Impotando datos
library(readr)
savings_and_loan <- read_csv("C:/Users/MINEDUCYT/Desktop/parcial 1 econometria/SavingsandLoan.csv")
#realizo el modelo lineal multiple
modelo_saving <- lm(profit ~ revenue+offices, data = savings_and_loan)
library(stargazer)
stargazer(modelo_saving, type = "text", title = "Modelo para el margem de las asociaciones de ahorro y credito")
##
## Modelo para el margem de las asociaciones de ahorro y credito
## ===============================================
## Dependent variable:
## ---------------------------
## profit
## -----------------------------------------------
## revenue 0.237***
## (0.056)
##
## offices -0.0002***
## (0.00003)
##
## Constant 1.564***
## (0.079)
##
## -----------------------------------------------
## Observations 25
## R2 0.865
## Adjusted R2 0.853
## Residual Std. Error 0.053 (df = 22)
## F Statistic 70.661*** (df = 2; 22)
## ===============================================
## Note: *p<0.1; **p<0.05; ***p<0.01
Literal b, relacion lineal entre dos variables
#Prueba T
#Nivel de confianza del 97.567%
alpha <- 1 - 0.97567
grados_de_libertad <- nrow(savings_and_loan) - 3 # n - k -1
valor_critico1 <- qt(1-alpha / 2, grados_de_libertad, lower.tail = TRUE)
t_values_offices <- summary(modelo_saving)$coefficients["offices", "t value"]
if(abs(t_values_offices) > valor_critico1){
print("rechazamos la hipotesis nula: existe evidencia suficiente para afirmar que existe una relacion lineal entre las variables")
} else {
print("no rechazamos la hipotesis nula. No hay evidencia suficeinte para afirmar una relacion lineal")
}
## [1] "rechazamos la hipotesis nula: existe evidencia suficiente para afirmar que existe una relacion lineal entre las variables"
Intervalo de confianza
confint_offices<- confint(modelo_saving, "offices", level = 0.97567)
#verifica si existe una relacion lineal sabiendo el intervalo
if (confint_offices[1] > 0 || confint_offices[2] < 0) {
print("El intervalo de confianza no incluye el cero: hay una relacion lineal parcial entre las dos variables")
} else {
print("El intervalo de confianza incluye cero: no hay relacion lineal entre parcial entre las dos variables")
}
## [1] "El intervalo de confianza no incluye el cero: hay una relacion lineal parcial entre las dos variables"
Prueba P
p_values_offices <- summary(modelo_saving)$coefficients["offices", "Pr(>|t|)"]
#comparacion con la significancia
if(p_values_offices < alpha){
print("rechamos la hipotesis nula: hay una evidencia suficiente para afirmar que existe una relacion lineal")
} else {
print("No rechazamos la hipotesis nula: no hay evidencia suficiente para afirmar que existe una relacion lineal")
}
## [1] "rechamos la hipotesis nula: hay una evidencia suficiente para afirmar que existe una relacion lineal"
Literal C, comparando residuos del modelo con los resiudos generados
por la mulriplicacion de la matriz m con el vector de terminos
dependientes
library(magrittr)
matriz_x <- model.matrix(modelo_saving)
matriz_xx <- t(matriz_x) %*% matriz_x
matriz_a <- solve(matriz_xx) %*% t(matriz_x)
matriz_p <- matriz_x %*% matriz_a
n <- nrow(matriz_x)
matriz_m <- diag(n) - matriz_p
#comparando
residuos_modelo_saving <- modelo_saving$residuals
datos_modelo_saving <- modelo_saving$model
residuos_mat <- matriz_m %*% savings_and_loan$profit
cbind(residuos_mat, residuos_modelo_saving, residuos_modelo_saving - residuos_mat) %>% round(digits = 2) -> comparando_saving
comparando_saving <- as.data.frame(comparando_saving)
names(comparando_saving) <- c("matriz", "modelo", "comparacion")
comparando_saving
## matriz modelo comparacion
## 1 0.07 0.07 0
## 2 0.00 0.00 0
## 3 -0.04 -0.04 0
## 4 -0.06 -0.06 0
## 5 0.02 0.02 0
## 6 0.01 0.01 0
## 7 0.03 0.03 0
## 8 -0.02 -0.02 0
## 9 0.11 0.11 0
## 10 0.03 0.03 0
## 11 -0.05 -0.05 0
## 12 -0.06 -0.06 0
## 13 -0.02 -0.02 0
## 14 0.04 0.04 0
## 15 0.04 0.04 0
## 16 -0.03 -0.03 0
## 17 -0.02 -0.02 0
## 18 0.03 0.03 0
## 19 -0.09 -0.09 0
## 20 0.02 0.02 0
## 21 -0.01 -0.01 0
## 22 -0.07 -0.07 0
## 23 0.07 0.07 0
## 24 0.07 0.07 0
## 25 -0.06 -0.06 0
evaluacion de todas las variables significativas en el modelo
