Path analysis: https://en.wikipedia.org/wiki/Path_analysis_(statistics) Knihy https://www.amazon.com/Latent-Variable-Models-John-Loehlin/dp/1138916072 https://books.google.cz/books?id=q9zhGIlYw7kC https://onlinelibrary.wiley.com/doi/book/10.1002/9781118619179 https://www.enbook.cz/catalog/product/view/id/399613?gclid=EAIaIQobChMI9N2Mv4yR9gIVVOJ3Ch1PeA5KEAQYASABEgJojvD_BwE Plán práce: korelace jednoduchá regrese (2 proměnné) vícenásobná regrese (3 proměnné) parciální korelace faktorová analýza (1 faktor) faktorová analýza (2 a více faktorů) v Excelu v dalších softwarech explorační vs. konfirmační FA strukturní modelování ##### Sheet/List 2 ##### i pohl (P) vyska (V) hmot (H) mV - Vi mH - Hi zVi zHi zVi * zHi H.stř e 1 0 172 87 -1.333333333 11.66666667 -0.115721897 0.604135788 -0.06991174 73.49170306 13.50829694 2 1 169 61 -4.333333333 -14.33333333 -0.376096166 -0.742223969 0.279147589 69.34803493 -8.348034934 3 0 170 63 -3.333333333 -12.33333333 -0.289304743 -0.638657833 0.18476674 70.72925764 -7.729257642 4 1 166 85 -7.333333333 9.666666667 -0.636470435 0.500569653 -0.318597785 65.20436681 19.79563319 5 0 183 77 9.666666667 1.666666667 0.838983755 0.086305113 0.072408587 88.68515284 -11.68515284 6 0 168 58 -5.333333333 -17.33333333 -0.462887589 -0.897573171 0.415475481 67.96681223 -9.966812227 7 1 170 65 -3.333333333 -10.33333333 -0.289304743 -0.535091698 0.154804566 70.72925764 -5.729257642 8 0 190 90 16.66666667 14.66666667 1.446523715 0.759484991 1.098613051 98.35371179 -8.35371179 9 1 165 63 -8.333333333 -12.33333333 -0.723261858 -0.638657833 0.461916851 63.8231441 -0.823144105 10 1 152 51 -21.33333333 -24.33333333 -1.851550356 -1.260054644 2.333054625 45.86724891 5.132751092 11 0 187 82 13.66666667 6.666666667 1.186149447 0.34522045 0.409483046 94.21004367 -12.21004367 12 0 185 125 11.66666667 49.66666667 1.012566601 2.571892356 2.6042123 91.44759825 33.55240175 13 0 193 97 19.66666667 21.66666667 1.706897984 1.121966464 1.915082296 102.4973799 -5.497379913 14 0 163 61 -10.33333333 -14.33333333 -0.896844703 -0.742223969 0.665659635 61.06069869 -0.06069869 15 1 150 44 -23.33333333 -31.33333333 -2.025133201 -1.622536117 3.285851762 43.10480349 0.895196507 16 1 173 68 -0.333333333 -7.333333333 -0.028930474 -0.379742496 0.010986131 74.87292576 -6.872925764 17 1 165 58 -8.333333333 -17.33333333 -0.723261858 -0.897573171 0.649180439 63.8231441 -5.823144105 18 1 171 65 -2.333333333 -10.33333333 -0.20251332 -0.535091698 0.108363196 72.11048035 -7.110480349 19 0 185 90 11.66666667 14.66666667 1.012566601 0.759484991 0.769029136 91.44759825 -1.447598253 20 0 172 72 -1.333333333 -3.333333333 -0.115721897 -0.172610225 0.019974783 73.49170306 -1.491703057 21 1 168 63 -5.333333333 -12.33333333 -0.462887589 -0.638657833 0.295626785 67.96681223 -4.966812227 22 0 194 113 20.66666667 37.66666667 1.793689407 1.950495545 3.498583198 103.8786026 9.12139738 23 1 174 83 0.666666667 