Url Ei2c15 Clase 11 e6 Regresión Ventas (Soln 2c15)

MES VENTAS1 2262 1,5893 3,3834 4,9305 12,4036 17,9897 20,5008 25,7489 24,262

10 29,93611 29,48912 30,07413 32,12414 33,21015 32,27716 36,15217 36,37718 33,92819 36,28520 34,86421 34,63522 34,86023 37,90524 35,865

OPCIONESA)

1) POLINÓMICA2) LOGARÍTMICA

B) POR SIMILITUD CON GRÁFICOS NO LINEALES3) INVERSA Y EXPONENCIAL

** COMENZAR CON LINEAL PORQUE LO PIDE EL ENUNCIADO DEL CASO

POR R2 EN DIAGRAMA DE DISPERSIÓN

AUNQUE SU R2 NO SEA MUY ALTO

0 5 10 15 20 25 300

5,000

10,000

15,000

20,000

25,000

30,000

35,000

40,000

GRÁFICA DATOS ORIGINALES

0 5 10 15 20 25 300

5,000

10,000

15,000

20,000

25,000

30,000

35,000

40,000f(x) = 3584.23197729482 exp( 0.129363719924764 x )R² = 0.535426084919673f(x) = 1570.29467391304 x + 6163.30615942029R² = 0.805533189791476f(x) = 14377.8067282347 ln(x) − 7028.18753936227

R² = 0.93151360926738f(x) = 0.0124666 x⁶ − 1.02205 x⁵ + 32.837 x⁴ − 515.395 x³ + 3865.06 x² − 8721.29 x + 5997.59R² = 0.988859581349932

f(x) = 735.676832696479 x^1.40209365452216R² = 0.867583691815373

Column CExponential (Column C)Linear (Column C)Logarithmic (Column C)Polynomial (Column C)Power (Column C)

POR SIMILITUD CON GRÁFICOS NO LINEALES


0 5 10 15 20 25 300

5,000

10,000

15,000

20,000

25,000

30,000

35,000

40,000

GRÁFICA DATOS ORIGINALES

0 5 10 15 20 25 300

5,000

10,000

15,000

20,000

25,000

30,000

35,000

40,000f(x) = 3584.23197729482 exp( 0.129363719924764 x )R² = 0.535426084919673f(x) = 1570.29467391304 x + 6163.30615942029R² = 0.805533189791476f(x) = 14377.8067282347 ln(x) − 7028.18753936227

R² = 0.93151360926738f(x) = 0.0124666 x⁶ − 1.02205 x⁵ + 32.837 x⁴ − 515.395 x³ + 3865.06 x² − 8721.29 x + 5997.59R² = 0.988859581349932

f(x) = 735.676832696479 x^1.40209365452216R² = 0.867583691815373

Column CExponential (Column C)Linear (Column C)Logarithmic (Column C)Polynomial (Column C)Power (Column C)

Resumen

Estadísticas de la regresiónCoeficiente de correlación múltiple 0.8975150081

Coeficiente de determinación R^2 0.8055332R^2 ajustado 0.7966937893Error típico 5,578.27298Observaciones 24

ANÁLISIS DE VARIANZAGrados de libertadSuma de cuadradosPromedio de los cuadrados

Regresión 1 2835699167 2835699167Residuos 22 684576848 31117129.4Total 23 3520276015

Coeficientes Error típico Estadístico tIntercepción 6163.3061594 2350.40803 2.62222818Variable X 1 1570.2946739 164.494296 9.54619529

Y = 6,163.3016 + 1,570.2947X

Análisis de los residuales

Observación Pronóstico para Y Residuos DATOS ORIG1 7,733.60083 -7508.10083 2262 9,303.89551 -7715.14551 1,5893 10,874.19018 -7491.69018 3,3834 12,444.48486 -7514.23486 4,9305 14,014.77953 -1612.27953 12,4036 15,585.07420 2403.6758 17,9897 17,155.36888 3344.63112 20,5008 18,725.66355 7022.33645 25,7489 20,295.95822 3965.79178 24,262

10 21,866.25290 8069.9971 29,93611 23,436.54757 6052.70243 29,48912 25,006.84225 5066.65775 30,07413 26,577.13692 5546.36308 32,12414 28,147.43159 5062.56841 33,21015 29,717.72627 2559.52373 32,27716 31,288.02094 4863.72906 36,15217 32,858.31562 3518.93438 36,37718 34,428.61029 -501.11029 33,92819 35,998.90496 286.095036 36,28520 37,569.19964 -2704.94964 34,86421 39,139.49431 -4504.74431 34,63522 40,709.78899 -5849.53899 34,86023 42,280.08366 -4375.58366 37,90524 43,850.37833 -7985.62833 35,865

F Valor crítico de F91.1298445 2.79114E-09

Probabilidad Inferior 95% Superior 95%Inferior 95.0%Superior 95.0%0.01555906 1288.85825 11037.7541 1288.85825 11037.7541

2.79114E-09 1229.15438 1911.43496 1229.15438 1911.43496

MENOR A 0.05: VÁLIDO

CALCULADO MAPE

7508.100833 3329.53%

7715.145507 485.61%

7491.690181 221.48%

7514.234855 152.41%

1612.279529 13.00%

2403.675797 13.36%

3344.631123 16.32%

7022.336449 27.27%

3965.791775 16.35%

VALOR ABSOLUTO RESIDUOS

VALOR ABS/REAL

8069.997101 26.96%

6052.702428 20.53%

5066.657754 16.85%

5546.36308 17.27%

5062.568406 15.24%

2559.523732 7.93%

4863.729058 13.45%

3518.934384 9.67%

501.1102899 1.48%

286.0950362 0.79%

2704.949638 7.76%

4504.744312 13.01%

5849.538986 16.78%

4375.583659 11.54%

7985.628333 22.27%

MAPE 186.54%

MES VENTAS1 2262 1,5893 3,3834 4,9305 12,4036 17,9897 20,5008 25,7489 24,262

10 29,93611 29,48912 30,07413 32,12414 33,21015 32,27716 36,152

17 36,377

18 33,92819 36,28520 34,864

21 34,635

22 34,860

23 37,90524 35,865

GRÁFICA TIPO (e)

LA ECUACIÓNY= Bo + B1 (lnX )

CONVERTIR (X,Y) EN: (LN X,Y)NOS DARÁ LA INFORMACIÓN PARA LA ECUACIÓN: Y´= Bo´ + B1´(LNX)

0 5 10 15 20 25 300

5,00010,00015,00020,00025,00030,00035,00040,000 GRÁFICA DATOS ORIGINALES

X Y

MES VENTAS LN(X)

1 226 0.000000000

2 1,589 0.693147181

3 3,383 1.098612289

4 4,930 1.3862943615 12,403 1.6094379126 17,989 1.7917594697 20,500 1.9459101498 25,748 2.0794415429 24,262 2.197224577

