Actividad 1
Adriana Madrigal
2026-08-13
#Importar paquetes y llamar librerias
#install.packages("readxl")
library(readxl)
#install.packages("plm")
library(plm)
#install.packages("gplots")
library(gplots)#Parte 1. Patentes INSTRUCCIONES: Genera el mejor modelo de la Base de Datos “Patentes” y genera predicciones.
df1 <- read_excel("/Users/adriana/Downloads/PATENT 3.xls")
summary(df1)## cusip merger employ return
## Min. : 800 Min. :0.0000 Min. : 0.085 Min. :-73.022
## 1st Qu.:368514 1st Qu.:0.0000 1st Qu.: 1.227 1st Qu.: 5.128
## Median :501116 Median :0.0000 Median : 3.842 Median : 7.585
## Mean :514536 Mean :0.0177 Mean : 18.826 Mean : 8.003
## 3rd Qu.:754688 3rd Qu.:0.0000 3rd Qu.: 15.442 3rd Qu.: 10.501
## Max. :878555 Max. :1.0000 Max. :506.531 Max. : 48.675
## NAs :21 NAs :8
## patents patentsg stckpr rnd
## Min. : 0.0 Min. : 0.00 Min. : 0.1875 Min. : 0.0000
## 1st Qu.: 1.0 1st Qu.: 1.00 1st Qu.: 7.6250 1st Qu.: 0.6847
## Median : 3.0 Median : 4.00 Median : 16.5000 Median : 2.1456
## Mean : 22.9 Mean : 27.14 Mean : 22.6270 Mean : 29.3398
## 3rd Qu.: 15.0 3rd Qu.: 19.00 3rd Qu.: 29.2500 3rd Qu.: 11.9168
## Max. :906.0 Max. :1063.00 Max. :402.0000 Max. :1719.3535
## NAs :2
## rndeflt rndstck sales sic
## Min. : 0.0000 Min. : 0.1253 Min. : 1.222 Min. :2000
## 1st Qu.: 0.4788 1st Qu.: 5.1520 1st Qu.: 52.995 1st Qu.:2890
## Median : 1.4764 Median : 13.3532 Median : 174.065 Median :3531
## Mean : 19.7238 Mean : 163.8234 Mean : 1219.601 Mean :3333
## 3rd Qu.: 8.7527 3rd Qu.: 74.5625 3rd Qu.: 728.964 3rd Qu.:3661
## Max. :1000.7876 Max. :9755.3516 Max. :44224.000 Max. :9997
## NAs :157 NAs :3
## year
## Min. :2012
## 1st Qu.:2014
## Median :2016
## Mean :2016
## 3rd Qu.:2019
## Max. :2021
## df1 <- pdata.frame(df1, index = c("cusip", "year"))
modelo_regresion <- lm(patents ~ rnd, data = df1)
summary(modelo_regresion) #Usando regresion simple, el modelo nos da que a mas gasto en I+D, mas patentes, pero esto mezcla 226 empresas muy distintas entre si, por eso usamos otros modelos.##
## Call:
## lm(formula = patents ~ rnd, data = df1)
##
## Residuals:
## Min 1Q Median 3Q Max
## -530.08 -13.85 -12.07 -5.13 789.56
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 13.810121 1.257238 10.98 <2e-16 ***
## rnd 0.309919 0.009839 31.50 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 58.17 on 2258 degrees of freedom
## Multiple R-squared: 0.3053, Adjusted R-squared: 0.305
## F-statistic: 992.2 on 1 and 2258 DF, p-value: < 2.2e-16#Prueba de Heterogeneidad
plotmeans(patents ~ cusip, data = df1)## Warning in arrows(x, li, x, pmax(y - gap, li), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, li, x, pmax(y - gap, li), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, li, x, pmax(y - gap, li), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, li, x, pmax(y - gap, li), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, li, x, pmax(y - gap, li), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, li, x, pmax(y - gap, li), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, li, x, pmax(y - gap, li), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, li, x, pmax(y - gap, li), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, li, x, pmax(y - gap, li), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, li, x, pmax(y - gap, li), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, li, x, pmax(y - gap, li), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, li, x, pmax(y - gap, li), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, li, x, pmax(y - gap, li), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, li, x, pmax(y - gap, li), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, li, x, pmax(y - gap, li), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, li, x, pmax(y - gap, li), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, li, x, pmax(y - gap, li), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, li, x, pmax(y - gap, li), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, li, x, pmax(y - gap, li), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, li, x, pmax(y - gap, li), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, li, x, pmax(y - gap, li), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, li, x, pmax(y - gap, li), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, li, x, pmax(y - gap, li), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, li, x, pmax(y - gap, li), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, li, x, pmax(y - gap, li), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, li, x, pmax(y - gap, li), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, li, x, pmax(y - gap, li), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, li, x, pmax(y - gap, li), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, li, x, pmax(y - gap, li), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, li, x, pmax(y - gap, li), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, li, x, pmax(y - gap, li), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, li, x, pmax(y - gap, li), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, li, x, pmax(y - gap, li), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, li, x, pmax(y - gap, li), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, li, x, pmax(y - gap, li), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, li, x, pmax(y - gap, li), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, li, x, pmax(y - gap, li), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, li, x, pmax(y - gap, li), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, li, x, pmax(y - gap, li), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, li, x, pmax(y - gap, li), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, li, x, pmax(y - gap, li), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, li, x, pmax(y - gap, li), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, li, x, pmax(y - gap, li), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, li, x, pmax(y - gap, li), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, li, x, pmax(y - gap, li), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, li, x, pmax(y - gap, li), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, li, x, pmax(y - gap, li), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, li, x, pmax(y - gap, li), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, li, x, pmax(y - gap, li), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, li, x, pmax(y - gap, li), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, li, x, pmax(y - gap, li), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, li, x, pmax(y - gap, li), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, li, x, pmax(y - gap, li), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, li, x, pmax(y - gap, li), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, li, x, pmax(y - gap, li), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, li, x, pmax(y - gap, li), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, li, x, pmax(y - gap, li), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, li, x, pmax(y - gap, li), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, li, x, pmax(y - gap, li), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, li, x, pmax(y - gap, li), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, li, x, pmax(y - gap, li), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, li, x, pmax(y - gap, li), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, li, x, pmax(y - gap, li), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, li, x, pmax(y - gap, li), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, li, x, pmax(y - gap, li), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, li, x, pmax(y - gap, li), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, li, x, pmax(y - gap, li), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, li, x, pmax(y - gap, li), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, li, x, pmax(y - gap, li), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, li, x, pmax(y - gap, li), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, li, x, pmax(y - gap, li), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, li, x, pmax(y - gap, li), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, li, x, pmax(y - gap, li), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, li, x, pmax(y - gap, li), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, li, x, pmax(y - gap, li), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, li, x, pmax(y - gap, li), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, li, x, pmax(y - gap, li), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, li, x, pmax(y - gap, li), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, li, x, pmax(y - gap, li), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, li, x, pmax(y - gap, li), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, li, x, pmax(y - gap, li), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, li, x, pmax(y - gap, li), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, li, x, pmax(y - gap, li), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, li, x, pmax(y - gap, li), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, li, x, pmax(y - gap, li), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, li, x, pmax(y - gap, li), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, li, x, pmax(y - gap, li), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, li, x, pmax(y - gap, li), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, li, x, pmax(y - gap, li), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, li, x, pmax(y - gap, li), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, li, x, pmax(y - gap, li), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, li, x, pmax(y - gap, li), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, li, x, pmax(y - gap, li), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, li, x, pmax(y - gap, li), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, li, x, pmax(y - gap, li), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, li, x, pmax(y - gap, li), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, li, x, pmax(y - gap, li), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, li, x, pmax(y - gap, li), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, li, x, pmax(y - gap, li), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, li, x, pmax(y - gap, li), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, li, x, pmax(y - gap, li), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, li, x, pmax(y - gap, li), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, li, x, pmax(y - gap, li), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, li, x, pmax(y - gap, li), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, li, x, pmax(y - gap, li), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, li, x, pmax(y - gap, li), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, li, x, pmax(y - gap, li), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, li, x, pmax(y - gap, li), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, li, x, pmax(y - gap, li), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, li, x, pmax(y - gap, li), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, li, x, pmax(y - gap, li), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, li, x, pmax(y - gap, li), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, li, x, pmax(y - gap, li), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, li, x, pmax(y - gap, li), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, li, x, pmax(y - gap, li), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, li, x, pmax(y - gap, li), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, li, x, pmax(y - gap, li), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, li, x, pmax(y - gap, li), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, li, x, pmax(y - gap, li), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, li, x, pmax(y - gap, li), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, li, x, pmax(y - gap, li), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, li, x, pmax(y - gap, li), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, li, x, pmax(y - gap, li), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, li, x, pmax(y - gap, li), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, li, x, pmax(y - gap, li), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, li, x, pmax(y - gap, li), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, li, x, pmax(y - gap, li), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, li, x, pmax(y - gap, li), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, li, x, pmax(y - gap, li), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, li, x, pmax(y - gap, li), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, li, x, pmax(y - gap, li), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, li, x, pmax(y - gap, li), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, li, x, pmax(y - gap, li), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, li, x, pmax(y - gap, li), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, li, x, pmax(y - gap, li), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, li, x, pmax(y - gap, li), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, li, x, pmax(y - gap, li), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, li, x, pmax(y - gap, li), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, li, x, pmax(y - gap, li), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, li, x, pmax(y - gap, li), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, li, x, pmax(y - gap, li), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, li, x, pmax(y - gap, li), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, li, x, pmax(y - gap, li), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, li, x, pmax(y - gap, li), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, li, x, pmax(y - gap, li), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, li, x, pmax(y - gap, li), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, li, x, pmax(y - gap, li), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, li, x, pmax(y - gap, li), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, li, x, pmax(y - gap, li), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, li, x, pmax(y - gap, li), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, li, x, pmax(y - gap, li), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, li, x, pmax(y - gap, li), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, li, x, pmax(y - gap, li), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, li, x, pmax(y - gap, li), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, li, x, pmax(y - gap, li), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, li, x, pmax(y - gap, li), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, li, x, pmax(y - gap, li), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, li, x, pmax(y - gap, li), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, li, x, pmax(y - gap, li), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, li, x, pmax(y - gap, li), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, li, x, pmax(y - gap, li), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, li, x, pmax(y - gap, li), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, li, x, pmax(y - gap, li), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, li, x, pmax(y - gap, li), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, li, x, pmax(y - gap, li), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, li, x, pmax(y - gap, li), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, li, x, pmax(y - gap, li), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, li, x, pmax(y - gap, li), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, li, x, pmax(y - gap, li), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, li, x, pmax(y - gap, li), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, li, x, pmax(y - gap, li), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, li, x, pmax(y - gap, li), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, li, x, pmax(y - gap, li), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, li, x, pmax(y - gap, li), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, li, x, pmax(y - gap, li), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, li, x, pmax(y - gap, li), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, li, x, pmax(y - gap, li), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, li, x, pmax(y - gap, li), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, li, x, pmax(y - gap, li), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, li, x, pmax(y - gap, li), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, li, x, pmax(y - gap, li), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, li, x, pmax(y - gap, li), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, li, x, pmax(y - gap, li), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, li, x, pmax(y - gap, li), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, li, x, pmax(y - gap, li), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, li, x, pmax(y - gap, li), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, li, x, pmax(y - gap, li), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, li, x, pmax(y - gap, li), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, li, x, pmax(y - gap, li), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, li, x, pmax(y - gap, li), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, li, x, pmax(y - gap, li), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, li, x, pmax(y - gap, li), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, li, x, pmax(y - gap, li), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, li, x, pmax(y - gap, li), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, li, x, pmax(y - gap, li), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, li, x, pmax(y - gap, li), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, li, x, pmax(y - gap, li), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, li, x, pmax(y - gap, li), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, li, x, pmax(y - gap, li), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, li, x, pmax(y - gap, li), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, li, x, pmax(y - gap, li), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, li, x, pmax(y - gap, li), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, li, x, pmax(y - gap, li), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, li, x, pmax(y - gap, li), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, li, x, pmax(y - gap, li), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, li, x, pmax(y - gap, li), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, li, x, pmax(y - gap, li), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, li, x, pmax(y - gap, li), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, li, x, pmax(y - gap, li), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, li, x, pmax(y - gap, li), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, li, x, pmax(y - gap, li), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, li, x, pmax(y - gap, li), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, li, x, pmax(y - gap, li), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, li, x, pmax(y - gap, li), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, li, x, pmax(y - gap, li), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, li, x, pmax(y - gap, li), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, li, x, pmax(y - gap, li), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, li, x, pmax(y - gap, li), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, li, x, pmax(y - gap, li), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, li, x, pmax(y - gap, li), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, li, x, pmax(y - gap, li), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped## Warning in arrows(x, ui, x, pmin(y + gap, ui), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, ui, x, pmin(y + gap, ui), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, ui, x, pmin(y + gap, ui), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, ui, x, pmin(y + gap, ui), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, ui, x, pmin(y + gap, ui), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, ui, x, pmin(y + gap, ui), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, ui, x, pmin(y + gap, ui), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, ui, x, pmin(y + gap, ui), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, ui, x, pmin(y + gap, ui), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, ui, x, pmin(y + gap, ui), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, ui, x, pmin(y + gap, ui), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, ui, x, pmin(y + gap, ui), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, ui, x, pmin(y + gap, ui), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, ui, x, pmin(y + gap, ui), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, ui, x, pmin(y + gap, ui), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, ui, x, pmin(y + gap, ui), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, ui, x, pmin(y + gap, ui), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, ui, x, pmin(y + gap, ui), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, ui, x, pmin(y + gap, ui), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, ui, x, pmin(y + gap, ui), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, ui, x, pmin(y + gap, ui), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, ui, x, pmin(y + gap, ui), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, ui, x, pmin(y + gap, ui), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, ui, x, pmin(y + gap, ui), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, ui, x, pmin(y + gap, ui), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, ui, x, pmin(y + gap, ui), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, ui, x, pmin(y + gap, ui), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, ui, x, pmin(y + gap, ui), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, ui, x, pmin(y + gap, ui), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, ui, x, pmin(y + gap, ui), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, ui, x, pmin(y + gap, ui), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, ui, x, pmin(y + gap, ui), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, ui, x, pmin(y + gap, ui), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, ui, x, pmin(y + gap, ui), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, ui, x, pmin(y + gap, ui), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, ui, x, pmin(y + gap, ui), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, ui, x, pmin(y + gap, ui), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, ui, x, pmin(y + gap, ui), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, ui, x, pmin(y + gap, ui), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, ui, x, pmin(y + gap, ui), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, ui, x, pmin(y + gap, ui), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, ui, x, pmin(y + gap, ui), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, ui, x, pmin(y + gap, ui), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, ui, x, pmin(y + gap, ui), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, ui, x, pmin(y + gap, ui), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, ui, x, pmin(y + gap, ui), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, ui, x, pmin(y + gap, ui), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, ui, x, pmin(y + gap, ui), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, ui, x, pmin(y + gap, ui), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, ui, x, pmin(y + gap, ui), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, ui, x, pmin(y + gap, ui), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, ui, x, pmin(y + gap, ui), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, ui, x, pmin(y + gap, ui), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, ui, x, pmin(y + gap, ui), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, ui, x, pmin(y + gap, ui), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, ui, x, pmin(y + gap, ui), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, ui, x, pmin(y + gap, ui), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, ui, x, pmin(y + gap, ui), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, ui, x, pmin(y + gap, ui), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, ui, x, pmin(y + gap, ui), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, ui, x, pmin(y + gap, ui), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, ui, x, pmin(y + gap, ui), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, ui, x, pmin(y + gap, ui), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, ui, x, pmin(y + gap, ui), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, ui, x, pmin(y + gap, ui), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, ui, x, pmin(y + gap, ui), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, ui, x, pmin(y + gap, ui), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, ui, x, pmin(y + gap, ui), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, ui, x, pmin(y + gap, ui), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, ui, x, pmin(y + gap, ui), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, ui, x, pmin(y + gap, ui), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, ui, x, pmin(y + gap, ui), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, ui, x, pmin(y + gap, ui), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, ui, x, pmin(y + gap, ui), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, ui, x, pmin(y + gap, ui), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, ui, x, pmin(y + gap, ui), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, ui, x, pmin(y + gap, ui), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, ui, x, pmin(y + gap, ui), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, ui, x, pmin(y + gap, ui), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, ui, x, pmin(y + gap, ui), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, ui, x, pmin(y + gap, ui), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, ui, x, pmin(y + gap, ui), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, ui, x, pmin(y + gap, ui), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, ui, x, pmin(y + gap, ui), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, ui, x, pmin(y + gap, ui), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, ui, x, pmin(y + gap, ui), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, ui, x, pmin(y + gap, ui), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, ui, x, pmin(y + gap, ui), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, ui, x, pmin(y + gap, ui), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, ui, x, pmin(y + gap, ui), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, ui, x, pmin(y + gap, ui), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, ui, x, pmin(y + gap, ui), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, ui, x, pmin(y + gap, ui), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, ui, x, pmin(y + gap, ui), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, ui, x, pmin(y + gap, ui), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, ui, x, pmin(y + gap, ui), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, ui, x, pmin(y + gap, ui), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, ui, x, pmin(y + gap, ui), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, ui, x, pmin(y + gap, ui), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, ui, x, pmin(y + gap, ui), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, ui, x, pmin(y + gap, ui), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, ui, x, pmin(y + gap, ui), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, ui, x, pmin(y + gap, ui), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, ui, x, pmin(y + gap, ui), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, ui, x, pmin(y + gap, ui), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, ui, x, pmin(y + gap, ui), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, ui, x, pmin(y + gap, ui), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, ui, x, pmin(y + gap, ui), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, ui, x, pmin(y + gap, ui), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, ui, x, pmin(y + gap, ui), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, ui, x, pmin(y + gap, ui), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, ui, x, pmin(y + gap, ui), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, ui, x, pmin(y + gap, ui), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, ui, x, pmin(y + gap, ui), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, ui, x, pmin(y + gap, ui), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, ui, x, pmin(y + gap, ui), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, ui, x, pmin(y + gap, ui), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, ui, x, pmin(y + gap, ui), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, ui, x, pmin(y + gap, ui), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, ui, x, pmin(y + gap, ui), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, ui, x, pmin(y + gap, ui), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, ui, x, pmin(y + gap, ui), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, ui, x, pmin(y + gap, ui), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, ui, x, pmin(y + gap, ui), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, ui, x, pmin(y + gap, ui), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, ui, x, pmin(y + gap, ui), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, ui, x, pmin(y + gap, ui), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, ui, x, pmin(y + gap, ui), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, ui, x, pmin(y + gap, ui), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, ui, x, pmin(y + gap, ui), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, ui, x, pmin(y + gap, ui), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, ui, x, pmin(y + gap, ui), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, ui, x, pmin(y + gap, ui), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, ui, x, pmin(y + gap, ui), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, ui, x, pmin(y + gap, ui), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, ui, x, pmin(y + gap, ui), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, ui, x, pmin(y + gap, ui), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, ui, x, pmin(y + gap, ui), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, ui, x, pmin(y + gap, ui), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, ui, x, pmin(y + gap, ui), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, ui, x, pmin(y + gap, ui), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, ui, x, pmin(y + gap, ui), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, ui, x, pmin(y + gap, ui), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, ui, x, pmin(y + gap, ui), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, ui, x, pmin(y + gap, ui), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, ui, x, pmin(y + gap, ui), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, ui, x, pmin(y + gap, ui), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, ui, x, pmin(y + gap, ui), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, ui, x, pmin(y + gap, ui), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, ui, x, pmin(y + gap, ui), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, ui, x, pmin(y + gap, ui), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, ui, x, pmin(y + gap, ui), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, ui, x, pmin(y + gap, ui), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, ui, x, pmin(y + gap, ui), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, ui, x, pmin(y + gap, ui), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, ui, x, pmin(y + gap, ui), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, ui, x, pmin(y + gap, ui), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, ui, x, pmin(y + gap, ui), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, ui, x, pmin(y + gap, ui), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, ui, x, pmin(y + gap, ui), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, ui, x, pmin(y + gap, ui), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, ui, x, pmin(y + gap, ui), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, ui, x, pmin(y + gap, ui), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, ui, x, pmin(y + gap, ui), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, ui, x, pmin(y + gap, ui), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, ui, x, pmin(y + gap, ui), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, ui, x, pmin(y + gap, ui), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, ui, x, pmin(y + gap, ui), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, ui, x, pmin(y + gap, ui), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, ui, x, pmin(y + gap, ui), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, ui, x, pmin(y + gap, ui), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, ui, x, pmin(y + gap, ui), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, ui, x, pmin(y + gap, ui), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, ui, x, pmin(y + gap, ui), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, ui, x, pmin(y + gap, ui), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, ui, x, pmin(y + gap, ui), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, ui, x, pmin(y + gap, ui), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, ui, x, pmin(y + gap, ui), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, ui, x, pmin(y + gap, ui), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, ui, x, pmin(y + gap, ui), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, ui, x, pmin(y + gap, ui), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, ui, x, pmin(y + gap, ui), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, ui, x, pmin(y + gap, ui), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, ui, x, pmin(y + gap, ui), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, ui, x, pmin(y + gap, ui), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, ui, x, pmin(y + gap, ui), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, ui, x, pmin(y + gap, ui), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, ui, x, pmin(y + gap, ui), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, ui, x, pmin(y + gap, ui), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, ui, x, pmin(y + gap, ui), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, ui, x, pmin(y + gap, ui), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, ui, x, pmin(y + gap, ui), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, ui, x, pmin(y + gap, ui), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, ui, x, pmin(y + gap, ui), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, ui, x, pmin(y + gap, ui), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, ui, x, pmin(y + gap, ui), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, ui, x, pmin(y + gap, ui), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, ui, x, pmin(y + gap, ui), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, ui, x, pmin(y + gap, ui), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, ui, x, pmin(y + gap, ui), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, ui, x, pmin(y + gap, ui), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, ui, x, pmin(y + gap, ui), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, ui, x, pmin(y + gap, ui), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, ui, x, pmin(y + gap, ui), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, ui, x, pmin(y + gap, ui), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, ui, x, pmin(y + gap, ui), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, ui, x, pmin(y + gap, ui), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, ui, x, pmin(y + gap, ui), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, ui, x, pmin(y + gap, ui), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, ui, x, pmin(y + gap, ui), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, ui, x, pmin(y + gap, ui), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, ui, x, pmin(y + gap, ui), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, ui, x, pmin(y + gap, ui), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, ui, x, pmin(y + gap, ui), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, ui, x, pmin(y + gap, ui), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, ui, x, pmin(y + gap, ui), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, ui, x, pmin(y + gap, ui), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, ui, x, pmin(y + gap, ui), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, ui, x, pmin(y + gap, ui), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, ui, x, pmin(y + gap, ui), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, ui, x, pmin(y + gap, ui), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
#INTERPRETACIÓN: La línea no es horizontal: hay empresas con muchas más patentes que otras, así que sí hay heterogeneidad.# Opcion 1 - Modelo de Regresión Agrupada (Pooled)
pooled <- plm(patents ~ rnd, data = df1, model = "pooling")
summary(pooled)## Pooling Model
##
## Call:
## plm(formula = patents ~ rnd, data = df1, model = "pooling")
##
## Balanced Panel: n = 226, T = 10, N = 2260
##
## Residuals:
## Min. 1st Qu. Median 3rd Qu. Max.
## -530.08 -13.85 -12.07 -5.13 789.56
##
## Coefficients:
## Estimate Std. Error t-value Pr(>|t|)
## (Intercept) 13.8101209 1.2572385 10.985 < 2.2e-16 ***
## rnd 0.3099192 0.0098392 31.499 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Total Sum of Squares: 10998000
## Residual Sum of Squares: 7640900
## R-Squared: 0.30526
## Adj. R-Squared: 0.30496
## F-statistic: 992.16 on 1 and 2258 DF, p-value: < 2.22e-16#Opcion 2 - Modelo de Efectos Fijos (within)
within <- plm(patents ~ rnd, data = df1, model = "within")
summary(within)## Oneway (individual) effect Within Model
##
## Call:
## plm(formula = patents ~ rnd, data = df1, model = "within")
##
## Balanced Panel: n = 226, T = 10, N = 2260
##
## Residuals:
## Min. 1st Qu. Median 3rd Qu. Max.
## -504.869 -1.565 -0.257 1.555 189.024
##
## Coefficients:
## Estimate Std. Error t-value Pr(>|t|)
## rnd -0.26365 0.01077 -24.48 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Total Sum of Squares: 1091400
## Residual Sum of Squares: 842960
## R-Squared: 0.22766
## Adj. R-Squared: 0.1418
## F-statistic: 599.259 on 1 and 2033 DF, p-value: < 2.22e-16#Prueba F
#INTERPRETACIÓN: Si la p es menor a 0.05 no usar POOLED, si p es mayor a 0.05 usar pooled.
