ANCOVA
J. Morales
4/30/2021
Intro
Ejercicio 9
Carga de datos y gráfico descriptivo
# Lectura de datos
edad <- c(40, 38, 40, 35, 36, 37, 41, 40, 37, 38, 40, 38,
40, 36, 40, 38, 42, 39, 40, 37, 36, 38, 39, 40)
peso <- c(2968, 2795, 3163, 2925, 2625, 2847, 3292, 3473,
2628, 3176, 3421, 2975, 3317, 2729, 2935, 2754,
3210, 2817, 3126, 2539, 2412, 2991, 2875, 3231)
sexo <- gl(2, 12, labels=c("H", "M"))
ejer09 <- data.frame(edad, peso, sexo)
# Gráfico
ggplot(ejer09, aes(x = edad, y = peso, color = sexo)) +
geom_point() 
Estimación
fit.M1 <- lm(peso ~ edad*sexo, data = ejer09)
ols_step_backward_p(fit.M1, prem = 0.05)##
##
## Elimination Summary
## ---------------------------------------------------------------------------
## Variable Adj.
## Step Removed R-Square R-Square C(p) AIC RMSE
## ---------------------------------------------------------------------------
## 1 edad:sexo 0.640 0.6057 2.1945 321.3909 177.1159
## ---------------------------------------------------------------------------fit.M1 <- lm(peso ~ edad + sexo, data = ejer09)
# Parámetros estimados
tab_model(fit.M1,
show.r2 = FALSE,
show.p = FALSE)| Â | peso | |
|---|---|---|
| Predictors | Estimates | CI |
| (Intercept) | -1610.28 | -3245.02 – 24.46 |
| edad | 120.89 | 78.34 – 163.45 |
| sexo [M] | -163.04 | -314.45 – -11.63 |
| Observations | 24 | |
Diagnóstico
Análisis gráfico
# Valores de diagnóstico
diagnostico <- fortify(fit.M1)
# Gráfico
ggplot(diagnostico,aes(x = edad, y = .stdresid, colour = sexo)) +
geom_point() +
geom_hline(yintercept = 0, col = "red") +
facet_wrap(. ~ sexo)
Tests estadÃsticos
# Tests de hipótesis
ols_test_normality(fit.M1)## -----------------------------------------------
## Test Statistic pvalue
## -----------------------------------------------
## Shapiro-Wilk 0.9286 0.0906
## Kolmogorov-Smirnov 0.1677 0.4601
## Cramer-von Mises 2.375 0.0000
## Anderson-Darling 0.7078 0.0562
## -----------------------------------------------leveneTest(.stdresid ~ sexo, data = diagnostico)## Levene's Test for Homogeneity of Variance (center = median)
## Df F value Pr(>F)
## group 1 0.4347 0.5165
## 22# Influencia
ols_plot_cooksd_chart(fit.M1)
Predicción
plot_model(fit.M1, "pred", terms = c("edad", "sexo"),
title ="Predicción de la media")
Ejercicio 9
Carga de datos y gráfico descriptivo
# Lectura de datos
ejer11 <- read_csv("https://goo.gl/OX9wgM", col_types = "ddddddc")
# Gráfico
g1 <- ggplot(ejer11, aes(x = claridad, y = calidad, color = region)) +
geom_point()
g2 <- ggplot(ejer11, aes(x = aroma, y = calidad, color = region)) +
geom_point()
g3 <- ggplot(ejer11, aes(x = cuerpo, y = calidad, color = region)) +
geom_point()
g4 <- ggplot(ejer11, aes(x = olor, y = calidad, color = region)) +
geom_point()
g5 <- ggplot(ejer11, aes(x = matiz, y = calidad, color = region)) +
geom_point()
library(ggpubr)
ggarrange(g1, g2, g3, g4, g5,
ncol = 2, nrow = 3)
Estimación
fit.M1 <- lm(calidad ~ (claridad + aroma + cuerpo + olor + matiz)*region, data = ejer11)
