SET 1

Muestra1 <- read.csv("Muestra1.csv")  
attach(Muestra1[,2:5])               
head(Muestra1[,2:5])

##          D       H         V        B
## 1 4.392676 19.5072 0.7050883 408.9512
## 2 3.342254 21.9456 0.4643955 269.3494
## 3 4.360845 21.6408 0.7277418 422.0902
## 4 2.641972 21.3360 0.2916630 169.1646
## 5 5.570423 24.9936 1.5772458 914.8025
## 6 3.533240 24.3840 0.6399597 371.1766

### variables 
D2<-D*D                  
H2<-H*H                 
DH2<-D*H2                  
D2H<-D2*H
D3<-D*D*D

## GENERAR VARIABLES Y CORRELACION
Set1<-data.frame(B, D, H, D2, H2, DH2, D2H,D3  ); Set1

##           B        D       H        D2       H2      DH2      D2H        D3
## 1  408.9512 4.392676 19.5072 19.295606 380.5309 1671.549 376.4032  84.75935
## 2  269.3494 3.342254 21.9456 11.170660 481.6094 1609.661 245.1468  37.33518
## 3  422.0902 4.360845 21.6408 19.016973 468.3242 2042.290 411.5425  82.93008
## 4  169.1646 2.641972 21.3360  6.980016 455.2249 1202.691 148.9256  18.44101
## 5  914.8025 5.570423 24.9936 31.029612 624.6800 3479.732 775.5417 172.84807
## 6  371.1766 3.533240 24.3840 12.483783 594.5795 2100.792 304.4046  44.10820
## 7  909.8754 5.506761 24.6888 30.324417 609.5368 3356.574 748.6735 166.98932
## 8  837.6109 5.729578 24.3840 32.828063 594.5795 3406.689 800.4795 188.09095
## 9  298.9121 3.501409 22.8600 12.259863 522.5796 1829.765 280.2605  42.92679
## 10 169.1646 2.737465 19.8120  7.493715 392.5153 1074.497 148.4655  20.51378
## 11 566.6192 4.456338 23.7744 19.858952 565.2221 2518.821 472.1347  88.49821
## 12 520.6327 4.520000 24.3840 20.430403 594.5795 2687.499 498.1750  92.34543
## 13 629.0294 5.092958 21.9456 25.938223 481.6094 2452.816 569.2299 132.10229
## 14 397.4546 3.596902 24.0792 12.937702 579.8079 2085.512 311.5295  46.53564
## 15 555.1225 4.106198 25.9080 16.860858 671.2245 2756.180 436.8311  69.23401
## 16 957.5043 5.697747 24.3840 32.464320 594.5795 3387.763 791.6100 184.97348
## 17 845.8228 5.729578 24.3840 32.828063 594.5795 3406.689 800.4795 188.09095
## 18 308.7664 3.405916 24.6888 11.600262 609.5368 2076.031 286.3966  39.50952
## 19 450.0106 4.233521 26.2128 17.922704 687.1109 2908.899 469.8043  75.87615
## 20 344.8986 3.628733 23.1648 13.167701 536.6080 1947.207 305.0272  47.78207
## 21 256.2104 3.501409 20.1168 12.259863 404.6856 1416.970 246.6292  42.92679
## 22 167.5222 2.801127 19.2024  7.846312 368.7322 1032.866 150.6680  21.97852
## 23 323.5478 3.437747 25.2984 11.818103 640.0090 2200.189 298.9791  40.62764
## 24 699.6515 5.188451 23.4696 26.920025 550.8221 2857.914 631.8022 139.67324
## 25 596.1819 4.615493 22.5552 21.302779 508.7370 2348.072 480.4884  98.32283

Corr<-cor(Set1, method = "pearson")           # Hacer la correlacion
round(Corr, digits = 3)

##         B     D     H    D2    H2   DH2   D2H    D3
## B   1.000 0.968 0.530 0.975 0.523 0.939 0.986 0.972
## D   0.968 1.000 0.441 0.995 0.433 0.907 0.985 0.981
## H   0.530 0.441 1.000 0.417 0.999 0.766 0.524 0.396
## D2  0.975 0.995 0.417 1.000 0.409 0.900 0.991 0.996
## H2  0.523 0.433 0.999 0.409 1.000 0.762 0.518 0.389
## DH2 0.939 0.907 0.766 0.900 0.762 1.000 0.947 0.888
## D2H 0.986 0.985 0.524 0.991 0.518 0.947 1.000 0.988
## D3  0.972 0.981 0.396 0.996 0.389 0.888 0.988 1.000

Rplot1.jpeg

Biomasa esta altamente correlacionada con D2H con el 0.99 ,y una baja correlacion con H2(0.52), en cuanto a las demas varibles se tiene una adecuada correlacion , pareciera que biomasa cumplira el supuesto de normalidad.

#correlacion set1 Rplot1.1.jpeg

la figura lo confirma , la mayoria de las variables estan aparentemente correlacionadas excepto H2 que es la que esta mas lejana a biomasa y su linea no es tan verde .

Paso 1: Hacer un modelo sin variables independientes (vacía).

regvacia1<-lm(formula = B~1, Set1); summary(regvacia1) # B, es la variable dependiente (Biomasa)

## 
## Call:
## lm(formula = B ~ 1, data = Set1)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -328.08 -186.84  -73.51  133.43  461.90 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)   495.60      49.57   9.998 4.94e-10 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 247.9 on 24 degrees of freedom

la intercepcion tiene un valor de 495.60 y un Pr(>|t|) significativo.

Paso 2: Hacer un modelo con todas variables independientes (completa)

regcompleta1<-lm(formula = B~.,Set1);
summary(regcompleta1)

## 
## Call:
## lm(formula = B ~ ., data = Set1)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -69.449 -18.025   3.301  18.364  72.382 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1212.107   2511.006   0.483    0.635
## D            205.025   1014.919   0.202    0.842
## H           -213.533    368.976  -0.579    0.570
## D2           -61.605    248.735  -0.248    0.807
## H2            10.354     14.795   0.700    0.493
## DH2           -2.941      3.437  -0.856    0.404
## D2H           18.439     19.341   0.953    0.354
## D3           -27.438     27.724  -0.990    0.336
## 
## Residual standard error: 46.11 on 17 degrees of freedom
## Multiple R-squared:  0.9755, Adjusted R-squared:  0.9654 
## F-statistic: 96.63 on 7 and 17 DF,  p-value: 1.946e-12

el modelo no tiene variables ni intercepcion con un Pr(>|t|) signicativo ,por ahora. aunque si tiene una Adjusted R-squared: 0.9654 aceptables , no quiere decir que sea estadisticamente bueno .

Paso 3: Hacer un modelo con el procedimiento Forward

regforw1<-step(regvacia1, scope = list(lower=regvacia1, upper=regcompleta1),direction = "forward"); summary(regforw1)

## Start:  AIC=276.62
## B ~ 1
## 
##        Df Sum of Sq     RSS    AIC
## + D2H   1   1434340   40030 188.46
## + D2    1   1400143   74227 203.90
## + D3    1   1393131   81239 206.16
## + D     1   1381912   92458 209.39
## + DH2   1   1299357  175013 225.34
## + H     1    414442 1059928 270.37
## + H2    1    402873 1071497 270.64
## <none>              1474370 276.62
## 
## Step:  AIC=188.46
## B ~ D2H
## 
##        Df Sum of Sq   RSS    AIC
## <none>              40030 188.46
## + D2    1    585.24 39445 190.09
## + D     1    425.25 39605 190.20
## + D3    1    409.01 39621 190.21
## + H     1    337.67 39692 190.25
## + H2    1    297.45 39732 190.28
## + DH2   1    293.79 39736 190.28

## 
## Call:
## lm(formula = B ~ D2H, data = Set1)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -79.981 -15.381  -4.984  33.975  62.654 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) -4.64135   19.32001   -0.24    0.812    
## D2H          1.13799    0.03964   28.71   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 41.72 on 23 degrees of freedom
## Multiple R-squared:  0.9728, Adjusted R-squared:  0.9717 
## F-statistic: 824.1 on 1 and 23 DF,  p-value: < 2.2e-16

Hacer un modelo con el procedimiento Stepwise

regstep1<-step(regvacia1,scope =list(lower=regvacia1, upper=regcompleta1),direction = "both"); summary(regstep1)

## Start:  AIC=276.62
## B ~ 1
## 
##        Df Sum of Sq     RSS    AIC
## + D2H   1   1434340   40030 188.46
## + D2    1   1400143   74227 203.90
## + D3    1   1393131   81239 206.16
## + D     1   1381912   92458 209.39
## + DH2   1   1299357  175013 225.34
## + H     1    414442 1059928 270.37
## + H2    1    402873 1071497 270.64
## <none>              1474370 276.62
## 
## Step:  AIC=188.46
## B ~ D2H
## 
##        Df Sum of Sq     RSS    AIC
## <none>                40030 188.46
## + D2    1       585   39445 190.09
## + D     1       425   39605 190.20
## + D3    1       409   39621 190.21
## + H     1       338   39692 190.25
## + H2    1       297   39732 190.28
## + DH2   1       294   39736 190.28
## - D2H   1   1434340 1474370 276.62