pFtest(within, pooled) ##
## F test for individual effects
##
## data: patents ~ rnd
## F = 72.866, df1 = 225, df2 = 2033, p-value < 2.2e-16
## alternative hypothesis: significant effects#Opcion 3 - Modelo de Efectos Aleatorios (Random)
random <- plm(patents ~ rnd, data = df1, model = "random")
summary(random)## Oneway (individual) effect Random Effect Model
## (Swamy-Arora's transformation)
##
## Call:
## plm(formula = patents ~ rnd, data = df1, model = "random")
##
## Balanced Panel: n = 226, T = 10, N = 2260
##
## Effects:
## var std.dev share
## idiosyncratic 414.64 20.36 0.147
## individual 2408.53 49.08 0.853
## theta: 0.8699
##
## Residuals:
## Min. 1st Qu. Median 3rd Qu. Max.
## -424.755 -4.456 -3.443 -0.733 225.888
##
## Coefficients:
## Estimate Std. Error z-value Pr(>|z|)
## (Intercept) 28.213748 3.622943 7.7875 6.834e-15 ***
## rnd -0.181005 0.011014 -16.4345 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Total Sum of Squares: 1259100
## Residual Sum of Squares: 1124600
## R-Squared: 0.10684
## Adj. R-Squared: 0.10644
## Chisq: 270.091 on 1 DF, p-value: < 2.22e-16#Prueba de Hausman
#INTERPRETACIÓN: Si la p es menor a 0.05 usar efectos fijos, si sale mayor usar efectos aleatorios.
phtest(random, within) ##
## Hausman Test
##
## data: patents ~ rnd
## chisq = 1286, df = 1, p-value < 2.2e-16
## alternative hypothesis: one model is inconsistent#Por lo tanto, el mejor modelo para este panel es el de EFECTOS FIJOS. La prueba F rechaza Pooled (sí hay heterogeneidad) y la prueba de Hausman rechaza Aleatorios (esa heterogeneidad está correlacionada con el gasto en I+D: las empresas que más patentan también son las que más invierten).df1_pronostico <- data.frame(
cusip = c("149123", "369604", "459200"),
year = c(2022, 2022, 2022),
rnd = c(226.5315, 813.7559, 1611.4912) * 1.10
)
intercepto <- fixef(within)
pendiente <- coef(within)["rnd"]
df1_pronostico$patentes <- intercepto[df1_pronostico$cusip] + pendiente * df1_pronostico$rnd
df1_pronostico[, c("patentes")]## [1] 217.4013 651.4144 245.4632CONCLUSIÓN: El mejor modelo es el de Efectos Fijos. Más gasto en I+D no reduce las patentes; simplemente toma tiempo convertirse en patentes solicitadas. Para las 3 empresas con más patentes, un aumento del 10% en I+D da un pronóstico distinto para cada una, porque cada empresa parte de un nivel distinto.
#Parte 2. Cuidado de la piel INSTRUCCIONES: ¿En cuál
categoría invertirías y por qué? Si tuvieras que invertir en alguna
subcategoría, ¿en cuál lo harías? Justifica de acuerdo al modelo.
df2_excel <- read_excel("/Users/adriana/Downloads/Market sizes.xls")
summary(df2_excel)## Geography Category Data Type Unit Current Constant
## Length :13 Length :13 Length :13 Length :13 Length :13
## N.unique : 1 N.unique :13 N.unique : 1 N.unique : 1 N.unique : 1
## N.blank : 0 N.blank : 0 N.blank : 0 N.blank : 0 N.blank : 0
## Min.nchar: 6 Min.nchar: 8 Min.nchar:16 Min.nchar:11 Min.nchar:14
## Max.nchar: 6 Max.nchar:39 Max.nchar:16 Max.nchar:11 Max.nchar:14
##
## 2011 2012 2013 2014 2015
## Length :13 Length :13 Length :13 Length :13 Length :13
## N.unique :12 N.unique :12 N.unique :12 N.unique :12 N.unique :12
## N.blank : 0 N.blank : 0 N.blank : 0 N.blank : 0 N.blank : 0
## Min.nchar: 1 Min.nchar: 1 Min.nchar: 1 Min.nchar: 1 Min.nchar: 1
## Max.nchar:18 Max.nchar:18 Max.nchar:18 Max.nchar:18 Max.nchar:18
##
## 2016 2017 2018 2019
## Min. : 1188 Min. : 1320 Min. : 1439 Min. : 1516
## 1st Qu.: 11482 1st Qu.: 12123 1st Qu.: 12490 1st Qu.: 12960
## Median : 21783 Median : 24478 Median : 26344 Median : 27806
## Mean : 37710 Mean : 40692 Mean : 42891 Mean : 44853
## 3rd Qu.: 32384 3rd Qu.: 34260 3rd Qu.: 35597 3rd Qu.: 37247
## Max. :170488 Max. :183580 Max. :192727 Max. :200916
## 2020 2021 2022 2023
## Min. : 1491 Min. : 1564 Min. : 1689 Min. : 1850
## 1st Qu.: 13835 1st Qu.: 15091 1st Qu.: 16815 1st Qu.: 19001
## Median : 23213 Median : 30225 Median : 37173 Median : 43366
## Mean : 42589 Mean : 47822 Mean : 53823 Mean : 61738
## 3rd Qu.: 36951 3rd Qu.: 39555 3rd Qu.: 42739 3rd Qu.: 46900
## Max. :191490 Max. :211921 Max. :236406 Max. :268852
## 2024 2025
## Min. : 1802 Min. : 1873
## 1st Qu.: 20235 1st Qu.: 21342
## Median : 47334 Median : 49508
## Mean : 68537 Mean : 72844
## 3rd Qu.: 53798 3rd Qu.: 58846
## Max. :296120 Max. :313593df2 <- data.frame(
categoria = c(rep("Bath and Shower",15), rep("Deodorants",15), rep("Depilatories",15),
rep("Fragrances",15), rep("Hair Care",15), rep("Mens Grooming",15),
rep("Skin Care",15), rep("Sun Care",15)),
anio = rep(2011:2025, 8),
valor = c(
8410.4, 9085, 9711.1, 10226.9, 10814.8, 11481.6, 12123.1, 12490.1, 12959.5, 14633.9, 15469.3, 16815.3, 19001, 20234.6, 21341.7,
9151, 10148.3, 10697.7, 11469.7, 12379.2, 13723.4, 14891.6, 15913.6, 16745.1, 13834.8, 15091.1, 17872.4, 19454.9, 20787.8, 21824.1,
802.5, 897.7, 969.9, 1036.3, 1106.4, 1187.9, 1319.5, 1439.1, 1516.1, 1491.2, 1563.5, 1688.6, 1850.2, 1802, 1872.8,
18727.9, 19957.2, 20651.8, 20979.6, 22567.6, 24208.9, 26152.3, 27536, 28483.1, 25516.1, 31800.8, 37172.8, 45318.9, 51579.2, 56742.1,
24853.9, 26565.6, 27672.5, 29154.6, 30416.2, 32383.6, 34260, 35597.2, 37247.4, 36950.7, 39554.7, 42738.8, 46900.3, 53024.9, 56289.8,
18672.1, 20694.4, 22133.4, 23175.3, 24774, 27446, 29497.2, 31498.1, 32693.3, 29669.4, 32938.6, 37702.4, 43366.2, 47333.8, 49508.4,
25650.3, 27306.2, 28366.9, 29438.3, 30964, 33054.3, 35787.8, 38067.5, 40637.5, 42196.5, 47980.6, 52939.6, 61023.6, 68590.4, 71830,
1144.7, 1303.1, 1417.3, 1552.8, 1693.3, 1944.1, 2143.3, 2266.5, 2443.8, 2042.9, 2293.6, 2862, 3736.4, 4183.4, 4326.4
)
)
df2$t <- df2$anio #copia numérica de anio; anio ya es el índice del panel, así que si lo usamos directo en el modelo R lo vuelve categórico (uno por año) en vez de número, y por eso salían los NA
df2 <- pdata.frame(df2, index = c("categoria","anio"))modelo_regresion2 <- lm(valor ~ t, data = df2)
summary(modelo_regresion2)##
## Call:
## lm(formula = valor ~ t, data = df2)
##
## Residuals:
## Min 1Q Median 3Q Max
## -30062 -10733 -673 13521 39895
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -2937049.2 670768.7 -4.379 2.60e-05 ***
## t 1466.2 332.4 4.411 2.29e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 15730 on 118 degrees of freedom
## Multiple R-squared: 0.1415, Adjusted R-squared: 0.1343
## F-statistic: 19.46 on 1 and 118 DF, p-value: 2.287e-05#Prueba de Heterogeneidad
plotmeans(valor ~ categoria, data = df2)## Warning in arrows(x, li, x, pmax(y - gap, li), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, li, x, pmax(y - gap, li), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped## Warning in arrows(x, ui, x, pmin(y + gap, ui), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, ui, x, pmin(y + gap, ui), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
#INTERPRETACIÓN: Skin Care y Hair Care operan en un nivel de mercado mucho más grande que Depilatories o Sun Care: sí hay heterogeneidad.# Opcion 1 - Modelo de Regresión Agrupada (Pooled)
pooled2 <- plm(valor ~ t, data = df2, model = "pooling")
