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.