Can root-deformation affect biomass predictions of Genipa americana seedlings?

Complete la información faltante de las celdas del Cuadro 1 y 2.

Table 1. Parameter estimates for “full” ANCOVA models of DM ~ D2, with parameters for root-deformation (Not or Yes) levels

La variable respuesta: pesos secos (DM) Variable categorica: deformacion (yes/no) Covariable: diametro (D2)

library(readxl)
ancova <- read_excel("C:/Users/La Enana/Desktop/I semestre 2021/Biosta/FASE-6-ANCOVA_2.xlsx")

## Registered S3 methods overwritten by 'tibble':
##   method     from  
##   format.tbl pillar
##   print.tbl  pillar

set.seed(2021) 

n <- nrow(ancova)
mu <- sample(n, n * 0.80) #muestra aleatoria del 80%

ancova.train <- ancova[mu, ]
ancova.test <- ancova[-mu, ]

Resultados

¿La relacion de los pesos secos (DM) con respecto al diametro (D2) difiere entre las deformaciones de las raices (yes/no)?

Parámetro 1. LDM (Peso seco foliar)

1.Normalidad

mon<-lm(LDM ~ Deformation + D2, data = ancova.train)
shapiro.test(mon$residuals)

## 
##  Shapiro-Wilk normality test
## 
## data:  mon$residuals
## W = 0.93991, p-value = 0.0009524

#Los datos no cumplen normalidad.

2. Homocedasticidad

library(car)

## Warning: package 'car' was built under R version 4.0.3

## Loading required package: carData

moH<-lm(LDM ~ Deformation, data = ancova.train) 
leveneTest(moH)

## Warning in leveneTest.default(y = y, group = group, ...): group coerced to
## factor.

## Levene's Test for Homogeneity of Variance (center = median)
##       Df F value Pr(>F)
## group  1  0.7643 0.3847
##       78

#Existe homogeneidad entre las varianzas.

3. Linealidad

mol<-lm(LDM ~ D2, data = ancova.train)
summary(mol)

## 
## Call:
## lm(formula = LDM ~ D2, data = ancova.train)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -2.51021 -0.46795 -0.07718  0.29440  2.88742 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 0.256207   0.206841   1.239    0.219    
## D2          0.067809   0.003331  20.359   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.9867 on 78 degrees of freedom
## Multiple R-squared:  0.8416, Adjusted R-squared:  0.8396 
## F-statistic: 414.5 on 1 and 78 DF,  p-value: < 2.2e-16

#El modelo es significativo.

4. Interacción

moi<-lm(LDM ~ Deformation * D2, data = ancova.train)
anova(moi)

## Analysis of Variance Table
## 
## Response: LDM
##                Df Sum Sq Mean Sq  F value    Pr(>F)    
## Deformation     1   8.62    8.62   8.6291  0.004377 ** 
## D2              1 394.93  394.93 395.3538 < 2.2e-16 ***
## Deformation:D2  1   0.01    0.01   0.0056  0.940585    
## Residuals      76  75.92    1.00                       
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

#No existe interacción

5. Modelo ANCOVA

moa<-lm(LDM ~ Deformation * D2, data = ancova.train)
summary(moa)

## 
## Call:
## lm(formula = LDM ~ Deformation * D2, data = ancova.train)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -2.53083 -0.46717 -0.08022  0.30631  2.87361 
## 
## Coefficients:
##                     Estimate Std. Error t value Pr(>|t|)    
## (Intercept)        0.2602733  0.3042009   0.856    0.395    
## DeformationYes    -0.0010296  0.4222119  -0.002    0.998    
## D2                 0.0679758  0.0045465  14.951   <2e-16 ***
## DeformationYes:D2 -0.0005135  0.0068672  -0.075    0.941    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.9995 on 76 degrees of freedom
## Multiple R-squared:  0.8417, Adjusted R-squared:  0.8354 
## F-statistic: 134.7 on 3 and 76 DF,  p-value: < 2.2e-16

moa

## 
## Call:
## lm(formula = LDM ~ Deformation * D2, data = ancova.train)
## 
## Coefficients:
##       (Intercept)     DeformationYes                 D2  DeformationYes:D2  
##         0.2602733         -0.0010296          0.0679758         -0.0005135

