Sumatorias= 21.00 132.50 91.00 441.00 2275.00 12201.00xᵢ yᵢ xᵢ² xᵢ³ xᵢ^4 xᵢ^5

0

6.3

0 0 0 0

6.7

1

5.7

1 1 1 1

5.2

2

6.3

4 8 16 32

5.9

3

7.3

9 27 81 243

7.5

4

9.9

16 64 256 1024

10.5

5

12.5

25 125 625 3125

12.1

6

18.1

36 216 1296 7776

18.5

6 36 216 1296 7776

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

Sumatorias= 21 132.5 91 441 2275 12201xᵢ yᵢ xᵢ² xᵢ³ xᵢ^4 xᵢ^5

b0 = 6.4726 b0 = 6.3310b1 = -1.3500 b1 = -0.8778b2 = 0.5417 b2 = 0.3292

b3 = 0.0236

67171.00 376761.00 2142595.00 503.90 2451.90 12794.30xᵢ^6 xᵢ^7 xᵢ^8 xᵢyᵢ xᵢ²yᵢ xᵢ³yᵢ

0 0 0

0 0 00 0 00 0 00 0 00 0 00 0 0

1 1 1

5.7 5.7 5.75.2 5.2 5.20 0 00 0 00 0 00 0 0

64 128 256

12.6 25.2 50.411.8 23.6 47.2

0 0 00 0 00 0 00 0 0

729 2187 6561

21.9 65.7 197.122.5 67.5 202.5

0 0 00 0 00 0 00 0 0

4096 16384 65536

39.6 158.4 633.642 168 6720 0 00 0 00 0 00 0 0

15625 78125 390625

62.5 312.5 1562.560.5 302.5 1512.5

0 0 00 0 00 0 00 0 0

46656 279936 1679616

108.6 651.6 3909.6111 666 3996

0 0 00 0 0

46656 279936 1679616

0 0 00 0 0

0 0 0

0 0 00 0 00 0 00 0 00 0 00 0 0

0 0 0

0 0 00 0 00 0 00 0 00 0 00 0 0

0 0 0

0 0 00 0 00 0 00 0 00 0 00 0 0

0 0 0

0 0 00 0 00 0 00 0 00 0 00 0 0

0 0 0

0 0 00 0 00 0 00 0 00 0 00 0 0

67171 376761 2142595 503.9 2451.9 12794.3xᵢ^6 xᵢ^7 xᵢ^8 xᵢyᵢ xᵢ²yᵢ xᵢ³yᵢ

b0 = 6.5423b1 = -2.9562b2 = 2.1551b3 = -0.4696b4 = 0.0411

69435.90 Sumatorias= 21.00 132.50 66.25 66.25xᵢ^4 yᵢ xᵢ yᵢ ŷij (k=2) ŷij (k=3)

0

0

6.3

6.473 6.331

0 6.70 00 00 00 0

5.7

1

5.7

5.664 5.806

5.2 5.20 00 00 00 0

100.8

2

6.3

5.939 6.081

94.4 5.90 00 00 00 0

591.3

3

7.3

7.298 7.298

607.5 7.50 00 00 00 0

2534.4

4

9.9

9.739 9.598

2688 10.50 00 00 00 0

7812.5

5

12.5

13.264 13.123

7562.5 12.10 00 00 00 0

23457.6

6

18.1

17.873 18.014

23976 18.50 00 0

0

6

0

17.873 18.014

0 00

0

00 00 00 00 00 00

0

00 00 00 00 00 00

0

00 00 00 00 00 00

0

00 00 00 00 00 00

0

00 00 00 00 00 0

69435.9 Sumatorias= 21 132.5 66.25 66.25xᵢ^4 yᵢ xᵢ yᵢ ŷij (k=2) ŷij (k=3)

66.25 1508.93 754.14 125.73 125.85ŷij (k=4) yij ² ӯᵢ..² (ŷij - ӯᵢ..²)² (k=2) (ŷij - ӯᵢ..²)² (k=3)

6.542

39.69

42.25 8.950 9.818

44.890000

5.313

32.49

29.70 14.440 13.383

27.040000

6.151

39.69

37.21 12.426 11.447

34.810000

7.720

53.29

54.76 4.694 4.694

56.250000

9.668

98.01

104.04 0.076 0.018

110.250000

12.629

156.25

151.29 14.440 13.383

146.410000

18.226

327.61

334.89 70.700 73.102

342.2500

18.226

0

334.89 70.700 73.102

0000000000000000000000000000000

66.25 1508.9300 754.1425 125.7258 125.8463ŷij (k=4) yij ² ӯᵢ.² (ŷij - ӯᵢ..²)² (k=2) (ŷij - ӯᵢ..²)² (k=3)

126.61(ŷij - ӯᵢ..²)² (k=4)