## 
## Call:
## lm(formula = B ~ D2H, data = Set1)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -79.981 -15.381  -4.984  33.975  62.654 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) -4.64135   19.32001   -0.24    0.812    
## D2H          1.13799    0.03964   28.71   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 41.72 on 23 degrees of freedom
## Multiple R-squared:  0.9728, Adjusted R-squared:  0.9717 
## F-statistic: 824.1 on 1 and 23 DF,  p-value: < 2.2e-16

Generar un modelo con Boostrap forward

library(pacman)                     
p_load(bootStepAIC,MASS )           

lmFit <-lm(formula = B~.,Set1)      
boot.stepAIC(regstep1, Set1)

## 
## Summary of Bootstrapping the 'stepAIC()' procedure for
## 
## Call:
## lm(formula = B ~ D2H, data = Set1)
## 
## Bootstrap samples: 100 
## Direction: backward 
## Penalty: 2 * df
## 
## Covariates selected
##     (%)
## D2H 100
## 
## Coefficients Sign
##     + (%) - (%)
## D2H   100     0
## 
## Stat Significance
##     (%)
## D2H 100
## 
## 
## The stepAIC() for the original data-set gave
## 
## Call:
## lm(formula = B ~ D2H, data = Set1)
## 
## Coefficients:
## (Intercept)          D2H  
##      -4.641        1.138  
## 
## 
## Stepwise Model Path 
## Analysis of Deviance Table
## 
## Initial Model:
## B ~ D2H
## 
## Final Model:
## B ~ D2H
## 
## 
##   Step Df Deviance Resid. Df Resid. Dev      AIC
## 1                         23   40029.75 188.4626

boot.stepAIC(regstep1, Set1, B = 100, alpha = 0.05, direction = "forward", # Hacer 100 remuestreos 

                          k = 2, verbose = F)    # Usar el procedimiento "forward"

## 
## Summary of Bootstrapping the 'stepAIC()' procedure for
## 
## Call:
## lm(formula = B ~ D2H, data = Set1)
## 
## Bootstrap samples: 100 
## Direction: forward 
## Penalty: 2 * df
## 
## Covariates selected
##     (%)
## D2H 100
## 
## Coefficients Sign
##     + (%) - (%)
## D2H   100     0
## 
## Stat Significance
##     (%)
## D2H 100
## 
## 
## The stepAIC() for the original data-set gave
## 
## Call:
## lm(formula = B ~ D2H, data = Set1)
## 
## Coefficients:
## (Intercept)          D2H  
##      -4.641        1.138  
## 
## 
## Stepwise Model Path 
## Analysis of Deviance Table
## 
## Initial Model:
## B ~ D2H
## 
## Final Model:
## B ~ D2H
## 
## 
##   Step Df Deviance Resid. Df Resid. Dev      AIC
## 1                         23   40029.75 188.4626

Ambos modelos (Forward Y Stepwis ) nos arroja una formula lm(formula = B ~ D2H, data = Set1), o B=B0 +B1D2H. SI remplazamos los valores tendremos que es B= -4.64135 +1.13799D2H ,tiene un error de 41.72 y una Adjusted R-squared: 0.9717 osea D2H explica el 97.17% de la biomasa .

si queremos mas exactitud o mas valides se aplica el modelo de con Boostrap forward notamos que efectivamente el modelo es el adecuado nos da unos valos iguales a los obtenidos en los anteriores modelos .

comprobar los supuestos en regresion multiple

De primera veremos si el modelo que se obtuvo , es adecuado o si cumple las condiciones de regresion .en caso de que no lo haga se ajusta el modelo .

MODELO1.1<-lm(B ~  D2H, data = Muestra1)  # Ajustar el moddelo
summary(MODELO1.1)

## 
## Call:
## lm(formula = B ~ D2H, data = Muestra1)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -79.981 -15.381  -4.984  33.975  62.654 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) -4.64135   19.32001   -0.24    0.812    
## D2H          1.13799    0.03964   28.71   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 41.72 on 23 degrees of freedom
## Multiple R-squared:  0.9728, Adjusted R-squared:  0.9717 
## F-statistic: 824.1 on 1 and 23 DF,  p-value: < 2.2e-16

observamos que la intercepcion no es significativa , lo tenemos que corregir.A continuacion se muestra la correccion .

MODELO1<-lm(B ~ D2H-1, data = Muestra1)
summary(MODELO1)

## 
## Call:
## lm(formula = B ~ D2H - 1, data = Muestra1)
## 
## Residuals:
##    Min     1Q Median     3Q    Max 
## -80.59 -17.61  -7.52  33.39  64.32 
## 
## Coefficients:
##     Estimate Std. Error t value Pr(>|t|)    
## D2H  1.12940    0.01678   67.31   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 40.89 on 24 degrees of freedom
## Multiple R-squared:  0.9947, Adjusted R-squared:  0.9945 
## F-statistic:  4530 on 1 and 24 DF,  p-value: < 2.2e-16

MODELO1$ residuals

##           1           2           3           4           5           6 
## -16.1595618  -7.5200710 -42.7069351   0.9675794  38.9037465  27.3813237 
##           7           8           9          10          11          12 
##  64.3216988 -66.4526398 -17.6147505   1.4872764  33.3890726 -42.0073802 
##          13          14          15          16          17          18 
## -13.8602645  45.6123809  61.7643764  63.4579389 -58.2407678 -14.6906119 
##          19          20          21          22          23          24 
## -80.5875406   0.4001729 -22.3332580  -2.6426679 -14.1199918 -13.9075461 
##          25 
##  53.5170433

ahora el modelo es significativo y con una Adjusted R-squared: 0.9945 , es decir la variable explica el 99.45% de la biomasa. Acontinuacion se hace el analisis de observaciones atipicas , pues , si ocurre que hay un dato mayor de 3 , este tiene que ser eliminado y volver a ajustar el modelo .

library(lmtest)

## Loading required package: zoo

## 
## Attaching package: 'zoo'

## The following objects are masked from 'package:base':
## 
##     as.Date, as.Date.numeric

library(car)

## Loading required package: carData

summary(influence.measures(MODELO1))

## Potentially influential observations of
##   lm(formula = B ~ D2H - 1, data = Muestra1) :
## 
##   dfb.D2H dffit   cov.r cook.d hat  
## 8 -0.63   -0.63_*  1.03  0.36   0.11

influencePlot(MODELO1)

##      StudRes        Hat     CookD
## 8  -1.798958 0.10790139 0.3580682
## 16  1.704780 0.10552349 0.3176312
## 17 -1.551544 0.10790139 0.2750397
## 19 -2.155657 0.03716726 0.1557165

la observacion 8 influye en el ajuste del modelo , pero no se necesita eliminar , asi tambien se tienen las observaciones 16,17,19.

set 2

### variables 
lnD2<-log(D)
lnH2<-log(H)
lnB<-log(B)
lnD3<-log(D)
lnDH2<-log(H)
H3<-H*H*H
lnH<-log(H)
lnD<-log(D)
lnH3<-log(H)
DH<-D*H
lnDH<-log(DH)

