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Ejercicio 1. Recta de mnimos cuadrados.
x 1 3 4 6 8 9 11 14 56
y 1 2 4 4 5 7 8 9 40
x2 1 9 16 36 64 81 121 196 524
xy 1 6 16 24 40 63 88 126 364
y2 1 4 16 16 25 49 64 81 25610
Incremento - seriey = 0.6364x + 0.5455 R = 0.9545
8 6 y 4 20
Incremento serie Linear (Incremento serie)
0
5 x
10
15
8 56 0.50 -0.05
56 524 -0.05 0.01
40 364 A 0.54545 B 0.63636
Ejercicio 2. Recta de mnimos cuadrados.
x 3 2 2 1 1 3 2 3 2 1 20
y 30 40 40 50 60 35 28 42 53 48 426
x2 9 4 4 1 1 9 4 9 4 1 46
xy 90 80 80 50 60 105 56 126 106 48 801
y2 900 1600 1600 2500 3600 1225 784 1764 2809 2304 1908680
Incremento - serie60 40 20 00 2 x 4y = -8.5x + 59.6 R = 0.462
y
Incremento serie Linear (Incremento serie)
10 20 0.77 -0.33
20 46 -0.33 0.17 A B
426 801 59.6 -8.5
Ejercicio 3. Recta de mnimos cuadrados. yest (yest 2
x65 63 67 64 68 62 70 66 68 67 69 71 800
y68 66 68 65 69 66 68 65 71 67 68 70 811
x24225 3969 4489 4096 4624 3844 4900 4356 4624 4489 4761 5041 53418
xy4420 4158 4556 4160 4692 4092 4760 4290 4828 4489 4692 4970 54107
y24624 4356 4624 4225 4761 4356 4624 4225 5041 4489 4624 4900 54849
x68 66 68 65 69 66 68 65 71 67 68 70 811
y65 63 67 64 68 62 70 66 68 67 69 71 800
yest66.791 65.8382 67.7438 66.3146 68.2202 65.3618 69.173 67.2674 68.2202 67.7438 68.6966 69.6494
y-yest (y-yest)21.209 0.1618 0.2562 0.7798 0.6382 -1.173 2.7798 1.4617 0.0262 0.0656 0.6081 0.4073 1.3759 7.7273
y-yprom (y-yprom)2 0.42 -1.58 0.42 -2.58 1.42 -1.58 0.42 -2.58 3.42 -0.58 0.42 2.42 r2 0.17 2.51 0.17 6.67 2.01 2.51 0.17 6.67 11.67 0.34 0.17 5.84 38.92 0.4938 0.7027
yprom yprom)-0.79 -1.75 0.16 -1.27 0.64 -2.22 1.59 -0.32 0.64 0.16 1.11 2.07 0.63 3.05 0.03 1.61 0.41 4.94 2.53 0.10 0.41 0.03 1.24 4.27 19.22 #REF!
-1.3146 1.7282
-2.2674 5.1411 -0.7438 0.5532 -0.6966 0.4853 0.3506 -0.02 n 0.1229 19.703 12 1.6419 1.28
y(prom) 7.58 6 x(prom) 66.7
Estaturas de padres e hijos (mayores).Estatura (padre)
75 70 65 60 60 65 70 Estatura (hijo)
x = 1.0364y - 3.3769 R = 0.4937
75
Estaturas de padres e hijos mayores
12 811 117.45 -1.74
811 54849 -1.74 0.03
800 54107 C -3.377 D 1.036
x - x prom -1.67 -3.67 0.33 -2.67 1.33 -4.67 3.33 -0.67 1.33 0.33 2.33 4.33
(x - x prom)(y - y prom)
-0.69 5.81 0.14 6.89 1.89 7.39 1.39 1.72 4.56 -0.19 0.97 10.47 40.333
Estaturas de padres e hijos mayores.Estatura (hijo). 72 70 68 66 64 60 65 70 75 Estatura (padre) y = 0.4764x + 35.825 R = 0.4937 Estaturas de padres e hijos
12 800
800 53418
811 54107
52.58 -0.79
-0.79 0.01
A 35.82 B 0.476
Ejercicio 4. Recta de mnimos cuadrados.
