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Ejercicio de Regresion Lineal Multiple
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Ejercicio de Regresion Lineal Multiple
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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
#N/A
#N/A
#N/A
#N/A
#N/A
#N/A
#N/A
#N/A
#N/A
#N/A
#N/A
#N/A
#N/A
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
#N/A
51.64235
3.2067
#N/A
#N/A
23.02517
0.666
#N/A
#N/A
#N/A
#N/A
0
#N/A
#N/A
#N/A
0
#N/A
#N/A
#N/A
0
#N/A
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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