## GENERAR VARIABLES Y CORRELACION
Set2<-data.frame(lnB, lnD2, lnH2, lnD3, lnDH2, lnH, lnD,lnH3 ,lnDH ); Set2

##         lnB      lnD2     lnH2      lnD3    lnDH2      lnH       lnD     lnH3
## 1  6.013596 1.4799387 2.970784 1.4799387 2.970784 2.970784 1.4799387 2.970784
## 2  5.596009 1.2066454 3.088567 1.2066454 3.088567 3.088567 1.2066454 3.088567
## 3  6.045219 1.4726659 3.074580 1.4726659 3.074580 3.074580 1.4726659 3.074580
## 4  5.130872 0.9715256 3.060396 0.9715256 3.060396 3.060396 0.9715256 3.060396
## 5  6.818708 1.7174710 3.218620 1.7174710 3.218620 3.218620 1.7174710 3.218620
## 6  5.916678 1.2622152 3.193927 1.2622152 3.193927 3.193927 1.2622152 3.193927
## 7  6.813308 1.7059766 3.206350 1.7059766 3.206350 3.206350 1.7059766 3.206350
## 8  6.730554 1.7456419 3.193927 1.7456419 3.193927 3.193927 1.7456419 3.193927
## 9  5.700150 1.2531654 3.129389 1.2531654 3.129389 3.129389 1.2531654 3.129389
## 10 5.130872 1.0070323 2.986288 1.0070323 2.986288 2.986288 1.0070323 2.986288
## 11 6.339687 1.4943274 3.168609 1.4943274 3.168609 3.168609 1.4943274 3.168609
## 12 6.255045 1.5085121 3.193927 1.5085121 3.193927 3.193927 1.5085121 3.193927
## 13 6.444178 1.6278588 3.088567 1.6278588 3.088567 3.088567 1.6278588 3.088567
## 14 5.985081 1.2800728 3.181348 1.2800728 3.181348 3.181348 1.2800728 3.181348
## 15 6.319189 1.4124974 3.254552 1.4124974 3.254552 3.254552 1.4124974 3.254552
## 16 6.864330 1.7400708 3.193927 1.7400708 3.193927 3.193927 1.7400708 3.193927
## 17 6.740310 1.7456419 3.193927 1.7456419 3.193927 3.193927 1.7456419 3.193927
## 18 5.732585 1.2255139 3.206350 1.2255139 3.206350 3.206350 1.2255139 3.206350
## 19 6.109271 1.4430341 3.266248 1.4430341 3.266248 3.266248 1.4430341 3.266248
## 20 5.843251 1.2888835 3.142634 1.2888835 3.142634 3.142634 1.2888835 3.142634
## 21 5.545999 1.2531654 3.001555 1.2531654 3.001555 3.001555 1.2531654 3.001555
## 22 5.121116 1.0300218 2.955035 1.0300218 2.955035 2.955035 1.0300218 2.955035
## 23 5.779347 1.2348162 3.230741 1.2348162 3.230741 3.230741 1.2348162 3.230741
## 24 6.550582 1.6464352 3.155706 1.6464352 3.155706 3.155706 1.6464352 3.155706
## 25 6.390546 1.5294188 3.115966 1.5294188 3.115966 3.115966 1.5294188 3.115966
##        lnDH
## 1  4.450722
## 2  4.295212
## 3  4.547246
## 4  4.031921
## 5  4.936091
## 6  4.456142
## 7  4.912326
## 8  4.939569
## 9  4.382554
## 10 3.993320
## 11 4.662937
## 12 4.702439
## 13 4.716426
## 14 4.461421
## 15 4.667049
## 16 4.933998
## 17 4.939569
## 18 4.431864
## 19 4.709282
## 20 4.431517
## 21 4.254721
## 22 3.985057
## 23 4.465557
## 24 4.802141
## 25 4.645384

Corr<-cor(Set2, method = "pearson")           # Hacer la correlacion
round(Corr, digits = 3)

##         lnB  lnD2  lnH2  lnD3 lnDH2   lnH   lnD  lnH3  lnDH
## lnB   1.000 0.977 0.611 0.977 0.611 0.611 0.977 0.611 0.986
## lnD2  0.977 1.000 0.474 1.000 0.474 0.474 1.000 0.474 0.963
## lnH2  0.611 0.474 1.000 0.474 1.000 1.000 0.474 1.000 0.694
## lnD3  0.977 1.000 0.474 1.000 0.474 0.474 1.000 0.474 0.963
## lnDH2 0.611 0.474 1.000 0.474 1.000 1.000 0.474 1.000 0.694
## lnH   0.611 0.474 1.000 0.474 1.000 1.000 0.474 1.000 0.694
## lnD   0.977 1.000 0.474 1.000 0.474 0.474 1.000 0.474 0.963
## lnH3  0.611 0.474 1.000 0.474 1.000 1.000 0.474 1.000 0.694
## lnDH  0.986 0.963 0.694 0.963 0.694 0.694 0.963 0.694 1.000

library(psych)

## 
## Attaching package: 'psych'

## The following object is masked from 'package:car':
## 
##     logit

pairs.panels(x = Set2, ellipses = FALSE, lm = TRUE, method = "pearson", hist.col = "#CD1076")

library(qgraph)

## Registered S3 methods overwritten by 'huge':
##   method    from   
##   plot.sim  BDgraph
##   print.sim BDgraph

Otra_Corr=cor(Set2) 
qgraph(Otra_Corr, shape="circle", posCol="darkgreen", negCol="darkred", layout="spring", vsize=10)

lnBiomasa , Tiene alta correlacion con con la mayoria de las variables , la valor de correlacion mas baja es de 0.61 .se puede comprobar con la figura verde , pues las variables lnDH2 , LnH3, lnH2 , son las que se encuantran mas distantes de la variable lnB

Paso 1: Hacer un modelo sin variables independientes (vacía).

regvacia2<-lm(formula = lnB~1, Set2); summary(regvacia2)

## 
## Call:
## lm(formula = lnB ~ 1, data = Set2)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.95554 -0.34407 -0.03144  0.36752  0.78767 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)   6.0767     0.1069   56.84   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5345 on 24 degrees of freedom

Paso 2: Hacer un modelo con todas variables independientes (completa)

regcompleta2<-lm(formula = lnB~.,Set2); # B, es la variable dependiente (Biomasa)
summary(regcompleta2)

## 
## Call:
## lm(formula = lnB ~ ., data = Set2)
## 
## Residuals:
##       Min        1Q    Median        3Q       Max 
## -0.175353 -0.052300 -0.004839  0.064461  0.120418 
## 
## Coefficients: (6 not defined because of singularities)
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) -0.29685    0.57340  -0.518     0.61    
## lnD2         1.98394    0.07335  27.046  < 2e-16 ***
## lnH2         1.13849    0.19593   5.811 7.59e-06 ***
## lnD3              NA         NA      NA       NA    
## lnDH2             NA         NA      NA       NA    
## lnH               NA         NA      NA       NA    
## lnD               NA         NA      NA       NA    
## lnH3              NA         NA      NA       NA    
## lnDH              NA         NA      NA       NA    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.07555 on 22 degrees of freedom
## Multiple R-squared:  0.9817, Adjusted R-squared:   0.98 
## F-statistic: 589.7 on 2 and 22 DF,  p-value: < 2.2e-16

Paso 3: Hacer un modelo con el procedimiento Forward

regforw2<-step(regvacia2, scope = list(lower=regvacia2, upper=regcompleta2),direction = "forward"); summary(regforw2)

## Start:  AIC=-30.34
## lnB ~ 1
## 
##         Df Sum of Sq    RSS      AIC
## + lnDH   1    6.6608 0.1967 -117.129
## + lnD2   1    6.5392 0.3183 -105.091
## + lnD3   1    6.5392 0.3183 -105.091
## + lnD    1    6.5392 0.3183 -105.091
## + lnH2   1    2.5566 4.3009  -40.001
## + lnDH2  1    2.5566 4.3009  -40.001
## + lnH    1    2.5566 4.3009  -40.001
## + lnH3   1    2.5566 4.3009  -40.001
## <none>               6.8575  -30.338
## 
## Step:  AIC=-117.13
## lnB ~ lnDH
## 
##         Df Sum of Sq     RSS     AIC
## + lnH2   1  0.071084 0.12557 -126.34
## + lnDH2  1  0.071084 0.12557 -126.34
## + lnH    1  0.071084 0.12557 -126.34
## + lnH3   1  0.071084 0.12557 -126.34
## + lnD2   1  0.071084 0.12557 -126.34
## + lnD3   1  0.071084 0.12557 -126.34
## + lnD    1  0.071084 0.12557 -126.34
## <none>               0.19666 -117.13
## 
## Step:  AIC=-126.34
## lnB ~ lnDH + lnH2
## 
##        Df Sum of Sq     RSS     AIC
## <none>              0.12557 -126.34

## 
## Call:
## lm(formula = lnB ~ lnDH + lnH2, data = Set2)
## 
## Residuals:
##       Min        1Q    Median        3Q       Max 
## -0.175353 -0.052300 -0.004839  0.064461  0.120418 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) -0.29685    0.57340  -0.518  0.60984    
## lnDH         1.98394    0.07335  27.046  < 2e-16 ***
## lnH2        -0.84545    0.23957  -3.529  0.00189 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.07555 on 22 degrees of freedom
## Multiple R-squared:  0.9817, Adjusted R-squared:   0.98 
## F-statistic: 589.7 on 2 and 22 DF,  p-value: < 2.2e-16

este modelo muestra que la intercept no es significativa , aunque las variables si lo son y se tiene una Adjusted R-squared: 0.98 ## Hacer un modelo con el procedimiento Stepwise

regstep2<-step(regvacia2, scope = list(lower=regvacia2, upper=regcompleta2),direction = "both"); summary(regstep2)

## Start:  AIC=-30.34
## lnB ~ 1
## 
##         Df Sum of Sq    RSS      AIC
## + lnDH   1    6.6608 0.1967 -117.129
## + lnD2   1    6.5392 0.3183 -105.091
## + lnD3   1    6.5392 0.3183 -105.091
## + lnD    1    6.5392 0.3183 -105.091
## + lnH2   1    2.5566 4.3009  -40.001
## + lnDH2  1    2.5566 4.3009  -40.001
## + lnH    1    2.5566 4.3009  -40.001
## + lnH3   1    2.5566 4.3009  -40.001
## <none>               6.8575  -30.338
## 
## Step:  AIC=-117.13
## lnB ~ lnDH
## 
##         Df Sum of Sq    RSS      AIC
## + lnH2   1    0.0711 0.1256 -126.343
## + lnDH2  1    0.0711 0.1256 -126.343
## + lnH    1    0.0711 0.1256 -126.343
## + lnH3   1    0.0711 0.1256 -126.343
## + lnD2   1    0.0711 0.1256 -126.343
## + lnD3   1    0.0711 0.1256 -126.343
## + lnD    1    0.0711 0.1256 -126.343
## <none>               0.1967 -117.129
## - lnDH   1    6.6608 6.8575  -30.338
## 
## Step:  AIC=-126.34
## lnB ~ lnDH + lnH2
## 
##        Df Sum of Sq    RSS      AIC
## <none>              0.1256 -126.343
## - lnH2  1    0.0711 0.1967 -117.129
## - lnDH  1    4.1753 4.3009  -40.001

