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 9 9 17 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 7 10 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 8 12 7 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 12 10 21 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 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0.465655035 1 0.564359377 0.52381415 0.916489686 0.320944483 0.406152765 0.828867356 0.584905427 9 7 13 18 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 8 16 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 10 7 12 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 10 15 7 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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