6. Plot

library(ggplot2)
p <- ggplot(ancova.train, (aes(x=D2, y=LDM, color=Deformation, shape=Deformation))) + ylab("Peso seco foliar (g)") + xlab("Diametro (cm)") + theme_classic()
p + geom_point() + geom_smooth(method=lm, se=FALSE, fullrange=TRUE)

## `geom_smooth()` using formula 'y ~ x'

Parámetro 2. SDM (Peso seco del vástago)

1. Normalidad

modn<-lm(SDM ~ Deformation + D2, data = ancova.train) 
shapiro.test(modn$residuals)

## 
##  Shapiro-Wilk normality test
## 
## data:  modn$residuals
## W = 0.94801, p-value = 0.002658

#No son normales

2. Homocedasticidad

library(car)

modh<-lm(SDM ~ Deformation, data = ancova.train) 
leveneTest(modh)

## Warning in leveneTest.default(y = y, group = group, ...): group coerced to
## factor.

## Levene's Test for Homogeneity of Variance (center = median)
##       Df F value Pr(>F)
## group  1  2.0177 0.1595
##       78

#Las varianzas son homogeneas

3. Linealidad

modl<-lm(SDM ~ D2, data = ancova.train)
summary(modl)

## 
## Call:
## lm(formula = SDM ~ D2, data = ancova.train)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -1.03262 -0.29316 -0.04105  0.23185  2.16830 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept) -0.462962   0.112910   -4.10    1e-04 ***
## D2           0.036475   0.001818   20.06   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5386 on 78 degrees of freedom
## Multiple R-squared:  0.8377, Adjusted R-squared:  0.8356 
## F-statistic: 402.5 on 1 and 78 DF,  p-value: < 2.2e-16

#El modelo es significativo

4. Interacción

modi<-lm(SDM ~ Deformation * D2, data = ancova.train)
anova(modi)

## Analysis of Variance Table
## 
## Response: SDM
##                Df  Sum Sq Mean Sq  F value    Pr(>F)    
## Deformation     1   4.554   4.554  16.6798 0.0001085 ***
## D2              1 112.599 112.599 412.3811 < 2.2e-16 ***
## Deformation:D2  1   1.485   1.485   5.4379 0.0223553 *  
## Residuals      76  20.751   0.273                       
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

#Se viola el supuesto de no interacción

5. Modelo ANCOVA

moda<-lm(SDM ~ Deformation * D2, data = ancova.train)
summary(moda)

## 
## Call:
## lm(formula = SDM ~ Deformation * D2, data = ancova.train)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -1.13881 -0.21032 -0.03857  0.18749  1.95663 
## 
## Coefficients:
##                    Estimate Std. Error t value Pr(>|t|)    
## (Intercept)       -0.586328   0.159041  -3.687 0.000424 ***
## DeformationYes     0.293565   0.220740   1.330 0.187524    
## D2                 0.039846   0.002377  16.763  < 2e-16 ***
## DeformationYes:D2 -0.008372   0.003590  -2.332 0.022355 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5225 on 76 degrees of freedom
## Multiple R-squared:  0.8511, Adjusted R-squared:  0.8452 
## F-statistic: 144.8 on 3 and 76 DF,  p-value: < 2.2e-16

moda

## 
## Call:
## lm(formula = SDM ~ Deformation * D2, data = ancova.train)
## 
## Coefficients:
##       (Intercept)     DeformationYes                 D2  DeformationYes:D2  
##         -0.586328           0.293565           0.039846          -0.008372

6. Plot

library(ggplot2)
p <- ggplot(ancova.train, (aes(x=D2, y=SDM, color=Deformation, shape=Deformation))) + ylab("Peso seco del vastago (g)") + xlab("Diametro (cm)") + theme_classic()
p + geom_point() + geom_smooth(method=lm, se=FALSE, fullrange=TRUE)

## `geom_smooth()` using formula 'y ~ x'

Parámetro 3. RDM (Peso seco de la raíz)

1. Normalidad

nmo<-lm(RDM ~ Deformation + D2, data = ancova.train) 
shapiro.test(nmo$residuals)

## 
##  Shapiro-Wilk normality test
## 
## data:  nmo$residuals
## W = 0.97303, p-value = 0.08855

#Son normales

2. Homocedasticidad

library(car)

hmo<-lm(RDM ~ Deformation, data = ancova.train) 
leveneTest(hmo)