## 
## Call:
## lm(formula = lnB ~ lnDH + lnH2, data = Set2)
## 
## Residuals:
##       Min        1Q    Median        3Q       Max 
## -0.175353 -0.052300 -0.004839  0.064461  0.120418 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) -0.29685    0.57340  -0.518  0.60984    
## lnDH         1.98394    0.07335  27.046  < 2e-16 ***
## lnH2        -0.84545    0.23957  -3.529  0.00189 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.07555 on 22 degrees of freedom
## Multiple R-squared:  0.9817, Adjusted R-squared:   0.98 
## F-statistic: 589.7 on 2 and 22 DF,  p-value: < 2.2e-16

Generar un modelo con Boostrap forward

library(pacman)                     
p_load(bootStepAIC,MASS ) 

lmFit <-lm(formula = lnB~.,Set2)      # El modelo, B = variable dependiente.
boot.stepAIC(regstep2, Set2)

## 
## Summary of Bootstrapping the 'stepAIC()' procedure for
## 
## Call:
## lm(formula = lnB ~ lnDH + lnH2, data = Set2)
## 
## Bootstrap samples: 100 
## Direction: backward 
## Penalty: 2 * df
## 
## Covariates selected
##      (%)
## lnDH 100
## lnH2  98
## 
## Coefficients Sign
##      + (%) - (%)
## lnDH   100     0
## lnH2     0   100
## 
## Stat Significance
##         (%)
## lnDH 100.00
## lnH2  93.88
## 
## 
## The stepAIC() for the original data-set gave
## 
## Call:
## lm(formula = lnB ~ lnDH + lnH2, data = Set2)
## 
## Coefficients:
## (Intercept)         lnDH         lnH2  
##     -0.2968       1.9839      -0.8454  
## 
## 
## Stepwise Model Path 
## Analysis of Deviance Table
## 
## Initial Model:
## lnB ~ lnDH + lnH2
## 
## Final Model:
## lnB ~ lnDH + lnH2
## 
## 
##   Step Df Deviance Resid. Df Resid. Dev       AIC
## 1                         22  0.1255738 -126.3434

boot.stepAIC(regstep2, Set2, lnB = 100, alpha = 0.05, direction = "forward", # Hacer 100 remuestreos 
             
             k = 2, verbose = F)

## 
## Summary of Bootstrapping the 'stepAIC()' procedure for
## 
## Call:
## lm(formula = lnB ~ lnDH + lnH2, data = Set2)
## 
## Bootstrap samples: 100 
## Direction: forward 
## Penalty: 2 * df
## 
## Covariates selected
##      (%)
## lnDH 100
## lnH2 100
## 
## Coefficients Sign
##      + (%) - (%)
## lnDH   100     0
## lnH2     0   100
## 
## Stat Significance
##      (%)
## lnDH 100
## lnH2  88
## 
## 
## The stepAIC() for the original data-set gave
## 
## Call:
## lm(formula = lnB ~ lnDH + lnH2, data = Set2)
## 
## Coefficients:
## (Intercept)         lnDH         lnH2  
##     -0.2968       1.9839      -0.8454  
## 
## 
## Stepwise Model Path 
## Analysis of Deviance Table
## 
## Initial Model:
## lnB ~ lnDH + lnH2
## 
## Final Model:
## lnB ~ lnDH + lnH2
## 
## 
##   Step Df Deviance Resid. Df Resid. Dev       AIC
## 1                         22  0.1255738 -126.3434

finalmente la formula que se obtuvo fue de Final Model: lnB ~ lnDH + lnH2 ## comprobar los supuestos en regresion multiple

MODELO2.1<-lm(lnB ~  lnDH+lnH2, data = Muestra1)  # SE TIENE QUE AJUSTAR
summary(MODELO2.1)

## 
## Call:
## lm(formula = lnB ~ lnDH + lnH2, data = Muestra1)
## 
## Residuals:
##       Min        1Q    Median        3Q       Max 
## -0.175353 -0.052300 -0.004839  0.064461  0.120418 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) -0.29685    0.57340  -0.518  0.60984    
## lnDH         1.98394    0.07335  27.046  < 2e-16 ***
## lnH2        -0.84545    0.23957  -3.529  0.00189 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.07555 on 22 degrees of freedom
## Multiple R-squared:  0.9817, Adjusted R-squared:   0.98 
## F-statistic: 589.7 on 2 and 22 DF,  p-value: < 2.2e-16

EL MODELO NO TIENE UNA INTERCEPCION SIGNIFICATIVA POR LO QUE SE TIENE QUE AJUSTAR Acontinuacion se presenta el modelo ajustado ,las variables son significativas y Adjusted R-squared: 0.9999 muy alto .
## MODELOS AJUSTADOS

MODELO2<-lm(lnB ~  lnDH+lnH2-1, data = Muestra1)  
summary(MODELO2)

## 
## Call:
## lm(formula = lnB ~ lnDH + lnH2 - 1, data = Muestra1)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.16320 -0.05116 -0.01278  0.06620  0.12610 
## 
## Coefficients:
##      Estimate Std. Error t value Pr(>|t|)    
## lnDH  1.99639    0.06818  29.279  < 2e-16 ***
## lnH2 -0.95801    0.09900  -9.677 1.42e-09 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.07434 on 23 degrees of freedom
## Multiple R-squared:  0.9999, Adjusted R-squared:  0.9999 
## F-statistic: 8.413e+04 on 2 and 23 DF,  p-value: < 2.2e-16

MODELO2$ residuals

##            1            2            3            4            5            6 
## -0.025750411 -0.020040265 -0.087388715  0.013465457  0.047805812  0.080284630 
##            7            8            9           10           11           12 
##  0.078093587 -0.070948422 -0.051161003  0.019532627  0.066196785 -0.073053507 
##           13           14           15           16           17           18 
## -0.012778619  0.126098150  0.119821895  0.073950025 -0.061192247 -0.043437442 
##           19           20           21           22           23           24 
## -0.163204107  0.006878959 -0.072571758 -0.003667531 -0.040574548 -0.013176269 
##           25 
##  0.101663522

ahora que el modelo ha sido corregido ,es significativo , y tiene como Multiple R-squared: 0.9999, Adjusted R-squared: 0.9999 ,que son valores muy altos .

library(lmtest)
library(car)
summary(influence.measures(MODELO2))

## Potentially influential observations of
##   lm(formula = lnB ~ lnDH + lnH2 - 1, data = Muestra1) :
## 
##    dfb.lnDH dfb.lnH2 dffit cov.r   cook.d hat  
## 4  -0.08     0.08     0.09  1.32_*  0.00   0.18
## 19  0.06    -0.09    -0.53  0.70_*  0.12   0.04

influencePlot(MODELO2)

##       StudRes        Hat       CookD
## 4   0.1954437 0.17696698 0.004285882
## 10  0.2763093 0.13203974 0.006050155
## 14  1.8384207 0.06058381 0.098763877
## 19 -2.4850911 0.04391987 0.115791015

4.- Observaciones influyentes y atípicas

se planteo tranajar de esta forma , primero observe que mi intercept sea significativa , si no lo era se ajustaba , y tambien se calculo los influyentes , son importantes pues influyen a que se vuelva a corregir un modelo .asi que todos los modelos tendran estas dos consideraciones para ajustarse . en este set 2 , no hay necesidad de volverlo ajustar otra vez pues no hay ningun valor mayor de 3 , se encuentra que el valor 4 influye en la coovarianza , pero no sobrepasa mas de 3 , asi que no es necesario eliminarlo e igualmente los datos 8,10,14 .