7.666666667 0.057860949 0.397003518 0.022971 76.25414847 6.745851528 24 0 175 87 1.666666667 11.66666667 0.144652372 0.604135788 0.087389675 77.63537118 9.364628821 m 173.3333333 75.33333333 -9.4739E-15 4.73695E-15 sd 11.52187585 19.31133181 koeficient determinace Matematický model rVH 0.824090059 H.stříška.i = a + b * V.i průměr 173.3333333 75.33333333 smodch 11.52187585 19.31133181 rVH 0.824090059 0.679124425 a -164.0786026 rPV -0.620301683 0.384774178 b 1.381222707 rPH -0.542610286 0.294425922 statistická významnost korelace t 6.823664807 df 22 p 8.29561E-07 ##### Sheet/List 3 ##### i pohl (P) vyska (V) hmot (H) mV - Vi mH - Hi zVi zHi zVi * zHi H.stř e 1 0 172 87 -1.333333333 11.66666667 -0.115721897 0.604135788 -0.06991174 74.45185246 12.54814754 2 1 169 61 -4.333333333 -14.33333333 -0.376096166 -0.742223969 0.279147589 68.52741618 -7.527416177 3 0 170 63 -3.333333333 -12.33333333 -0.289304743 -0.638657833 0.18476674 71.79574982 -8.795749824 a -153.9729744 4 1 166 85 -7.333333333 9.666666667 -0.636470435 0.500569653 -0.318597785 64.54326222 20.45673778 b1 1.328051319 5 0 183 77 9.666666667 1.666666667 0.838983755 0.086305113 0.072408587 89.06041697 -12.06041697 b2 -1.940282327 6 0 168 58 -5.333333333 -17.33333333 -0.462887589 -0.897573171 0.415475481 69.13964719 -11.13964719 7 1 170 65 -3.333333333 -10.33333333 -0.289304743 -0.535091698 0.154804566 69.8554675 -4.855467497 8 0 190 90 16.66666667 14.66666667 1.446523715 0.759484991 1.098613051 98.35677621 -8.356776206 Kritéria 9 1 165 63 -8.333333333 -12.33333333 -0.723261858 -0.638657833 0.461916851 63.2152109 -0.215210901 10 1 152 51 -21.33333333 -24.33333333 -1.851550356 -1.260054644 2.333054625 45.95054375 5.049456248 R 0.825063427 R2 0.680729659 11 0 187 82 13.66666667 6.666666667 1.186149447 0.34522045 0.409483046 94.37262225 -12.37262225 12 0 185 125 11.66666667 49.66666667 1.012566601 2.571892356 2.6042123 91.71651961 33.28348039 SS 2738.488136 13 0 193 97 19.66666667 21.66666667 1.706897984 1.121966464 1.915082296 102.3409302 -5.340930164 14 0 163 61 -10.33333333 -14.33333333 -0.896844703 -0.742223969 0.665659635 62.49939059 -1.49939059 VÝSLEDEK 15 1 150 44 -23.33333333 -31.33333333 -2.025133201 -1.622536117 3.285851762 43.29444111 0.705558886 16 1 173 68 -0.333333333 -7.333333333 -0.028930474 -0.379742496 0.010986131 73.83962145 -5.839621454 Regresní statistika 17 1 165 58 -8.333333333 -17.33333333 -0.723261858 -0.897573171 0.649180439 63.2152109 -5.215210901 Násobné R 0.825063429 18 1 171 65 -2.333333333 -10.33333333 -0.20251332 -0.535091698 0.108363196 71.18351882 -6.183518816 Hodnota spolehlivosti R 0.680729661 19 0 185 90 11.66666667 14.66666667 1.012566601 0.759484991 0.769029136 91.71651961 -1.716519611 Nastavená hodnota spolehlivosti R 0.650322963 20 0 172 72 -1.333333333 -3.333333333 -0.115721897 -0.172610225 0.019974783 74.45185246 -2.451852462 Chyba stř. hodnoty 11.41946566 21 1 168 