## Warning in leveneTest.default(y = y, group = group, ...): group coerced to
## factor.

## Levene's Test for Homogeneity of Variance (center = median)
##       Df F value Pr(>F)
## group  1  0.0065  0.936
##       78

#Las varianzas son homogéneas

3. Linealidad

lmo<-lm(RDM ~ D2, data = ancova.train)
summary(lmo)

## 
## Call:
## lm(formula = RDM ~ D2, data = ancova.train)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -2.9712 -0.9829 -0.0301  0.7542  4.6328 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept) -0.803990   0.291599  -2.757  0.00726 ** 
## D2           0.105687   0.004696  22.508  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.391 on 78 degrees of freedom
## Multiple R-squared:  0.8666, Adjusted R-squared:  0.8649 
## F-statistic: 506.6 on 1 and 78 DF,  p-value: < 2.2e-16

#El modelo es significativo

4. Interacción

imo<-lm(RDM ~ Deformation * D2, data = ancova.train)
anova(imo)

## Analysis of Variance Table
## 
## Response: RDM
##                Df Sum Sq Mean Sq  F value Pr(>F)    
## Deformation     1   0.21    0.21   0.1188 0.7313    
## D2              1 995.82  995.82 568.0682 <2e-16 ***
## Deformation:D2  1   1.95    1.95   1.1097 0.2955    
## Residuals      76 133.23    1.75                    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

#La variable respuesta y la covariable no interaccionan

5. Modelo ANCOVA

amo<-lm(RDM ~ Deformation * D2, data = ancova.train)
summary(amo)

## 
## Call:
## lm(formula = RDM ~ Deformation * D2, data = ancova.train)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -2.6190 -0.8771 -0.0611  0.6187  3.8996 
## 
## Coefficients:
##                    Estimate Std. Error t value Pr(>|t|)    
## (Intercept)       -1.111639   0.402978  -2.759  0.00727 ** 
## DeformationYes     0.398477   0.559309   0.712  0.47837    
## D2                 0.103382   0.006023  17.165  < 2e-16 ***
## DeformationYes:D2  0.009583   0.009097   1.053  0.29548    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.324 on 76 degrees of freedom
## Multiple R-squared:  0.8822, Adjusted R-squared:  0.8776 
## F-statistic: 189.8 on 3 and 76 DF,  p-value: < 2.2e-16

amo

## 
## Call:
## lm(formula = RDM ~ Deformation * D2, data = ancova.train)
## 
## Coefficients:
##       (Intercept)     DeformationYes                 D2  DeformationYes:D2  
##         -1.111639           0.398477           0.103382           0.009583

6. Plot

p <- ggplot(ancova.train, (aes(x=D2, y=RDM, color=Deformation, shape=Deformation))) + ylab("Peso seco de la raiz (g)") + xlab("Diametro (cm)") + theme_classic()
p + geom_point() + geom_smooth(method=lm, se=FALSE, fullrange=TRUE)

## `geom_smooth()` using formula 'y ~ x'

Parámetro 4. TDM (Peso seco total)

1. Normalidad de los residuos

nmod<-lm(TDM ~ Deformation + D2, data = ancova.train)
shapiro.test(nmod$residuals)

## 
##  Shapiro-Wilk normality test
## 
## data:  nmod$residuals
## W = 0.96848, p-value = 0.04543

#Son normales

2. Homocedasticidad

library(car)

hmod<-lm(TDM ~ Deformation, data = ancova.train) 
leveneTest(hmod)

## Warning in leveneTest.default(y = y, group = group, ...): group coerced to
## factor.

## Levene's Test for Homogeneity of Variance (center = median)
##       Df F value Pr(>F)
## group  1  0.2369 0.6278
##       78

#Son homogéneas las varianzas

3. Linealidad

lmod<-lm(TDM ~ D2, data = ancova.train)
summary(lmod)

## 
## Call:
## lm(formula = TDM ~ D2, data = ancova.train)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -4.5169 -1.5956 -0.1005  1.1195  6.9438 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept) -1.010746   0.481723  -2.098   0.0391 *  
## D2           0.209971   0.007757  27.068   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 2.298 on 78 degrees of freedom
## Multiple R-squared:  0.9038, Adjusted R-squared:  0.9026 
## F-statistic: 732.7 on 1 and 78 DF,  p-value: < 2.2e-16