SET 3

##  [1] 408.9512 269.3494 422.0902 169.1646 914.8025 371.1766 909.8754 837.6109
##  [9] 298.9121 169.1646 566.6192 520.6327 629.0294 397.4546 555.1225 957.5043
## [17] 845.8228 308.7664 450.0106 344.8986 256.2104 167.5222 323.5478 699.6515
## [25] 596.1819

lnD2H<-log(D)
lnD<-log(D)
lnH<-log(H)
lnDH<-log(DH)
lnDH3<-log(D)
lnD3<-log(D)
DH3<-D*H3

Set3<-data.frame(B, lnD2H, lnD, lnH, lnDH, lnDH3, lnD3  ); Set3

##           B     lnD2H       lnD      lnH     lnDH     lnDH3      lnD3
## 1  408.9512 1.4799387 1.4799387 2.970784 4.450722 1.4799387 1.4799387
## 2  269.3494 1.2066454 1.2066454 3.088567 4.295212 1.2066454 1.2066454
## 3  422.0902 1.4726659 1.4726659 3.074580 4.547246 1.4726659 1.4726659
## 4  169.1646 0.9715256 0.9715256 3.060396 4.031921 0.9715256 0.9715256
## 5  914.8025 1.7174710 1.7174710 3.218620 4.936091 1.7174710 1.7174710
## 6  371.1766 1.2622152 1.2622152 3.193927 4.456142 1.2622152 1.2622152
## 7  909.8754 1.7059766 1.7059766 3.206350 4.912326 1.7059766 1.7059766
## 8  837.6109 1.7456419 1.7456419 3.193927 4.939569 1.7456419 1.7456419
## 9  298.9121 1.2531654 1.2531654 3.129389 4.382554 1.2531654 1.2531654
## 10 169.1646 1.0070323 1.0070323 2.986288 3.993320 1.0070323 1.0070323
## 11 566.6192 1.4943274 1.4943274 3.168609 4.662937 1.4943274 1.4943274
## 12 520.6327 1.5085121 1.5085121 3.193927 4.702439 1.5085121 1.5085121
## 13 629.0294 1.6278588 1.6278588 3.088567 4.716426 1.6278588 1.6278588
## 14 397.4546 1.2800728 1.2800728 3.181348 4.461421 1.2800728 1.2800728
## 15 555.1225 1.4124974 1.4124974 3.254552 4.667049 1.4124974 1.4124974
## 16 957.5043 1.7400708 1.7400708 3.193927 4.933998 1.7400708 1.7400708
## 17 845.8228 1.7456419 1.7456419 3.193927 4.939569 1.7456419 1.7456419
## 18 308.7664 1.2255139 1.2255139 3.206350 4.431864 1.2255139 1.2255139
## 19 450.0106 1.4430341 1.4430341 3.266248 4.709282 1.4430341 1.4430341
## 20 344.8986 1.2888835 1.2888835 3.142634 4.431517 1.2888835 1.2888835
## 21 256.2104 1.2531654 1.2531654 3.001555 4.254721 1.2531654 1.2531654
## 22 167.5222 1.0300218 1.0300218 2.955035 3.985057 1.0300218 1.0300218
## 23 323.5478 1.2348162 1.2348162 3.230741 4.465557 1.2348162 1.2348162
## 24 699.6515 1.6464352 1.6464352 3.155706 4.802141 1.6464352 1.6464352
## 25 596.1819 1.5294188 1.5294188 3.115966 4.645384 1.5294188 1.5294188

Corr<-cor(Set3, method = "pearson")           
round(Corr, digits = 3)

##           B lnD2H   lnD   lnH  lnDH lnDH3  lnD3
## B     1.000 0.950 0.950 0.536 0.941 0.950 0.950
## lnD2H 0.950 1.000 1.000 0.474 0.963 1.000 1.000
## lnD   0.950 1.000 1.000 0.474 0.963 1.000 1.000
## lnH   0.536 0.474 0.474 1.000 0.694 0.474 0.474
## lnDH  0.941 0.963 0.963 0.694 1.000 0.963 0.963
## lnDH3 0.950 1.000 1.000 0.474 0.963 1.000 1.000
## lnD3  0.950 1.000 1.000 0.474 0.963 1.000 1.000

library(psych)
pairs.panels(x = Set3, ellipses = FALSE, lm = TRUE, method = "pearson", hist.col = "#CD1076")

biomasa tiene buena correlacion con la mayoria de las variables , la mas baja es lnH , que tambien se puede observar en figura verde ,lnH es la mas mas lejana a biomasa

*CORRELACION

Otra_Corr=cor(Set3) 
library(qgraph)
qgraph(Otra_Corr, shape="circle", posCol="darkgreen", negCol="darkred", layout="spring", vsize=10)

Paso 1: Hacer un modelo sin variables independientes (vacía).

regvacia3<-lm(formula = B~1, Set3); summary(regvacia3)

## 
## Call:
## lm(formula = B ~ 1, data = Set3)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -328.08 -186.84  -73.51  133.43  461.90 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)   495.60      49.57   9.998 4.94e-10 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 247.9 on 24 degrees of freedom

Paso 2: Hacer un modelo con todas variables independientes (completa)

regcompleta3<-lm(formula = B~.,Set3); 
summary(regcompleta3)

## 
## Call:
## lm(formula = B ~ ., data = Set3)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -114.11  -46.38  -15.47   23.04  138.61 
## 
## Coefficients: (4 not defined because of singularities)
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) -1779.65     581.17  -3.062  0.00571 ** 
## lnD2H         932.14      74.35  12.538 1.71e-11 ***
## lnD               NA         NA      NA       NA    
## lnH           305.75     198.58   1.540  0.13790    
## lnDH              NA         NA      NA       NA    
## lnDH3             NA         NA      NA       NA    
## lnD3              NA         NA      NA       NA    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 76.57 on 22 degrees of freedom
## Multiple R-squared:  0.9125, Adjusted R-squared:  0.9046 
## F-statistic: 114.7 on 2 and 22 DF,  p-value: 2.3e-12

Paso 3: Hacer un modelo con el procedimiento Forward

regforw3<-step(regvacia3, scope = list(lower=regvacia3, upper=regcompleta3),direction = "forward"); summary(regforw3)

## Start:  AIC=276.62
## B ~ 1
## 
##         Df Sum of Sq     RSS    AIC
## + lnD2H  1   1331470  142900 220.28
## + lnD    1   1331470  142900 220.28
## + lnDH3  1   1331470  142900 220.28
## + lnD3   1   1331470  142900 220.28
## + lnDH   1   1306351  168019 224.32
## + lnH    1    423655 1050715 270.15
## <none>               1474370 276.62
## 
## Step:  AIC=220.28
## B ~ lnD2H
## 
##        Df Sum of Sq    RSS    AIC
## + lnDH  1     13901 128999 219.72
## + lnH   1     13901 128999 219.72
## <none>              142900 220.28
## 
## Step:  AIC=219.72
## B ~ lnD2H + lnDH
## 
##        Df Sum of Sq    RSS    AIC
## <none>              128999 219.72

## 
## Call:
## lm(formula = B ~ lnD2H + lnDH, data = Set3)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -114.11  -46.38  -15.47   23.04  138.61 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)   
## (Intercept)  -1779.7      581.2  -3.062  0.00571 **
## lnD2H          626.4      242.8   2.580  0.01710 * 
## lnDH           305.8      198.6   1.540  0.13790   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 76.57 on 22 degrees of freedom
## Multiple R-squared:  0.9125, Adjusted R-squared:  0.9046 
## F-statistic: 114.7 on 2 and 22 DF,  p-value: 2.3e-12

Hacer un modelo con el procedimiento Stepwise

regstep3<-step(regvacia3, scope = list(lower=regvacia3, upper=regcompleta3),direction = "both"); summary(regstep3)

## Start:  AIC=276.62
## B ~ 1
## 
##         Df Sum of Sq     RSS    AIC
## + lnD2H  1   1331470  142900 220.28
## + lnD    1   1331470  142900 220.28
## + lnDH3  1   1331470  142900 220.28
## + lnD3   1   1331470  142900 220.28
## + lnDH   1   1306351  168019 224.32
## + lnH    1    423655 1050715 270.15
## <none>               1474370 276.62
## 
## Step:  AIC=220.28
## B ~ lnD2H
## 
##         Df Sum of Sq     RSS    AIC
## + lnDH   1     13901  128999 219.72
## + lnH    1     13901  128999 219.72
## <none>                142900 220.28
## - lnD2H  1   1331470 1474370 276.62
## 
## Step:  AIC=219.72
## B ~ lnD2H + lnDH
## 
##         Df Sum of Sq    RSS    AIC
## <none>               128999 219.72
## - lnDH   1     13901 142900 220.28
## - lnD2H  1     39019 168019 224.32

## 
## Call:
## lm(formula = B ~ lnD2H + lnDH, data = Set3)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -114.11  -46.38  -15.47   23.04  138.61 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)   
## (Intercept)  -1779.7      581.2  -3.062  0.00571 **
## lnD2H          626.4      242.8   2.580  0.01710 * 
## lnDH           305.8      198.6   1.540  0.13790   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 76.57 on 22 degrees of freedom
## Multiple R-squared:  0.9125, Adjusted R-squared:  0.9046 
## F-statistic: 114.7 on 2 and 22 DF,  p-value: 2.3e-12

Generar un modelo con Boostrap forward

lmFit <-lm(formula = B~.,Set3)      # El modelo, B = variable dependiente.
boot.stepAIC(regstep3, Set3)

