Minimo Cuadardos

METODO DE MINIMOS CUADRADOS Y=5*4X1-3X2 y

x1

x2

x1^2

x2^2

x1*x2

5 10 9 0 3 27

0 2 2.5 1 4 7

0 1 2 3 6 2

0 4 6.25 1 16 49

0 1 4 9 36 4

0 2 5 3 24 14

54

16.5

14

Sumatorias() 76.25 54

48

n= 6 matiz de coefactores

6 16.5 14

16.5 76.25 48

14 48 54

54 243.5 100

matriz inverza 0.53 -0.06 -0.08

-0.06 0.04 -0.02

-0.08 -0.02 0.05

a= b= c=

5 4 -3

OS

y*x1

y*x2

0 20 22.5 0 12 189

0 10 18 0 18 54

243.5

100

(Porcentaje de impurzas) Pi y 14.05 14.93 10.55 9.48 7.55 6.59 16.56 15.87 13.63 11.75 9.23 8.78 22.41 21.66 18.55 17.98 15.93 16.44

(Temperatura ) T x1 75 75 75 75 75 75 100 100 100 100 100 100 125 125 125 125 125 125

251.94

1800

numero de datos=

Porcentaje de impureas en el proceso de fabricacion de una bebida (Tiempode exterilizacion) Tiem x2 x3 x4 15 5625 225 15 5625 225 15 5625 225 15 5625 225 15 5625 225 15 5625 225 20 10000 400 20 10000 400 20 10000 400 20 10000 400 20 10000 400 20 10000 400 25 15625 625 25 15625 625 25 15625 625 25 15625 625 25 15625 625 25 15625 625

360

187500

7500

x1 1800 187500

x2 360 37500

x3 187500 20250000

18 a 18 1800

e fabricacion de una bebida

x5 1125 1125 1125 1125 1125 1125 2000 2000 2000 2000 2000 2000 3125 3125 3125 3125 3125 3125

x1^2 5625 5625 5625 5625 5625 5625 10000 10000 10000 10000 10000 10000 15625 15625 15625 15625 15625 15625

37500

187500

x4 7500 810000

x5 37500 4050000

x1*x2 1125 1125 1125 1125 1125 1125 2000 2000 2000 2000 2000 2000 3125 3125 3125 3125 3125 3125

37500

x1*x3 421875 421875 421875 421875 421875 421875 1000000 1000000 1000000 1000000 1000000 1000000 1953125 1953125 1953125 1953125 1953125 1953125

20250000

y 251.94 26439.5

x1*x4 16875 16875 16875 16875 16875 16875 40000 40000 40000 40000 40000 40000 78125 78125 78125 78125 78125 78125

810000

x1*x5 84375 84375 84375 84375 84375 84375 200000 200000 200000 200000 200000 200000 390625 390625 390625 390625 390625 390625

4050000

x2^2 225 225 225 225 225 225 400 400 400 400 400 400 625 625 625 625 625 625

x2*x3 84375 84375 84375 84375 84375 84375 200000 200000 200000 200000 200000 200000 390625 390625 390625 390625 390625 390625

sumatorias 7500 4050000

x2*x4 3375 3375 3375 3375 3375 3375 8000 8000 8000 8000 8000 8000 15625 15625 15625 15625 15625 15625

x2*x5 16875 16875 16875 16875 16875 16875 40000 40000 40000 40000 40000 40000 78125 78125 78125 78125 78125 78125

x3^2 31640625 31640625 31640625 31640625 31640625 31640625 100000000 100000000 100000000 100000000 100000000 100000000 244140625 244140625 244140625 244140625 244140625 244140625

x3*x4 1265625 1265625 1265625 1265625 1265625 1265625 4000000 4000000 4000000 4000000 4000000 4000000 9765625 9765625 9765625 9765625 9765625 9765625

x3*x5 x4^2 6328125 6328125 6328125 6328125 6328125 6328125 20000000 20000000 20000000 20000000 20000000 20000000 48828125 48828125 48828125 48828125 48828125 48828125

50625 50625 50625 50625 50625 50625 160000 160000 160000 160000 160000 160000 390625 390625 390625 390625 390625 390625

x4*x5 253125 253125 253125 253125 253125 253125 800000 800000 800000 800000 800000 800000 1953125 1953125 1953125 1953125 1953125 1953125

x5^2 1265625 1265625 1265625 1265625 1265625 1265625 4000000 4000000 4000000 4000000 4000000 4000000 9765625 9765625 9765625 9765625 9765625 9765625

rias 162000

810000

2254687500

90187500

450937500

3607500

18037500

90187500

y*x1 1053.75 1119.75 791.25 711 566.25 494.25 1656 1587 1363 1175 923 878 2801.25 2707.5 2318.75 2247.5 1991.25 2055

26439.5

y*x2 210.75 223.95 158.25 142.2 113.25 98.85 331.2 317.4 272.6 235 184.6 175.6 560.25 541.5 463.75 449.5 398.25 411

5287.9

y*x3 79031.25 83981.25 59343.75 53325 42468.75 37068.75 165600 158700 136300 117500 92300 87800 350156.25 338437.5 289843.75 280937.5 248906.25 256875

2878575

y*x4 3161.25 3359.25 2373.75 2133 1698.75 1482.75 6624 6348 5452 4700 3692 3512 14006.25 13537.5 11593.75 11237.5 9956.25 10275

115143

y*x5 15806.25 16796.25 11868.75 10665 8493.75 7413.75 33120 31740 27260 23500 18460 17560 70031.25 67687.5 57968.75 56187.5 49781.25 51375

575715