63 -5.333333333 -12.33333333 -0.462887589 -0.638657833 0.295626785 67.19936486 -4.199364858 Pozorování 24 22 0 194 113 20.66666667 37.66666667 1.793689407 1.950495545 3.498583198 103.6689815 9.331018517 23 1 174 83 0.666666667 7.666666667 0.057860949 0.397003518 0.022971 75.16767277 7.832327227 ANOVA 24 0 175 87 1.666666667 11.66666667 0.144652372 0.604135788 0.087389675 78.43600642 8.563993581 Rozdíl SS MS F Významnost F Regrese 2 5838.845216 2919.422608 22.38748979 6.2182E-06 m 173.3333333 75.33333333 -9.4739E-15 4.73695E-15 Rezidua 21 2738.488117 130.4041961 sd 11.52187585 19.31133181 koeficient determinace Matematický model Celkem 23 8577.333333 rVH 0.824090059 H.stříška.i = a + b1 * V.i + b2 * P.i průměr 173.3333333 75.33333333 Koeficienty Chyba stř. hodnoty t Stat Hodnota P Dolní 95% Horní 95% "Dolní 95,0%" "Horní 95,0%" smodch 11.52187585 19.31133181 rVH 0.824090059 0.679124425 Hranice -153.9852731 47.4706878 -3.243796967 0.003887109 -252.7059727 -55.26457354 -252.7059727 -55.26457354 rPV -0.620301683 0.384774178 pohl (P) -1.938054679 5.964391017 -0.324937562 0.748443234 -14.34168481 10.46557546 -14.34168481 10.46557546 rPH -0.542610286 0.294425922 vyska (V) 1.328116624 0.263476203 5.040746032 5.44428E-05 0.780187865 1.876045383 0.780187865 1.876045383 statistická významnost korelace t 6.823664807 REZIDUA PRAVDĚPODOBNOST df 22 p 8.29561E-07 Pozorování Očekávané hmot (H) Rezidua Normovaná rezidua Percentil hmot (H) 1 74.45078623 12.54921377 1.150071934 2.083333333 44 Parciální korelace 2 68.52838168 -7.528381678 -0.689938081 6.25 51 rVH.P 0.739934279 3 71.79455298 -8.794552981 -0.805976274 10.41666667 58 rPV.H -0.363883734 4 64.54403181 20.45596819 1.874685962 14.58333333 58 rPH.V -0.070729604 5 89.06006909 -12.06006909 -1.105244299 18.75 61 6 69.13831973 -11.13831973 -1.020770635 22.91666667 61 7 69.8564983 -4.856498302 -0.445073492 27.08333333 63 8 98.35688546 -8.356885461 -0.76586626 31.25 63 9 63.21591518 -0.215915183 -0.019787534 35.41666667 63 10 45.95039907 5.049600929 0.46277037 39.58333333 65 11 94.37253559 -12.37253559 -1.133880272 43.75 65 12 91.71630234 33.28369766 3.05028245 47.91666667 68 13 102.3412353 -5.341235333 -0.489497188 52.08333333 72 14 62.49773661 -1.497736613 -0.137259981 56.25 77 15 43.29416582 0.705834177 0.06468613 60.41666667 82 16 73.84084817 -5.840848174 -0.535284176 64.58333333 83 17 63.21591518 -5.215915183 -0.47801223 68.75 85 18 71.18461493 -6.184614926 -0.566788659 72.91666667 87 19 91.71630234 -1.716302341 -0.157290424 77.08333333 87 20 74.45078623 -2.450786229 -0.224602155 81.25 90 21 67.20026505 -4.200265054 -0.384933036 85.41666667 90 22 103.669352 9.330648043 0.855106673 89.58333333 97 23 75.1689648 7.831035202 0.717674745 93.75 113 24 78.4351361 8.564863899 0.784926432 97.91666667 125 ##### Sheet/List 4 ##### i pohl (P) vyska (V) hmot (H) mV - Vi mH - Hi zVi zHi zPi H.stř e.H P.stř e.P 1 0 172 87 -1.333333333 