Problemas Examen Diseño
26
PROBLEMA 1.- N Utilice la Regresion por minimos cuadrados para ajustar una linea recta a xi yi xi.yi ei 0 5 0 25 0 4.9 0.1 2 6 4 36 12 5.6 0.4 4 7 16 49 28 6.3 0.7 6 6 36 36 36 7.0 -1.0 9 9 81 81 81 8.0 1.0 11 8 121 64 88 8.7 -0.7 12 7 144 49 84 9.1 -2.1 15 10 225 100 150 10.1 -0.1 17 12 289 144 204 10.8 1.2 19 12 361 144 228 11.5 0.5 95 82 1277 728 911 144.30 0.8368 0.9148 1.07 xi 2 yi 2 0 2 4 6 8 10 12 14 16 18 20 0.0 2.0 4.0 6.0 8.0 10.0 12.0 14.0 f(x) = − 1.57501465E-17 x² + 0.3524699599466 x + 4.851535380507 Column F Polynomial (Co F) 0 2 4 6 8 10 12 14 16 18 20 0 2 4 6 8 10 12 14 f(x) = 0.352469959946595 x + 4.85153538050734 Column B
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problemas en excel de diseño de experimentos de regresion lineal
Transcript of Problemas Examen Diseño
PROBLEMA 1.- N 10
Utilice la Regresion por minimos cuadrados para ajustar una linea recta a: 9.50
8.20
xi yi xi.yi ei0 5 0 25 0 4.9 0.12 6 4 36 12 5.6 0.4 132.004 7 16 49 28 6.3 0.76 6 36 36 36 7.0 -1.09 9 81 81 81 8.0 1.0 374.50
11 8 121 64 88 8.7 -0.712 7 144 49 84 9.1 -2.1 0.352515 10 225 100 150 10.1 -0.117 12 289 144 204 10.8 1.2 4.851519 12 361 144 228 11.5 0.595 82 1277 728 911 55.60
144.30 46.530.8368 0.9148 1.07
xi2 yi2
0 2 4 6 8 10 12 14 16 18 200.0
2.0
4.0
6.0
8.0
10.0
12.0
14.0
f(x) = − 1.5750146469162E-17 x² + 0.352469959946596 x + 4.85153538050734
Column FPolynomial (Column F)
0 2 4 6 8 10 12 14 16 18 200
2
4
6
8
10
12
14
f(x) = 0.352469959946595 x + 4.85153538050734
Column BLinear (Column B)
0 2 4 6 8 10 12 14 16 18 200.0
2.0
4.0
6.0
8.0
10.0
12.0
14.0
f(x) = − 1.5750146469162E-17 x² + 0.352469959946596 x + 4.85153538050734
Column FPolynomial (Column F)
0 2 4 6 8 10 12 14 16 18 200
2
4
6
8
10
12
14
f(x) = 0.352469959946595 x + 4.85153538050734
Column BLinear (Column B)
PROBLEMA 1a.- n 10
Utilice la Regresion por minimos cuadrados para ajustar una linea recta a: 8.20
9.50
xi yi xi.yi ei5 0 25 0 0 1.9 -1.96 2 36 4 12 4.3 -2.3 132.007 4 49 16 28 6.7 -2.76 6 36 36 36 4.3 1.79 9 81 81 81 11.4 -2.4 55.608 11 64 121 88 9.0 2.07 12 49 144 84 6.7 5.3 2.3741
10 15 100 225 150 13.8 1.212 17 144 289 204 18.5 -1.5 -9.967612 19 144 361 228 18.5 0.582 95 728 1277 911 374.50
144.30 313.380.8368 0.9148 2.76
xi2 yi2
4 5 6 7 8 9 10 11 12 130.0
2.0
4.0
6.0
8.0
10.0
12.0
14.0
16.0
18.0
20.0
f(x) = 2.7931655354878E-17 x² + 2.37410071942446 x − 9.96762589928057
Column FPolynomial (Column F)
4 5 6 7 8 9 10 11 12 130
2
4
6
8
10
12
14
16
18
20
f(x) = 2.37410071942446 x − 9.96762589928058
Column B
Linear (Column B)
4 5 6 7 8 9 10 11 12 130.0
2.0
4.0
6.0
8.0
10.0
12.0
14.0
16.0
18.0
20.0
f(x) = 2.7931655354878E-17 x² + 2.37410071942446 x − 9.96762589928057
Column FPolynomial (Column F)
4 5 6 7 8 9 10 11 12 130
2
4
6
8
10
12
14
16
18
20
f(x) = 2.37410071942446 x − 9.96762589928058
Column B
Linear (Column B)
PROBLEMA 2.- n 11
Utilice la Regresion por minimos cuadrados para ajustar una linea recta a: 21.27
14.45