coeficientes1 <- summary(modelo_saving)$coefficients
#Evaluar la significancia de cada variable
for(variable in rownames(coeficientes1)){
t_value <- coeficientes1[variable, "t value"]
if(abs(t_value)> valor_critico1){
print(paste("rechazamos la hipotesis nula: hay una relacion lineal entre", variable,"y profit"))
}else{
print(paste("no rechazamos la hipotesis nula: no hay una relacion lineal entre",variable,"y profit"))
}
}
## [1] "rechazamos la hipotesis nula: hay una relacion lineal entre (Intercept) y profit"
## [1] "rechazamos la hipotesis nula: hay una relacion lineal entre revenue y profit"
## [1] "rechazamos la hipotesis nula: hay una relacion lineal entre offices y profit"
Literal d, demostrar que existe la idempotencia usando la matriz
p
# comprobando que son idempotente
# la multiplicacion de p * p debe ser igual a P
P <- matriz_p %*% matriz_p
# por lo tanto al ser el resultado de P igual a mat_p, la resta de ambos sera una matriz nula, por lo tanto
ort_p <- P - matriz_p
print(round(ort_p,2))
## 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
## 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 10 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 11 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 12 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 13 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 14 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 15 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 16 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 17 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 18 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 19 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 20 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 21 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 22 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 23 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 24 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 25 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
Ejercicio 2
Literal A; estimando el modelo lineal para la base de datos
motors
motors <- read.csv("C:/Users/MINEDUCYT/Desktop/parcial 1 econometria/motors.csv")
model_motors <- lm(formula = milpgal ~horspwr+weight, data = motors)
library(stargazer)
stargazer(model_motors, type = "text", title = "modelo para el rendimiento de vehiculos automotor")
##
## modelo para el rendimiento de vehiculos automotor
## ===============================================
## Dependent variable:
## ---------------------------
## milpgal
## -----------------------------------------------
## horspwr -0.105***
## (0.022)
##
## weight -0.007***
## (0.001)
##
## Constant 55.769***
## (1.448)
##
## -----------------------------------------------
## Observations 150
## R2 0.723
## Adjusted R2 0.720
## Residual Std. Error 3.901 (df = 147)
## F Statistic 192.228*** (df = 2; 147)
## ===============================================
## Note: *p<0.1; **p<0.05; ***p<0.01
Ejercicio 2, literal b
#Prueba T
#Nivel de confianza del 97.567%
alpha2 <- 1 - 0.96078
grados_de_libertad2 <- nrow(motors) - 3 # n - k -1
valor_critico2 <- qt(1-alpha2 / 2, grados_de_libertad2, lower.tail = TRUE)
t_values_weight <- summary(model_motors)$coefficients["weight", "t value"]
if(abs(t_values_weight) > valor_critico2){
print("Rechazamos la hipotesis nula: hay evidencia suficiente para afirmar que existe una relacion lineal entre las variables")
} else {
print("No rechazamos la hipotesis nula: No hay evidencia suficiente para afirmar una relacion lineal")
}
## [1] "Rechazamos la hipotesis nula: hay evidencia suficiente para afirmar que existe una relacion lineal entre las variables"
Ejercicio 2, literal b
confint_weight<- confint(model_motors, "weight", level = 0.96078)
#verifica si existe una relacion lineal sabiendo el intervalo
if (confint_weight[1] > 0 || confint_weight[2] < 0) {
print("El intervalo de confianza no incluye el cero: hay una relacion lineal parcial entre las dos variables")
