EXAMEN PARCIAL DE ESTADÍSTICA 1
josephleo3Apuntes14 de Diciembre de 2019
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RESOLUCION DEL I EXAMEN PARCIAL DE ESTADISTICA I (ES-241)
Parte I: REGRESION Y CORRELACIÓN LINAL SIMPLE
CUADRO I:
Conocimientos (X) | 12 | 17 | 20 | 13 | 8 | 9 | 11 | 13 | 19 | 10 |
Psicotécnico (Y) | 40 | 42 | 32 | 20 | 20 | 7 | 24 | 20 | 40 | 30 |
i | XI | YI | xi=( XI-x) | yi=(YI-y) | xi2 | yi2 | xiyi |
1 | 12 | 40 | x1=-1,2 | y1=12,5 | 1,44 | 156,25 | -15 |
2 | 17 | 42 | x2=3,8 | y2=14,5 | 14,44 | 210,25 | 55,1 |
3 | 20 | 32 | x3=6,8 | y3=4,5 | 46,24 | 20,25 | 30,6 |
4 | 13 | 20 | x4=-0,2 | y4=-7,5 | 0,04 | 56,25 | 1,5 |
5 | 8 | 20 | x5=-5,2 | y5=-7,5 | 27,04 | 56,25 | 39 |
6 | 9 | 7 | x6=-4,2 | y6=-20,5 | 17,64 | 420,25 | 86,1 |
7 | 11 | 24 | x7=-2,2 | y7=-3,5 | 4,84 | 12,25 | 7,7 |
8 | 13 | 20 | x8=-0,2 | y8=-7,5 | 0,04 | 56,25 | 1,5 |
9 | 19 | 40 | x9=5,8 | y9=12,5 | 33,64 | 156,25 | 72,5 |
10 | 10 | 30 | x10=-3,2 | y10=2,5 | 10,24 | 6,25 | -8 |
x=13,2 , y=27,5 | ∑=132 | ∑=275 | ∑=0 | ∑=0 | ∑=155,6 | ∑=1150,5 | ∑=271 |
I-a) Media muestral de X: x=13,2 I-b) Media muestral de Y: y=27,5
I-c) Variancia muestral de las X: Sx2=155,6 I-d) Variancia muestral de las Y: SY2=1150,5
I-e) [pic 1]
I-f) [pic 2]
I-g)[pic 3]
I-h) Regresión lineal simple (RLS)
[pic 4]
I-i) [pic 5]
I-j) [pic 6]
I-k) [pic 7]
I-l) [pic 8]
I-m) %[pic 9]
Parte II: Sumatorias
II-a) [pic 10]
[pic 11]
+- 5[pic 12][pic 13]
[pic 14]
553
II-b) [pic 15]
[pic 16]
[pic 17]
0
II-c) [pic 18]
[pic 19]
[pic 20]
] A[pic 21]
[pic 22]
[22(9)+22(6)+81]A=411A
II-d) = [pic 23][pic 24]
[pic 25]
[pic 26]
[pic 27]
II-e) [pic 28]
[pic 29]
[pic 30]
[pic 31]
Parte III: Organización de datos clasificación y distribución de datos del caso III:
3.1 n = 50 > 30, es una muestra grande por tener más de 30.
3.2 Xmax – Xmin = 61.50 - 45.70 = 15,80
3.3 m=1+ 3,32 log (50)=6,64058 = 7
3.3 [pic 32]
3.4 [pic 33]
3.5 16,1 – 15,80= 0.3 | y’i-1 = 45.70-0.15=45.55|y’i = 61.50+0.15=61.65
i | y’i-1 ,y’i | ci | yi | tabulación | ni | hi | Hix100 | Nj | Hj | Hjx100 | Nj* | Hj* | Hj*x100 | yini | yihi |
1 | 45.55,47.85 | 2,3 | 46.7 | 3 | 0.06 | 6% | 3 | 0.06 | 6% | 50 | 1.00 | 100% | 140.1 | 2.802 | |
2 | 47.85,50.15 | 2,3 | 49 | 7 | 0.14 | 14% | 10 | 0.20 | 20% | 47 | 0.94 | 94% | 343 | 6.86 | |
3 | 50.15,52.45 | 2,3 | 51.3 | 6 | 0.12 | 12% | 16 | 0.32 | 32% | 40 | 0.80 | 80% | 307.8 | 6.156 | |
4 | 52.45,54.75 | 2,3 | 53.6 | 11 | 0.22 | 22% | 27 | 0.54 | 54% | 34 | 0.68 | 68% | 589.6 | 11.792 | |
5 | 54.75,57.75 | 2,3 | 55.9 | 19 | 0.38 | 38% | 46 | 0.96 | 96% | 23 | 0.46 | 46% | 1062.1 | 21.242 | |
6 | 57.75,59.35 | 2,3 | 58.2 | 2 | 0.04 | 4% | 48 | 0.98 | 98% | 4 | 0.08 | 8% | 116.4 | 2.328 | |
7 | 59.35,61.65 | 2,3 | 60.5 | 2 | 0.04 | 4% | 50 | 1.00 | 100% | 2 | 0.04 | 4% | 121 | 2.42 | |
∑ | N=50 | ∑=50 | 1 | 100% | 0 | 0 | 0 | 2680 | 53.6 |
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