#El modelo es significativo

4. Interacción

imod<-lm(TDM ~ Deformation * D2, data = ancova.train)
anova(imod)

## Analysis of Variance Table
## 
## Response: TDM
##                Df Sum Sq Mean Sq  F value  Pr(>F)    
## Deformation     1   30.5    30.5   5.7810 0.01864 *  
## D2              1 3849.1  3849.1 728.5526 < 2e-16 ***
## Deformation:D2  1    0.0     0.0   0.0019 0.96490    
## Residuals      76  401.5     5.3                     
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

#No hay interacción

5. Modelo ANCOVA

amod<-lm(TDM ~ Deformation * D2, data = ancova.train)
summary(amod)

## 
## Call:
## lm(formula = TDM ~ Deformation * D2, data = ancova.train)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -4.9773 -1.5883 -0.2934  1.1806  6.5094 
## 
## Coefficients:
##                     Estimate Std. Error t value Pr(>|t|)    
## (Intercept)       -1.4376934  0.6995822  -2.055   0.0433 *  
## DeformationYes     0.6910122  0.9709766   0.712   0.4788    
## D2                 0.2112037  0.0104558  20.200   <2e-16 ***
## DeformationYes:D2  0.0006972  0.0157928   0.044   0.9649    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 2.299 on 76 degrees of freedom
## Multiple R-squared:  0.9062, Adjusted R-squared:  0.9025 
## F-statistic: 244.8 on 3 and 76 DF,  p-value: < 2.2e-16

amod

## 
## Call:
## lm(formula = TDM ~ Deformation * D2, data = ancova.train)
## 
## Coefficients:
##       (Intercept)     DeformationYes                 D2  DeformationYes:D2  
##        -1.4376934          0.6910122          0.2112037          0.0006972

6. Plot

p <- ggplot(ancova.train, (aes(x=D2, y=TDM, color=Deformation, shape=Deformation))) + ylab("Peso seco total (g)") + xlab("Diametro (cm)") + theme_classic()
p + geom_point() + geom_smooth(method=lm, se=FALSE, fullrange=TRUE)

## `geom_smooth()` using formula 'y ~ x'

Table 2. Relative prediction error (RPE, % mean ± standard deviation) from validation data (n = 40) (Eq. 3)

Parámetro 1. LDM (Peso seco foliar)

Modelo ancova

modancova<-lm(ancova.train$LDM ~ ancova.train$Deformation*ancova.train$D2)
summary(modancova)

## 
## Call:
## lm(formula = ancova.train$LDM ~ ancova.train$Deformation * ancova.train$D2)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -2.53083 -0.46717 -0.08022  0.30631  2.87361 
## 
## Coefficients:
##                                               Estimate Std. Error t value
## (Intercept)                                  0.2602733  0.3042009   0.856
## ancova.train$DeformationYes                 -0.0010296  0.4222119  -0.002
## ancova.train$D2                              0.0679758  0.0045465  14.951
## ancova.train$DeformationYes:ancova.train$D2 -0.0005135  0.0068672  -0.075
##                                             Pr(>|t|)    
## (Intercept)                                    0.395    
## ancova.train$DeformationYes                    0.998    
## ancova.train$D2                               <2e-16 ***
## ancova.train$DeformationYes:ancova.train$D2    0.941    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.9995 on 76 degrees of freedom
## Multiple R-squared:  0.8417, Adjusted R-squared:  0.8354 
## F-statistic: 134.7 on 3 and 76 DF,  p-value: < 2.2e-16

s<-summary(modancova)

Modelo predictivo

pv<-predict(modancova, newdata=data.frame(ancova.test$LDM, ancova.test$Deformation, ancova.test$D2), interval="prediction")

## Warning: 'newdata' had 20 rows but variables found have 80 rows

RPE_mean=mean(((pv[,1]-ancova.test$LDM)/ancova.test$LDM)*100)
RPE_sd= sd(((pv[,1]-ancova.test$LDM)/ancova.test$LDM)*100)

RPE_mean

## [1] 107.3573

RPE_sd

## [1] 364.0816

Parámetro 2. SDM (Peso seco del vástago)