## 
## Summary of Bootstrapping the 'stepAIC()' procedure for
## 
## Call:
## lm(formula = B ~ lnD2H + lnDH, data = Set3)
## 
## Bootstrap samples: 100 
## Direction: backward 
## Penalty: 2 * df
## 
## Covariates selected
##       (%)
## lnD2H  94
## lnDH   62
## 
## Coefficients Sign
##        + (%) - (%)
## lnD2H 100.00  0.00
## lnDH   98.39  1.61
## 
## Stat Significance
##         (%)
## lnD2H 76.60
## lnDH  56.45
## 
## 
## The stepAIC() for the original data-set gave
## 
## Call:
## lm(formula = B ~ lnD2H + lnDH, data = Set3)
## 
## Coefficients:
## (Intercept)        lnD2H         lnDH  
##     -1779.7        626.4        305.8  
## 
## 
## Stepwise Model Path 
## Analysis of Deviance Table
## 
## Initial Model:
## B ~ lnD2H + lnDH
## 
## Final Model:
## B ~ lnD2H + lnDH
## 
## 
##   Step Df Deviance Resid. Df Resid. Dev      AIC
## 1                         22   128999.4 219.7172

boot.stepAIC(regstep3, Set3, B = 100, alpha = 0.05, direction = "forward", # Hacer 100 remuestreos 
             
             k = 2, verbose = T)

## 
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##  100 replicate finished

## 
## Summary of Bootstrapping the 'stepAIC()' procedure for
## 
## Call:
## lm(formula = B ~ lnD2H + lnDH, data = Set3)
## 
## Bootstrap samples: 100 
## Direction: forward 
## Penalty: 2 * df
## 
## Covariates selected
##       (%)
## lnD2H 100
## lnDH  100
## 
## Coefficients Sign
##       + (%) - (%)
## lnD2H   100     0
## lnDH     95     5
## 
## Stat Significance
##       (%)
## lnD2H  67
## lnDH   41
## 
## 
## The stepAIC() for the original data-set gave
## 
## Call:
## lm(formula = B ~ lnD2H + lnDH, data = Set3)
## 
## Coefficients:
## (Intercept)        lnD2H         lnDH  
##     -1779.7        626.4        305.8  
## 
## 
## Stepwise Model Path 
## Analysis of Deviance Table
## 
## Initial Model:
## B ~ lnD2H + lnDH
## 
## Final Model:
## B ~ lnD2H + lnDH
## 
## 
##   Step Df Deviance Resid. Df Resid. Dev      AIC
## 1                         22   128999.4 219.7172

Final Model: B ~ lnD2H + lnDH
## ajuste de modelo

MODELO3<-lm(B ~  lnD2H+lnDH, data = Muestra1)  # SIGNIFICATIVO
summary(MODELO3)

## 
## Call:
## lm(formula = B ~ lnD2H + lnDH, data = Muestra1)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -114.11  -46.38  -15.47   23.04  138.61 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)   
## (Intercept)  -1779.7      581.2  -3.062  0.00571 **
## lnD2H          626.4      242.8   2.580  0.01710 * 
## lnDH           305.8      198.6   1.540  0.13790   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 76.57 on 22 degrees of freedom
## Multiple R-squared:  0.9125, Adjusted R-squared:  0.9046 
## F-statistic: 114.7 on 2 and 22 DF,  p-value: 2.3e-12

MODELO3$ residuals

##           1           2           3           4           5           6 
##  -99.235732  -20.102386 -111.053723  107.490701  109.425427   -2.288401 
##           7           8           9          10          11          12 
##  118.964300   13.524470  -46.384289   97.052248  -15.465997  -82.415554 
##          13          14          15          16          17          18 
##  -53.052434   11.189789   23.037253  138.610797   21.736342  -34.286033 
##          19          20          21          22          23          24 
## -114.115322  -37.741842  -50.000541   83.535987  -35.633567  -20.274200 
##          25 
##   -2.517292

la intercept es significativa y la variable lnD2H tambien , Adjusted R-squared: 0.9046 es decir este modelo explica el 90.46% de la biomasa

library(lmtest)
library(car)
summary(influence.measures(MODELO3))

## Potentially influential observations of
##   lm(formula = B ~ lnD2H + lnDH, data = Muestra1) :
## NONE

## numeric(0)

influencePlot(MODELO3)

##      StudRes       Hat     CookD
## 1  -1.556575 0.2620115 0.2693216
## 4   1.606181 0.1813363 0.1777172
## 7   1.712845 0.1050029 0.1054642
## 16  2.067082 0.1190629 0.1675693
## 22  1.265875 0.2369847 0.1614785

deacuerdo a lo anterior se tienen los valores de 1, 4, ,7 ,16, y 22, tienen influencia pero no sobrepasa el valor de 3 , asi que no es necesario eliminarlo.

SET 4

#*VARIABLES*
B

##  [1] 408.9512 269.3494 422.0902 169.1646 914.8025 371.1766 909.8754 837.6109
##  [9] 298.9121 169.1646 566.6192 520.6327 629.0294 397.4546 555.1225 957.5043
## [17] 845.8228 308.7664 450.0106 344.8986 256.2104 167.5222 323.5478 699.6515
## [25] 596.1819

lnD2<-log(D)
lnDH<-log(D)
lnD2H<-log(D)
D3H<-D3*H                 
H2D2<-H2*D2                  
D

##  [1] 4.392676 3.342254 4.360845 2.641972 5.570423 3.533240 5.506761 5.729578
##  [9] 3.501409 2.737465 4.456338 4.520000 5.092958 3.596902 4.106198 5.697747
## [17] 5.729578 3.405916 4.233521 3.628733 3.501409 2.801127 3.437747 5.188451
## [25] 4.615493

##  [1] 19.5072 21.9456 21.6408 21.3360 24.9936 24.3840 24.6888 24.3840 22.8600
## [10] 19.8120 23.7744 24.3840 21.9456 24.0792 25.9080 24.3840 24.3840 24.6888
## [19] 26.2128 23.1648 20.1168 19.2024 25.2984 23.4696 22.5552

Set4<-data.frame(B, lnD2, lnDH, lnD2H, D3H, H2D2,D,H  ); Set4

##           B      lnD2      lnDH     lnD2H       D3H      H2D2        D       H
## 1  408.9512 1.4799387 1.4799387 1.4799387 1653.4177  7342.573 4.392676 19.5072
## 2  269.3494 1.2066454 1.2066454 1.2066454  819.3430  5379.895 3.342254 21.9456
## 3  422.0902 1.4726659 1.4726659 1.4726659 1794.6733  8906.109 4.360845 21.6408
## 4  169.1646 0.9715256 0.9715256 0.9715256  393.4573  3177.477 2.641972 21.3360
## 5  914.8025 1.7174710 1.7174710 1.7174710 4320.0955 19383.580 5.570423 24.9936
## 6  371.1766 1.2622152 1.2622152 1.2622152 1075.5343  7422.601 3.533240 24.3840
## 7  909.8754 1.7059766 1.7059766 1.7059766 4122.7659 18483.850 5.506761 24.6888
## 8  837.6109 1.7456419 1.7456419 1.7456419 4586.4097 19518.892 5.729578 24.3840
## 9  298.9121 1.2531654 1.2531654 1.2531654  981.3065  6406.754 3.501409 22.8600
## 10 169.1646 1.0070323 1.0070323 1.0070323  406.4190  2941.398 2.737465 19.8120
## 11 566.6192 1.4943274 1.4943274 1.4943274 2103.9919 11224.718 4.456338 23.7744
## 12 520.6327 1.5085121 1.5085121 1.5085121 2251.7510 12147.498 4.520000 24.3840
## 13 629.0294 1.6278588 1.6278588 1.6278588 2899.0639 12492.091 5.092958 21.9456
## 14 397.4546 1.2800728 1.2800728 1.2800728 1120.5410  7501.381 3.596902 24.0792
## 15 555.1225 1.4124974 1.4124974 1.4124974 1793.7148 11317.420 4.106198 25.9080
## 16 957.5043 1.7400708 1.7400708 1.7400708 4510.3934 19302.618 5.697747 24.3840
## 17 845.8228 1.7456419 1.7456419 1.7456419 4586.4097 19518.892 5.729578 24.3840
## 18 308.7664 1.2255139 1.2255139 1.2255139  975.4426  7070.787 3.405916 24.6888
## 19 450.0106 1.4430341 1.4430341 1.4430341 1988.9264 12314.885 4.233521 26.2128
## 20 344.8986 1.2888835 1.2888835 1.2888835 1106.8620  7065.893 3.628733 23.1648
## 21 256.2104 1.2531654 1.2531654 1.2531654  863.5497  4961.391 3.501409 20.1168
## 22 167.5222 1.0300218 1.0300218 1.0300218  422.0403  2893.188 2.801127 19.2024
## 23 323.5478 1.2348162 1.2348162 1.2348162 1027.8144  7563.693 3.437747 25.2984
## 24 699.6515 1.6464352 1.6464352 1.6464352 3278.0750 14828.146 5.188451 23.4696
## 25 596.1819 1.5294188 1.5294188 1.5294188 2217.6912 10837.513 4.615493 22.5552

Corr<-cor(Set4, method = "pearson")           # Hacer la correlacion
round(Corr, digits = 3)

##           B  lnD2  lnDH lnD2H   D3H  H2D2     D     H
## B     1.000 0.950 0.950 0.950 0.980 0.982 0.968 0.530
## lnD2  0.950 1.000 1.000 1.000 0.946 0.945 0.994 0.467
## lnDH  0.950 1.000 1.000 1.000 0.946 0.945 0.994 0.467
## lnD2H 0.950 1.000 1.000 1.000 0.946 0.945 0.994 0.467
## D3H   0.980 0.946 0.946 0.946 1.000 0.984 0.974 0.463
## H2D2  0.982 0.945 0.945 0.945 0.984 1.000 0.963 0.604
## D     0.968 0.994 0.994 0.994 0.974 0.963 1.000 0.441
## H     0.530 0.467 0.467 0.467 0.463 0.604 0.441 1.000

library(psych)
pairs.panels(x = Set4, ellipses = FALSE, lm = TRUE, method = "pearson", hist.col = "#CD1076")

library(qgraph)

biomasa tiene alta correlacion con la mayoria de las variables unicamente , la variable H(altura) , es la mas baja con 0.53,este se comprueba tambien con la figura verde .