lgebra (x) Fsica (y) 75 80 93 65 87 71 98 68 84 77 798 82 78 86 72 91 80 95 72 89 74 819
x2 5625 6400 8649 4225 7569 5041 9604 4624 7056 5929 64722
xy 6150 6240 7998 4680 7917 5680 9310 4896 7476 5698 66045
y2 6724 6084 7396 5184 8281 6400 9025 5184 7921 5476 67675
Fsica (x) lgebra (y) 82 78 86 72 91 80 95 72 89 74 819 75 80 93 65 87 71 98 68 84 77 798y = 0.6613x + 29.129 R = 0.7606
Calificaciones100 8060 y
40 200
Calificaciones Linear (Calificaciones) 0 20 40 60 x 80 100 120
10 798 6.21 -0.08
798 64722 -0.08 0.00
819 66045 A 29.12903 B 0.66129
Calificaciones150
y = 1.1501x - 14.394 R = 0.7606
100 y 50 00 20 40 x 60 80 100
Calificaciones Linear (Calificaciones)
10 819
819 67675
798 66045
11.30 -0.14
-0.14 0.00
C -14.393889 D 1.15010853
2.15 -1.76
Ejercicio 5. Recta de mnimos cuadrados.
Nivel de hid. (x) Pureza (y)
x2
y2
xy
Nivel de hid. (y)
Pureza (x)
0.99 1.02 1.15 1.29 1.46 1.36 0.87 1.23 1.55 1.4 1.19 1.15 0.98 1.01 1.11 1.2 1.26 1.32 1.43 0.95 23.92
90.01 89.05 91.43 93.74 96.73 94.45 87.59 91.77 99.42 93.65 93.54 92.52 90.56 89.54 89.85 90.39 93.25 93.41 94.98 87.33 1843.21
0.9801 1.0404 1.3225 1.6641 2.1316 1.8496 0.7569 1.5129 2.4025 1.96 1.4161 1.3225 0.9604 1.0201 1.2321 1.44 1.5876 1.7424 2.0449 0.9025 29.2892
8101.8001 7929.9025 8359.4449 8787.1876 9356.6929 8920.8025 7672.0081 8421.7329 9884.3364 8770.3225 8749.7316 8559.9504 8201.1136 8017.4116 8073.0225 8170.3521 8695.5625 8725.4281 9021.2004 7626.5289 170044.532
89.1099 90.831 105.1445 120.9246 141.2258 128.452 76.2033 112.8771 154.101 131.11 111.3126 106.398 88.7488 90.4354 99.7335 108.468 117.495 123.3012 135.8214 82.9635 2214.6566
0.99 1.02 1.15 1.29 1.46 1.36 0.87 1.23 1.55 1.4 1.19 1.15 0.98 1.01 1.11 1.2 1.26 1.32 1.43 0.95 23.92y = 0.0587x - 4.2139 R = 0.8774
90.01 89.05 91.43 93.74 96.73 94.45 87.59 91.77 99.42 93.65 93.54 92.52 90.56 89.54 89.85 90.39 93.25 93.41 94.98 87.33 1843.21
Destilacin qumica2 1.5 10.5
y
Destilacin qumica Linear (Destilacin qumica) 85 90 95 x 100 105
0
20 1843.21 49.04 -0.53
1843.21 170044.532 -0.53 0.01
23.92 2214.6566 C -4.213936307 D 0.058701247
Destilacin qumica105 10095
y = 14.947x + 74.283 R = 0.8774
y
90 85 0 0.5 1 x 1.5 2
Destilacin qumica Linear (Destilacin qumica)
20 23.92 2.15 -1.76
23.92 29.2892 -1.76 1.47 A B
1843.21 2214.6566 74.28331424 14.94747973
Ejercicio 6. Recta de mnimos cuadrados.