10 29,936 2.30258509311 29,489 2.39789527312 30,074 2.48490665013 32,124 2.56494935714 33,210 2.63905733015 32,277 2.70805020116 36,152 2.77258872217 36,377 2.83321334418 33,928 2.89037175819 36,285 2.94443897920 34,864 2.99573227421 34,635 3.04452243822 34,860 3.09104245323 37,905 3.13549421624 35,865 3.178053830

Resumen LOGARÍTMICA

Estadísticas de la regresiónCoeficiente de correlación múlti 0.9651495268959

Coeficiente de determinación R 0.93151360927 VER "DISPERSIÓN (24 DATOS) MISMA R2 QUE LOGARÍTMICA

R^2 ajustado 0.928400591506807

Error típico 3,310.389971

Observaciones 24

ANÁLISIS DE VARIANZAGrados de libertad Suma de cuadrados

Regresión 1 3279185016Residuos 22 241090998.7Total 23 3520276015

Coeficientes Error típicoIntercepción -7028.18753936229 2014.045046

Variable X 1 14377.8067282347 831.1680458

Y´= Bo´ + B1´(LNX)

Y´= -7,028.187539 + 14,377.80673(LNX)Análisis de los residuales

Observación Pronóstico para Y Residuos1 -7,028.187539 7253.687539

2 2,937.748657 -1348.9986573 8,767.447616 -5384.9476164 12,903.684853 -7973.4348535 16,111.999707 -3709.4997076 18,733.383813 -744.6338127

7 20,949.732494 -449.73249438 22,869.621050 2878.378959 24,563.082772 -301.3327721

10 26,077.935903 3858.31409711 27,448.287247 2040.96275312 28,699.320009 1374.179991

13 29,850.158590 2273.3414114 30,915.668691 2294.33130915 31,907.634862 369.615137616 32,835.557246 3316.19275417 33,707.206341 2670.04365918 34,529.018968 -601.518968419 35,306.387026 978.612973820 36,043.872099 -1179.62209921 36,745.367650 -2110.6176522 37,414.223444 -2553.97344423 38,053.342295 -148.842294824 38,665.256205 -2800.506205

Y= Bo + B1 (lnX )

CONVERTIR (X,Y) EN: (LN X,Y)NOS DARÁ LA INFORMACIÓN PARA LA ECUACIÓN:

0 5 10 15 20 25 300


LN(X) = VALOR AL QUE HAY QUE ELEVAR ePARA OBTENER EL NÚMERO X

Y e= 2.7183226 EXCEL: =LN(X) 1

1,589 2.000

3,383 3.0004,930

12,40317,98920,50025,74824,26229,93629,48930,07432,12433,21032,27736,15236,37733,92836,28534,86434,63534,86037,90535,865

e0 = 1e0.6931 = 2e1.09861 = 3

VER "DISPERSIÓN (24 DATOS) MISMA R2 QUE LOGARÍTMICA

Promedio de los cuadrados F Valor crítico de F3279185016 299.2317040606 2.70101E-14

10958681.757

Estadístico t Probabilidad Inferior 95% Superior 95%Inferior 95.0%-3.489588058 0.002075282203 -11205.0613 -2851.313762 -11205.0613

17.298315064 2.701012E-14 12654.0697 16101.54375 12654.0697

MENOR A 0.05: VÁLIDO

Y´= -7,028.187539 + 14,377.80673(LNX)

CALCULADO MAPE

DATOS ORIG226 7253.6875393623 3216.71% Y´= -7,028.187539 + 14,377.80673(LNX)

1,589 1348.9986569494 84.91% CON X = 1 (CELDA A39)3,383 5384.9476163713 159.20%

4,930 7973.4348532611 161.72%

12,403 3709.4997067087 29.91%

17,989 744.63381268302 4.14%

20,500 449.73249426532 2.19%

25,748 2878.3789504273 11.18%

24,262 301.33277210498 1.24%

29,936 3858.3140969796 12.89%

29,489 2040.9627525198 6.92%

30,074 1374.1799910053 4.57%


VALOR ABS/REAL

32,124 2273.3414100706 7.08%

33,210 2294.331309423 6.91%

32,277 369.61513755769 1.15%

36,152 3316.1927541156 9.17%

36,377 2670.0436586666 7.34%

33,928 601.51896841664 1.77%

36,285 978.61297382663 2.70%

34,864 1179.622099332 3.38%

34,635 2110.617649999 6.09%

34,860 2553.9734437919 7.33%

37,905 148.84229476472 0.39%

35,865 2800.5062053064 7.81%

MAPE 156.53%LOGARÍTMICA

LN(X) = VALOR AL QUE HAY QUE ELEVAR e

Superior 95.0%-2851.313762

16101.54375

Y´= -7,028.187539 + 14,377.80673(LNX)

-7028.187539CELDA B88

GRÁFICA TIPO (i)LA ECUACIÓN ES: Y=EXP (Bo + B1/X )

CONVERTIR (X,Y) EN: (1/X, LN Y)NOS DARÁ LA INFORMACIÓN PARA LA ECUACIÓN:

X Y 1/XMES VENTAS 1/MES

1 226 1.0000000002 1,589 0.5000000003 3,383 0.333333333

Y´=EXP (Bo + B1´/X + SE2/2)

0 5 10 15 20 25 300


4 4,930 0.2500000005 12,403 0.2000000006 17,989 0.1666666677 20,500 0.1428571438 25,748 0.1250000009 24,262 0.111111111

10 29,936 0.10000000011 29,489 0.09090909112 30,074 0.08333333313 32,124 0.07692307714 33,210 0.07142857115 32,277 0.06666666716 36,152 0.06250000017 36,377 0.05882352918 33,928 0.05555555619 36,285 0.05263157920 34,864 0.05000000021 34,635 0.04761904822 34,860 0.04545454523 37,905 0.04347826124 35,865 0.041666667

Resumen INVERSA Y EXPONENCIAL

Estadísticas de la regresiónCoeficiente de correlación múlti 0.976967083952055

Coeficiente de determinación R 0.95446468312578 ´C69/C71R^2 ajustado 0.952394895995136

Error típico 0.272756113843RAIZ(C70/B70)

Observaciones 24

SE = STD ERRORANÁLISIS DE VARIANZA

Grados de libertad

Regresión 1 34.3070337111Residuos 22 1.63670974806Total 23 35.9437434591

VER M110Coeficientes Error típico

Intercepción 10.71827764756 0.07016446311

1/MES -5.828019956949 0.27139631074

Y=EXP (10.7555 - 5.8280/X)

ESTO ES LO QUE NOS DA EXCEL (SÓLO SE COPIÓ PARTE)Análisis de los residuales

Observación Pronóstico para Y Residuos1 4.8902576906084 0.528062468332 7.80426766908274 -0.4335648466

23 10.4648854755158 0.0779396420224 10.4754434826842 0.01206671527

????????