Otra_Corr=cor(Set4) 
library(qgraph)
qgraph(Otra_Corr, shape="circle", posCol="darkgreen", negCol="darkred", layout="spring", vsize=10)

Paso 1: Hacer un modelo sin variables independientes (vacía).

regvacia4<-lm(formula = B~1, Set4); summary(regvacia4)

## 
## Call:
## lm(formula = B ~ 1, data = Set4)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -328.08 -186.84  -73.51  133.43  461.90 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)   495.60      49.57   9.998 4.94e-10 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 247.9 on 24 degrees of freedom

Paso 2: Hacer un modelo con todas variables independientes (completa)

regcompleta4<-lm(formula = B~.,Set4); 
summary(regcompleta4)

## 
## Call:
## lm(formula = B ~ ., data = Set4)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -91.935 -15.642  -1.829  32.251  62.102 
## 
## Coefficients: (2 not defined because of singularities)
##               Estimate Std. Error t value Pr(>|t|)
## (Intercept) -5.181e+01  4.340e+02  -0.119    0.906
## lnD2        -4.878e+02  1.677e+03  -0.291    0.774
## lnDH                NA         NA      NA       NA
## lnD2H               NA         NA      NA       NA
## D3H         -7.097e-03  2.093e-01  -0.034    0.973
## H2D2         2.777e-02  3.955e-02   0.702    0.491
## D            2.216e+02  5.724e+02   0.387    0.703
## H            1.212e+00  2.031e+01   0.060    0.953
## 
## Residual standard error: 45.75 on 19 degrees of freedom
## Multiple R-squared:  0.973,  Adjusted R-squared:  0.9659 
## F-statistic: 137.1 on 5 and 19 DF,  p-value: 3.164e-14

Paso 3: Hacer un modelo con el procedimiento Forward

regforw4<-step(regvacia4, scope = list(lower=regvacia4, upper=regcompleta4),direction = "forward"); summary(regforw4)

## Start:  AIC=276.62
## B ~ 1
## 
##         Df Sum of Sq     RSS    AIC
## + H2D2   1   1422292   52078 195.04
## + D3H    1   1416589   57781 197.64
## + D      1   1381912   92458 209.39
## + lnD2   1   1331470  142900 220.28
## + lnDH   1   1331470  142900 220.28
## + lnD2H  1   1331470  142900 220.28
## + H      1    414442 1059928 270.37
## <none>               1474370 276.62
## 
## Step:  AIC=195.04
## B ~ H2D2
## 
##         Df Sum of Sq   RSS    AIC
## + D      1   10251.0 41827 191.56
## + H      1    9282.7 42795 192.13
## + D3H    1    8486.3 43592 192.59
## + lnD2   1    6683.8 45394 193.61
## + lnDH   1    6683.8 45394 193.61
## + lnD2H  1    6683.8 45394 193.61
## <none>               52078 195.04
## 
## Step:  AIC=191.56
## B ~ H2D2 + D
## 
##         Df Sum of Sq   RSS    AIC
## <none>               41827 191.56
## + lnD2   1    2050.3 39777 192.30
## + lnDH   1    2050.3 39777 192.30
## + lnD2H  1    2050.3 39777 192.30
## + D3H    1    1887.9 39939 192.41
## + H      1    1597.8 40229 192.59

## 
## Call:
## lm(formula = B ~ H2D2 + D, data = Set4)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -106.635  -20.793   -1.803   26.534   70.215 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept) -1.544e+02  8.279e+01  -1.865   0.0756 .  
## H2D2         3.105e-02  6.018e-03   5.160 3.58e-05 ***
## D            7.761e+01  3.342e+01   2.322   0.0299 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 43.6 on 22 degrees of freedom
## Multiple R-squared:  0.9716, Adjusted R-squared:  0.9691 
## F-statistic: 376.7 on 2 and 22 DF,  p-value: < 2.2e-16

Hacer un modelo con el procedimiento Stepwise

regstep4<-step(regvacia4, scope = list(lower=regvacia4, upper=regcompleta4),direction = "both"); summary(regstep4)

## Start:  AIC=276.62
## B ~ 1
## 
##         Df Sum of Sq     RSS    AIC
## + H2D2   1   1422292   52078 195.04
## + D3H    1   1416589   57781 197.64
## + D      1   1381912   92458 209.39
## + lnD2   1   1331470  142900 220.28
## + lnDH   1   1331470  142900 220.28
## + lnD2H  1   1331470  142900 220.28
## + H      1    414442 1059928 270.37
## <none>               1474370 276.62
## 
## Step:  AIC=195.04
## B ~ H2D2
## 
##         Df Sum of Sq     RSS    AIC
## + D      1     10251   41827 191.56
## + H      1      9283   42795 192.13
## + D3H    1      8486   43592 192.59
## + lnD2   1      6684   45394 193.61
## + lnDH   1      6684   45394 193.61
## + lnD2H  1      6684   45394 193.61
## <none>                 52078 195.04
## - H2D2   1   1422292 1474370 276.62
## 
## Step:  AIC=191.56
## B ~ H2D2 + D
## 
##         Df Sum of Sq   RSS    AIC
## <none>               41827 191.56
## + lnD2   1      2050 39777 192.30
## + lnDH   1      2050 39777 192.30
## + lnD2H  1      2050 39777 192.30
## + D3H    1      1888 39939 192.41
## + H      1      1598 40229 192.59
## - D      1     10251 52078 195.04
## - H2D2   1     50630 92458 209.39

## 
## Call:
## lm(formula = B ~ H2D2 + D, data = Set4)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -106.635  -20.793   -1.803   26.534   70.215 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept) -1.544e+02  8.279e+01  -1.865   0.0756 .  
## H2D2         3.105e-02  6.018e-03   5.160 3.58e-05 ***
## D            7.761e+01  3.342e+01   2.322   0.0299 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 43.6 on 22 degrees of freedom
## Multiple R-squared:  0.9716, Adjusted R-squared:  0.9691 
## F-statistic: 376.7 on 2 and 22 DF,  p-value: < 2.2e-16

Aambos analisis muestran los mismos resultados ## Generar un modelo con Boostrap forward

#set4
lmFit <-lm(formula = B~.,Set4)      
boot.stepAIC(regstep4, Set4)

## 
## Summary of Bootstrapping the 'stepAIC()' procedure for
## 
## Call:
## lm(formula = B ~ H2D2 + D, data = Set4)
## 
## Bootstrap samples: 100 
## Direction: backward 
## Penalty: 2 * df
## 
## Covariates selected
##      (%)
## H2D2  99
## D     90
## 
## Coefficients Sign
##      + (%) - (%)
## D      100     0
## H2D2   100     0
## 
## Stat Significance
##        (%)
## H2D2 93.94
## D    74.44
## 
## 
## The stepAIC() for the original data-set gave
## 
## Call:
## lm(formula = B ~ H2D2 + D, data = Set4)
## 
## Coefficients:
## (Intercept)         H2D2            D  
##  -154.36426      0.03105     77.61324  
## 
## 
## Stepwise Model Path 
## Analysis of Deviance Table
## 
## Initial Model:
## B ~ H2D2 + D
## 
## Final Model:
## B ~ H2D2 + D
## 
## 
##   Step Df Deviance Resid. Df Resid. Dev      AIC
## 1                         22    41827.1 191.5606

boot.stepAIC(regstep4, Set4, B = 100, alpha = 0.05, direction = "forward",
             
             k = 2, verbose = F)

## 
## Summary of Bootstrapping the 'stepAIC()' procedure for
## 
## Call:
## lm(formula = B ~ H2D2 + D, data = Set4)
## 
## Bootstrap samples: 100 
## Direction: forward 
## Penalty: 2 * df
## 
## Covariates selected
##      (%)
## D    100
## H2D2 100
## 
## Coefficients Sign
##      + (%) - (%)
## D      100     0
## H2D2   100     0
## 
## Stat Significance
##      (%)
## H2D2  95
## D     67
## 
## 
## The stepAIC() for the original data-set gave
## 
## Call:
## lm(formula = B ~ H2D2 + D, data = Set4)
## 
## Coefficients:
## (Intercept)         H2D2            D  
##  -154.36426      0.03105     77.61324  
## 
## 
## Stepwise Model Path 
## Analysis of Deviance Table
## 
## Initial Model:
## B ~ H2D2 + D
## 
## Final Model:
## B ~ H2D2 + D
## 
## 
##   Step Df Deviance Resid. Df Resid. Dev      AIC
## 1                         22    41827.1 191.5606

*AJUSTE DE MODELO .