xi yi xi.yi ei6 29 36 841 174 26.4 2.67 21 49 441 147 25.6 -4.6 -1002.36
11 29 121 841 319 22.5 6.515 14 225 196 210 19.4 -5.417 21 289 441 357 17.8 3.2 1284.1821 15 441 225 315 14.7 0.323 7 529 49 161 13.1 -6.1 -0.780529 7 841 49 203 8.4 -1.429 13 841 169 377 8.4 4.6 31.058937 0 1369 0 0 2.2 -2.239 3 1521 9 117 0.6 2.4
234 159 6262 3261 2380 962.73
1111.90-0.9015 4.48
xi2 yi2
0 5 10 15 20 25 30 35 40 450.0
5.0
10.0
15.0
20.0
25.0
30.0
f(x) = − 0.780546509981594 x + 31.058898485063
Column FLinear (Column F)
0 5 10 15 20 25 30 35 40 450
5
10
15
20
25
30
35
f(x) = − 0.780546509981594 x + 31.058898485063
Column BLinear (Column B)
0 5 10 15 20 25 30 35 40 450.0
5.0
10.0
15.0
20.0
25.0
30.0
f(x) = − 0.780546509981594 x + 31.058898485063
Column FLinear (Column F)
0 5 10 15 20 25 30 35 40 450
5
10
15
20
25
30
35
f(x) = − 0.780546509981594 x + 31.058898485063
Column BLinear (Column B)
PROBLEMA 3.- n 9
Utilice la Regresion por minimos cuadrados para ajustar una linea recta a: 5.00
5.28
xi yi xi.yi ei1 1 1 1 1 -0.6 1.62 1.5 4 2.25 3 0.9 0.6 87.503 2 9 4 6 2.4 -0.44 3 16 9 12 3.8 -0.85 4 25 16 20 5.3 -1.3 60.006 5 36 25 30 6.7 -1.77 8 49 64 56 8.2 -0.2 1.45838 10 64 100 80 9.7 0.39 13 81 169 117 11.1 1.9 -2.0139
45 47.5 285 390.25 325139.56
91.510.9562 1.31
xi2 yi2
0 1 2 3 4 5 6 7 8 9 10
-2.0
0.0
2.0
4.0
6.0
8.0
10.0
12.0
f(x) = 5.4790227189293E-17 x² + 1.45833333333333 x − 2.01388888888889
Column FPolynomial (Column F)
0 1 2 3 4 5 6 7 8 9 100
2
4
6
8
10
12
14
f(x) = 1.45833333333333 x − 2.01388888888889
Column B
Linear (Column B)
EJEMPLO 2.-Xi Yi Xi.Yi
1 1 1 1 1 1 12 1.5 4 8 16 3 63 2 9 27 81 6 184 3 16 64 256 12 485 4 25 125 625 20 1006 5 36 216 1296 30 1807 8 49 343 2401 56 3928 10 64 512 4096 80 6409 13 81 729 6561 117 1053
∑Xi ∑Yi ∑Xi.Yi ∑Xi2.Yi45 47.5 285 2025 15333 325 2438
9 + 45 + 285 = 47.5 n 9
45 + 285 + 2025 = 325
285 + 2025 + 15333 = 2438 ###
### x
polinomio ###
1.4880952 + -0.45184 + -0.45184 x + 0.19102
Xi2 Xi3 Xi4 Xi2.Yi
∑Xi2 ∑Xi3 ∑Xi4
a0 a1 a2
a0 a1 a2
a0 a1 a2 a0
a1
a2 x2
x2
0 1 2 3 4 5 6 7 8 9 100
2
4
6
8
10
12
14
f(x) = 0.1910173160173 x² − 0.4518398268398 x + 1.4880952380952R² = 0.994889465629911
Column B
Polynomial (Column B)
eje Xi
eje
Yi
0 1 2 3 4 5 6 7 8 9 100
2
4
6
8
10
12
14
f(x) = 0.1910173160173 x² − 0.4518398268398 x + 1.4880952380952R² = 0.994889465629911
Column B
Polynomial (Column B)
eje Xi
eje
Yi
PROBLEMA 4.- n 8
Ajuste una ecuacion cúbica a los datos siguientes: 7.38
3.30
xi yi xi.yi ei3 1.6 9 2.56 4.8 2.7 -1.14 3.6 16 12.96 14.4 2.8 0.8 10.105 4.4 25 19.36 22 3.0 1.47 3.4 49 11.56 23.8 3.2 0.28 2.2 64 4.84 17.6 3.4 -1.2 73.889 2.8 81 7.84 25.2 3.5 -0.7
11 3.8 121 14.44 41.8 3.8 0.0 0.136712 4.6 144 21.16 55.2 3.9 0.759 26.4 509 94.72 204.8 2.2917
23.69 7.600.1817 0.4263 1.02
1.38
xi2 yi2
2 4 6 8 10 12 140.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
f(x) = 0.136717428087986 x + 2.29170896785111
Column FLinear (Column F)
2 4 6 8 10 12 140
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
f(x) = 0.136717428087986 x + 2.2917089678511