ESTO SUCEDE PORQUE EXCEL HACE LOS PRONÓSTICOS EN BASE A LA FÓRMULA Y = a + bx

Por ejemplo, para el primer pronóstico: Y = 10.7183 - 5.8280(1) =

Suma de cuadrados

Y´=EXP (Bo + B1´/X + SE2/2)Y=EXP (10.71827765 - 5.828019957/X + 0.5*0.2727561142)

ERROR TÍPICO Y R 2 CON INVERSA Y EXPONENCIAL

POR LO ANTERIOR, hay que calcular los residuos con la fórmula de la INVERSA Y EXPONENCIAL

CÁLCULO DE MAPE Análisis de los residuales

ObservaciónDATOS ORIG

1 138.03400 226

2 2,544.01800 1,589

3 6,719.93213 3,383

4 10,921.62448 4,930

5 14,616.40782 12,403

6 17,750.45923 17,989

7 20,392.62452 20,500

8 22,629.28177 25,748

9 24,537.17134 24,262

10 26,178.66382 29,936

11 27,603.05732 29,489

12 28,849.07859 30,074

13 29,947.23587 32,124

14 30,921.72486 33,210

15 31,791.89515 32,277

16 32,573.35820 36,152

17 33,278.82110 36,377

18 33,918.71555 33,928

19 34,501.67518 36,285

20 35,034.90047 34,864

21 35,524.44004 34,635

22 35,975.40930 34,860

PRONÓSTICO CON LA FÓRMULA (CELDA B79)

23 36,392.16181 37,905

24 36,778.42469 35,865

Observación

DATOS ORIG

1 138.03400 2262 2,544.01800 1,5893 6,719.93213 3,3834 10,921.62448 4,9305 14,616.40782 12,4036 17,750.45923 17,9897 20,392.62452 20,5008 22,629.28177 25,7489 24,537.17134 24,262

10 26,178.66382 29,93611 27,603.05732 29,48912 28,849.07859 30,07413 29,947.23587 32,12414 30,921.72486 33,21015 31,791.89515 32,27716 32,573.35820 36,15217 33,278.82110 36,37718 33,918.71555 33,92819 34,501.67518 36,28520 35,034.90047 34,864

CÁLCULO DEL ERROR TÍPICO Y R2

PRONÓSTICO CON LA FÓRMULA (CELDA B79)

21 35,524.44004 34,63522 35,975.40930 34,86023 36,392.16181 37,90524 36,778.42469 35,865

PROM DATOS ORIGINALES 25,792

Coeficiente de determinación R^2 0.998217281006 ´C166/C168R^2 ajustado

Error típico 482.4243225938RAIZ(C167/B167)

Observaciones 24

ANÁLISIS DE VARIANZA

Grados de libertad

Regresión 1 ###Residuos 22 5120130.99466Total 23 ###

Suma de cuadrados

LN (Y)ln (VENTAS)

5.41832015894277.37070282250378.1263703600449

0 5 10 15 20 25 300


8.50314497569029.42565334417529.79750184148449.928180165126510.15611223317310.09665631509810.30682539962810.29178106913610.311399664287

10.377343128510.41060631437110.38211792668510.49548063582

10.50169885823110.43198117395610.49915971171210.45921722787910.45261279229910.45910249059210.54282511753110.487510197952

SUMA DE LOS CUADRADOS DE LA REGRESIÓN ENTRE EL TOTAL DE LOS CUADRADOS

RAIZ(SUMA DE RESIDUOS AL CUADRADO/GL)

F Valor crítico de F

34.30703371109 461.1414715038 2.9983883E-160.074395897639

Estadístico t Probabilidad Inferior 95% Superior 95% Inferior 95.0%

152.75934813911 8.708814782E-35 10.5727654572 10.8637898379 10.57276546

-21.474204793281 2.998388318E-16 -6.3908614565 -5.26517845738 -6.39086146VÁLIDO

10.75547559638

Y = 10.7182-5.8280X

IMPORTANTE: X LINEALIZADO ES 1/XESTO ES LO QUE NOS DA EXCEL (SÓLO SE COPIÓ PARTE)

COMPARANDO CON DATOS HISTÓRICOS DE "Y"Y (HISTÓRICO)

2261,589

37,90535,865

????????

ESTO SUCEDE PORQUE EXCEL HACE LOS PRONÓSTICOS EN BASE A LA FÓRMULA Y = a + bx

4.8902576906084 VER B87

Promedio de los cuadrados

Y=EXP (10.71827765 - 5.828019957/X + 0.5*0.2727561142) SE2 = ERROR TÍPICO2

POR LO ANTERIOR, hay que calcular los residuos con la fórmula de la INVERSA Y EXPONENCIAL

CALCULADO MAPE

VALOR ABS/REAL

-87 87.466004365051 38.79%

955 955.26800023741 60.13%

3337.4321271072 3337.4321271072 98.67%

5991.3744784742 5991.3744784742 121.52%

2213.907820476 2213.907820476 17.85%

-238.29077026439 238.29077026439 1.32%

-107.37547783848 107.37547783848 0.52%

-3118.7182337443 3118.7182337443 12.11%

275.4213434841 275.4213434841 1.14%

-3757.5861790655 3757.5861790655 12.55%

-1886.1926759251 1886.1926759251 6.40%

-1224.4214139796 1224.4214139796 4.07%

-2176.2641331851 2176.2641331851 6.77%

-2288.2751411318 2288.2751411318 6.89%

-485.35485381492 485.35485381492 1.50%

-3578.3918035481 3578.3918035481 9.90%

-3098.4289013841 3098.4289013841 8.52%

-8.7844475086313 8.7844475086313 0.03%

-1783.3248161338 1783.3248161338 4.91%

170.65047255102 170.65047255102 0.49%

889.69004198747 889.69004198747 2.57%

1115.1593019672 1115.1593019672 3.20%

RESIDUOS CON FÓRMULA


-1512.3381861665 1512.3381861665 3.99%

### 913.67469147391 2.55%

MAPE 17.77%

ERROR TÍPICO

-87 7650.301919587 -25,653.95559 658,125,437.3955 912536.9522776 -23,247.97158 540,468,182.7

3337.4321271072 11138453.20305 -19,072.05746 363,743,375.65991.3744784742 35896568.14131 -14,870.36510 221,127,758.42213.907820476 4901387.837565 -11,175.58176 124,893,627.7

