Ejercicio de Regresion Lineal Multiple

Probeta: Diametro: Altura: Área =

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

8 cm 16 cm 50.27 cm2

Presión de cámara σ3

Fuerza

Esfuerzo Desviador σd

Deformación

Kg/cm2 0.21 0.21 0.21 0.35 0.35 0.35 0.7 0.7 0.7 1.05 1.05 1.05 1.4 1.4 1.4

Kg 10.55 21.11 31.66 17.59 35.18 52.77 35.18 70.36 105.55 35.18 52.77 105.55 52.77 70.36 140.73

Kg/cm2 0.21 0.42 0.63 0.35 0.7 1.05 0.7 1.4 2.1 0.7 1.05 2.1 1.05 1.4 2.8

cm 0.00208696 0.00440367 0.00631579 0.00242424 0.00470588 0.00685714 0.00326531 0.00627451 0.0090566 0.00301887 0.00444444 0.00857143 0.00428571 0.00561404 0.01084746

Deformación Unitaria 0.000130435 0.0002752294 0.0003947369 0.000151515 0.0002941175 0.0004285713 0.0002040819 0.0003921569 0.0005660375 0.0001886794 0.0002777775 0.0005357144 0.0002678569 0.0003508775 0.0006779663

Modulo Resiliente

Primer Invariante ϴ

Log Mr

Log ϴ

Kg/cm2 1610 1526 1596 2310 2380 2450 3430 3570 3710 3710 3780 3920 3920 3990 4130

Kg/cm2 0.84 1.05 1.26 1.4 1.75 2.1 2.8 3.5 4.2 3.85 4.2 5.25 5.25 5.6 7

y 3.20682515 3.18355451 3.20303285 3.36361241 3.37657717 3.38916627 3.5352936 3.5526682 3.56937409 3.56937361 3.57749223 3.59328599 3.5932865 3.60097252 3.61594996

x -0.07572071 0.0211893 0.10037055 0.14612804 0.24303805 0.32221929 0.44715803 0.54406804 0.62324929 0.58546073 0.62324929 0.7201593 0.7201593 0.74818803 0.84509804

ϴ

Ʈ

ϴ

n 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Sumatoria

Xi -0.075720714 0.021189299 0.100370545 0.146128036 0.243038049 0.322219295 0.447158031 0.544068044 0.62324929 0.58546073 0.62324929 0.720159303 0.720159303 0.748188027 0.84509804 6.61401457

Yi 3.2068252 3.1835545 3.2030329 3.3636124 3.3765772 3.3891663 3.5352936 3.5526682 3.5693741 3.5693736 3.5774922 3.593286 3.5932865 3.6009725 3.61595 51.93047

β1 = ӯ= Ẋ= β0 =

0.525 3.462031 0.4409343

Xi^2 0.005734 0.000449 0.010074 0.021353 0.059067 0.103825 0.19995 0.29601 0.38844 0.342764 0.38844 0.518629 0.518629 0.559785 0.714191 4.12734

Yi^2 10.28372756 10.1350193 10.25941944 11.31388847 11.40127341 11.48644797 12.49830087 12.62145136 12.7404314 12.74042798 12.79845069 12.91170424 12.91170788 12.96700306 13.07509409 180.144348

Xi*Yi -0.242823 0.067457 0.32149 0.491518 0.820637 1.092055 1.580835 1.932893 2.22461 2.089728 2.229669 2.587738 2.587739 2.694205 3.055832 23.5336

+ *

0.525 ϴ

x ^

3.231

Y = β0 + β1*X + є Y= Mr =

3.23 1700.52

0.525

3.7 f(x) = 0.5249066395x + 3.2305816609 R² = 0.9282119683 3.6

3.5

3.4

3.3

3.2

3.1

3

2.9 -0.2

0

0.2

0.4

0.6

0.8

1

SECUENCIA DE ENSAYO 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Esfuerzo Confinamiento

