Cours de statistique sur l'étude de 2 variables, de couples de variables et de régression linéaire avec présence de nombreux schémas, graphiques, calculs et explications qui permettent une parfaite compréhension du cours.
[...] L'effectif total est : n = n ij 2. Tableau de contingence, distributions marginales, distributions conditionnelles On représente les données dans un tableau à double entrée : n = n ij nombre d'individus ayant les modalités x i n distribution marginale de X n = n ij nombre d'individus ayant les modalités y j n distribution marginale de Y Y Xy 1y 2 .y j .y lMargex 1n 11n 12n 1jn 1kn 2n 21x in i1n ijn kn k1n kln k•Margen Ex 1 : Distribution de la population française de 65 ans suivant le sexe et l'état matrimonial. [...]
[...] Moyenne de la distribution marginale de x : picscalex1000100090000039b00000000003d000000000004000000030108000500000 00b0200000000050000000c020d000e00030000001e003d000000410b8600ee000c000d0 0000000000c000d0000000000280000000d0000000c00000001000100000000000000000 00000000000000000000000000000000000000000ffffff003300c530120000000a00494 c0400ffff0400a702060011001d80000000000100000000003ff00000000000000000000 03d000000410bc60088000c000d00000000000c000d0000000000280000000d0000000c0 000000100010000000000000000000000000000000000000000000000000000000000fff fff00ccf80000edf80000f5f80101fbf80000fbf80100f9f80001e2780101fff80000fff 80101c0080001fff80101fff80000040000002701ffff030000000000 = 1/n n x i = f x i Moyenne de la distribution marginale de y : picscalex1000100090000037000000000004f000000000004000000030108000500000 00b0200000000050000000c0216001200030000001e004f000000410b2000cc 00000000000000000000000000000000000000000ffffff00ffff8001ffff8001ffff800 1f83f8001feff8011feff8001feff8001feff8001feff8001fd7f8047fdbf8001fbbf800 1fbdf8001e1878001ffff8030ffff8001e0038000ffff8001ffff8001ffff8018ffff800 1040000002701ffff030000000000 = 1/n n y j = f y j Variance de la distribution marginale de x : x = 1/n n x - (picscalex1000100090000039b00000000003d000000000004000000030108000500000 00b0200000000050000000c020d000e00030000001e003d000000410b8600ee000c000d0 0000000000c000d0000000000280000000d0000000c00000001000100000000000000000 00000000000000000000000000000000000000000ffffff003300c530120000000a00494 c0400ffff0400a702060011001d80000000000100000000003ff00000000000000000000 03d000000410bc60088000c000d00000000000c000d0000000000280000000d0000000c0 000000100010000000000000000000000000000000000000000000000000000000000fff fff00ccf80000edf80000f5f80101fbf80000fbf80100f9f80001e2780101fff80000fff 80101c0080001fff80101fff80000040000002701ffff030000000000n)² Variance de la distribution marginale de y : y = 1/n n y - (picscalex1000100090000037000000000004f000000000004000000030108000500000 00b0200000000050000000c0216001200030000001e004f000000410b2000cc 00000000000000000000000000000000000000000ffffff00ffff8001ffff8001ffff800 1f83f8001feff8011feff8001feff8001feff8001feff8001fd7f8047fdbf8001fbbf800 1fbdf8001e1878001ffff8030ffff8001e0038000ffff8001ffff8001ffff8018ffff800 1040000002701ffff030000000000 Moyenne conditionnelle de x sachant y = y j : picscalex1000100090000039b00000000003d000000000004000000030108000500000 00b0200000000050000000c020d000e00030000001e003d000000410b8600ee000c000d0 0000000000c000d0000000000280000000d0000000c00000001000100000000000000000 00000000000000000000000000000000000000000ffffff003300c530120000000a00494 c0400ffff0400a702060011001d80000000000100000000003ff00000000000000000000 03d000000410bc60088000c000d00000000000c000d0000000000280000000d0000000c0 000000100010000000000000000000000000000000000000000000000000000000000fff fff00ccf80000edf80000f5f80101fbf80000fbf80100f9f80001e2780101fff80000fff 80101c0080001fff80101fff80000040000002701ffff030000000000׀j = 1/n n ij x i Moyenne conditionnelle de y sachant x = x i : picscalex1000100090000037000000000004f0000000000040000000301080005000000 