-238.29077026439 56782.4911932 -8,041.53035 64,666,210.4-107.37547783848 11529.49324104 -5,399.36506 29,153,143.1-3118.7182337443 9726403.421489 -3,162.70782 10,002,720.7275.4213434841 75856.91644658 -1,254.81824 1,574,568.8

-3757.5861790655 14119453.8931 386.67424 149,517.0-1886.1926759251 3557722.810714 1,811.06774 3,279,966.4-1224.4214139796 1499207.799012 3,057.08900 9,345,793.2-2176.2641331851 4736125.577388 4,155.24628 17,266,071.7-2288.2751411318 5236203.121522 5,129.73528 26,314,184.0-485.35485381492 235569.3341217 5,999.90556 35,998,866.8-3578.3918035481 12804887.8997 6,781.36861 45,986,960.3-3098.4289013841 9600261.656933 7,486.83152 56,052,646.1-8.7844475086313 77.1665180319 8,126.72597 66,043,675.0-1783.3248161338 3180247.399839 8,709.68560 75,858,623.3170.65047255102 29121.58378189 9,242.91089 85,431,401.7

NO SE CALCULA EL MAPE CON LOS RESIDUOS QUE DA EXCEL

RESIDUOS CON FÓRMULA

RESIDUOS AL CUADRADO

DIF PRONÓSTICO Y PROMEDIO DE LOS DATOS ORIGINALES = "DIF"

"DIF"2

889.69004198747 791548.3708117 9,732.45046 94,720,591.91115.1593019672 1243580.268764 10,183.41972 103,702,037.2-1512.3381861665 2287166.789337 10,600.17223 112,363,651.3

### 834801.4418399 10,986.43511 120,701,756.45120130.994662 2,866,970,766.9 EN LUGAR DE C69

EN LUGAR DE C70 SUMA CUADRADOS REGRESIÓN

PROMEDIO DE PRONÓSTICOS AL CUADRADO

RAIZ(C167/B167)

Superior 95.0%

10.86378984

-5.26517846

1: CELDA C32

Y = 10.7182-5.8280X Y = 10.7182-5.8280 (1) = 4.890257691

IMPORTANTE: X LINEALIZADO ES 1/X CELDA H86

Y 1/X LN (Y)VENTAS 1/MES ln (VENTAS)

226 1.000000000 5.418320159

SUMA CUADRADOS REGRESIÓN

Y 1/X LN (Y)VENTAS 1/MES ln (VENTAS)

226 1.000000000 5.418320159

POLINOMIAL GRADO 6:DIAGRAMA DISPERSIÓN:

CONVERSIÓN PARA REGRESIÓNObservación

1 1 12 2 43 3 94 4 165 5 256 6 367 7 498 8 649 9 81

10 10 10011 11 12112 12 14413 13 16914 14 19615 15 22516 16 25617 17 28918 18 32419 19 36120 20 40021 21 44122 22 48423 23 52924 24 576

CORRIENDO LA REGRESIÓN LINEAL MÚLTIPLEResumen

y = 0.00125x6 - 1.0221x5 + 32.837x4 - 515.39x3 + 3965.1x2 - 8721.3x + 5997.6

X1 X2

Estadísticas de la regresiónCoeficiente de correlación 0.99441419Coeficiente de determina 0.9888595813R^2 ajustado 0.9849276689

Error típico 1,518.85Observaciones 24

ANÁLISIS DE VARIANZAGrados de libertad

Regresión 6Residuos 17Total 23

CoeficientesIntercepción 5997.5861352Variable X 1 -8721.285698Variable X 2 3865.0599362Variable X 3 -515.3947578Variable X 4 32.837023164Variable X 5 -1.02205085Variable X 6 0.0124665682

IGUAL A LA FÓRMULA QUE NOS DIO DISPERSIÓN


Observación Pronóstico para Y1 657.793052 385.581033 3,124.138654 7,378.898755 12,117.332036 16,677.71679

y = 0.00125x6 - 1.0221x5 + 32.837x4 - 515.39x3 + 3965.1x2 - 8721.3x + 5997.6

7 20,686.884478 23,986.941179 26,570.96507

10 28,527.6798311 29,995.1038512 31,123.1755013 32,045.3543114 32,859.1980115 33,615.9155416 34,318.8960317 34,931.2136518 35,392.1083919 35,642.4428020 35,659.1346921 35,498.5656322 35,348.9655323 35,591.7731024 36,871.97213

FÓRMULA COPIADA DEL DIAGRAMA DE DISPERSIÓN

1 1 1 18 16 32 64 ´= POTENCIA (A8,2)

27 81 243 72964 256 1024 4096

125 625 3125 15625216 1296 7776 46656343 2401 16807 117649512 4096 32768 262144729 6561 59049 531441

1000 10000 100000 10000001331 14641 161051 17715611728 20736 248832 29859842197 28561 371293 48268092744 38416 537824 75295363375 50625 759375 113906254096 65536 1048576 167772164913 83521 1419857 241375695832 104976 1889568 340122246859 130321 2476099 470458818000 160000 3200000 640000009261 194481 4084101 85766121

10648 234256 5153632 11337990412167 279841 6436343 14803588913824 331776 7962624 191102976

CORRIENDO LA REGRESIÓN LINEAL MÚLTIPLE

+ 32.837x4 - 515.39x3 + 3965.1x2 - 8721.3x + 5997.6

X3 X4 X5 X6

1,518.85 SUMA DE RESIDUOS AL CUADRADO/GLD45/C45

Suma de cuadradosPromedio de los cuadrados F Valor crítico de F3481058666.4883 580176444 251.495828104 1.22418E-15

39,217,348.57 2306902.863520276015.0599

VER H86Error típico Estadístico t Probabilidad Inferior 95% Superior 95%

3901.2977243896 1.53733105 0.14261591342 -2233.43258 14228.60484792633852.77366602 -2.26363821 0.03696904462 -16849.9276 -592.643799654881

1242.4701411547 3.11078698 0.00635588109 1243.677077 6486.44279497771179.22843450733 -2.87563053 0.01049017551 -893.533701 -137.25581464674612.784447481855 2.56851328 0.01993499013 5.864196712 59.80984961485070.4407900993943 -2.31867923 0.03312682202 -1.95203667 -0.09206503181115330.0058595264762 2.12757264 0.04830541915 0.000104048 0.0248290884282359

IGUAL A LA FÓRMULA QUE NOS DIO DISPERSIÓN

CALCULADO MAPE

Residuos DATOS ORIG-432.29305445113 226 432.293054451 191.70% 186,877.281203.1689745368 1,589 1203.16897454 75.73% 1,447,615.58258.36134508274 3,383 258.361345083 7.64% 66,750.58

-2448.6487477385 4,930 2448.64874774 49.67% 5,995,880.69285.16797212639 12,403 285.167972126 2.30% 81,320.77