Modelo ancova

modancova2<-lm(ancova.train$SDM ~ ancova.train$Deformation*ancova.train$D2)
summary(modancova2)

## 
## Call:
## lm(formula = ancova.train$SDM ~ ancova.train$Deformation * ancova.train$D2)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -1.13881 -0.21032 -0.03857  0.18749  1.95663 
## 
## Coefficients:
##                                              Estimate Std. Error t value
## (Intercept)                                 -0.586328   0.159041  -3.687
## ancova.train$DeformationYes                  0.293565   0.220740   1.330
## ancova.train$D2                              0.039846   0.002377  16.763
## ancova.train$DeformationYes:ancova.train$D2 -0.008372   0.003590  -2.332
##                                             Pr(>|t|)    
## (Intercept)                                 0.000424 ***
## ancova.train$DeformationYes                 0.187524    
## ancova.train$D2                              < 2e-16 ***
## ancova.train$DeformationYes:ancova.train$D2 0.022355 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5225 on 76 degrees of freedom
## Multiple R-squared:  0.8511, Adjusted R-squared:  0.8452 
## F-statistic: 144.8 on 3 and 76 DF,  p-value: < 2.2e-16

m<-summary(modancova2)

Modelo predictivo

mp<-predict(modancova, newdata=data.frame(ancova.test$SDM, ancova.test$Deformation, ancova.test$D2), interval="prediction")

## Warning: 'newdata' had 20 rows but variables found have 80 rows

Parametros

RPE_mean=mean(((mp[,1]-ancova.test$SDM)/ancova.test$SDM)*100)
RPE_sd= sd(((mp[,1]-ancova.test$SDM)/ancova.test$SDM)*100)
RPE_mean

## [1] 1005.321

RPE_sd

## [1] 2132.889

Parámetro 3. RDM (Peso seco de la raíz)

Modelo ancova

modancova3<-lm(ancova.train$RDM ~ ancova.train$Deformation*ancova.train$D2)
summary(modancova3)

## 
## Call:
## lm(formula = ancova.train$RDM ~ ancova.train$Deformation * ancova.train$D2)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -2.6190 -0.8771 -0.0611  0.6187  3.8996 
## 
## Coefficients:
##                                              Estimate Std. Error t value
## (Intercept)                                 -1.111639   0.402978  -2.759
## ancova.train$DeformationYes                  0.398477   0.559309   0.712
## ancova.train$D2                              0.103382   0.006023  17.165
## ancova.train$DeformationYes:ancova.train$D2  0.009583   0.009097   1.053
##                                             Pr(>|t|)    
## (Intercept)                                  0.00727 ** 
## ancova.train$DeformationYes                  0.47837    
## ancova.train$D2                              < 2e-16 ***
## ancova.train$DeformationYes:ancova.train$D2  0.29548    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.324 on 76 degrees of freedom
## Multiple R-squared:  0.8822, Adjusted R-squared:  0.8776 
## F-statistic: 189.8 on 3 and 76 DF,  p-value: < 2.2e-16

o<-summary(modancova3)

Modelo predictivo

pv2<-predict(modancova3, newdata=data.frame(ancova.test$RDM, ancova.test$Deformation, ancova.test$D2), interval="prediction")

## Warning: 'newdata' had 20 rows but variables found have 80 rows

Parametros

RPE_mean=mean(((pv2[,1]-ancova.test$RDM)/ancova.test$RDM)*100)
RPE_sd= sd(((pv2[,1]-ancova.test$RDM)/ancova.test$RDM)*100)
RPE_mean

## [1] 253.2045

RPE_sd

## [1] 797.2929

Parámetro 4. TDM (Peso seco total)

Modelo ancova

modancova4<-lm(ancova.train$TDM ~ ancova.train$Deformation*ancova.train$D2)
summary(modancova4)