8.538

17.235

10.975

3.041

0.042

10.018

76.761

76.761

126.6107(ŷij - ӯᵢ..²)² (k=4)

k = 2 orden del polinomio

a = 7 numero de valores de xi k = 3=

n = 2 réplicas yᵢ 132.5xᵢyᵢ 503.9

x̅. = 3.0000 xᵢ²yᵢ 2451.9xᵢ³yᵢ 12794.3

y̅..= 9.4643k = 2

5% =Sumatorias yᵢ 132.5

xᵢ 21 xᵢyᵢ 503.9xᵢ² 91 xᵢ²yᵢ 2451.9xᵢ³ 441

xᵢ^4 2275 k = 4xᵢ^5 12201 =xᵢ^6 67171 yᵢ 132.5xᵢ^7 376761 xᵢyᵢ 503.9xᵢ^8 2142595 xᵢ²yᵢ 2451.9

xᵢ³yᵢ 12794.3yᵢ 132.5 xᵢ^4 yᵢ 69435.9

xᵢyᵢ 503.9xᵢ²yᵢ 2451.9xᵢ³yᵢ 12794.3

xᵢ^4 yᵢ 69435.9SI

NONO

ANÁLISIS ESTADÍSTICO

SS USAR k = 2FV k=2 k=3 k=4 FVT 254.9121 254.9121 254.9121 tt 251.4517 251.6925 253.2214 de 0.6450 0.6450 0.6450 ed 2.8155 2.5746 1.0458 T

NO USAR k = 3FV

a =

tdeT

NO USAR k = 4FVtdeT

Ecuaciones

NO Matriz inversab0 b1 b2 b3 b014 42 182 882 0.464342 182 882 4550 -0.5099182 882 4550 24402 0.1548882 4550 24402 134342 -0.0139

SIb0 b1 b2 b014 42 182 0.381042 182 882 -0.2321182 882 4550 0.0298

NOb0 b1 b2 b3 b4 b014 42 182 882 4550 0.493542 182 882 4550 24402 -0.7973182 882 4550 24402 134342 0.4072882 4550 24402 134342 753522 -0.0821

4550 24402 134342 753522 4285190 0.0057

POLINOMIOSk = 2 ŷij = 6.4726 + -1.3500 xᵢ +k = 3 ŷij = 6.3310 + -0.8778 xᵢ +k = 4 ŷij = 6.5423 + -2.9562 xᵢ +

SS u MS F251.4517 2 125.7258 1364.4664 4.74 Cierto

2.8155 4 0.7039 7.6389 4.12 Falso0.6450 7 0.0921

254.9121 13

SS u MS F

Fa F>Fa F<Fa

Fa F>Fa F<Fa

251.6925 3 83.8975 910.5155 4.35 Cierto2.5746 3 0.8582 9.3140 4.35 Falso0.6450 7 0.0921

254.9121 13

SS u MS F253.2214 4 63.3053 687.0347 4.12 Cierto

1.0458 2 0.5229 5.6748 4.74 Falso0.6450 7 0.0921

254.9121 13

Fa F>Fa F<Fa

b1 b2 b3-0.5099 0.1548 -0.0139 b0 = 6.33101.1581 -0.4524 0.0463 b1 = -0.8778-0.4524 0.1935 -0.0208 b2 = 0.32920.0463 -0.0208 0.0023 b3 = 0.0236

b1 b2-0.2321 0.0298 b0 = 6.47260.2321 -0.0357 b1 = -1.3500-0.0357 0.0060 b2 = 0.5417

b1 b2 b3 b4-0.7973 0.4072 -0.0821 0.0057 b0 =3.9836 -2.9347 0.7168 -0.0559 b1 =-2.9347 2.3742 -0.6098 0.0491 b2 =0.7168 -0.6098 0.1614 -0.0133 b3 =-0.0559 0.0491 -0.0133 0.0011 b4 =

0.5417 xᵢ²0.3292 xᵢ² + 0.0236 xᵢ³2.1551 xᵢ² + -0.4696 xᵢ³ +

ConclusiónLa regresión es suficiente Si NO hay falta de ajuste

Con falta de ajuste Se acepta el modelo propuesto

Conclusión

La regresión es suficiente Si NO hay falta de ajusteCon falta de ajuste Se acepta el modelo propuesto