1311.033211878 17,989 1311.03321188 7.29% 1,718,808.08

+ 32.837x4 - 515.39x3 + 3965.1x2 - 8721.3x + 5997.6


VALOR ABS/REAL RESIDUOS2

-186.8844690632 20,500 186.884469063 0.91% 34,925.801761.0588329185 25,748 1761.05883292 6.84% 3,101,328.21

-2309.2150714876 24,262 2309.21507149 9.52% 5,332,474.251408.570169263 29,936 1408.57016926 4.71% 1,984,069.92

-505.85384774432 29,489 505.853847744 1.72% 255,888.12-1049.6755042971 30,074 1049.6755043 3.49% 1,101,818.66

78.14568543715 32,124 78.1456854371 0.24% 6,106.75350.80199230363 33,210 350.801992304 1.06% 123,062.04

-1338.6655395407 32,277 1338.66553954 4.15% 1,792,025.431832.8539665715 36,152 1832.85396657 5.07% 3,359,353.661446.0363499226 36,377 1446.03634992 3.98% 2,091,021.13

-1464.6083865833 33,928 1464.60838658 4.32% 2,145,077.73642.55719549005 36,285 642.55719549 1.77% 412,879.75

-794.88468707915 34,864 794.884687079 2.28% 631,841.67-863.81562544717 34,635 863.815625447 2.49% 746,177.43

-488.7155340942 34,860 488.715534094 1.40% 238,842.872312.7269047021 37,905 2312.7269047 6.10% 5,348,705.74

-1007.2221327045 35,865 1007.2221327 2.81% 1,014,496.42

MAPE 16.55% 39,217,348.57

MES VENTAS1 2262 1,5893 3,3834 4,9305 12,4036 17,9897 20,5008 25,7489 24,262

10 29,93611 29,48912 30,07413 32,12414 33,21015 32,27716 36,15217 36,37718 33,92819 36,28520 34,86421 34,63522 34,86023 37,90524 35,865

Inferior 95.0%Superior 95.0%-2233.43258 14228.6048-16849.9276 -592.64381243.67708 6486.44279

-893.533701 -137.2558155.86419671 59.8098496

-1.95203667 -0.092065030.00010405 0.02482909

SUMATORIA

RESUMEN DE LAS OPCIONES DE PRONÓSTICO

TODAS LAS OPCIONESFÓRMULA

POLINOMIAL y = 0.0125x6 - 1.0221x5 + 32.837x4 - 515.39x3 + 3865.1x2 - 8721.3x + 5997.6

INVERSA Y LN Y=EXP (10.7555 - 5.8280/X)LOGARÍTMICA Y = -7,028.1875 + 14,377.8067 (LNX)LINEAL Y = 6,163.3016 + 1,570.2947X

PROYECCIONES MESES 25 Y 40

USANDO LAS 2 MEJORES Y LA LINEAL

0 5 10 15 20 25 300 Column C

POLINOMIAL INV Y LNPROYECCION MES 25 40,177.40 37,118.84PROYECCION MES 40 3,323,813.12 40,509.83PROYECCIÓN MES 30 157,535.81 38,589.42MEJOR INV Y LN PORQUE POLINOMIAL HACE PRONÓSTICOS ILÓGICOS (AÑO 40)

0.0124665681900886

-1.0220508500679132.8370231636404 y = 0.0125x6 - 1.0221x5 + 32.837x4 - 515.39x3 + 3865.1x2 - 8721.3x + 5997.6-515.3947577609913865.05993617682-8721.285698089915997.58613524346 MES

123456789

101112

131415161718192021222324

25

40

30

GRAFICANDO

MES VENTAS (POLIN) VENTAS (INV Y LN)

1 226 2262 1,589 1,5893 3,383 3,3834 4,930 4,930

5 12,403 12,4036 17,989 17,9897 20,500 20,5008 25,748 25,7489 24,262 24,262

10 29,936 29,93611 29,489 29,48912 30,074 30,07413 32,124 32,12414 33,210 33,21015 32,277 32,27716 36,152 36,15217 36,377 36,37718 33,928 33,92819 36,285 36,28520 34,864 34,86421 34,635 34,63522 34,860 34,86023 37,905 37,90524 35,865 35,86525 40,177 37,11930 157,536 38,58940 3,323,813 40,510

POLINOMIAL INV Y LN

RESUMEN DE LAS OPCIONES DE PRONÓSTICO


y = 0.0125x6 - 1.0221x5 + 32.837x4 - 515.39x3 + 3865.1x2 - 8721.3x + 5997.6 0.9889

Y=EXP (10.7555 - 5.8280/X) 0.9982

Y = -7,028.1875 + 14,377.8067 (LNX) 0.9315

Y = 6,163.3016 + 1,570.2947X 0.8055


R2

LINEAL 6163.345,420.65 1570.2968,975.0653,272.12ADICIONAL

MEJOR INV Y LN PORQUE POLINOMIAL HACE PRONÓSTICOS ILÓGICOS (AÑO 40)254030

y = 0.0125x6 - 1.0221x5 + 32.837x4 - 515.39x3 + 3865.1x2 - 8721.3x + 5997.6

VENTAS226

1,5893,3834,930

12,40317,98920,50025,74824,26229,93629,48930,074

32,12433,21032,27736,15236,37733,92836,28534,86434,63534,86037,90535,865

POLINOMIAL INV Y LN LINEAL40,177 37,119 45,421

3,323,813 40,510 68,975

157,536 38,589 53,272

VTAS (LINEAL)226

1,5893,3834,930

0 5 10 15 20 25 30 35 40 450

500,000

1,000,000

1,500,000

2,000,000

2,500,000

3,000,000

3,500,000

VENTAS (POLINOMIAL)

VENTAS (POLIN)

12,40317,98920,50025,74824,26229,93629,48930,07432,12433,21032,27736,15236,37733,92836,28534,86434,63534,86037,90535,86545,42153,27268,975

LINEAL

0 5 10 15 20 25 30 35 40 450

500,000

1,000,000

1,500,000

2,000,000

2,500,000

3,000,000

3,500,000

VENTAS (POLINOMIAL)

VENTAS (POLIN)

0 5 10 15 20 25 30 35 40 450

5,000

10,000

15,000

20,000

25,000

30,000

35,000

40,000

45,000

VENTAS (INV Y LN)

VENTAS (INV Y LN)

0 5 10 15 20 25 30 35 40 450

10,000

20,000

30,000

40,000

50,000

60,000

70,000

80,000

VENTAS (LINEAL)

VTAS (LINEAL)

0 5 10 15 20 25 30 35 40 450

10,000

20,000

30,000

40,000

50,000

60,000

70,000

80,000

VENTAS (LINEAL)

VTAS (LINEAL)

MAPE (%) ERROR TÍPICOVALIDEZ

16.55 1,518.8492 SI POLINOMIAL

17.77% 482.24SÍINVERSA Y LN

156.53% 3,310.3900 SI LOGARÍTMICA

186.54% 5,578.2730 SI LINEAL

NO SE PUEDE COMPARAR CON LOS OTROS MAPES POR TENER MÁS VARIABLES INDEPENDIENTES. EL ERROR TÍPICO SÍ TOMA EN CUENTA LA CANTIDAD DE VARIABLES.