11.66666667 -0.115721897 0.604135788 0.900498437 73.49170306 13.50829694 0.494868996 -0.494868996 2 1 169 61 -4.333333333 -14.33333333 -0.376096166 -0.742223969 -1.064225426 69.34803493 -8.348034934 0.577074236 0.422925764 3 0 170 63 -3.333333333 -12.33333333 -0.289304743 -0.638657833 0.900498437 70.72925764 -7.729257642 0.549672489 -0.549672489 4 1 166 85 -7.333333333 9.666666667 -0.636470435 0.500569653 -1.064225426 65.20436681 19.79563319 0.659279476 0.340720524 5 0 183 77 9.666666667 1.666666667 0.838983755 0.086305113 0.900498437 88.68515284 -11.68515284 0.193449782 -0.193449782 6 0 168 58 -5.333333333 -17.33333333 -0.462887589 -0.897573171 0.900498437 67.96681223 -9.966812227 0.604475983 -0.604475983 7 1 170 65 -3.333333333 -10.33333333 -0.289304743 -0.535091698 -1.064225426 70.72925764 -5.729257642 0.549672489 0.450327511 8 0 190 90 16.66666667 14.66666667 1.446523715 0.759484991 0.900498437 98.35371179 -8.35371179 0.001637555 -0.001637555 9 1 165 63 -8.333333333 -12.33333333 -0.723261858 -0.638657833 -1.064225426 63.8231441 -0.823144105 0.686681223 0.313318777 10 1 152 51 -21.33333333 -24.33333333 -1.851550356 -1.260054644 -1.064225426 45.86724891 5.132751092 1.04290393 -0.04290393 11 0 187 82 13.66666667 6.666666667 1.186149447 0.34522045 0.900498437 94.21004367 -12.21004367 0.083842795 -0.083842795 Předpověď H z V 12 0 185 125 11.66666667 49.66666667 1.012566601 2.571892356 0.900498437 91.44759825 33.55240175 0.138646288 -0.138646288 13 0 193 97 19.66666667 21.66666667 1.706897984 1.121966464 0.900498437 102.4973799 -5.497379913 -0.080567686 0.080567686 b 1.381222707 14 0 163 61 -10.33333333 -14.33333333 -0.896844703 -0.742223969 0.900498437 61.06069869 -0.06069869 0.741484716 -0.741484716 a -164.0786026 15 1 150 44 -23.33333333 -31.33333333 -2.025133201 -1.622536117 -1.064225426 43.10480349 0.895196507 1.097707424 -0.097707424 16 1 173 68 -0.333333333 -7.333333333 -0.028930474 -0.379742496 -1.064225426 74.87292576 -6.872925764 0.467467249 0.532532751 Předpověď P z V 17 1 165 58 -8.333333333 -17.33333333 -0.723261858 -0.897573171 -1.064225426 63.8231441 -5.823144105 0.686681223 0.313318777 18 1 171 65 -2.333333333 -10.33333333 -0.20251332 -0.535091698 -1.064225426 72.11048035 -7.110480349 0.522270742 0.477729258 b -0.027401747 19 0 185 90 11.66666667 14.66666667 1.012566601 0.759484991 0.900498437 91.44759825 -1.447598253 0.138646288 -0.138646288 a 5.207969432 20 0 172 72 -1.333333333 -3.333333333 -0.115721897 -0.172610225 0.900498437 73.49170306 -1.491703057 0.494868996 -0.494868996 21 1 168 63 -5.333333333 -12.33333333 -0.462887589 -0.638657833 -1.064225426 67.96681223 -4.966812227 0.604475983 0.395524017 22 0 194 113 20.66666667 37.66666667 1.793689407 1.950495545 0.900498437 103.8786026 9.12139738 -0.107969432 0.107969432 23 1 174 83 0.666666667 7.666666667 0.057860949 0.397003518 -1.064225426 76.25414847 6.745851528 0.440065502 0.559934498 24 0 175 