} else {
print("El intervalo de confianza incluye cero: no hay relacion lineal parcial entre las dos variables")
}
## [1] "El intervalo de confianza no incluye el cero: hay una relacion lineal parcial entre las dos variables"
Ejercicio 2, literal B
p_values_weight <- summary(model_motors)$coefficients["weight", "Pr(>|t|)"]
#comparacion con la significancia
if(p_values_weight < alpha2){
print("rechamos la hipotesis nula: hay una evidencia suficiente para afirmar que existe una relacion lineal")
} else {
print("No rechazamos la hipotesis nula: no hay evidencia suficiente para afirmar que existe una relacion lineal")
}
## [1] "rechamos la hipotesis nula: hay una evidencia suficiente para afirmar que existe una relacion lineal"
Ejercicio 2, literal c
library(magrittr)
mat_x <- model.matrix(model_motors)
mat_xx <- t(mat_x) %*% mat_x
mat_a <- solve(mat_xx) %*% t(mat_x)
mat_p <- mat_x %*% mat_a
n_2 <- nrow(mat_x)
mat_m <- diag(n_2) - mat_p
#comparando
residuos_model_motors <- model_motors$residuals
datos_modelo_motors <- model_motors$model
residuos_mat2 <- mat_m %*% datos_modelo_motors$milpgal
cbind(residuos_mat2, residuos_model_motors, residuos_model_motors - residuos_mat2) %>% round(digits = 2) -> comparando_motors
comparando_motors <- as.data.frame(comparando_motors)
names(comparando_motors) <- c("matriz", "modelo", "comparacion")
comparando_motors
## matriz modelo comparacion
## 1 5.49 5.49 0
## 2 -0.84 -0.84 0
## 3 -4.39 -4.39 0
## 4 4.66 4.66 0
## 5 -1.47 -1.47 0
## 6 -2.07 -2.07 0
## 7 3.02 3.02 0
## 8 2.62 2.62 0
## 9 -2.17 -2.17 0
## 10 -4.44 -4.44 0
## 11 -7.04 -7.04 0
## 12 -3.45 -3.45 0
## 13 -2.09 -2.09 0
## 14 -5.70 -5.70 0
## 15 -1.80 -1.80 0
## 16 -5.75 -5.75 0
## 17 -1.69 -1.69 0
## 18 -2.53 -2.53 0
## 19 1.29 1.29 0
## 20 2.02 2.02 0
## 21 -1.89 -1.89 0
## 22 3.40 3.40 0
## 23 -4.38 -4.38 0
## 24 -1.37 -1.37 0
## 25 -3.18 -3.18 0
## 26 -2.25 -2.25 0
## 27 -8.07 -8.07 0
## 28 -3.40 -3.40 0
## 29 -4.17 -4.17 0
## 30 -5.79 -5.79 0
## 31 -5.95 -5.95 0
## 32 -4.89 -4.89 0
## 33 -3.62 -3.62 0
## 34 -3.06 -3.06 0
## 35 -3.66 -3.66 0
## 36 -5.02 -5.02 0
## 37 -0.74 -0.74 0
## 38 -7.28 -7.28 0
## 39 -5.12 -5.12 0
## 40 -4.53 -4.53 0
## 41 -1.41 -1.41 0
## 42 0.27 0.27 0
## 43 0.00 0.00 0
## 44 1.36 1.36 0
## 45 1.92 1.92 0
## 46 6.23 6.23 0
## 47 1.44 1.44 0
## 48 0.39 0.39 0
## 49 4.52 4.52 0
## 50 -3.69 -3.69 0
## 51 -1.79 -1.79 0
## 52 0.99 0.99 0
## 53 -2.32 -2.32 0
## 54 1.06 1.06 0
## 55 6.14 6.14 0
## 56 -0.02 -0.02 0
## 57 0.19 0.19 0
## 58 0.32 0.32 0
## 59 0.29 0.29 0
## 60 -3.79 -3.79 0
## 61 2.86 2.86 0
## 62 -0.27 -0.27 0
## 63 2.26 2.26 0
## 64 0.95 0.95 0
## 65 4.08 4.08 0
## 66 7.88 7.88 0
## 67 1.64 1.64 0
## 68 -2.30 -2.30 0
## 69 1.60 1.60 0
## 70 -0.62 -0.62 0
## 71 -1.16 -1.16 0
## 72 -2.17 -2.17 0
## 73 -4.87 -4.87 0
## 74 1.18 1.18 0
## 75 1.40 1.40 0
## 76 0.21 0.21 0
## 77 6.98 6.98 0
## 78 -0.72 -0.72 0
## 79 11.60 11.60 0
## 80 1.66 1.66 0
## 81 5.80 5.80 0
## 82 7.36 7.36 0
## 83 8.11 8.11 0
## 84 7.17 7.17 0
## 85 3.15 3.15 0
## 86 8.09 8.09 0
## 88 -0.75 -0.75 0
## 89 -7.26 -7.26 0
## 90 10.02 10.02 0
## 91 -5.57 -5.57 0
## 92 5.00 5.00 0
## 94 -0.67 -0.67 0
## 95 -3.29 -3.29 0
## 96 -2.93 -2.93 0
## 97 -2.99 -2.99 0
## 98 -2.71 -2.71 0
## 99 -1.18 -1.18 0
## 100 1.02 1.02 0
## 101 2.35 2.35 0
## 102 -2.73 -2.73 0
## 103 -2.78 -2.78 0
## 104 1.11 1.11 0
## 105 1.99 1.99 0
## 106 -1.41 -1.41 0
## 107 0.19 0.19 0
## 108 -1.03 -1.03 0
## 109 -3.31 -3.31 0
## 110 -0.52 -0.52 0
## 112 0.41 0.41 0
## 113 0.04 0.04 0
## 114 4.92 4.92 0
## 115 1.02 1.02 0
## 116 2.09 2.09 0
## 118 3.80 3.80 0
## 119 0.98 0.98 0
## 120 0.40 0.40 0
## 121 0.76 0.76 0
## 122 6.48 6.48 0
## 123 -6.10 -6.10 0
## 124 -6.34 -6.34 0
## 125 -1.31 -1.31 0
## 126 -2.08 -2.08 0
## 127 3.30 3.30 0
## 128 1.18 1.18 0
## 129 -1.26 -1.26 0
## 130 -1.24 -1.24 0
## 131 -3.17 -3.17 0
## 133 1.09 1.09 0
## 134 1.76 1.76 0
## 135 -4.61 -4.61 0
## 136 2.89 2.89 0
## 137 1.63 1.63 0
## 138 3.75 3.75 0
## 139 2.68 2.68 0
## 140 0.42 0.42 0
## 141 2.26 2.26 0
## 142 -3.74 -3.74 0
## 143 2.45 2.45 0
## 144 0.25 0.25 0
## 145 11.09 11.09 0
## 146 -3.02 -3.02 0
## 147 -3.27 -3.27 0
## 148 3.93 3.93 0
## 149 4.72 4.72 0
## 150 0.18 0.18 0
## 151 -1.29 -1.29 0
## 152 7.77 7.77 0
## 153 0.22 0.22 0
## 154 -2.12 -2.12 0
## 155 1.82 1.82 0
Ejercicio 2, literal D
# comprobando que son idempotente la multiplicacion de p * p debe ser igual a P
p <- mat_p %*% mat_p
# por lo tanto al ser el resultado de P igual a mat_p, la resta de ambos sera una matriz nula, por lo tanto
ot_p <- p - mat_p
print(round(ot_p,2))
## 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28
## 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 10 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 11 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 12 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 13 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 14 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 15 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 16 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 17 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 18 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 19 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 20 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 21 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 22 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 23 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 24 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 25 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 26 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 27 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 28 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 29 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 30 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 31 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 32 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 33 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 34 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 35 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 36 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 37 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 38 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 39 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 40 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 41 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 42 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 43 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 44 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 45 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 46 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 47 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 48 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 49 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 50 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 51 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 52 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 53 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 54 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 55 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 56 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 57 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 58 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 59 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 60 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 61 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 62 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 63 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 64 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 65 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 66 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 67 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 68 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
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