0 5 10 15 20 25 30 35 40 450

500,000

1,000,000

1,500,000

2,000,000

2,500,000

3,000,000

3,500,000

VENTAS (POLINOMIAL)

VENTAS (POLIN)

0 5 10 15 20 25 30 35 40 450

500,000

1,000,000

1,500,000

2,000,000

2,500,000

3,000,000

3,500,000

VENTAS (POLINOMIAL)

VENTAS (POLIN)

0 5 10 15 20 25 30 35 40 450

5,000

10,000

15,000

20,000

25,000

30,000

35,000

40,000

45,000

VENTAS (INV Y LN)

VENTAS (INV Y LN)

0 5 10 15 20 25 30 35 40 450

10,000

20,000

30,000

40,000

50,000

60,000

70,000

80,000

VENTAS (LINEAL)

VTAS (LINEAL)

0 5 10 15 20 25 30 35 40 450

10,000

20,000

30,000

40,000

50,000

60,000

70,000

80,000

VENTAS (LINEAL)

VTAS (LINEAL)

0 5 10 15 20 25 30 35 40 450

500,000

1,000,000

1,500,000

2,000,000

2,500,000

3,000,000

3,500,000

VENTAS (POLINOMIAL)

VENTAS (POLIN)

0 5 10 15 20 25 30 35 40 450

500,000

1,000,000

1,500,000

2,000,000

2,500,000

3,000,000

3,500,000

VENTAS (POLINOMIAL)

VENTAS (POLIN)

0 5 10 15 20 25 30 35 40 450

5,000

10,000

15,000

20,000

25,000

30,000

35,000

40,000

45,000

VENTAS (INV Y LN)

VENTAS (INV Y LN)

0 5 10 15 20 25 30 35 40 450

10,000

20,000

30,000

40,000

50,000

60,000

70,000

80,000

VENTAS (LINEAL)

VTAS (LINEAL)

0 5 10 15 20 25 30 35 40 450

10,000

20,000

30,000

40,000

50,000

60,000

70,000

80,000

VENTAS (LINEAL)

VTAS (LINEAL)

MES VENTAS10 29,93611 29,48912 30,07413 32,12414 33,21015 32,27716 36,15217 36,37718 33,92819 36,28520 34,86421 34,63522 34,86023 37,90524 35,865

OPCIONESA)

1) POLINÓMICA2) POTENCIAL

B) POR SIMILITUD CON GRÁFICOS NO LINEALES3) INVERSA Y EXPONENCIAL


REGRESIÓN LINEAL

Resumen

POR R2 EN DIAGRAMA DE DISPERSIÓN

AUNQUE SU R2 NO SEA MUY ALTO

8 10 12 14 16 18 20 22 24 260

5,000

10,000

15,000

20,000

25,000

30,000

35,000

40,000

f(x) = 26284.6086483636 exp( 0.0147395268359627 x )R² = 0.706188921294069f(x) = 488.299107142857 x + 25564.2318452381R² = 0.700991089273815f(x) = 8180.47094639999 ln(x) + 10969.3227075992R² = 0.749835728620568

f(x) = − 0.126646922660011 x⁶ + 12.44757472865 x⁵ − 497.592249637718 x⁴ + 10337.6574303245 x³ − 117591.337076418 x² + 694882.011240729 x − 1639761.90953187R² = 0.868226350747498

f(x) = 16891.1051863923 x^0.247518027660556R² = 0.758990547328932

Column CLinear (Column C)Exponential (Column C)Logarithmic (Column C)Logarithmic (Column C)Power (Column C)Polynomial (Column C)Exponential (Column C)Linear (Column C)Logarithmic (Column C)Polynomial (Column C)Power (Column C)

Estadísticas de la regresiónCoeficiente de correl 0.8372521062Coeficiente de deter 0.7009910893 ÍDEM A DISPERSIÓNR^2 ajustado 0.6779904038Error típico 1480.0591986Observaciones 15

ANÁLISIS DE VARIANZAGrados de libertadSuma de cuadradosPromedio de los cuadradosF

Regresión 1 66762085.1 66762085.05 30.47696518Residuos 13 28477478 2190575.231Total 14 95239563.1

Coeficientes Error típico Estadístico t ProbabilidadIntercepción 25564.231845 1551.45897 16.477543 4.309305E-10Variable X 1 488.29910714 88.4504549 5.52059464 9.863888E-05


Observación Pronóstico para Y Residuos1 30447.222917 -510.9729172 30935.522024 -1446.272023 31423.821131 -1350.321134 31912.120238 211.3797625 32400.419345 809.5806556 32888.718452 -611.4684527 33377.01756 2774.732448 33865.316667 2511.933339 34353.615774 -426.115774

10 34841.914881 1443.0851211 35330.213988 -465.96398812 35818.513095 -1183.763113 36306.812202 -1446.562214 36795.11131 1109.3886915 37283.410417 -1418.66042

POLINÓMICA

Observación10 10 100 1000 1000011 11 121 1331 1464112 12 144 1728 2073613 13 169 2197 2856114 14 196 2744 3841615 15 225 3375 5062516 16 256 4096 6553617 17 289 4913 8352118 18 324 5832 10497619 19 361 6859 13032120 20 400 8000 16000021 21 441 9261 19448122 22 484 10648 23425623 23 529 12167 27984124 24 576 13824 331776

Resumen

Estadísticas de la regresiónCoeficiente de correl 0.9317866444Coeficiente de deter 0.8682263507 ÍDEM A DISPERSIÓNR^2 ajustado 0.7693961138Error típico 1252.5007374Observaciones 15


Regresión 6 82689498.3 13781583.05 8.785027514Residuos 8 12550064.8 1568758.097Total 14 95239563.1

Coeficientes Error típico Estadístico t ProbabilidadIntercepción -1639761.91 2207250.87 -0.742897841 0.47878822

X1 X2 X3 X4

Variable X 1 694882.01128 848626.322 0.818831555 0.436593Variable X 2 -117591.3371 133461.848 -0.881085788 0.403964Variable X 3 10337.657431 10995.021 0.940212615 0.374626Variable X 4 -497.5922497 500.762384 -0.993669383 0.349484Variable X 5 12.447574729 11.9634997 1.040462662 0.328546Variable X 6 -0.126646923 0.11722222 -1.080400305 0.311455


