Modelos

EJERCICIO Nº2
Y | X1 | X2 | X3 | X4 | X5 |
15.0 | 17.4 | 157.4 | 40.1 | 66.2 | 273.4 |
18.7 | 14.3 | 196.8 | 194.9 | 55.1 | 251.4 |
14.6 | 17.9 | 152.8 | 112.9 | 77.2 | 235.9 |
11.0 | 16.3 | 115.8 | 119.7 | 88.2 | 255.8 |
13.7 | 4.9 | 143.5 | 31.3 | 66.2 | 249.2 |
17.1 | 5.1 | 179.8 | 24.0 | 66.2 | 235.9 |
15.9 | 5.5 | 167.5 | 25.4 | 55.1 | 244.8 |
13.5 | 5.7 | 141.2 | 188.1 |55.1 | 282.2 |
12.3 | 9.0 | 129.7 | 134.7 | 22.1 | 293.3 |
15.1 | 12.1 | 158.2 | 35.3 | 66.2 | 293.3 |
13.5 | 10.4 | 141.2 | 22.9 | 66.2 | 310.9 |
13.5 | 13.0 | 142.0 | 22.5 | 77.2 | 295.5 |
13.7 | 10.4 | 144.3 | 24.5 | 66.2 | 297.7 |
13.4 | 11.0 | 140.5 | 13.7 | 77.2 | 293.3 |
13.6 | 11.5 | 142.8 | 37.3 | 66.2 | 317.5 |
12.9 | 10.4 | 135.1 | 26.9 | 44.1 | 310.9 |
11.1 | 9.3 |116.5 | 47.0 | 66.2 | 337.4 |
10.1 | 8.2 | 106.5 | 32.4 | 44.1 | 308.7 |

Ploteando los puntos tenemos:

Con estos datos nos damos cuenta que hay 5 variables para esto uformamos nuestra ecuación y* y luego la derivamos con respecto a cada una de esas variables para tener nuestro sistema de ecuaciones
S= [y-y*]2
y* =a+bx1+cx2+dx3+ex4+fx5
dSda=2[y-(a+bx1+cx2+dx3+ex4+fx5)]-1=0
dSdb=2[y-(a+bx1+cx2+dx3+ex4+fx5)]-x1= 0
dSdc =2 [y-(a+bx1+cx2+dx3+ex4+fx5)]-x2= 0
dSdd=2[y-(a+bx1+cx2+dx3+ex4+fx5)]-x3= 0
dSde=2[y-(a+bx1+cx2+dx3+ex4+fx5)]-x4= 0
dSdf=2[y-(a+bx1+cx2+dx3+ex4+fx5)]-x5= 0

na+bx1+cx2+dx3+ex4+fx5= y
ax1+bx12+cx1x2+dx1x3+ex1x4+fx1x5= x1y
ax2+bx1x2+cx22+dx2x3+ex2x4+fx2x5= x2y
ax3+bx1x3+cx2x3+dx32+ex3x4+fx3x5= x3y
ax4+bx1x4+cx2x4+dx3x4+ex42+fx4x5= x4yax5+bx1x5+cx2x5+dx3x5+ex4x5+fx52= x5y
Teniendo este sistema hallamos usando el Excel los valores de las sumatorias las cuales son las siguientes:

| Y | X1 | X2 | X3 | X4 | X5 | X12 | X22 | X32 | X42 | X52 |
| 15.0 | 17.4 | 157.4 | 40.1 | 66.2 | 273.4 | 302.8 | 24774.76 | 1608.01 | 4382.44 | 74747.56 |
| 18.7 | 14.3 | 196.8 | 194.9 | 55.1 | 251.4 | 204.5 | 38730.24 | 37986.01 | 3036.01 | 63201.96 |
| 14.6| 17.9 | 152.8 | 112.9 | 77.2 | 235.9 | 320.4 | 23347.84 | 12746.41 | 5959.84 | 55648.81 |
| 11.0 | 16.3 | 115.8 | 119.7 | 88.2 | 255.8 | 265.7 | 13409.64 | 14328.09 | 7779.24 | 65433.64 |
| 13.7 | 4.9 | 143.5 | 31.3 | 66.2 | 249.2 | 24.0 | 20592.25 | 979.69 | 4382.44 | 62100.64 |
| 17.1 | 5.1 | 179.8 | 24.0 | 66.2 | 235.9 | 26.0 | 32328.04 | 576 | 4382.44 | 55648.81 |
| 15.9 | 5.5 |167.5 | 25.4 | 55.1 | 244.8 | 30.3 | 28056.25 | 645.16 | 3036.01 | 59927.04 |
| 13.5 | 5.7 | 141.2 | 188.1 | 55.1 | 282.2 | 32.5 | 19937.44 | 35381.61 | 3036.01 | 79636.84 |
| 12.3 | 9.0 | 129.7 | 134.7 | 22.1 | 293.3 | 81.0 | 16822.09 | 18144.09 | 488.41 | 86024.89 |
| 15.1 | 12.1 | 158.2 | 35.3 | 66.2 | 293.3 | 146.4 | 25027.24 | 1246.09 | 4382.44 | 86024.89 |
| 13.5 | 10.4 | 141.2 |22.9 | 66.2 | 310.9 | 108.2 | 19937.44 | 524.41 | 4382.44 | 96658.81 |
| 13.5 | 13.0 | 142.0 | 22.5 | 77.2 | 295.5 | 169.0 | 20164 | 506.25 | 5959.84 | 87320.25 |
| 13.7 | 10.4 | 144.3 | 24.5 | 66.2 | 297.7 | 108.2 | 20822.49 | 600.25 | 4382.44 | 88625.29 |
| 13.4 | 11.0 | 140.5 | 13.7 | 77.2 | 293.3 | 121.0 | 19740.25 | 187.69 | 5959.84 | 86024.89 |
| 13.6 | 11.5 | 142.8 | 37.3 |66.2 | 317.5 | 132.3 | 20391.84 | 1391.29 | 4382.44 | 100806.25 |
| 12.9 | 10.4 | 135.1 | 26.9 | 44.1 | 310.9 | 108.2 | 18252.01 | 723.61 | 1944.81 | 96658.81 |
| 11.1 | 9.3 | 116.5 | 47.0 | 66.2 | 337.4 | 86.5 | 13572.25 | 2209 | 4382.44 | 113838.76 |
| 10.1 | 8.2 | 106.5 | 32.4 | 44.1 | 308.7 | 67.2 | 11342.25 | 1049.76 | 1944.81 | 95295.69 |
∑ | 248.7 | 192.4 | 2611.6 | 1133.6 | 1125.0| 5087.1 | 2334.0 | 387248.3 | 130833.4 | 74204.3 | 1453623.8 |

X1X2 | X1X3 | X1X4 | X1X5 | X2X3 | X2X4 | X2X5 | X3X4 | X3X5 |
2738.76 | 697.74 | 1151.88 | 4757.16 | 6311.74 | 10419.88 | 43033.16 | 2654.62 | 10963.34 |
2814.24 | 2787.07 | 787.93 | 3595.02 | 38356.32 | 10843.68 | 49475.52 | 10738.99 | 48997.86 |
2735.12 | 2020.91 | 1381.88 | 4222.61 | 17251.12 | 11796.16 | 36045.52 |...