Esfuerzo MODULO Desviador RESILIENTE

σ3

σd

PSI 3.02 3.01 3.01 5.01 5 5 10.02 10.01 10.01 15.03 15.03 15.03 20 20 20

PSI 3.13 6 9.1 5.24 10.2 15.22 10.27 20.29 30.42 10.47 15.48 30.64 15.76 20.27 40.21

TETA ϴ

PSI 22758 22085 23318 28464 30383 32507 44394 47361 47258 51209 52123 57798 61609 64428 70512

12.19 15.03 18.13 20.27 25.2 30.22 40.33 50.32 60.45 55.56 60.57 75.73 75.76 80.27 100.21

Esfuerzo Octoedral

τ

octoedral

1.47549615 2.82842712 4.28978114 2.47015969 4.80832611 7.17477681 4.84132443 9.56479773 14.3401255 4.93560533 7.29734198 14.4438345 7.42933525 9.55536964 18.9551758

Log

Log

Mr/Pa

ϴ/Pa

3.18993643 3.17689974 3.20049363 3.28709827 3.31543299 3.34477923 3.48012661 3.5082232 3.50727767 3.54214863 3.54983174 3.59471514 3.62244649 3.64187698 3.68106537

-0.08119396 0.00976131 0.09120014 0.13965608 0.23420288 0.31309679 0.43843056 0.53454297 0.61419864 0.57756457 0.61505991 0.71207029 0.7122423 0.7373556 0.8337134

Log

τ

octoedral

/Pa

0.04155119 0.07644492 0.11122966 0.06747422 0.12293217 0.17266555 0.12366631 0.21770652 0.29574025 0.12575704 0.17509257 0.29728867 0.17769121 0.21753771 0.35980193

Observación Número 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 SUMA

x1

x2

x3

x4

-0.08119396 0.00976131 0.09120014 0.13965608 0.23420288 0.31309679 0.43843056 0.53454297 0.61419864 0.57756457 0.61505991 0.71207029 0.7122423 0.7373556 0.8337134 6.4819015

0.0415511932 0.0764449249 0.1112296607 0.0674742176 0.1229321707 0.17266555 0.1236663111 0.2177065162 0.2957402516 0.1257570427 0.1750925742 0.2972886702 0.1776912128 0.21753771 0.3598019322 2.5825799384

0

0

MATRIZ

n

 x1

 x2  x3  x4

 x5 15.00 6.48 2.58 0.00 0.00 0.00

 x2  x1 x 2

 x1

 x12  x1 x 2  x1 x 3  x1 x 4  x1 x 5

 x22

 x 2 x3  x2 x4  x 2 x5 6.48 4.01 1.43 0.00 0.00 0.00

MATRIZ 2.58 1.43 0.56 0.00 0.00 0.00

 x3  x1 x 3  x 2 x3  x32

 x3 x 4  x3 x5 0.00 0.00 0.00 0.00 0.00 0.00

MATRIZ INVERSA (Esta matriz inversa se calcula con la función MINVERSA(B40:G45) luego das F2 y después Ctrl+Shift+Enter 0.31957839

0.0734454764 -1.65328556

#N/A

0.07344548

2.7266613395 -7.27010693

#N/A

-1.65328556

-7.2701069263 27.8494381

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Ecuación de regresión múltiple resultante Y = β0 + β1x1 + β2x2 + β3x3 +β4 y= Observación Número 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Suma =

Pronósticos Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y

= = = = = = = = = = = = = = =

Promedio de los cuadrados =

0.00052762

Error típico de la regresión =

0.02297

3.14011675 3.19022875 3.23403513 3.27943484 3.32576989 3.36339682 3.46157323 3.49737678 3.52702127 3.55361470 3.56378792 3.59174309 3.62773561 3.63250852 3.65400881

Residuos u

u2

0.04981968 -0.01332902 -0.0335415 0.00766343 -0.0103369 -0.0186176 0.01855338 0.01084642 -0.01974359 -0.01146607 -0.01395618 0.00297206 -0.00528912 0.00936846 0.02705655