0b0200000000050000000c0216001200030000001e004f000000410b2000cc 0000000000000000000000000000000000000000ffffff00ffff8001ffff8001ffff8001 f83f8001feff8011feff8001feff8001feff8001feff8001fd7f8047fdbf8001fbbf8001 fbdf8001e1878001ffff8030ffff8001e0038000ffff8001ffff8001ffff8018ffff8001 040000002701ffff030000000000 Ði = 1/n n ij y j Variance conditionnelle de x sachant y = y j : xÐj = 1/n x - (picscalex1000100090000039b00000000003d000000000004000000030108000500000 00b0200000000050000000c020d000e00030000001e003d000000410b8600ee000c000d0 0000000000c000d0000000000280000000d0000000c00000001000100000000000000000 00000000000000000000000000000000000000000ffffff003300c530120000000a00494 c0400ffff0400a702060011001d80000000000100000000003ff00000000000000000000 03d000000410bc60088000c000d00000000000c000d0000000000280000000d0000000c0 000000100010000000000000000000000000000000000000000000000000000000000fff fff00ccf80000edf80000f5f80101fbf80000fbf80100f9f80001e2780101fff80000fff 80101c0080001fff80101fff80000040000002701ffff030000000000 Ex picscalex1000100090000039b00000000003d0000000000040000000301080005000000 0b0200000000050000000c020d000e00030000001e003d000000410b8600ee000c000d00 000000000c000d0000000000280000000d0000000c000000010001000000000000000000 0000000000000000000000000000000000000000ffffff003300c530120000000a00494c 0400ffff0400a702060011001d80000000000100000000003ff000000000000000000000 3d000000410bc60088000c000d00000000000c000d0000000000280000000d0000000c00 00000100010000000000000000000000000000000000000000000000000000000000ffff ff00ccf80000edf80000f5f80101fbf80000fbf80100f9f80001e2780101fff80000fff8 0101c0080001fff80101fff80000040000002701ffff030000000000 Ð[5,6] = 1/5500 (1200 * 21 + 2500 * 23 + 1800 * 25) = 23.21 picscalex1000100090000039b00000000003d000000000004000000030108000500000 00b0200000000050000000c020d000e00030000001e003d000000410b8600ee000c000d0 0000000000c000d0000000000280000000d0000000c00000001000100000000000000000 00000000000000000000000000000000000000000ffffff003300c530120000000a00494 c0400ffff0400a702060011001d80000000000100000000003ff00000000000000000000 03d000000410bc60088000c000d00000000000c000d0000000000280000000d0000000c0 000000100010000000000000000000000000000000000000000000000000000000000fff fff00ccf80000edf80000f5f80101fbf80000fbf80100f9f80001e2780101fff80000fff 80101c0080001fff80101fff80000040000002701ffff030000000000 Ð[6,7] = 24 picscalex1000100090000039b00000000003d0000000000040000000301080005000000 0b0200000000050000000c020d000e00030000001e003d000000410b8600ee000c000d00 000000000c000d0000000000280000000d0000000c000000010001000000000000000000 0000000000000000000000000000000000000000ffffff003300c530120000000a00494c 0400ffff0400a702060011001d80000000000100000000003ff000000000000000000000 3d000000410bc60088000c000d00000000000c000d0000000000280000000d0000000c00 00000100010000000000000000000000000000000000000000000000000000000000ffff ff00ccf80000edf80000f5f80101fbf80000fbf80100f9f80001e2780101fff80000fff8 0101c0080001fff80101fff80000040000002701ffff030000000000 Ð[7,8] = 24.46 picscalex1000100090000039b00000000003d000000000004000000030108000500000 00b0200000000050000000c020d000e00030000001e003d000000410b8600ee000c000d0 0000000000c000d0000000000280000000d0000000c00000001000100000000000000000 00000000000000000000000000000000000000000ffffff003300c530120000000a00494 c0400ffff0400a702060011001d80000000000100000000003ff00000000000000000000 03d000000410bc60088000c000d00000000000c000d0000000000280000000d0000000c0 000000100010000000000000000000000000000000000000000000000000000000000fff fff00ccf80000edf80000f5f80101fbf80000fbf80100f9f80001e2780101fff80000fff 80101c0080001fff80101fff80000040000002701ffff030000000000 = 1/17500 (1800 * 21 + 6600 * 23 + 9100 * 25) = 1/17500 (5500 * 23.21 + 9000 * 24 + 3000 * 24.46 ) = 23.83 IV. Résumé d'un couple de variables quantitatives, Courbes de régression 1. [...]