summary(pooled2)## Pooling Model
##
## Call:
## plm(formula = valor ~ t, data = df2, model = "pooling")
##
## Balanced Panel: n = 8, T = 15, N = 120
##
## Residuals:
## Min. 1st Qu. Median 3rd Qu. Max.
## -30062 -10733 -673 13521 39895
##
## Coefficients:
## Estimate Std. Error t-value Pr(>|t|)
## (Intercept) -2937049.22 670768.71 -4.3786 2.598e-05 ***
## t 1466.17 332.39 4.4110 2.287e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Total Sum of Squares: 3.4018e+10
## Residual Sum of Squares: 2.9203e+10
## R-Squared: 0.14155
## Adj. R-Squared: 0.13427
## F-statistic: 19.4565 on 1 and 118 DF, p-value: 2.2866e-05#Opcion 2 - Modelo de Efectos Fijos (within)
within2 <- plm(valor ~ t, data = df2, model = "within")
summary(within2)## Oneway (individual) effect Within Model
##
## Call:
## plm(formula = valor ~ t, data = df2, model = "within")
##
## Balanced Panel: n = 8, T = 15, N = 120
##
## Residuals:
## Min. 1st Qu. Median 3rd Qu. Max.
## -9760 -3015 -1523 2555 19311
##
## Coefficients:
## Estimate Std. Error t-value Pr(>|t|)
## t 1466.17 116.12 12.626 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Total Sum of Squares: 8.168e+09
## Residual Sum of Squares: 3352800000
## R-Squared: 0.58952
## Adj. R-Squared: 0.55993
## F-statistic: 159.413 on 1 and 111 DF, p-value: < 2.22e-16#Prueba F
pFtest(within2, pooled2) ##
## F test for individual effects
##
## data: valor ~ t
## F = 122.26, df1 = 7, df2 = 111, p-value < 2.2e-16
## alternative hypothesis: significant effects#Opcion 3 - Modelo de Efectos Aleatorios (Random)
random2 <- plm(valor ~ t, data = df2, model = "random")
summary(random2)## Oneway (individual) effect Random Effect Model
## (Swamy-Arora's transformation)
##
## Call:
## plm(formula = valor ~ t, data = df2, model = "random")
##
## Balanced Panel: n = 8, T = 15, N = 120
##
## Effects:
## var std.dev share
## idiosyncratic 30205839 5496 0.11
## individual 244180653 15626 0.89
## theta: 0.9096
##
## Residuals:
## Min. 1st Qu. Median 3rd Qu. Max.
## -11596 -3144 -709 1841 21173
##
## Coefficients:
## Estimate Std. Error z-value Pr(>|z|)
## (Intercept) -2937049.22 234403.59 -12.530 < 2.2e-16 ***
## t 1466.17 116.12 12.626 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Total Sum of Squares: 8379500000
## Residual Sum of Squares: 3564300000
## R-Squared: 0.57464
## Adj. R-Squared: 0.57104
## Chisq: 159.413 on 1 DF, p-value: < 2.22e-16#Prueba de Hausman
#INTERPRETACIÓN: Si la p es menor a 0.05 usar efectos fijos, si sale mayor usar efectos aleatorios.
phtest(random2, within2) ##
## Hausman Test
##
## data: valor ~ t
## chisq = 1.9543e-12, df = 1, p-value = 1
## alternative hypothesis: one model is inconsistent#Por lo tanto, el mejor modelo para este panel es el de EFECTOS ALEATORIOS.#Pronóstico 2026 para cada categoría de producto
df2_pronostico <- data.frame(
categoria = c("Bath and Shower","Deodorants","Depilatories","Fragrances","Hair Care","Mens Grooming","Skin Care","Sun Care"),
t = rep(2026, 8)
)
intercepto2 <- coef(random2)["(Intercept)"]
pendiente2 <- coef(random2)["t"]
efectos2 <- ranef(random2)
df2_pronostico$valor <- intercepto2 + efectos2[df2_pronostico$categoria] + pendiente2*df2_pronostico$t
df2_pronostico[order(-df2_pronostico$valor), c("categoria","valor")]## categoria valor
## 7 Skin Care 53816.52
## 5 Hair Care 48512.05
## 6 Mens Grooming 43056.53
## 4 Fragrances 42150.12
## 2 Deodorants 26716.76
## 1 Bath and Shower 25448.13
## 8 Sun Care 14244.21
## 3 Depilatories 13264.96df3 <- data.frame(
categoria = c(rep("Premium",10), rep("Prestige",10), rep("Mass",10), rep("Dermocosmetics",10)),
anio = rep(2016:2025, 4),
valor = c(
21782.8, 24478.4, 26344, 27806.3, 23212.9, 30224.8, 37374.7, 46017.8, 53798.1, 58845.9,
19715, 21722.1, 23189.7, 24244.8, 19409.1, 25615.4, 31797.5, 38290.7, 44287.3, 48538.1,
129002.7, 138197.6, 145032.6, 151178.5, 146414.9, 158941.4, 174599.9, 195814, 213682.8, 225083.1,
3808.3, 4841.9, 5483.3, 6216.3, 6792.4, 8288.2, 9733.7, 12967.4, 15551.4, 17172.2
)
)
df3$t <- df3$anio #misma razón: copia numérica para el modelo, anio se queda como índice del panel
df3 <- pdata.frame(df3, index = c("categoria","anio"))#Prueba de Heterogeneidad
plotmeans(valor ~ categoria, data = df3)## Warning in arrows(x, li, x, pmax(y - gap, li), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, li, x, pmax(y - gap, li), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped## Warning in arrows(x, ui, x, pmin(y + gap, ui), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, ui, x, pmin(y + gap, ui), col = barcol, lwd = lwd, :
## zero-length arrow is of indeterminate angle and so skipped
#INTERPRETACIÓN: Mass es mucho más grandes que Dermocosmetics: sí hay heterogeneidad.# Opcion 1 - Modelo de Regresión Agrupada (Pooled)
pooled3 <- plm(valor ~ t, data = df3, model = "pooling")
summary(pooled3)## Pooling Model
##
## Call:
## plm(formula = valor ~ t, data = df3, model = "pooling")
##
## Balanced Panel: n = 4, T = 10, N = 40
##
## Residuals:
## Min. 1st Qu. Median 3rd Qu. Max.
## -64823 -37524 -27657 9359 143088
##
## Coefficients:
## Estimate Std. Error t-value Pr(>|t|)
## (Intercept) -9641543.5 7277989.5 -1.3248 0.1932
## t 4801.7 3602.1 1.3331 0.1905
##
## Total Sum of Squares: 1.7031e+11
## Residual Sum of Squares: 1.6271e+11
## R-Squared: 0.044675
## Adj. R-Squared: 0.019535
## F-statistic: 1.77703 on 1 and 38 DF, p-value: 0.19045#Opcion 2 - Modelo de Efectos Fijos (within)
within3 <- plm(valor ~ t, data = df3, model = "within")