0.002482 0.00017766 0.00112503 5.8728E-005 0.00010685 0.00034661 0.00034423 0.00011764 0.00038981 0.00013147 0.00019478 8.8331E-006 2.7975E-005 8.7768E-005 0.00073206 0.0063315

x5

y

x1^2

x2^2

0

3.18993643 3.17689974 3.20049363 3.28709827 3.31543299 3.34477923 3.48012661 3.5082232 3.50727767 3.54214863 3.54983174 3.59471514 3.62244649 3.64187698 3.68106537 51.642352

0.0066 1E-004 0.0083 0.0195 0.0549 0.098 0.1922 0.2857 0.3772 0.3336 0.3783 0.507 0.5073 0.5437 0.6951 4.0076

0.001727 0.005844 0.012372 0.004553 0.015112 0.029813 0.015293 0.047396 0.087462 0.015815 0.030657 0.088381 0.031574 0.047323 0.129457 0.56278

 x4  x1 x 4  x2 x4  x3 x 4  x42

 x 4 x5 0.00 0.00 0.00 0.00 0.00 0.00

 x5

*

 x5 2

0.00 -1 0.00 0.00 0.00 * 0.00 0.00

x4^2

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

51.64235 23.02517 9.065714 0 0 0

x5^2

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

y

-1

 x1 x 5  x 2 x5  x3 x5  x 4 x5

x3^2

 x1 y

 x2 y  x3 y  x4 y  x5 y

0

x1x2 0 -0.0033737 0 0.0007462 0 0.0101442 0 0.0094232 0 0.0287911 0 0.054061 0 0.0542191 0 0.1163735 0 0.1816433 0 0.0726328 0 0.1076924 0 0.2116904 0 0.1265592 0 0.1604026 0 0.2999717 1.430977

e calcula con la función pués Ctrl+Shift+Enter #N/A

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51.64235

3.2067

#N/A

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23.02517

0.666

#N/A

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0

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0

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0

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últiple resultante β3x3 +β4x4 +β5x5

*

9.065714

=

β0 = β1 = β2 = β3 = β4 = β5 =

-0.300

Hugo: Esta columna es el resultado de la MMU seleccionas el espacio presionas F2 y l

��=( 〖 10 〗 ^�� ) ∗��∗(�/��)^β1∗(�/��+1)^�2 20291.512

x1x3

x1x4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0

x1x5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0

x2x3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0

x2x4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0

x2x5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0

x3x4 x3x5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

3.207

1609.3852

0.666 -0.300 #N/A #N/A #N/A

es el resultado de la MMULT(B40:G45; I40:I45) y luego el espacio presionas F2 y luego Ctrl+shift+enter

x4x5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

x1y

x2y

-0.259 0.03101 0.29189 0.45906 0.77648 1.04724 1.52579 1.8753 2.15417 2.04582 2.18336 2.55969 2.58006 2.68536 3.06895 23.025

0.132546 0.242858 0.35599 0.221794 0.407573 0.577528 0.430374 0.763763 1.037243 0.44545 0.621549 1.068668 0.643677 0.792246 1.324454 9.06571

x3y

x4y 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0

x5y 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

Resumen Estadísticas de la regresión Coeficiente de correlación múltiple Coeficiente de determinación R^2 R^2 ajustado Error típico Observaciones

0.99254685 0.98514925 0.98267412 0.02297 15

ANÁLISIS DE VARIANZA Regresión Residuos Total

Intercepción Variable X 1 Variable X 2

Grados de libertadSuma 2 12 14 Coeficientes 3.20666 0.6660389 -0.29998934

de cuadrados 0.4200072002 0.0063314506 0.4263386509

Error típico 0.0129852313 0.0379294539 0.1212185846

Promedio de los cuadrados F Valor crítico de F 0.2100036001 398.019876 1.072731697E-011 0.0005276209

Estadístico t 246.9466992448 17.5599391676 -2.4747800869

Probabilidad 1.3082E-023 6.3347E-010 0.02923637

Inferior 95% Superior 95%Inferior 95.0% 3.1783676127 3.23495239 3.17836761 0.5833977224 0.74868008 0.58339772 -0.5641019464 -0.03587673 -0.56410195

Superior 95.0% 3.23495239 0.74868008 -0.03587673

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