[...] + ( 2.75 = 0.9375 y = 0.0625 â = 0.066 b = 2.57 y = 0.066 x + 2.57 = var / y = [cov / á x á Proche de donc l'ajuste- = [ 0.0625 / 0.0625 0.9375 = 0.0656 ment est mauvais. X22222444Y Y .83å- 0.2 - 0.2 Var = ( 2.7 + . + 2.83 ( 2.7482 = 0.0041 = 0.0041 / 0.0625 = 0.0656 Var = 0.2 + . + 0.27 ( 0.019 = 0.0584 = y var = 0.0625 0.0041 = 0.0584 x = â y + b â = 0.0625 / 0.0625 = 1 b = picscalex1000100090000039b00000000003d0000000000040000000301080005000000 0b0200000000050000000c020d000e00030000001e003d000000410b8600ee000c000d00 000000000c000d0000000000280000000d0000000c000000010001000000000000000000 0000000000000000000000000000000000000000ffffff003300c530120000000a00494c 0400ffff0400a702060011001d80000000000100000000003ff000000000000000000000 3d000000410bc60088000c000d00000000000c000d0000000000280000000d0000000c00 00000100010000000000000000000000000000000000000000000000000000000000ffff ff00ccf80000edf80000f5f80101fbf80000fbf80100f9f80001e2780101fff80000fff8 0101c0080001fff80101fff80000040000002701ffff030000000000 - â picscalex75010009000003a600000000008500000000000400000003010800050000000 b0200000000050000000c0212000d00030000001e0085000000410b2000cc0011000c000 000000011000c0000000000280000000c000000110000000100040000000000000000000 000000000000000000000000000000000000000ffffff00fefefe004444440099999900c ccccc00666666005555550077777700aaaaaa0011111100eeeeee00bbbbbb00222222003 3333300dddddd0022866ef222220f0222a825a522220a082283228a222202022222fcba4 222080a2228ec7a72220202222d922702220202222a42290b22070a22237222a422020d2 2260222372202022cb50c22602202092542372290b20203227263222a420202225675222 89202022222222222220b052222222222220202233333333334020222222222222207020 40000002701ffff030000000000 = 0 x = y Ex : Le tableau suivant donne la distance de freinage d'un véhicule roulant sur route sèche en fonction de la vitesse. [...]
[...] Donner les 2 tableaux de fréquences conditionnelles. 8[n ij f 22 = 3500 / 17500 = f 2/Y = y 2 = 3500 / 9000 = f = 9000 / 17500 = 0.51 picscalex1000100090000037b2500000a001610000000001610000026060f002220 574d46430100000000000100e760000000000200000000200000d80e0000d82e00000100 00006c000000230000001200000016010000ab0000000000000000000000ba270000701a 000020454d4600000100d82e00005d020000050000000000000000000000000000000005 000020030000c40100001a010000000000000000000000000000e3e306006e4e04004600 00002c00000020000000454d462b014001001c000000100000000110c0db010000006000 000060000000460000005c00000050000000454d462b224004000c000000000000001e40 01000c00000000000000244001000c00000000000000214007000c000000000000003040 020010000000040000000000803f044000000c00000000000000180000000c0000000000 0000190000000c000000ffffff00140000000c0000000d000000120000000c0000000200 00002100000008000000220000000c000000ffffffff2100000008000000220000000c00 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[...]
[...] Proportion des salariés âgés de 22 à 24ans et gagnant entre 6000 et 7000 ? 3. Parmi les employés gagnant entre 6000 et 7000, quelle est la proportion de ceux qui ont entre 22 et 24ans ? 4. [...]
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