Observación Pronóstico para Y Residuos1 29769.979386 166.2706142 29893.949355 -404.6993553 30258.067633 -184.5676334 31266.26081 857.239195 32724.174992 485.8250086 34193.062465 -1915.812477 35252.482575 899.2674258 35671.816821 705.4331799 35490.598168 -1563.09817

10 35007.654571 1277.3454311 34679.066716 185.18328412 34924.939984 -290.18998413 35844.990615 -984.74061514 36842.946104 1061.553915 36159.759804 -295.009804

POTENCIAL

LN(X) LN (Y)2.302585093 10.3068254

2.3978952728 10.29178112.4849066498 10.31139972.5649493575 10.37734312.6390573296 10.41060632.7080502011 10.38211792.7725887222 10.49548062.8332133441 10.50169892.8903717579 10.43198122.9444389792 10.49915972.9957322736 10.45921723.0445224377 10.45261283.0910424534 10.45910253.1354942159 10.54282513.1780538303 10.4875102

Resumen

Estadísticas de la regresiónCoeficiente de correl 0.8712006355Coeficiente de deter 0.7589905473R^2 ajustado 0.7404513587Error típico 0.0399620234Observaciones 15



Coeficientes Error típico Estadístico t ProbabilidadIntercepción 9.734542442 0.1087623 89.50290694 1.581618E-19Variable X 1 0.2475180277 0.03868424 6.398421137 2.34921E-05


Observación Pronóstico para Y Residuos Y FÓRMULA Y REAL1 10.304473763 0.00235164 29864.50783 29,9362 10.32806475 -0.03628368 30577.36458 29,4893 10.349601635 -0.03820197 31242.99939 30,0744 10.369413648 0.00792948 31868.1125 32,1245 10.387756707 0.02284961 32458.02204 33,2106 10.404833687 -0.02271576 33017.02576 32,277

Y = EXP (Bo + Se2/2)XB1

7 10.420808134 0.0746725 33548.65068 36,1528 10.435813821 0.06588504 34055.83006 36,3779 10.449961559 -0.01798038 34541.03183 33,928

10 10.463344171 0.03581554 35006.35383 36,28511 10.476040186 -0.01682296 35453.59554 34,86412 10.488116631 -0.03550384 35884.3131 34,63513 10.499631173 -0.04052868 36299.86212 34,86014 10.510633786 0.03219133 36701.43129 37,90515 10.521168058 -0.03365786 37090.06925 35,865

INVERSA Y EXPONENCIAL

X Y 1/X LN (Y)MES VENTAS 1/MES ln (VENTAS)

10 29,936 0.100000000 10.306825411 29,489 0.090909091 10.2917810712 30,074 0.083333333 10.3113996613 32,124 0.076923077 10.3773431314 33,210 0.071428571 10.41060631

15 32,277 0.066666667 10.3821179316 36,152 0.062500000 10.4954806417 36,377 0.058823529 10.5016988618 33,928 0.055555556 10.4319811719 36,285 0.052631579 10.4991597120 34,864 0.050000000 10.4592172321 34,635 0.047619048 10.4526127922 34,860 0.045454545 10.4591024923 37,905 0.043478261 10.5428251224 35,865 0.041666667 10.4875102

Resumen

Estadísticas de la regresiónCoeficiente de correl 0.8883540413

Coeficiente de deter 0.789173 MAYOR QUE TODOS LOS DEL DIAGRAMA DE DISPERSIÓN (EX POLINÓMICA)R^2 ajustado 0.7729554337

Error típico 0.037376Observaciones 15

ANÁLISIS DE VARIANZAGrados de libertadSuma de cuadradosPromedio de los cuadrados F


Coeficientes Error típico Estadístico t ProbabilidadIntercepción 10.670811073 0.03621585 294.6448124 2.992111E-26Variable X 1 -3.856962255 0.55290542 -6.975808405 9.685078E-06

Y =Y =


Y = EXP(10.6715096 - 3.8569623/X)

Observación Pronóstico para Y ResiduosY REAL

EXP(Bo + B1/X + SE2/2)EXP(10.6708111 - 3.8569623/X + 0.037382/2)

Y CON FÓRMULA

1 10.285114848 0.02171055 63399.15322 29,9362 10.320178141 -0.02839707 61214.69114 29,4893 10.349397552 -0.03799789 59451.91301 30,0744 10.374121669 0.00322146 58000.03906 32,1245 10.395313769 0.01529254 56783.82895 33,2106 10.413680256 -0.03156233 55750.42852 32,2777 10.429750932 0.0657297 54861.64227 36,1528 10.443930941 0.05776792 54089.19334 36,3779 10.456535393 -0.02455422 53411.70734 33,928

10 10.46781306 0.03134665 52812.73174 36,28511 10.477962961 -0.01874573 52279.39898 34,86412 10.487146204 -0.03453341 51801.50221 34,63513 10.495494607 -0.03639212 51370.84255 34,86014 10.503117062 0.03970806 50980.75919 37,90515 10.510104313 -0.02259411 50625.78545 35,865

RESUMEN DE LAS OPCIONES DE PRONÓSTICO (15 DATOS)


POLINOMIAL

INVERSA Y LN Y = EXP(10.6715096 - 3.8569623/X)POTENCIAL Y =LINEAL Y = 25,564.23 + 488.2991X

16,904.5978 X 0.247518

PROYECCIONES MESES 25 Y 40PROYECTANDO CON INV Y LINEAL

INV Y LN 25PROYECCION MES 25 36,946.68 40PROYECCION MES 40 39,147.25

COMPARANDO SOLUCIONES CON 24 Y CON 15 DATOS

24 DATOS INV Y LN 0.9545 0.2728 37,118.8415 DATOS INV Y LN 0.7891 0.0379 36,946.68

MEJOR REGRESIÓN

R2 ERROR TÍPICO

PROY MES 25

POR SIMILITUD CON GRÁFICOS NO LINEALESINVERSA Y EXPONENCIAL


EN DIAGRAMA DE DISPERSIÓN

8 10 12 14 16 18 20 22 24 260

5,000

10,000

15,000

20,000

25,000

30,000

35,000

40,000


f(x) = − 0.126646922660011 x⁶ + 12.44757472865 x⁵ − 497.592249637718 x⁴ + 10337.6574303245 x³ − 117591.337076418 x² + 694882.011240729 x − 1639761.90953187R² = 0.868226350747498

f(x) = 16891.1051863923 x^0.247518027660556R² = 0.758990547328932


Valor crítico de F9.863888E-05

Inferior 95% Superior 95%Inferior 95.0%Superior 95.0%22212.50852 28915.9552 22212.508521 28915.9552297.2135168 679.384698 297.21351676 679.384698

VENTAS100000 1000000 29,936161051 1771561 29,489248832 2985984 30,074371293 4826809 32,124537824 7529536 33,210759375 11390625 32,277