MODELO4<-lm(B ~  H2D2+D, data = Muestra1)  
summary(MODELO4)

## 
## Call:
## lm(formula = B ~ H2D2 + D, data = Muestra1)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -106.635  -20.793   -1.803   26.534   70.215 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept) -1.544e+02  8.279e+01  -1.865   0.0756 .  
## H2D2         3.105e-02  6.018e-03   5.160 3.58e-05 ***
## D            7.761e+01  3.342e+01   2.322   0.0299 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 43.6 on 22 degrees of freedom
## Multiple R-squared:  0.9716, Adjusted R-squared:  0.9691 
## F-statistic: 376.7 on 2 and 22 DF,  p-value: < 2.2e-16

MODELO4$ residuals

##            1            2            3            4            5            6 
##   -5.6344090   -2.7594937  -38.5797448   19.8018045   34.8806015   20.8094341 
##            7            8            9           10           11           12 
##   62.8351699  -58.8655913  -17.4379151   19.7216100   26.5344011  -53.0495689 
##           13           14           15           16           17           18 
##    0.1768685   39.6999218   39.3345325   70.2145341  -50.6537193  -20.7933673 
##           19           20           21           22           23           24 
## -106.6352313   -1.8026894  -15.2545816   14.6353685  -23.7894409   -9.1575857 
##           25 
##   55.7690917

modelo ajustado

rm(list=ls(all=TRUE))
setwd("C:/tarea2/tarea2")
Muestra3 <- read.csv("Muestra3.csv")  
attach(Muestra3[,2:5])

## The following objects are masked from Muestra1[, 2:5]:
## 
##     B, D, H, V

head(Muestra3[,2:5])

##          D       H         V        B
## 1 4.392676 19.5072 0.7050883 408.9512
## 2 3.342254 21.9456 0.4643955 269.3494
## 3 4.360845 21.6408 0.7277418 422.0902
## 4 2.641972 21.3360 0.2916630 169.1646
## 5 5.570423 24.9936 1.5772458 914.8025
## 6 3.533240 24.3840 0.6399597 371.1766

##  [1] 408.9512 269.3494 422.0902 169.1646 914.8025 371.1766 909.8754 837.6109
##  [9] 298.9121 169.1646 566.6192 520.6327 629.0294 397.4546 555.1225 957.5043
## [17] 845.8228 308.7664 344.8986 256.2104 167.5222 323.5478 699.6515 596.1819

D2<-D*D
H2<-H*H                 
H2D2<-H2*D2                 
D

##  [1] 4.392676 3.342254 4.360845 2.641972 5.570423 3.533240 5.506761 5.729578
##  [9] 3.501409 2.737465 4.456338 4.520000 5.092958 3.596902 4.106198 5.697747
## [17] 5.729578 3.405916 3.628733 3.501409 2.801127 3.437747 5.188451 4.615493

##  [1] 19.5072 21.9456 21.6408 21.3360 24.9936 24.3840 24.6888 24.3840 22.8600
## [10] 19.8120 23.7744 24.3840 21.9456 24.0792 25.9080 24.3840 24.3840 24.6888
## [19] 23.1648 20.1168 19.2024 25.2984 23.4696 22.5552

MODELO4.1<-lm(B ~  H2D2+D-1, data = Muestra3)  
summary(MODELO4.1)

## 
## Call:
## lm(formula = B ~ H2D2 + D - 1, data = Muestra3)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -68.873 -21.287  -0.661  25.785  69.467 
## 
## Coefficients:
##       Estimate Std. Error t value Pr(>|t|)    
## H2D2  0.041651   0.002485  16.764 5.14e-14 ***
## D    16.319268   6.704469   2.434   0.0235 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 38.02 on 22 degrees of freedom
## Multiple R-squared:  0.9957, Adjusted R-squared:  0.9953 
## F-statistic:  2553 on 2 and 22 DF,  p-value: < 2.2e-16

MODELO4.1$ residuals

##          1          2          3          4          5          6          7 
##  31.440237  -9.271870 -20.024174  -6.295676  16.551324   4.357778  50.137799 
##          8          9         10         11         12         13         14 
## -68.873471 -25.076187   1.978890  26.373939 -59.086184  25.607631  26.315563 
##         15         16         17         18         19         20         21 
##  16.730226  60.547358 -60.661599 -41.321216  -8.621343  -7.577035   1.305604 
##         22         23         24 
## -47.589321  -2.627715  69.466898

este modelo se ajusto dos veces , uno por la intercept y otro por un dato atipico(num.19), se ha corregido como se deberia , la estadistica nos arroja que las variables son significativas , y que tiene una Rcuadrada ajustada de 0.9953 es decir el 99.53 % .que es muy alto .

library(lmtest)
library(car)
summary(influence.measures(MODELO4.1))

## Potentially influential observations of
##   lm(formula = B ~ H2D2 + D - 1, data = Muestra3) :
## 
##   dfb.H2D2 dfb.D dffit   cov.r   cook.d hat  
## 5  0.17    -0.12  0.21    1.30_*  0.02   0.17
## 8 -0.71     0.51 -0.95_*  0.89    0.39   0.16

influencePlot(MODELO4.1)

##       StudRes        Hat      CookD
## 5   0.4697941 0.17163073 0.02370386
## 8  -2.1362192 0.16430976 0.38608524
## 17 -1.8372820 0.16430976 0.29950699
## 24  2.0021860 0.05321191 0.09909817

lo anterior muestra que efectivamente ya no hay datos atipicos .el modelo ya es correcto .

combrobacion de supuestos

se trabajo de la siguinte manera , para comprobobar los supuestos , se organizaron los resultados que buscamos en unas tablas ,para poder comparar mejor los modelos y porteriormente escoger el mejor .

VARIANZA1.jpg

EL MODELO 2,3 son los que tienen un p-value alto , en comparacion a los demas , es decir la probabilidad de que los errores se distribuyan homogeneamente es alta .

LINEALIDAD1.jpg

DISTRIBUCION1.jpg

El p-value es muy alto en los modelos 2 y 4, es decir; la probabilidad es muy alta que los errores se distribuyan normal.

AUTOCOR1.jpg

un valor cercano a 2, demuestra ausencia de autocorrelación o independencia de los residuales (errores).en este caso el unico modelo mas de 2 , es el modelo 4 .

para concluir , se observa que los modelos 2 y 3 , cumplen por lo menos la mayoria de los supuestos , no los cumplen todos , pero escojo el modelo 2 , pues este modelo tiene mas supuestos cumplidos ademas que ,si considera su Rcuadrada ajustada es del 99.99% es un valor muy alto . el modelo 3 sigue muy de cerca con una Rcuadrada ajustada de 99.53.

para concluir se escoje el modelo 2 es el mas adecuado.

regresion de stepwise

erika paola vicuña espinosa

7/5/2020

SET 1

Paso 1: Hacer un modelo sin variables independientes (vacía).

Paso 2: Hacer un modelo con todas variables independientes (completa)

Paso 3: Hacer un modelo con el procedimiento Forward

Hacer un modelo con el procedimiento Stepwise

Generar un modelo con Boostrap forward

comprobar los supuestos en regresion multiple

set 2

Paso 1: Hacer un modelo sin variables independientes (vacía).

Paso 2: Hacer un modelo con todas variables independientes (completa)

Paso 3: Hacer un modelo con el procedimiento Forward

Generar un modelo con Boostrap forward

4.- Observaciones influyentes y atípicas

SET 3

*CORRELACION

Paso 1: Hacer un modelo sin variables independientes (vacía).

Paso 2: Hacer un modelo con todas variables independientes (completa)

Paso 3: Hacer un modelo con el procedimiento Forward

Hacer un modelo con el procedimiento Stepwise

Generar un modelo con Boostrap forward

SET 4

Paso 1: Hacer un modelo sin variables independientes (vacía).

Paso 2: Hacer un modelo con todas variables independientes (completa)

Paso 3: Hacer un modelo con el procedimiento Forward

Hacer un modelo con el procedimiento Stepwise

*AJUSTE DE MODELO .

modelo ajustado

combrobacion de supuestos