ConclusiónLa regresión es suficiente Si NO hay falta de ajuste

Con falta de ajuste Se acepta el modelo propuesto

6.5423-2.95622.1551-0.46960.0411

0.0411 xᵢ^4

Sumatorias= 21.00 132.50 91.00 441.00 2275.00 12201.00xᵢ yᵢ xᵢ² xᵢ³ xᵢ^4 xᵢ^5

0

6.3

0 0 0 0

6.7

1

5.7

1 1 1 1

5.2

2

6.3

4 8 16 32

5.9

3

7.3

9 27 81 243

7.5

4

9.9

16 64 256 1024

10.5

5

12.5

25 125 625 3125

12.1

6

18.1

36 216 1296 7776

18.5

6 36 216 1296 7776

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

Sumatorias= 21 132.5 91 441 2275 12201

67171.00 376761.00 2142595.00 ### ### 503.90 2451.90xᵢ^6 xᵢ^7 xᵢ^8 xᵢ^9 xᵢ^10 xᵢyᵢ xᵢ²yᵢ

0 0 0 0 0

0 00 00 00 00 00 0

1 1 1 1 1

5.7 5.75.2 5.20 00 00 00 0

64 128 256 512 1024

12.6 25.211.8 23.6

0 00 00 00 0

729 2187 6561 19683 59049

21.9 65.722.5 67.5

0 00 00 00 0

4096 16384 65536 262144 1048576

39.6 158.442 1680 00 00 00 0

15625 78125 390625 1953125 9765625

62.5 312.560.5 302.5

0 00 00 00 0

46656 279936 1679616 10077696 60466176

108.6 651.6111 666

0 00 0

46656 279936 1679616 10077696 60466176

0 00 0

0 0 0 0 0

0 00 00 00 00 00 0

0 0 0 0 0

0 00 00 00 00 00 0

0 0 0 0 0

0 00 00 00 00 00 0

0 0 0 0 0

0 00 00 00 00 00 0

0 0 0 0 0

0 00 00 00 00 00 0

67171 376761 2142595 12313161 71340451 503.9 2451.9

12122.30 66747.90 375611.90 2144115.90 ### ###xᵢ³yᵢ xᵢ^4 yᵢ xᵢ^5 yᵢ xᵢ^6 yᵢ xᵢ^7 yᵢ xᵢ^8 yᵢ

0 0 0 0 0 00 0 0 0 0 00 0 0 0 0 00 0 0 0 0 00 0 0 0 0 00 0 0 0 0 0

5.7 5.7 5.7 5.7 5.7 5.75.2 5.2 5.2 5.2 5.2 5.20 0 0 0 0 00 0 0 0 0 00 0 0 0 0 00 0 0 0 0 0

50.4 100.8 201.6 403.2 806.4 1612.847.2 94.4 188.8 377.6 755.2 1510.4

0 0 0 0 0 00 0 0 0 0 00 0 0 0 0 00 0 0 0 0 0

197.1 591.3 1773.9 5321.7 15965.1 47895.3202.5 607.5 1822.5 5467.5 16402.5 49207.5

0 0 0 0 0 00 0 0 0 0 00 0 0 0 0 00 0 0 0 0 0

633.6 2534.4 10137.6 40550.4 162201.6 648806.40 0 0 0 0 00 0 0 0 0 00 0 0 0 0 00 0 0 0 0 00 0 0 0 0 0

1562.5 7812.5 39062.5 195312.5 976562.5 4882812.51512.5 7562.5 37812.5 189062.5 945312.5 4726562.5

0 0 0 0 0 00 0 0 0 0 00 0 0 0 0 00 0 0 0 0 0

3909.6 23457.6 140745.6 844473.6 5066841.6 30401049.63996 23976 143856 863136 5178816 31072896

0 0 0 0 0 00 0 0 0 0 0

0 0 0 0 0 00 0 0 0 0 00 0 0 0 0 00 0 0 0 0 00 0 0 0 0 00 0 0 0 0 00 0 0 0 0 00 0 0 0 0 00 0 0 0 0 00 0 0 0 0 00 0 0 0 0 00 0 0 0 0 00 0 0 0 0 00 0 0 0 0 00 0 0 0 0 00 0 0 0 0 00 0 0 0 0 00 0 0 0 0 00 0 0 0 0 00 0 0 0 0 00 0 0 0 0 00 0 0 0 0 00 0 0 0 0 00 0 0 0 0 00 0 0 0 0 00 0 0 0 0 00 0 0 0 0 00 0 0 0 0 00 0 0 0 0 00 0 0 0 0 00 0 0 0 0 00 0 0 0 0 0

12122.3 66747.9 375611.9 2144115.9 12363674.3 71832363.9

419783339.90 2464563747.90xᵢ^9 yᵢ xᵢ^10 yᵢ

0 00 00 00 00 00 0

5.7 5.75.2 5.20 00 00 00 0

3225.6 6451.23020.8 6041.6

0 00 00 00 0

143685.9 431057.7147622.5 442867.5

0 00 00 00 0

2595225.6 10380902.40 00 00 00 00 0

24414062.5 122070312.523632812.5 118164062.5

0 00 00 00 0

182406297.6 1094437785.6186437376 1118624256

0 00 0

0 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 0

419783339.9 2464563747.9