87 1.666666667 11.66666667 0.144652372 0.604135788 0.900498437 77.63537118 9.364628821 0.412663755 -0.412663755 m 0.458333333 173.3333333 75.33333333 -9.4739E-15 4.73695E-15 -8.17633E-16 2.03541E-16 0 sd 0.508977378 11.52187585 19.31133181 1 1 1 průměr 173.3333333 75.33333333 smodch 11.52187585 19.31133181 koeficient determinace rVH 0 rVH 0.824090059 0.679124425 rPV -0.620301683 0.384774178 rPH -0.542610286 0.294425922 statistická významnost korelace t 6.823664807 df 22 p 8.29561E-07 Parciální korelace pomocí vzorce Excelu (pearson) rVH.P 0.739934279 rPV.H -0.363883734 rPH.V -0.070729604 -0.070729604 ##### Sheet/List 5 ##### b1 b1 b2 b3 … bk b1b1 b1b2 b1b3 … b1bk b2 b2b1 b2b2 b2b3 b2bk b3 x b3b1 bk 1 10 20 30 40 50 10 20 30 40 50 2 20 40 60 80 100 3 x 30 60 90 120 150 4 40 80 120 160 200 5 50 100 150 200 250 1 -1 10 20 30 40 50 -990 -1980 -2970 -3960 -4950 2 -2 1000 2000 3000 4000 5000 -1980 -3960 -5940 -7920 -9900 3 -3 -2970 -5940 -8910 -11880 -14850 4 -4 -3960 -7920 -11880 -15840 -19800 5 -5 -4950 -9900 -14850 -19800 -24750 1 -1 1 2 3 4 5 2 4 6 8 10 2 -2 -1 -2 -3 -4 -5 4 8 12 16 20 3 -3 6 12 18 24 30 4 -4 8 16 24 32 40 5 -5 10 20 30 40 50 ##### Sheet/List 6 ##### X Y Z oXY oXZ oYZ sXY sXZ xYZ uXY uXZ uYZ vXYZ uXYZ X 1 Y -0.021385845 1 Z 0.008204409 0.103949793 1 oXY 0.61281165 0.776942783 0.087329374 1 oXZ 0.533445891 0.076667471 0.850182333 0.396517721 1 oYZ -0.006386958 0.664852598 0.812039169 0.521484028 0.683510841 1 sXY 0.685430109 0.674834413 0.092770258 0.965021496 0.439354022 0.465655035 1 sXZ 0.709487891 0.069971538 0.670419402 0.502081519 0.940632433 0.54457204 0.564359377 1 xYZ 0.005191309 0.725392212 0.729465539 0.576626141 0.619760919 0.973507171 0.52381415 0.497850897 1 uXY 0.514930639 0.837859308 0.080486463 0.986511854 0.33919461 0.552089414 0.916489686 0.426878305 0.608440268 1 uXZ 0.361226712 0.07926043 0.929567706 0.290118181 0.976474677 0.744654196 0.320944483 0.851439189 0.674547282 0.250668184 1 uYZ -0.010276094 0.588626399 0.857485227 0.458785047 0.71990431 0.989403812 0.406152765 0.573862443 0.935151999 0.488337077 0.785733485 1 vXYZ 0.514343464 0.591022953 0.582405346 0.791040233 0.763439901 0.784213158 0.828867356 0.804000646 0.818280993 0.749743986 0.702794115 0.74884096 1 uXYZ 0.288691621 0.553579665 0.823727635 0.619348289 0.848758345 0.943485612 0.584905427 0.748247472 0.898932873 0.62261584 0.867239675 0.951494096 0.858283398 1 ##### Sheet/List 7 ##### i gX gY gZ X Y Z oXY oXZ oYZ sXY sXZ xYZ uXY uXZ uYZ vXYZ uXYZ 1 6 7 15 11 7 21 36 64 56 77 231 147 13.03840481 23.70653918 22.13594362 1617 24.71841419 R X Y Z oXY oXZ oYZ sXY sXZ xYZ uXY uXZ uYZ vXYZ uXYZ 2 11 12 8 5 13 7 36 24 40 65 35 91 13.92838828 8.602325267 14.76482306 455 15.58845727 X 1 -0.021385845 0.008204409 0.61281165 0.533445891 -0.006386958 0.685430109 0.709487891 0.005191309 0.514930639 0.361226712 -0.010276094 0.514343464 0.288691621 3 9 7 20 8 13 21 42 58 68 104 