.117940616 2.500000068 12 155 52 1 -17.7 -1.264591372 -23.25 -1.46434475 1.851797737 13 174 80 1 1.3 0.092879592 4.75 0.299167207 0.027786528 14 185 110 0 12.3 0.878783835 34.75 2.188644305 1.923345235 15 169 70 1 -3.7 -0.264349609 -5.25 -0.330658492 0.087409443 16 173 65 0 0.3 0.021433752 -10.25 -0.645571342 -0.013837016 17 189 74 0 16.3 1.164567196 -1.25 -0.078728212 -0.091684294 18 154 60 0 -18.7 -1.336037212 -15.25 -0.960484191 1.283242621 19 176 68 1 3.3 0.235771273 -7.25 -0.456623632 -0.107658735 20 168 94 0 -4.7 -0.335795449 18.75 1.180923186 -0.396548632 kontrola r2 kovariance t df p m 172.7 75.25 rVH 0.586992629 0.586992629 0.344560347 130.4473684 3.076114836 18 0.007111186 s 13.99661613 15.87740864 rVP 0.139273582 0.019397131 0.596703272 18 0.326637698 rHP -0.003230938 1.0439E-05 -0.013707779 18 0.393403501 kontrola m 172.7 s 13.99661613 N t 20 50 100 200 1000 Poznámka kovariance různé 0 0 0 0 0 0 hodnoty 0.1 0.426401433 0.696310624 0.994936676 1.414213562 3.175028831 cVH = sV * rVH * sH r 0.2 0.866025404 1.414213562 2.020725942 2.872281323 6.448514041 0.3 1.33424877 2.178819118 3.11324713 4.425202547 9.934953281 rVH = cVH/(sV*sH) 0.4 1.8516402 3.023715784 4.320493799 6.141195789 13.78750297 0.5 2.449489743 4 5.715476066 8.124038405 18.23915203 0.6 3.181980515 5.196152423 7.424621202 10.55343546 23.6933535 0.7 4.158619681 6.790997501 9.703445921 13.79258113 30.96550896 0.8 5.656854249 9.237604307 13.19932658 18.76166304 42.12151733 0.9 8.759956741 14.30494946 20.43989906 29.05348969 65.22753697 0.99 29.7745296 48.62160324 69.47390241 98.750943 221.7042033 ##### Sheet/List 2 ##### i V(ýška) H(motnost) P(ohlaví) Vi-mV zVi Hi-mH zHi zVi x zHi Hi.stř ei 1 172 85 1 -0.7 -0.050012088 9.75 0.614080057 -0.030711426 74.78389125 10.21610875 2 170 59 0 -2.7 -0.192903769 -16.25 -1.023466761 0.197430595 73.45215195 -14.45215195 3 149 86 0 -23.7 -1.693266414 10.75 0.677062627 -1.146447405 59.46888937 26.53111063 b 0.665869647 4 176 79 1 3.3 0.235771273 3.75 0.236184637 0.055685553 77.44736984 1.552630165 a -39.74568803 5 185 86 1 12.3 0.878783835 10.75 0.677062627 0.594991691 83.44019666 2.559803342 6 162 57 0 -10.7 -0.76447049 -18.25 -1.149431901 0.878706769 68.12519478 -11.12519478 7 182 73 1 9.3 0.664446314 -2.25 -0.141710782 -0.094159207 81.44258772 -8.442587717 8 190 96 1 17.3 1.236013036 20.75 1.306888326 1.615331007 86.76954489 9.230455107 9 154 55 0 -18.7 -1.336037212 -20.25 -1.275397041 1.703977907 62.7982376 -7.798237601 10 167 63 1 -5.7 -0.407241289 -12.25 -0.771536481 0.314201511 71.45454301 -8.454543012 11 204 93 0 31.3 2.236254799 17.75 1.117940616 2.500000068 96.09171995 -3.091719951 12 155 52 1 -17.7 -1.264591372 -23.25 -1.46434475 1.851797737 63.46410725 -11.46410725 13 174 80 1 1.3 0.092879592 4.75 0.299167207 0.027786528 76.11563054 3.884369459 14 185 110 0 12.3 0.878783835 34.75 2.188644305 1.923345235 83.44019666 26.55980334 15 169 70 1 -3.7 -0.264349609 -5.25 -0.330658492 0.087409443 72.78628231 -2.786282306 16 173 65 0 0.3 0.021433752 -10.25 -0.645571342 -0.013837016 75.44976089 -10.44976089 17 189 74 0 16.3 1.164567196 -1.25 -0.078728212 -0.091684294 86.10367525 -12.10367525 18 154 60 0 -18.7 -1.336037212 -15.25 -0.960484191 1.283242621 62.7982376 -2.798237601 19 176 68 1 3.3 0.235771273 -7.25 -0.456623632 -0.107658735 77.44736984 -9.447369835 20 168 94 0 -4.7 -0.335795449 18.75 1.180923186 -0.396548632 72.12041266 21.87958734 m 172.7 75.25 s 13.99661613 15.87740864 kontrola r2 kovariance t df p rVH 0.586992629 0.586992629 0.344560347 130.4473684 3.076114836 18 0.007111186 kontrola rVP 0.139273582 0.019397131 0.596703272 18 0.326637698 m 172.7 rHP -0.003230938 1.0439E-05 -0.013707779 18 0.393403501 s 13.99661613 R 0.586992629 0.344560347 pro vztah H = a+bV+e Poznámka kovariance cVH = sV * rVH * sH rVH = cVH/(sV*sH) ##### Sheet/List 3 ##### i V(ýška) H(motnost) P(ohlaví) Vi-mV zVi Hi-mH zHi zVi x zHi Hi.stř ei ei 1 172 85 1 -0.7 -0.050012088 9.75 0.614080057 -0.030711426 73.43278627 11.56721373 10.21610875 VÝSLEDEK 2 170 59 0 -2.7 -0.192903769 -16.25 -1.023466761 0.197430595 74.75684434 -15.75684434 -14.45215195 3 149 86 0 -23.7 -1.693266414 10.75 0.677062627 -1.146447405 60.48702243 25.51297757 a -40.76076161 26.53111063 Regresní statistika 4 176 79 1 3.3 0.235771273 3.75 0.236184637 0.055685553 76.15084759 2.849152414 b1 0.679515329 1.552630165 Násobné R 0.593233009 5 185 86 1 12.3 0.878783835 10.75 0.677062627 0.594991691 82.26648555 3.733514451 b2 -2.68308873 2.559803342 Hodnota spolehlivosti R 0.351925403 6 162 57 0 -10.7 -0.76447049 -18.25 -1.149431901 0.878706769 69.32072171 -12.32072171 -11.12519478 Nastavená hodnota spolehlivosti R 0.275681333 7 182 73 1 9.3 0.664446314 -2.25 -0.141710782 -0.094159207 80.22793956 -7.227939561 SS 3104.115311 -8.442587717 Chyba stř. hodnoty 13.51277239 8 190 96 1 17.3 1.236013036 20.75 1.306888326 1.615331007 85.66406219 10.33593781 9.230455107 Pozorování 20 9 154 55 0 -18.7 -1.336037212 -20.25 -1.275397041 1.703977907 63.88459907 -8.884599075 R 0.593233009 -7.798237601 10 167 63 1 -5.7 -0.407241289 -12.25 -0.771536481 0.314201511 70.03520962 -7.035209624 R2 0.351925403 -8.454543012 ANOVA 11 204 93 0 31.3 2.236254799 17.75 1.117940616 2.500000068 97.86036553 -4.860365532 -3.091719951 Rozdíl SS MS F Významnost F 12 155 52 1 -17.7 -1.264591372 -23.25 -1.46434475 1.851797737 61.88102567 -9.881025674 -11.46410725 Regrese 2 1685.634701 842.8173507 4.615774088 0.025050274 13 174 80 1 1.3 0.092879592 4.75 0.299167207 0.027786528 74.79181693 5.208183072 3.884369459 Rezidua 17 3104.115299 182.5950176 14 185 110 0 12.3 0.878783835 34.75 2.188644305 1.923345235 84.94957428 25.05042572 26.55980334 Celkem 19 4789.75 15 169 70 1 -3.7 -0.264349609 -5.25 -0.330658492 0.087409443 71.39424028 -1.394240282 -2.786282306 16 173 65 0 0.3 0.021433752 -10.25 -0.645571342 -0.013837016 76.79539033 -11.79539033 -10.44976089 Koeficienty Chyba stř. hodnoty t Stat Hodnota P Dolní 95% Horní 95% "Dolní 95,0%" "Horní 95,0%" 17 189 74 0 16.3 1.164567196 -1.25 -0.078728212 -0.091684294 87.6676356 -13.6676356 -12.10367525 Hranice -40.76912877 38.44022542 -1.06058506 0.303714932 -121.8709152 40.33265763 -121.8709152 40.33265763 18 154 60 0 -18.7 -1.336037212 -15.25 -0.960484191 1.283242621 63.88459907 -3.884599075 -2.798237601 V(ýška) 0.679561644 0.223665 3.038301227 0.007422476 0.207669743 1.151453545 0.207669743 1.151453545 19 176 68 1 3.3 0.235771273 -7.25 -0.456623632 -0.107658735 76.15084759 -8.150847586 -9.447369835 P(ohlaví) -2.682334247 6.102571541 -0.439541631 0.665805497 -15.55763475 10.19296626 -15.55763475 10.19296626 20 168 94 0 -4.7 -0.335795449 18.75 1.180923186 -0.396548632 73.39781368 20.60218632 21.87958734 m 172.7 75.25 s 13.99661613 15.87740864 kontrola r2 kovariance t df p REZIDUA PRAVDĚPODOBNOST rVH 0.586992629 0.586992629 0.344560347 130.4473684 3.076114836 18 0.007111186 kontrola rVP 0.139273582 0.019397131 0.596703272 18 0.326637698 Pozorování Očekávané H(motnost) Rezidua Normovaná rezidua Percentil H(motnost) m 172.7 rHP -0.003230938 1.0439E-05 -0.013707779 18 0.393403501 1 73.43313973 11.56686027 0.904947465 2.5 52 s 13.99661613 2 74.75635068 -15.75635068 -1.232717373 7.5 55 R 0.593233009 0.351925403 3 60.48555616 25.51444384 1.996153729 12.5 57 pro vztah H = a+bV+e 4 76.1513863 2.848613699 0.222864778 17.5 59 5 82.2674411 3.732558904 0.292021312 22.5 60 6 69.31985753 -12.31985753 -0.963859127 27.5 63 7 80.22875616 -7.228756164 -0.565550582 32.5 65 Poznámka kovariance 8 85.66524932 10.33475068 0.808551864 37.5 68 9 63.88336438 -8.883364384 -0.695000881 42.5 70 cVH = sV * rVH * sH 10 70.03533151 -7.035331507 -0.550417768 47.5 73 11 97.86144658 -4.861446575 -0.380341221 52.5 74 rVH = cVH/(sV*sH) 12 61.88059178 -9.880591781 -0.773020186 57.5 79 13 74.79226301 5.207736986 0.407433674 62.5 80 i V(ýška) P(ohlaví) H(motnost) 14 84.94977534 25.05022466 1.959834974 67.5 85 1 172 1 85 15 71.39445479 -1.394454795 -0.109096877 72.5 86 2 170 0 59 16 76.79503562 -11.79503562 -0.922799042 77.5 86 3 149 0 86 17 87.66802192 -13.66802192 -1.069334417 82.5 93 4 176 1 79 18 63.88336438 -3.883364384 -0.303819764 87.5 94 5 185 1 86 19 76.1513863 -8.151386301 -0.63773368 92.5 96 6 162 0 57 20 73.3972274 20.6027726 1.611883121 97.5 110 7 182 1 73 8 190 1 96 9 154 0 55 10 167 1 63 11 204 0 93 12 155 1 52 13 174 1 80 14 185 0 110 15 169 1 70 16 173 0 65 17 189 0 74 18 154 0 60 19 176 1 68 20 168 0 94 ##### Sheet/List 4 ##### i V(ýška) H(motnost) P(ohlaví) Vi-mV zVi Hi-mH zHi zPi zVi.stř. (z P) zHi.stř. (z P) eVi eHi 1 172 85 1 -0.7 -0.050012088 9.75 0.614080057 0.974679434 0.135747096 -0.003149128 -0.185759185 0.617229185 1. model 2 170 59 0 -2.7 -0.192903769 -16.25 -1.023466761 -0.974679434 -0.135747096 0.003149128 -0.057156672 -1.02661589 V = bV * P 3 149 86 0 -23.7 -1.693266414 10.75 0.677062627 -0.974679434 -0.135747096 0.003149128 -1.557519317 0.673913498 4 176 79 1 3.3 0.235771273 3.75 0.236184637 0.974679434 0.135747096 -0.003149128 0.100024176 0.239333766 rVP 0.139273582 0.139273582 5 185 86 1 12.3 0.878783835 10.75 0.677062627 0.974679434 0.135747096 -0.003149128 0.743036738 0.680211755 6 162 57 0 -10.7 -0.76447049 -18.25 -1.149431901 -0.974679434 -0.135747096 0.003149128 -0.628723394 -1.152581029 bV 0.139273582 7 182 73 1 9.3 0.664446314 -2.25 -0.141710782 0.974679434 0.135747096 -0.003149128 0.528699218 -0.138561654 8 190 96 1 17.3 1.236013036 20.75 1.306888326 0.974679434 0.135747096 -0.003149128 1.10026594 1.310037454 2. model 9 154 55 0 -18.7 -1.336037212 -20.25 -1.275397041 -0.974679434 -0.135747096 0.003149128 -1.200290116 -1.278546169 H = bH * P 10 167 63 1 -5.7 -0.407241289 -12.25 -0.771536481 0.974679434 0.135747096 -0.003149128 -0.542988386 -0.768387353 11 204 93 0 31.3 2.236254799 17.75 1.117940616 -0.974679434 -0.135747096 0.003149128 2.372001896 1.114791487 rHP -0.003230938 -0.003230938 12 155 52 1 -17.7 -1.264591372 -23.25 -1.46434475 0.974679434 0.135747096 -0.003149128 -1.400338469 -1.461195622 13 174 80 1 1.3 0.092879592 4.75 0.299167207 0.974679434 0.135747096 -0.003149128 -0.042867504 0.302316336 bH -0.003230938 14 185 110 0 12.3 0.878783835 34.75 2.188644305 -0.974679434 -0.135747096 0.003149128 1.014530931 2.185495176 15 169 70 1 -3.7 -0.264349609 -5.25 -0.330658492 0.974679434 0.135747096 -0.003149128 -0.400096705 -0.327509364 rVH.P 0.593227307 16 173 65 0 0.3 0.021433752 -10.25 -0.645571342 -0.974679434 -0.135747096 0.003149128 0.157180849 -0.64872047 17 189 74 0 16.3 1.164567196 -1.25 -0.078728212 -0.974679434 -0.135747096 0.003149128 1.300314292 -0.081877341 Kontrola 18 154 60 0 -18.7 -1.336037212 -15.25 -0.960484191 -0.974679434 -0.135747096 0.003149128 -1.200290116 -0.96363332 19 176 68 1 3.3 0.235771273 -7.25 -0.456623632 0.974679434 0.135747096 -0.003149128 0.100024176 -0.453474503 vzorec 0.593227307 20 168 94 0 -4.7 -0.335795449 18.75 1.180923186 -0.974679434 -0.135747096 0.003149128 -0.200048353 1.177774057 0.593233009 m 172.7 75.25 0.5 rVH 0.586992629 s 13.99661613 15.87740864 kontrola m 172.7 75.25 0.5 s 13.99661613 15.87740864 0.512989176 i V(ýška) P(ohlaví) H(motnost) 1 172 1 85 2 170 0 59 3 149 0 86 4 176 1 79 5 185 1 86 6 162 0 57 7 182 1 73 8 190 1 96 9 154 0 55 10 167 1 63 11 204 0 93 12 155 1 52 13 174 1 80 14 185 0 110 15 169 1 70 16 173 0 65 17 189 0 74 18 154 0 60 19 176 1 68 20 168 0 94 ##### Sheet/List 5 ##### Maticové násobení 1 b1 2 b2 B = 3 BT = 1 2 3 4 5 B = b3 BT = b1 b2 b3 b4 b5 4 b4 5 b5 b1 b1 b1 b2 b1 b3 b1 b4 b1 b5 b2 b1 b2 b2 b2 b3 b2 b4 b2 b5 B x BT b3 b1 b3 b2 b3 b3 b3 b4 b3 b5 BT x B b1 b1 + b2 b2 + b3 b3 + b4 b4 + b5 b5 b4 b1 b4 b2 b4 b3 b4 b4 b4 b5 b5 b1 b5 b2 b5 b3 b5 b4 b5 b5 1 2 3 4 5 2 4 6 8 10 B x BT 3 6 9 12 15 4 8 12 16 20 5 10 15 20 25 2faktorové řešení s nekorelovanými faktory (nákres chybí) Implikované korelace r12^ = b11*b12 + b21*b22 sloupec pro každý faktor r13^ = b11*b13 + b21*b23 b11 b21 řádek pro každou proměnnou b12 b22 r2k^ = b12*b1k + b22*b2k B = b13 b23 BT = b11 b12 b13 b14 b15 b14 b24 b21 b22 b23 b24 b25 b15 b25 B - matice faktorových nábojů tzn. regresních koeficientů mezi faktory a proměnnými b11*b11+b21*b21 b11*b12+b21*b22 b11*b13+b21*b23 B x BT b13*b14+b23*b24 r11^ r12^ r13^ B x BT r34^ 1 100 BT = 1 2 3 4 5 2 200 100 200 300 400 500 B = 3 300 4 400 10001 20002 30003 40004 50005 5 500 20002 40004 60006 80008 100010 R2=BxBT= 30003 60006 90009 120012 150015 40004 80008 120012 160016 200020 50005 100010 150015 200020 250025 2faktorové řešení s korelovanými faktory (nákres chybí) Implikované korelace B F BT F1 F2 F3 r12^ = b11*b12 + b21*b22 + b11*rF12*b22 + b12*rF12*b21 X1 F1 F2 F3 X1 X2 X3 X4 X5 r13^ = b11*b13 + b21*b23 + b11*rF12*b23 + b13*rF12*b21 X2 F1 F1 R2 = B x F x BT = X3 F2 F2 r2k^ = b12*b1k + b22*b2k + b12*rF12*b2k + b1k*rF12*b22 X4 F3 F3 X5 Příklad násobení B F BT F1 F2 F3 X1 1 10 100 F1 F2 F3 X1 X2 X3 X4 X5 X2 2 20 200 F1 1 0.1 0.2 F1 1 2 3 4 5 X3 3 30 300 F2 0.1 1 0.3 F2 10 20 30 40 50 X4 4 40 400 F3 0.2 0.3 1 F3 100 200 300 400 500 X5 5 50 500 Mezivýpočet B x F Finální výpočet B x F x BT 22 40.1 103.2 10743 21486 32229 42972 53715 44 80.2 206.4 21486 42972 64458 85944 107430 66 120.3 309.6 32229 64458 96687 128916 161145 88 160.4 412.8 42972 85944 128916 171888 214860 110 200.5 516 53715 107430 161145 214860 268575 ##### Sheet/List 6 ##### Generování dat (mění se při každém přepočtu listu) Jedna z variant vygenerovaných (simulovaných) dat i X Y Z oXY oXZ xYZ sXY sXZ sYZ uXY uXZ uYZ V i X Y Z oXY oXZ xYZ sXY sXZ sYZ uXY uXZ uYZ V oXY oXZ xYZ sXY sXZ sYZ uXY uXZ uYZ V 1 9 9 4 36.61073371 26.10347421 26.31474444 81.87565354 36.96984175 36.10719674 13.28421204 10.66123269 10.42472901 324.7811421 1 5 13 4 36.42163361 18.1709762 34.55589816 65.77883872 20.33979518 52.33232542 14.76319366 6.84009735 14.13318461 260.3318014 oXY 1 0.370818591 0.770466401 0.927531246 0.244236953 0.569535633 0.969728263 0.437381808 0.815349977 0.723869046 2 7 5 4 24.49002579 22.1360554 18.59970624 35.40385037 28.14571579 20.0310094 9.079685801 8.664688915 6.941589416 140.4717048 2 9 8 4 34.23967128 26.95883558 24.30217281 72.6613672 36.55567758 32.01130822 12.98680308 10.08066656 9.715835277 288.2635553 oXZ 0.370818591 1 0.037416136 0.432516743 0.938120582 0.165386043 0.289280138 0.968057012 -0.034906115 0.601515965 3 7 13 5 40.95385601 24.63535606 36.08764841 91.10086231 35.90622961 65.99639553 15.60696727 8.663774997 14.1156043 455.0190354 3 2 2 3 8.478387023 10.39464462 10.24642274 4.705854493 6.422325146 6.223874937 3.161377522 4.079486964 3.800283973 12.53778242 xYZ 0.770466401 0.037416136 1 0.617410268 0.067270645 0.902950737 0.818492009 0.009836628 0.975592827 0.685904977 4 9 14 5 46.86225805 28.81525768 38.03821211 126.4432518 45.36641791 70.33174036 16.73174452 11.22574508 15.6892891 630.4282556 4 2 16 6 36.5298348 16.91765705 44.5901128 32.88246181 12.44234355 96.79591246 16.59405585 7.168067499 17.57797272 192.6108568 sXY 0.927531246 0.432516743 0.617410268 1 0.285871008 0.431611675 0.827222316 0.510988037 0.663815352 0.759759568 5 7 13 3 40.80929362 20.28231826 32.27336293 91.30932003 21.42162494 39.97523604 15.72417842 8.430886396 14.0530759 273.712153 5 8 10 2 36.83239934 20.61299686 24.06939057 80.6279146 16.45103443 20.78127482 12.85993976 9.187229376 10.55394975 160.6190128 sXZ 0.244236953 0.938120582 0.067270645 0.285871008 1 0.250885664 0.18363588 0.842546275 -0.035437367 0.633918579 6 10 3 4 26.33647965 28.00821335 14.0760686 30.14420586 40.21216995 12.38383614 10.53463126 11.27083894 5.466565869 120.2667767 6 3 12 4 30.25269676 14.80534061 32.6389039 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