Edad (x) Presin (y)
x2
y2
xy
x-xprom
y-yprom
56 147 42 125 72 160 36 118 63 149 47 128 55 150 49 145 38 115 42 140 68 152 60 155 628 1684 52.3333 140.3333
3136 1764 5184 1296 3969 2209 3025 2401 1444 1764 4624 3600 34416
0.89 80.78 1.138
12 628
21609 8232 3.6667 6.66667 24.444444 13.444 44.4444 15625 5250 -10.33 -15.333 158.44444 106.78 235.111 25600 11520 19.667 19.6667 386.77778 386.78 386.778 13924 4248 -16.33 -22.333 364.77778 266.78 498.778 22201 9387 10.667 8.66667 92.444444 113.78 75.1111 16384 6016 -5.333 -12.333 65.777778 28.444 152.111 22500 8250 2.6667 9.66667 25.777778 7.1111 93.4444 21025 7105 -3.333 4.66667 -15.55556 11.111 21.7778 13225 4370 -14.33 -25.333 363.11111 205.44 641.778 19600 5880 -10.33 -0.3333 3.4444444 106.78 0.11111 23104 10336 15.667 11.6667 182.77778 245.44 136.111 24025 9300 7.6667 14.6667 112.44444 58.778 215.111 238822 89894 1764.6667 1550.7 2500.67 4E+06 1969 628 1684 0.896139 34416 89894 80.778 1.138
1.84953 -0.0337 -0.0337 0.00064
Nota en la primera evaluacin (x) evaluacin2 (y). y2 Nota en la segunda x6 5 8 8 7 6 10 4 9 7 70 8 7 7 10 5 8 10 6 8 6 75 36 25 64 64 49 36 100 16 81 49 520 64 49 49 100 25 64 100 36 64 36 587
712
7.5
Segunda evaluacin (y)
10 8 6 42
00 5 10 Primera evaluacin (x)
10 75
75 587
2.396 -0.31 -0.306 0.04
10 70
70 520
1.733 -0.23 -0.233 0.03
xy Ecuac 1 (x est) 2 (y est) Ecuac48 35 56 80 35 48 100 24 72 42 540 7.30612 6.69388 6.69388 8.53061 5.46939 7.30612 8.53061 6.08163 7.30612 6.08163 7 6.5 8 8 7.5 7 9 6 8.5 7.5
-0.5 6.5 8 8 7.5 7 9 6 8.5 7.5
0.25 42.3 64 64 56.3 49 81 36 72.3 56.3 521
y = 0.5x + 4 R = 0.3061
Evaluaciones
Ecuacin 1 Ecuacin 2 Linear (Evaluaciones)
15
70 540 C 2.40816 D 0.61224
75 540 A B 4 0.5
Ejercicio 1. Parbola de mnimos cuadrados.x y x2 y2 x3 x4 xy x2y
1.2 1.8 3.1 4.9 5.7 7.1 8.6 9.8 42.2
4.5 5.9 7 7.8 7.2 6.8 4.5 2.7 46.4
1.44 3.24 9.61 24 32.5 50.4 74 96 291
20.25 34.81 49 60.84 51.84 46.24 20.25 7.29 290.5
1.728 5.832 29.791 117.649 185.193 357.911 636.056 941.192 2275.35
2.0736 10.4976 92.3521 576.48 1055.6 2541.17 5470.08 9223.68 18971.9
5.4 10.62 21.7 38.22 41.04 48.28 38.7 26.46 230.42
6.48 19.116 67.27 187.278 233.928 342.788 332.82 259.308 1448.988
8 42.2 291.2 42.2 291.2 2275.35 291 2275 18971.9 1.56 -0.62 0.05051 -0.6 0.301 -0.02662 0.05 -0.03 0.00247
46.4 230.4 1448.99 A 2.600731 B 2.05863 C -0.21044
Ahora comprobaremos si se satisfacen las igualdades.
46.4
46.4
Ejercicio 2. Parbola de mnimos cuadrados.x y x2 y2 x3 x4 xy x2y
0 1 2 3 4 5 6 21
2.4 2.1 3.2 5.6 9.3 15 22 59
0 1 4 9 16 25 36 91 7 21 91
5.76 4.41 10.24 31.36 86.49 213.2 479.6 831 21 91 441
0 1 8 27 64 125 216 441 91 441 2275
0 1 16 81 256 625 1296 2275 59.1 266.9 1367.5
0 2.1 6.4 16.8 37.2 73 131.4 266.9
0 2.1 12.8 50.4 148.8 365 788.4 1367.5
0.762 -0.46 0.06 -0.464 0.464 -0.071 0.06 -0.07 0.012
A 2.509524 B -1.2 C 0.733333
Ahora comprobaremos si se satisfacen las igualdades.