summary(within3)## Oneway (individual) effect Within Model
##
## Call:
## plm(formula = valor ~ t, data = df3, model = "within")
##
## Balanced Panel: n = 4, T = 10, N = 40
##
## Residuals:
## Min. 1st Qu. Median 3rd Qu. Max.
## -18979 -7934 -1587 5709 35680
##
## Coefficients:
## Estimate Std. Error t-value Pr(>|t|)
## t 4801.75 667.31 7.1957 2.14e-08 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Total Sum of Squares: 1.2752e+10
## Residual Sum of Squares: 5143300000
## R-Squared: 0.59667
## Adj. R-Squared: 0.55058
## F-statistic: 51.7777 on 1 and 35 DF, p-value: 2.1398e-08#Prueba F
pFtest(within3, pooled3)##
## F test for individual effects
##
## data: valor ~ t
## F = 357.4, df1 = 3, df2 = 35, p-value < 2.2e-16
## alternative hypothesis: significant effects#Opcion 3 - Modelo de Efectos Aleatorios (Random)
random3 <- plm(valor ~ t, data = df3, model = "random")
summary(random3)## Oneway (individual) effect Random Effect Model
## (Swamy-Arora's transformation)
##
## Call:
## plm(formula = valor ~ t, data = df3, model = "random")
##
## Balanced Panel: n = 4, T = 10, N = 40
##
## Effects:
## var std.dev share
## idiosyncratic 1.470e+08 1.212e+04 0.027
## individual 5.237e+09 7.237e+04 0.973
## theta: 0.9471
##
## Residuals:
## Min. 1st Qu. Median 3rd Qu. Max.
## -16235 -7355 -3169 5035 41362
##
## Coefficients:
## Estimate Std. Error z-value Pr(>|z|)
## (Intercept) -9641543.53 1348787.76 -7.1483 8.786e-13 ***
## t 4801.75 667.31 7.1957 6.215e-13 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Total Sum of Squares: 1.3193e+10
## Residual Sum of Squares: 5584100000
## R-Squared: 0.57673
## Adj. R-Squared: 0.56559
## Chisq: 51.7777 on 1 DF, p-value: 6.2154e-13#Prueba de Hausman
phtest(random3, within3)##
## Hausman Test
##
## data: valor ~ t
## chisq = 5.1971e-13, df = 1, p-value = 1
## alternative hypothesis: one model is inconsistent#Por lo tanto, el mejor modelo para este panel también es el de EFECTOS ALEATORIOS, por la misma razón que en las categorías de producto.#Pronóstico 2026 para cada subcategoría
categorias_tier <- c("Premium", "Prestige", "Mass", "Dermocosmetics")
df3_pronostico <- data.frame(categoria = categorias_tier, t = rep(2026, 4))
intercepto3 <- coef(random3)["(Intercept)"]
pendiente3 <- coef(random3)["t"]
efectos3 <- ranef(random3)
df3_pronostico$valor <- intercepto3 + efectos3[df3_pronostico$categoria] + pendiente3*df3_pronostico$t
df3_pronostico[order(-df3_pronostico$valor), c("categoria","valor")]## categoria valor
## 3 Mass 193903.84
## 1 Premium 61469.25
## 2 Prestige 56176.50
## 4 Dermocosmetics 35638.66CONCLUSIÓN: En los dos paneles el modelo que mejor funcionó fue el de Efectos Aleatorios, porque sí hay diferencias de tamaño entre categorías pero no interfieren con la tendencia en el tiempo. Invertiría en Skin Care porque ya es la categoría más grande del mercado y sigue proyectándose como la de mayor valor para 2026. Y a una subcategoría, invertiria en Dermocosmetics: todavía es chica, pero es la que más rápido está creciendo (casi el doble que las demás), así que es donde veo más potencial a futuro.
#Parte 3. Banco mundial PIB (crecimiento anual, %) y Desempleo (% de la fuerza laboral) — 5 países, 2000-2023 INSTRUCCIONES: Importa datos del Banco Mundial y genera el mejor modelo, incluyendo predicciones, conclusiones y gráficas.
wb <- tryCatch({
library(WDI)
d <- WDI(country = c("MX","BR","CA","US","AR"),
indicator = c(pib_crecimiento = "NY.GDP.MKTP.KD.ZG",
desempleo = "SL.UEM.TOTL.ZS"),
start = 2000, end = 2023)
d <- na.omit(d[, c("country","year","pib_crecimiento","desempleo")])
names(d) <- c("pais","anio","pib_crecimiento","desempleo")
d
}, error = function(e) read.csv("panel_wb.csv"))
pdfWB <- pdata.frame(wb, index = c("pais", "anio"))modelo_regresion4 <- lm(pib_crecimiento ~ desempleo, data = pdfWB)
summary(modelo_regresion4)##
## Call:
## lm(formula = pib_crecimiento ~ desempleo, data = pdfWB)
##
## Residuals:
## Min 1Q Median 3Q Max
## -11.1604 -1.4021 0.2238 1.3557 8.6690
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 3.4172 0.8283 4.126 6.92e-05 ***
## desempleo -0.1882 0.1039 -1.811 0.0726 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 3.586 on 118 degrees of freedom
## Multiple R-squared: 0.02706, Adjusted R-squared: 0.01881
## F-statistic: 3.282 on 1 and 118 DF, p-value: 0.07261#Prueba de Heterogeneidad
plotmeans(pib_crecimiento ~ pais, data = wb, n.label = FALSE)
#INTERPRETACIÓN: Aquí la línea sale más plana el crecimiento promedio del PIB no varía tanto entre estos 5 países, así que podría no haber heterogeneidad fuerte.# Opcion 1 - Modelo de Regresión Agrupada (Pooled)
pooled4 <- plm(pib_crecimiento ~ desempleo, data = pdfWB, model = "pooling")
summary(pooled4)## Pooling Model
##
## Call:
## plm(formula = pib_crecimiento ~ desempleo, data = pdfWB, model = "pooling")
##
## Balanced Panel: n = 5, T = 24, N = 120
##
## Residuals:
## Min. 1st Qu. Median 3rd Qu. Max.
## -11.160 -1.402 0.224 1.356 8.669
##
## Coefficients:
## Estimate Std. Error t-value Pr(>|t|)
## (Intercept) 3.41718 0.82826 4.1257 6.915e-05 ***
## desempleo -0.18823 0.10391 -1.8115 0.07261 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Total Sum of Squares: 1559.7
## Residual Sum of Squares: 1517.5
## R-Squared: 0.027057
## Adj. R-Squared: 0.018812
## F-statistic: 3.28151 on 1 and 118 DF, p-value: 0.072608#Opcion 2 - Modelo de Efectos Fijos (within)
within4 <- plm(pib_crecimiento ~ desempleo, data = pdfWB, model = "within")
summary(within4)## Oneway (individual) effect Within Model
##
## Call:
## plm(formula = pib_crecimiento ~ desempleo, data = pdfWB, model = "within")
##
## Balanced Panel: n = 5, T = 24, N = 120
##
## Residuals:
## Min. 1st Qu. Median 3rd Qu. Max.
## -11.025 -0.982 0.106 1.504 9.647
##
## Coefficients:
## Estimate Std. Error t-value Pr(>|t|)
## desempleo -0.49609 0.15661 -3.1677 0.001972 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Total Sum of Squares: 1553
## Residual Sum of Squares: 1427.3
## R-Squared: 0.080901
## Adj. R-Squared: 0.040589
## F-statistic: 10.0345 on 1 and 114 DF, p-value: 0.001972#Prueba F
#INTERPRETACIÓN: Si la p es menor a 0.05 no usar POOLED, si p es mayor a 0.05 usar pooled.
pFtest(within4, pooled4)##
## F test for individual effects
##
## data: pib_crecimiento ~ desempleo
## F = 1.8007, df1 = 4, df2 = 114, p-value = 0.1335
## alternative hypothesis: significant effects#Opcion 3 - Modelo de Efectos Aleatorios (Random)
random4 <- plm(pib_crecimiento ~ desempleo, data = pdfWB, model = "random")