1048576 16777216 36,1521419857 24137569 36,3771889568 34012224 33,9282476099 47045881 36,2853200000 64000000 34,8644084101 85766121 34,6355153632 113379904 34,8606436343 148035889 37,9057962624 191102976 35,865

Valor crítico de F0.003621564

Inferior 95% Superior 95%Inferior 95.0%Superior 95.0%-6729691.554 3450167.74 -6729691.554 3450167.74

X5 X6

-1262053.797 2651817.82 -1262053.797 2651817.82

-425354.9094 190172.235 -425354.9094 190172.235

-15016.90644 35692.2213 -15016.90644 35692.2213

-1652.352379 657.16788 -1652.352379 657.16788

-15.14030501 40.0354545 -15.14030501 40.0354545

-0.396961848 0.143668 -0.396961848 0.143668


Inferior 95% Superior 95%Inferior 95.0%Superior 95.0%9.499575768 9.96950912 9.4995757678 9.969509120.163945819 0.33109024 0.1639458186 0.33109024

Y =

Y =

LA ECUACIÓN DE DISPERSIÓN ES CASI LA MISMA:

Y =

RESIDUOS RESID CUADR-72 5146.93899

1,088 1183993.351,169 1367728.82

-255 65222.7756-752 565470.859740 547268.172

Y = EXP (Bo + Se2/2)XB1 EXP(9.734542 + 0.039962/2)X0.247518

EXP ( 9.7353)X0.247518

16,904.5978 X 0.247518

16,891 X 0.2475

-2,603 6776126.07-2,321 5388990.56

614 376421.307-1,279 1634936.03

589 347328.1611,250 1561407.941,440 2072483.05

-1,203 1447374.311,225 1501407.28

1656087.04 PROMEDIO DE PRONÓSTICOS AL CUADRADO

NUEVO ERROR TÍPICO= RAIZ(PROM PRON AL CUAD/GL)NUEVO ERROR TÍPICO=

356.919194

X YMES VENTAS

1 27,4362 26,9893 27,5744 29623.55 30710

0 2 4 6 8 10 12 14 160

5,000

10,000

15,000

20,000

25,000

30,000

35,000

40,000

Column H

6 29777.257 33651.758 33877.259 31427.5

10 3378511 32364.2512 32134.7513 32360.2514 35404.515 33364.75

MAYOR QUE TODOS LOS DEL DIAGRAMA DE DISPERSIÓN (EX POLINÓMICA)


Inferior 95% Superior 95% Inferior 95.0%Superior 95.0%10.5925715 10.7490507 10.592571495 10.7490507

-5.051441788 -2.66248272 -5.051441788 -2.66248272

EXP(10.6715096 - 3.8569623/X)RESIDUOS RESIDUOS C

EXP(Bo + B1/X + SE2/2)EXP(10.6708111 - 3.8569623/X + 0.037382/2)

0 2 4 6 8 10 12 14 160

5,000

10,000

15,000

20,000

25,000

30,000

35,000

40,000

Column H

33,463 111976589231,725 100650361629,378 86309115125,877 66959527423,574 55572541223,473 55099011018,710 35006006917,712 31371293719,484 37963433616,528 27316591717,415 30328741417,167 29469738116,511 27259966613,076 17098855514,761 217888168

489447060 PROMEDIO RESIDUOS AL CUADRADONUEVO ERROR TÍPICO = RAIZ (PROME RESIDUOS AL CUADRADO/GL)NUEVO ERROR TÍPICO = 6135.94115207497

RESUMEN DE LAS OPCIONES DE PRONÓSTICO (15 DATOS)

TODAS LAS OPCIONESFÓRMULA MAPE (%) ERROR TÍPICO

0.8682 1,252.5000

EXP(10.6715096 - 3.8569623/X) 0.7891 0.037880.7589 0.03996

Y = 25,564.23 + 488.2991X 0.7009 1480.06000

R2


COMPARANDO SOLUCIONES CON 24 Y CON 15 DATOS

40,509.8339,147.25

PROY MES 40

8 10 12 14 16 18 20 22 24 260

5,000

10,000

15,000

20,000

25,000

30,000

35,000

40,000


f(x) = − 0.126646922660011 x⁶ + 12.44757472865 x⁵ − 497.592249637718 x⁴ + 10337.6574303245 x³ − 117591.337076418 x² + 694882.011240729 x − 1639761.90953187R² = 0.868226350747498

f(x) = 16891.1051863923 x^0.247518027660556R² = 0.758990547328932


9.73534092

16904.5978

NUEVO ERROR TÍPICO= RAIZ(PROM PRON AL CUAD/GL) GL = 13

0 2 4 6 8 10 12 14 160

5,000

10,000

15,000

20,000

25,000

30,000

35,000

40,000

Column H

0.00069849

10.6715096

0 2 4 6 8 10 12 14 160

5,000

10,000

15,000

20,000

25,000

30,000

35,000

40,000

Column H

NUEVO ERROR TÍPICO = RAIZ (PROME RESIDUOS AL CUADRADO/GL) GL =13

VALIDEZ

NO POLINOMIAL

SÍ INVERSA Y LN

SI POTENCIAL

SI LINEAL

Resumen

Estadísticas de la regresiónCoeficiente d 0.88835404Coeficiente d 0.7891729R^2 ajustado 0.77295543Error típico 0.03737607Observacione 15

ANÁLISIS DE VARIANZAGrados de libertadSuma de cuadradosPromedio de los cuadradosF Valor crítico de F

Regresión 1 0.06797925 0.06797925 48.6619029 9.68508E-06Residuos 13 0.01816062 0.00139697Total 14 0.08613987

Coeficientes Error típico Estadístico t Probabilidad Inferior 95%Intercepción 10.6708111 0.03621585 294.644812 2.99211E-26 10.5925715Variable X 1 -3.85696226 0.55290542 -6.9758084 9.68508E-06 -5.05144179


ObservaciónPronóstico para YResiduos1 10.2851148 0.021710552 10.3201781 -0.028397073 10.3493976 -0.037997894 10.3741217 0.003221465 10.3953138 0.015292546 10.4136803 -0.031562337 10.4297509 0.06572978 10.4439309 0.057767929 10.4565354 -0.02455422

10 10.4678131 0.0313466511 10.477963 -0.0187457312 10.4871462 -0.0345334113 10.4954946 -0.0363921214 10.5031171 0.03970806

15 10.5101043 -0.02259411

Valor crítico de F

Superior 95%Inferior 95.0%Superior 95.0%10.7490507 10.5925715 10.7490507

-2.66248272 -5.05144179 -2.66248272

Url Ei2c15 Clase 11 e6 Regresión Ventas (Soln 2c15)

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