59 59
Ejercicio 3. Parbola de mnimos cuadrados.x y x2 y2 x3 x4 xy x2y
20 30 40 50 60 70 270
54 90 138 206 292 396 1176
400 900 1600 2500 3600 4900 13900
2916 8100 19044 42436 85264 156816 314576
8000 27000 64000 125000 216000 343000 783000
160000 810000 2560000 6250000 12960000 24010000 46750000
1080 2700 5520 10300 17520 27720 64840
21600 81000 220800 515000 1051200 1940400 3830000
6 270 13900
270 13900 783000
13900 783000 46750000
1176 64840 3830000 A 41.7714286 B -1.0957143 C 0.08785714
9.37143 -0.4435714 0.004642857 -0.4436 0.02226786 -0.00024107 0.00464 -0.0002411 2.67857E-06
1176
1176
Para estimar cuando x= 45 y 80
170.367
516.394
Ejercicio 4. Parbola de mnimos cuadrados.Esfuerzo (x) Resistencia (y) x2 y2 x3 x4
15.5 23.75 8 17 5 19 24 2.5 7.5 11 13 3.75 25 9.75 22 18 6 12.5 2 21.5 266.75
2158.7 1678.15 2316 2061.3 2207.5 1708.3 1784.7 2575 2357.9 2277.7 2165.2 2399.55 1779.8 2336.75 1765.3 2053.5 2414.4 2200.5 2654.2 1753.7 42648.15 20 266.75 4672.4375 0.604699114 -0.09576765 0.003093041
240.25 564.0625 64 289 25 361 576 6.25 56.25 121 169 14.0625 625 95.0625 484 324 36 156.25 4 462.25 4672.4375 266.75 4672.4375 92518.95313 -0.095767654 0.018671469 -0.00065603
4659985.69 2816187.423 5363856 4248957.69 4873056.25 2918288.89 3185154.09 6630625 5559692.41 5187917.29 4688091.04 5757840.203 3167688.04 5460400.563 3116284.09 4216862.25 5829327.36 4842200.25 7044777.64 3075463.69 92642655.86 4672.4375 92518.95313 1951123.449 0.003093041 -0.00065603 2.42133E-05
3723.875 13396.48438 512 4913 125 6859 13824 15.625 421.875 1331 2197 52.734375 15625 926.859375 10648 5832 216 1953.125 8 9938.375 92518.95313
57720.0625 318166.5039 4096 83521 625 130321 331776 39.0625 3164.0625 14641 28561 197.7539063 390625 9036.878906 234256 104976 1296 24414.0625 16 213675.0625 1951123.449 42648.15 527619.888 8839272.303
A B C
2600.608753 -31.70668548 -0.193960157
42648.15
42648.15
1966.47504
Ejercicio 1. Regresin de mnimos cuadrados. Peso (z) 64 71 53 67 55 58 77 57 56 51 76 68 753 Estatura (x) 57 59 49 62 51 50 55 48 52 42 61 57 643 Edad (y) 8 10 6 11 8 7 10 9 10 6 12 9 106 x2 3249 3481 2401 3844 2601 2500 3025 2304 2704 1764 3721 3249 34843 y2 64 100 36 121 64 49 100 81 100 36 144 81 976 xy 456 590 294 682 408 350 550 432 520 252 732 513 5779 xz 3648 4189 2597 4154 2805 2900 4235 2736 2912 2142 4636 3876 40830 yz 512 710 318 737 440 406 770 513 560 306 912 612 6796 753 40830 6796 A 3.651216 B 0.85461 C 1.506332
12 643 106 643 34843 5779 106 5779 976 9.088 -0.22 0.336 -0.22 0.007 -0.02 0.336 -0.02 0.07
Obtener el valor de z, dados los de x y y, sustituyendo en la ecuacin. Peso (z) Estatura (x) Edad (y) 64.41 57 8 69.14 59 10 54.57 49 6 73.21 62 11 59.29 51 8 56.93 50 7 65.72 55 10 58.23 48 9 63.15 52 10 48.58 42 6 73.86 61 12 65.92 57 9 Determinar el peso de un nio dados los datos 63.36 Libras
609927 14994 22539
-3088329 476 1190
22539 1190 4667
+ +
609927 -14994 22539
-3088329 476 1190
22539 -1190 4667
418116 69312
69348 11715
413449 68158
3715897 627568
68158 7347072 -63491 -7345918
3693358 1241472 -7339907 -1857325
Laboratorio 8 3 9 2 7 10 4 6 1 5
Teora 9 5 10 1 8 7 3 4 2 6
Diferencia de grados
-1 -2 -1 1 -1 3 1 2 -1 -1
d2 1 4 1 1 1 9 1 4 1 1 24
0.854545455 NOTA: Si el resultado es menor a 1 se ve correlacin en los datos.
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