summary(random4)## Oneway (individual) effect Random Effect Model
## (Swamy-Arora's transformation)
##
## Call:
## plm(formula = pib_crecimiento ~ desempleo, data = pdfWB, model = "random")
##
## Balanced Panel: n = 5, T = 24, N = 120
##
## Effects:
## var std.dev share
## idiosyncratic 12.520 3.538 1
## individual 0.000 0.000 0
## theta: 0
##
## Residuals:
## Min. 1st Qu. Median 3rd Qu. Max.
## -11.160 -1.402 0.224 1.356 8.669
##
## Coefficients:
## Estimate Std. Error z-value Pr(>|z|)
## (Intercept) 3.41718 0.82826 4.1257 3.696e-05 ***
## desempleo -0.18823 0.10391 -1.8115 0.07006 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Total Sum of Squares: 1559.7
## Residual Sum of Squares: 1517.5
## R-Squared: 0.027057
## Adj. R-Squared: 0.018812
## Chisq: 3.28151 on 1 DF, p-value: 0.070064#Prueba de Hausman
phtest(random4, within4)##
## Hausman Test
##
## data: pib_crecimiento ~ desempleo
## chisq = 6.9035, df = 1, p-value = 0.008603
## alternative hypothesis: one model is inconsistent#Por lo tanto, el mejor modelo para este panel es el de POOLED. La prueba F da p > 0.05: con solo 5 países, no hay evidencia suficiente de heterogeneidad como para justificar Efectos Fijos o Aleatorios.#Pronóstico 2024 para cada país, a partir de su desempleo observado en 2023
intercepto4 <- coef(pooled4)["(Intercept)"]
pendiente4 <- coef(pooled4)["desempleo"]
df4_pronostico <- wb[wb$anio == max(wb$anio), c("pais", "desempleo", "pib_crecimiento")]
names(df4_pronostico)[3] <- "pib_observado"
df4_pronostico$pib_2024_pred <- intercepto4 + pendiente4 * df4_pronostico$desempleo
df4_pronostico[order(-df4_pronostico$pib_2024_pred), ]## pais desempleo pib_observado pib_2024_pred
## 96 Mexico 2.765 3.106796 2.896729
## 120 United States 3.638 2.934363 2.732406
## 72 Canada 5.415 1.953086 2.397927
## 24 Argentina 6.139 -1.855788 2.261650
## 48 Brazil 7.947 3.241655 1.921335#Gráfica: relación PIB vs. desempleo
plot(wb$desempleo, wb$pib_crecimiento, col = as.factor(wb$pais), pch = 19,
xlab = "Desempleo (%)", ylab = "PIB, crecimiento anual (%)",
main = "PIB vs. Desempleo, 2000-2023 (5 países)")
abline(a = intercepto4, b = pendiente4, col = "black", lwd = 2)
legend("topright", legend = levels(as.factor(wb$pais)), col = 1:5, pch = 19, cex = 0.8)
CONCLUSIÓN: El mejor modelo para el panel de PIB y desempleo es el
Pooled, porque con solo 5 países la prueba F no encuentra evidencia
suficiente de heterogeneidad entre ellos. Existe una relación negativa
entre desempleo y crecimiento del PIB: por cada punto porcentual
adicional de desempleo, el PIB crece en promedio 0.19 puntos
porcentuales menos.
---
title: "Actividad 1"
author: "Adriana Madrigal"
date: "2026-08-13"
output:
  html_document:
    toc: true
    toc_float: true
    code_download: true
  pdf_document:
    toc: true
---

#Importar paquetes y llamar librerias 
```{r message=FALSE, warning=FALSE}
#install.packages("readxl")
library(readxl)
#install.packages("plm")
library(plm)
#install.packages("gplots")
library(gplots)
```

#Parte 1. 
**Patentes**
INSTRUCCIONES: Genera el mejor modelo de la Base de Datos "Patentes" y genera predicciones. 

```{r}
df1 <- read_excel("/Users/adriana/Downloads/PATENT 3.xls")
summary(df1)
```

```{r}
df1 <- pdata.frame(df1, index = c("cusip", "year"))
modelo_regresion <- lm(patents ~ rnd, data = df1)
summary(modelo_regresion) #Usando regresion simple, el modelo nos da que a mas gasto en I+D, mas patentes, pero esto mezcla 226 empresas muy distintas entre si, por eso usamos otros modelos.
```
```{r}
#Prueba de Heterogeneidad
plotmeans(patents ~ cusip, data = df1)
#INTERPRETACIÓN: La línea no es horizontal: hay empresas con muchas más patentes que otras, así que sí hay heterogeneidad.
```

```{r}
# Opcion 1 - Modelo de Regresión Agrupada (Pooled)
pooled <- plm(patents ~ rnd, data = df1, model = "pooling")
summary(pooled)
```

```{r}
#Opcion 2 - Modelo de Efectos Fijos (within)
within <- plm(patents ~ rnd, data = df1, model = "within")
summary(within)
```

```{r}
#Prueba F
#INTERPRETACIÓN: Si la p es menor a 0.05 no usar POOLED, si p es mayor a 0.05 usar pooled.
pFtest(within, pooled) 
```

```{r}
#Opcion 3 - Modelo de Efectos Aleatorios (Random)
random <- plm(patents ~ rnd, data = df1, model = "random")
summary(random)
```

```{r}
#Prueba de Hausman
#INTERPRETACIÓN: Si la p es menor a 0.05 usar efectos fijos, si sale mayor usar efectos aleatorios.
phtest(random, within) 
#Por lo tanto, el mejor modelo para este panel es el de EFECTOS FIJOS. La prueba F rechaza Pooled (sí hay heterogeneidad) y la prueba de Hausman rechaza Aleatorios (esa heterogeneidad está correlacionada con el gasto en I+D: las empresas que más patentan también son las que más invierten).
```
```{r}
df1_pronostico <- data.frame(
  cusip = c("149123", "369604", "459200"),
  year = c(2022, 2022, 2022),
  rnd = c(226.5315, 813.7559, 1611.4912) * 1.10
)
intercepto <- fixef(within)
pendiente <- coef(within)["rnd"]
df1_pronostico$patentes <- intercepto[df1_pronostico$cusip] + pendiente * df1_pronostico$rnd
df1_pronostico[, c("patentes")]
```
CONCLUSIÓN: El mejor modelo es el de Efectos Fijos. Más gasto en I+D no reduce las patentes; simplemente toma tiempo convertirse en patentes solicitadas. Para las 3 empresas con más patentes, un aumento del 10% en I+D da un pronóstico distinto para cada una, porque cada empresa parte de un nivel distinto.

#Parte 2. 
**Cuidado de la piel**
INSTRUCCIONES: ¿En cuál categoría invertirías y por qué? Si tuvieras que invertir en alguna subcategoría, ¿en cuál lo harías? Justifica de acuerdo al modelo.
![]()
```{r}
df2_excel <- read_excel("/Users/adriana/Downloads/Market sizes.xls")
summary(df2_excel)
```

```{r}
df2 <- data.frame(
  categoria = c(rep("Bath and Shower",15), rep("Deodorants",15), rep("Depilatories",15),
                rep("Fragrances",15), rep("Hair Care",15), rep("Mens Grooming",15),
                rep("Skin Care",15), rep("Sun Care",15)),
  anio = rep(2011:2025, 8),
  valor = c(
    8410.4, 9085, 9711.1, 10226.9, 10814.8, 11481.6, 12123.1, 12490.1, 12959.5, 14633.9, 15469.3, 16815.3, 19001, 20234.6, 21341.7,
    9151, 10148.3, 10697.7, 11469.7, 12379.2, 13723.4, 14891.6, 15913.6, 16745.1, 13834.8, 15091.1, 17872.4, 19454.9, 20787.8, 21824.1,
    802.5, 897.7, 969.9, 1036.3, 1106.4, 1187.9, 1319.5, 1439.1, 1516.1, 1491.2, 1563.5, 1688.6, 1850.2, 1802, 1872.8,
    18727.9, 19957.2, 20651.8, 20979.6, 22567.6, 24208.9, 26152.3, 27536, 28483.1, 25516.1, 31800.8, 37172.8, 45318.9, 51579.2, 56742.1,
    24853.9, 26565.6, 27672.5, 29154.6, 30416.2, 32383.6, 34260, 35597.2, 37247.4, 36950.7, 39554.7, 42738.8, 46900.3, 53024.9, 56289.8,
    18672.1, 20694.4, 22133.4, 23175.3, 24774, 27446, 29497.2, 31498.1, 32693.3, 29669.4, 32938.6, 37702.4, 43366.2, 47333.8, 49508.4,
    25650.3, 27306.2, 28366.9, 29438.3, 30964, 33054.3, 35787.8, 38067.5, 40637.5, 42196.5, 47980.6, 52939.6, 61023.6, 68590.4, 71830,
    1144.7, 1303.1, 1417.3, 1552.8, 1693.3, 1944.1, 2143.3, 2266.5, 2443.8, 2042.9, 2293.6, 2862, 3736.4, 4183.4, 4326.4
  )
)
df2$t <- df2$anio #copia numérica de anio; anio ya es el índice del panel, así que si lo usamos directo en el modelo R lo vuelve categórico (uno por año) en vez de número, y por eso salían los NA
df2 <- pdata.frame(df2, index = c("categoria","anio"))
```


```{r}
modelo_regresion2 <- lm(valor ~ t, data = df2)
summary(modelo_regresion2)
```
```{r}
#Prueba de Heterogeneidad
plotmeans(valor ~ categoria, data = df2)
#INTERPRETACIÓN: Skin Care y Hair Care operan en un nivel de mercado mucho más grande que Depilatories o Sun Care: sí hay heterogeneidad.