168 273 15.26433752 22.47220505 24.69817807 2184 25.96150997 Y -0.021385845 1 0.103949793 0.776942783 0.076667471 0.664852598 0.674834413 0.069971538 0.725392212 0.837859308 0.07926043 0.588626399 0.591022953 0.553579665 4 5 14 18 7 9 18 32 50 54 63 126 162 11.40175425 19.31320792 20.1246118 1134 21.30727575 Z 0.008204409 0.103949793 1 0.087329374 0.850182333 0.812039169 0.092770258 0.670419402 0.729465539 0.080486463 0.929567706 0.857485227 0.582405346 0.823727635 5 12 6 19 6 9 14 30 40 46 54 84 126 10.81665383 15.23154621 16.64331698 756 17.69180601 oXY 0.61281165 0.776942783 0.087329374 1 0.396517721 0.521484028 0.965021496 0.502081519 0.576626141 0.986511854 0.290118181 0.458785047 0.791040233 0.619348289 6 12 16 21 11 12 15 46 52 54 132 165 180 16.2788206 18.60107524 19.20937271 1980 22.13594362 oXZ 0.533445891 0.076667471 0.850182333 0.396517721 1 0.683510841 0.439354022 0.940632433 0.619760919 0.33919461 0.976474677 0.71990431 0.763439901 0.848758345 7 8 6 14 11 10 10 42 42 40 110 110 100 14.86606875 14.86606875 14.14213562 1100 17.91647287 oYZ -0.006386958 0.664852598 0.812039169 0.521484028 0.683510841 1 0.465655035 0.54457204 0.973507171 0.552089414 0.744654196 0.989403812 0.784213158 0.943485612 8 4 13 21 5 13 8 36 26 42 65 40 104 13.92838828 9.433981132 15.26433752 520 16.0623784 sXY 0.685430109 0.674834413 0.092770258 0.965021496 0.439354022 0.465655035 1 0.564359377 0.52381415 0.916489686 0.320944483 0.406152765 0.828867356 0.584905427 9 10 9 13 8 9 19 34 54 56 72 152 171 12.04159458 20.61552813 21.02379604 1368 22.49444376 sXZ 0.709487891 0.069971538 0.670419402 0.502081519 0.940632433 0.54457204 0.564359377 1 0.497850897 0.426878305 0.851439189 0.573862443 0.804000646 0.748247472 10 12 14 19 10 17 18 54 56 70 170 180 306 19.72308292 20.59126028 24.75883681 3060 26.70205985 xYZ 0.005191309 0.725392212 0.729465539 0.576626141 0.619760919 0.973507171 0.52381415 0.497850897 1 0.608440268 0.674547282 0.935151999 0.818280993 0.898932873 11 6 6 11 9 10 18 38 54 56 90 162 180 13.45362405 20.1246118 20.59126028 1620 22.47220505 uXY 0.514930639 0.837859308 0.080486463 0.986511854 0.33919461 0.552089414 0.916489686 0.426878305 0.608440268 1 0.250668184 0.488337077 0.749743986 0.62261584 12 6 13 14 6 17 8 46 28 50 102 48 136 18.02775638 10 18.78829423 816 19.72308292 uXZ 0.361226712 0.07926043 0.929567706 0.290118181 0.976474677 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24.18677324 25.23885893 3528 27.94637722 96 7 7 9 8 7 10 30 36 34 56 80 70 10.63014581 12.80624847 12.20655562 560 14.59451952 97 11 12 7 12 15 15 54 54 60 180 180 225 19.20937271 19.20937271 21.21320344 2700 24.37211521 98 9 7 13 9 16 21 50 60 74 144 189 336 18.35755975 22.84731932 26.40075756 3024 27.89265136 99 12 6 17 8 17 10 50 36 54 136 80 170 18.78829423 12.80624847 19.72308292 1360 21.28379665 100 4 12 13 12 6 8 36 40 28 72 96 48 13.41640786 14.4222051 10 576 15.62049935