## 
## Call:
## lm(formula = ancova.train$TDM ~ ancova.train$Deformation * ancova.train$D2)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -4.9773 -1.5883 -0.2934  1.1806  6.5094 
## 
## Coefficients:
##                                               Estimate Std. Error t value
## (Intercept)                                 -1.4376934  0.6995822  -2.055
## ancova.train$DeformationYes                  0.6910122  0.9709766   0.712
## ancova.train$D2                              0.2112037  0.0104558  20.200
## ancova.train$DeformationYes:ancova.train$D2  0.0006972  0.0157928   0.044
##                                             Pr(>|t|)    
## (Intercept)                                   0.0433 *  
## ancova.train$DeformationYes                   0.4788    
## ancova.train$D2                               <2e-16 ***
## ancova.train$DeformationYes:ancova.train$D2   0.9649    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 2.299 on 76 degrees of freedom
## Multiple R-squared:  0.9062, Adjusted R-squared:  0.9025 
## F-statistic: 244.8 on 3 and 76 DF,  p-value: < 2.2e-16

s<-summary(modancova4)

Modelo predictivo

pv3<-predict(modancova4, newdata=data.frame(ancova.test$TDM, ancova.test$Deformation, ancova.test$D2), interval="prediction")

## Warning: 'newdata' had 20 rows but variables found have 80 rows

Parametros

RPE_mean=mean(((pv3[,1]-ancova.test$TDM)/ancova.test$TDM)*100)
RPE_sd= sd(((pv3[,1]-ancova.test$TDM)/ancova.test$TDM)*100)
RPE_mean

## [1] 170.0881

RPE_sd

## [1] 553.2315

¿Cuáles variables demostraron efectos significativos del tratamiento? ¿Explicar por qué? ¿Plantear algunas conclusiones del experimento (no olvidar incluir toda la información estadística que válida sus conclusiones)?

La relación que existe entre el peso seco foliar y el diámetro de la raíz al cuadrado es significativa (t (3, 76) = 14.951, p < 0.05), en adición, la deformación en la raíz no mostró efectos estadísticamente significativos sobre la biomasa foliar y el diámetro de la raíz al cuadrado (t (3, 76) = 0.856, p > 0.05). El modelo es significativo (F(3, 76) = 134.7, p < 0.05).

En el caso del peso seco del vástago, se encontró interacción entre las variables, por esto, se decidió no llevar a cabo la prueba de ANCOVA.

La relación entre el peso seco radicular y el diámetro de la raíz al cuadrado es significativa (t (3, 76) = 17.165, p < 0.05), también, la deformación en la raíz no mostró efectos estadísticamente significativos sobre la biomasa radicular y el diámetro de la raíz al cuadrado (t (3, 76) = 0.856, p > 0.05). El modelo es significativo (F (3, 76) = 190, p < 0.05).

Se encontró una relación estadísticamente significativa entre la biomasa total y el diámetro de la raíz al cuadrado (t (3, 76) = 20.200, p < 0.05)). No se encontró un efecto de la deformación de la raíz sobre biomasa total y el diámetro de la raíz al cuadrado (t (3,76) = -2.055, p > 0.05)). Por último, el modelo es significativo (F(3, 76) = 244.8, p < 0.05).

Elaborar algunas figuras que permita demostrar o aclarar los resultados obtenido en la Cuadro 1 y 2.

Las figuras están adjuntas en los resultados de la primera pregunta.

Modelo (LDM): y = (0.2603 + coeficiente) + (0.0680 + coeficiente) * x

y (valor de biomasa foliar), x (diámetro al cuadrado de la raíz) Los coefecientes se usan en caso de ser significativos, de lo contrario se trabaja con el modelo simplificado:

y = (0.2603) + (0.0680) * x

Practica ANCOVA

Fiorella Gazo Bryan

11/6/2021

Can root-deformation affect biomass predictions of Genipa americana seedlings?

Resultados

1.Normalidad

2. Homocedasticidad

3. Linealidad

4. Interacción

5. Modelo ANCOVA

6. Plot

1. Normalidad

2. Homocedasticidad

3. Linealidad

4. Interacción

5. Modelo ANCOVA

6. Plot

1. Normalidad

2. Homocedasticidad

3. Linealidad

4. Interacción

5. Modelo ANCOVA

6. Plot

1. Normalidad de los residuos

2. Homocedasticidad

3. Linealidad

4. Interacción

5. Modelo ANCOVA

6. Plot

Modelo ancova

Modelo predictivo

Modelo ancova

Modelo predictivo

Parametros

Modelo ancova

Modelo predictivo

Parametros

Modelo ancova

Modelo predictivo

Parametros