```

```{r}
# Opcion 1 - Modelo de Regresión Agrupada (Pooled)
pooled2 <- plm(valor ~ t, data = df2, model = "pooling")
summary(pooled2)
```
```{r}
#Opcion 2 - Modelo de Efectos Fijos (within)
within2 <- plm(valor ~ t, data = df2, model = "within")
summary(within2)
```

```{r}
#Prueba F
pFtest(within2, pooled2) 
```
```{r}
#Opcion 3 - Modelo de Efectos Aleatorios (Random)
random2 <- plm(valor ~ t, data = df2, model = "random")
summary(random2)
```
```{r}
#Prueba de Hausman
#INTERPRETACIÓN: Si la p es menor a 0.05 usar efectos fijos, si sale mayor usar efectos aleatorios.
phtest(random2, within2) 
#Por lo tanto, el mejor modelo para este panel es el de EFECTOS ALEATORIOS.
```
```{r}
#Pronóstico 2026 para cada categoría de producto
df2_pronostico <- data.frame(
  categoria = c("Bath and Shower","Deodorants","Depilatories","Fragrances","Hair Care","Mens Grooming","Skin Care","Sun Care"),
  t = rep(2026, 8)
)
intercepto2 <- coef(random2)["(Intercept)"]
pendiente2 <- coef(random2)["t"]
efectos2 <- ranef(random2)
df2_pronostico$valor <- intercepto2 + efectos2[df2_pronostico$categoria] + pendiente2*df2_pronostico$t
df2_pronostico[order(-df2_pronostico$valor), c("categoria","valor")]
```

```{r}
df3 <- data.frame(
  categoria = c(rep("Premium",10), rep("Prestige",10), rep("Mass",10), rep("Dermocosmetics",10)),
  anio = rep(2016:2025, 4),
  valor = c(
    21782.8, 24478.4, 26344, 27806.3, 23212.9, 30224.8, 37374.7, 46017.8, 53798.1, 58845.9,
    19715, 21722.1, 23189.7, 24244.8, 19409.1, 25615.4, 31797.5, 38290.7, 44287.3, 48538.1,
    129002.7, 138197.6, 145032.6, 151178.5, 146414.9, 158941.4, 174599.9, 195814, 213682.8, 225083.1,
    3808.3, 4841.9, 5483.3, 6216.3, 6792.4, 8288.2, 9733.7, 12967.4, 15551.4, 17172.2
  )
)
df3$t <- df3$anio #misma razón: copia numérica para el modelo, anio se queda como índice del panel
df3 <- pdata.frame(df3, index = c("categoria","anio"))

```

```{r}
#Prueba de Heterogeneidad
plotmeans(valor ~ categoria, data = df3)
#INTERPRETACIÓN: Mass es mucho más grandes que Dermocosmetics: sí hay heterogeneidad.
```
```{r}
# Opcion 1 - Modelo de Regresión Agrupada (Pooled)
pooled3 <- plm(valor ~ t, data = df3, model = "pooling")
summary(pooled3)

#Opcion 2 - Modelo de Efectos Fijos (within)
within3 <- plm(valor ~ t, data = df3, model = "within")
summary(within3)

#Prueba F
pFtest(within3, pooled3)

#Opcion 3 - Modelo de Efectos Aleatorios (Random)
random3 <- plm(valor ~ t, data = df3, model = "random")
summary(random3)

#Prueba de Hausman
phtest(random3, within3)
#Por lo tanto, el mejor modelo para este panel también es el de EFECTOS ALEATORIOS, por la misma razón que en las categorías de producto.
```
```{r}
#Pronóstico 2026 para cada subcategoría
categorias_tier <- c("Premium", "Prestige", "Mass", "Dermocosmetics")
df3_pronostico <- data.frame(categoria = categorias_tier, t = rep(2026, 4))
intercepto3 <- coef(random3)["(Intercept)"]
pendiente3 <- coef(random3)["t"]
efectos3 <- ranef(random3)
df3_pronostico$valor <- intercepto3 + efectos3[df3_pronostico$categoria] + pendiente3*df3_pronostico$t
df3_pronostico[order(-df3_pronostico$valor), c("categoria","valor")]
```
CONCLUSIÓN: En los dos paneles el modelo que mejor funcionó fue el de Efectos Aleatorios, porque sí hay diferencias de tamaño entre categorías pero no interfieren con la tendencia en el tiempo. Invertiría en Skin Care porque ya es la categoría más grande del mercado y  sigue proyectándose como la de mayor valor para 2026. Y a una subcategoría, invertiria en Dermocosmetics: todavía es chica, pero es la que más rápido está creciendo (casi el doble que las demás), así que es donde veo más potencial a futuro.


#Parte 3. 
**Banco mundial** **PIB (crecimiento anual, %) y Desempleo (% de la fuerza laboral) — 5 países, 2000-2023**
INSTRUCCIONES: Importa datos del Banco Mundial y genera el mejor modelo, incluyendo predicciones, conclusiones y gráficas.
```{r}
wb <- tryCatch({
  library(WDI)
  d <- WDI(country = c("MX","BR","CA","US","AR"),
           indicator = c(pib_crecimiento = "NY.GDP.MKTP.KD.ZG",
                         desempleo = "SL.UEM.TOTL.ZS"),
           start = 2000, end = 2023)
  d <- na.omit(d[, c("country","year","pib_crecimiento","desempleo")])
  names(d) <- c("pais","anio","pib_crecimiento","desempleo")
  d
}, error = function(e) read.csv("panel_wb.csv"))

pdfWB <- pdata.frame(wb, index = c("pais", "anio"))
```

```{r}
modelo_regresion4 <- lm(pib_crecimiento ~ desempleo, data = pdfWB)
summary(modelo_regresion4)
```

```{r}
#Prueba de Heterogeneidad
plotmeans(pib_crecimiento ~ pais, data = wb, n.label = FALSE)
#INTERPRETACIÓN: Aquí la línea sale más plana el crecimiento promedio del PIB no varía tanto entre estos 5 países, así que podría no haber heterogeneidad fuerte.
```
```{r}
# Opcion 1 - Modelo de Regresión Agrupada (Pooled)
pooled4 <- plm(pib_crecimiento ~ desempleo, data = pdfWB, model = "pooling")
summary(pooled4)

#Opcion 2 - Modelo de Efectos Fijos (within)
within4 <- plm(pib_crecimiento ~ desempleo, data = pdfWB, model = "within")
summary(within4)

#Prueba F
#INTERPRETACIÓN: Si la p es menor a 0.05 no usar POOLED, si p es mayor a 0.05 usar pooled.
pFtest(within4, pooled4)

#Opcion 3 - Modelo de Efectos Aleatorios (Random)
random4 <- plm(pib_crecimiento ~ desempleo, data = pdfWB, model = "random")
summary(random4)

#Prueba de Hausman
phtest(random4, within4)
#Por lo tanto, el mejor modelo para este panel es el de POOLED. La prueba F da p > 0.05: con solo 5 países, no hay evidencia suficiente de heterogeneidad como para justificar Efectos Fijos o Aleatorios.
```
```{r}

#Pronóstico 2024 para cada país, a partir de su desempleo observado en 2023
intercepto4 <- coef(pooled4)["(Intercept)"]
pendiente4 <- coef(pooled4)["desempleo"]
df4_pronostico <- wb[wb$anio == max(wb$anio), c("pais", "desempleo", "pib_crecimiento")]
names(df4_pronostico)[3] <- "pib_observado"
df4_pronostico$pib_2024_pred <- intercepto4 + pendiente4 * df4_pronostico$desempleo
df4_pronostico[order(-df4_pronostico$pib_2024_pred), ]

#Gráfica: relación PIB vs. desempleo
plot(wb$desempleo, wb$pib_crecimiento, col = as.factor(wb$pais), pch = 19,
     xlab = "Desempleo (%)", ylab = "PIB, crecimiento anual (%)",
     main = "PIB vs. Desempleo, 2000-2023 (5 países)")
abline(a = intercepto4, b = pendiente4, col = "black", lwd = 2)
legend("topright", legend = levels(as.factor(wb$pais)), col = 1:5, pch = 19, cex = 0.8)
```
CONCLUSIÓN: El mejor modelo para el panel de PIB y desempleo es el Pooled, porque con solo 5 países la prueba F no encuentra evidencia suficiente de heterogeneidad entre ellos. Existe una relación negativa entre desempleo y crecimiento del PIB: por cada punto porcentual adicional de desempleo, el PIB crece en promedio 0.19 puntos porcentuales menos.