Column B
Linear (Column B)
Utilice Regresion Lineal Multiple para ajustar
Yi ei15.1 0 0 0 0 0 0 0 8.75 6.35 40.289117.9 1 1 1 1 1 17.9 17.9 1.91 15.99 255.66312.7 1 2 1 4 2 12.7 25.4 1.91 10.79 116.41325.6 2 1 4 1 2 51.2 25.6 5.33 20.27 410.80920.5 2 2 4 4 4 41 41 1.91 18.59 345.56935.1 3 1 9 1 3 105.3 35.1 5.33 29.77 886.15929.7 3 2 9 4 6 89.1 59.4 1.91 27.79 772.25545.4 4 1 16 1 4 181.6 45.4 5.33 40.07 1605.4840.2 4 2 16 4 8 160.8 80.4 1.91 38.29 1466.08
242.2 20 12 60 20 30 659.6 330.2 5898.72
n 10
-110 20 12 242.2 0.39473684 -0.05263 -0.1579 242.2 8.752631579
= 20 60 30 * 659.6 = -0.05263158 0.07368 -0.0789 659.6 = 9.78631578912 30 20 330.2 -0.15789474 -0.07895 0.26316 330.2 -3.421052632
X1 X2 X12 X2
2 X1X2 X1Yi X2Yi ei2
y=8.753+9.786x1-3.421x2
Resumen
Estadísticas de la regresiónCoeficiente de correlación múltiple 0.99775916245Coeficiente de determinación R^2 0.99552334626R^2 ajustado 0.99403112835Error típico 0.88878682989Observaciones 9
ANÁLISIS DE VARIANZA
Grados de libertad Suma de cuadrados Promedio de los cuadrados F Valor crítico de F
Regresión 2 1054.00923671498 527.004618357488 667.14341 8.971406E-08Residuos 6 4.73965217391302 0.789942028985503Total 8 1058.74888888889
Coeficientes Error típico Estadístico t Probabilidad Inferior 95%
Intercepción 14.4608695652 0.717760116000451 20.1472180507844 9.7114E-07 12.704573831Variable X 1 9.0252173913 0.248639397711862 36.2984204207384 2.9161E-08 8.4168187024Variable X 2 -5.7043478261 0.490323504695071 -11.6338453520283 2.4293E-05 -6.904126221
Superior 95% Inferior 95.0% Superior 95.0%
16.2171652993 12.7045738310967 16.21716529933819.63361608023 8.41681870238165 9.63361608022705-4.5045694316 -6.90412622062026 -4.50456943155365
Utilice Regresion Lineal Multiple para ajustar
Yi14 0 0 0 0 0 0 021 0 2 0 4 0 0 4211 1 2 1 4 2 11 2212 2 4 4 16 8 24 4823 0 4 0 16 0 0 9223 1 6 1 36 6 23 13814 2 6 4 36 12 28 84
6 2 2 4 4 4 12 1211 1 1 1 1 1 11 11
135 9 27 15 117 33 109 449
n 10
-110 9 27 135 0.2913386 -0.0708661 -0.0472 135 10.39370079
B= 9 15 33 * 109 = -0.070866 0.19291339 -0.0381 109 = -5.62729658827 33 117 449 -0.047244 -0.0380577 0.03018 449 3.026246719
X1 X2 X12 X2
2 X1X2 X1Yi X2Yi
y=10.393-5627x1+3.026x2
Resumen
Estadísticas de la regresiónCoeficiente de correlación múltiple 0.9789450103726Coeficiente de determinación R^2 0.9583333333333R^2 ajustado 0.9444444444444Error típico 1.4142135623731Observaciones 9
ANÁLISIS DE VARIANZA
Grados de libertad Suma de cuadradosPromedio de los cuadrados F Valor crítico de F
Regresión 2 276 138 69 7.233796E-05Residuos 6 12 2Total 8 288
Coeficientes Error típico Estadístico t Probabilidad Inferior 95% Superior 95% Inferior 95.0% Superior 95.0%
Intercepción 14.666666666667 0.9067647 16.1747217 3.55161E-06 12.447893375 16.88544 12.4478934 16.88544Variable X 1 -6.666666666667 0.63245553 -10.5409255 4.28583E-05 -8.214229603 -5.11910373 -8.2142296 -5.11910373Variable X 2 2.3333333333333 0.25819889 9.03696114 0.00010287 1.7015434101 2.96512326 1.70154341 2.96512326