ols_step_backward_p(fit.M1, prem = 0.05)##
##
## Elimination Summary
## --------------------------------------------------------------------------------
## Variable Adj.
## Step Removed R-Square R-Square C(p) AIC RMSE
## --------------------------------------------------------------------------------
## 1 aroma:region 0.905 0.8402 4.0312 105.7803 0.8178
## 2 aroma 0.9039 0.8453 2.2624 104.2163 0.8044
## 3 claridad 0.9039 0.8453 0.2624 104.2163 0.8044
## 4 cuerpo 0.9039 0.8453 -1.7376 104.2163 0.8044
## 5 olor:region 0.8971 0.8476 -2.3044 102.8133 0.7984
## 6 matiz 0.8971 0.8476 -4.3044 102.8133 0.7984
## 7 matiz:region 0.875 0.8348 -1.6521 104.1960 0.8313
## 8 claridad:region 0.8456 0.8158 2.5310 106.2064 0.8779
## 9 cuerpo:region 0.8242 0.8087 5.0522 105.1516 0.8946
## --------------------------------------------------------------------------------fit.M1 <- lm(calidad ~ olor + region, data = ejer11)
# Parámetros estimados
tab_model(fit.M1,
show.r2 = FALSE,
show.p = FALSE)| Â | calidad | |
|---|---|---|
| Predictors | Estimates | CI |
| (Intercept) | 7.09 | 5.49 – 8.70 |
| olor | 1.12 | 0.76 – 1.47 |
| region [B] | -1.53 | -2.28 – -0.78 |
| region [C] | 1.22 | 0.41 – 2.04 |
| Observations | 38 | |
Diagnóstico
Análisis gráfico
# Valores de diagnóstico
diagnostico <- fortify(fit.M1)
# Gráfico
ggplot(diagnostico,aes(x = olor, y = .stdresid, colour = region)) +
geom_point() +
geom_hline(yintercept = 0, col = "red") +
facet_wrap(. ~ region)
Tests estadÃsticos
# Tests de hipótesis
ols_test_normality(fit.M1)## Warning in ks.test(y, "pnorm", mean(y), sd(y)): ties should not be present for
## the Kolmogorov-Smirnov test## -----------------------------------------------
## Test Statistic pvalue
## -----------------------------------------------
## Shapiro-Wilk 0.9884 0.9577
## Kolmogorov-Smirnov 0.0849 0.9472
## Cramer-von Mises 3.0963 0.0000
## Anderson-Darling 0.2026 0.8686
## -----------------------------------------------leveneTest(.stdresid ~ region, data = diagnostico)## Warning in leveneTest.default(y = y, group = group, ...): group coerced to
## factor.## Levene's Test for Homogeneity of Variance (center = median)
## Df F value Pr(>F)
## group 2 0.0851 0.9186
## 35# Influencia
ols_plot_cooksd_chart(fit.M1)
Predicción
plot_model(fit.M1, "pred", terms = c("olor", "region"),
title ="Predicción de la media")
Ejercicio 13
Carga de datos y gráfico descriptivo
# Lectura de datos
ejer13 <- read_csv("https://goo.gl/V6hyVW", col_types = "ddc")
ejer13 <- ejer13 %>%
mutate_if(sapply(ejer13, is.character), as.factor)
ggplot(ejer13, aes(x = TempExt, y = Calor, color = Cristal)) +
geom_point()
Estimación
fit.M1 <- lm(Calor ~ TempExt*Cristal, data = ejer13)
ols_step_backward_p(fit.M1, prem = 0.05)##
##
## Elimination Summary
## --------------------------------------------------------------------------------
## Variable Adj.
## Step Removed R-Square R-Square C(p) AIC RMSE
## --------------------------------------------------------------------------------
## 1 TempExt:Cristal 0.9828 0.9816 -1.6468 103.5045 0.5418
## --------------------------------------------------------------------------------fit.M1 <- lm(Calor ~ TempExt + Cristal, data = ejer13)
# Parámetros estimados
tab_model(fit.M1,
show.r2 = FALSE,
show.p = FALSE)| Â | Calor | |
|---|---|---|
| Predictors | Estimates | CI |
| (Intercept) | 12.66 | 12.18 – 13.15 |
| TempExt | -0.14 | -0.15 – -0.13 |
| Cristal [B] | 4.07 | 3.67 – 4.46 |
| Cristal [C] | 6.87 | 6.48 – 7.27 |
| Cristal [D] | 9.01 | 8.61 – 9.40 |
| Observations | 60 | |
Diagnóstico
Análisis gráfico
# Valores de diagnóstico
diagnostico <- fortify(fit.M1)
# Gráfico
ggplot(diagnostico,aes(x = TempExt, y = .stdresid, colour = Cristal)) +
geom_point() +
geom_hline(yintercept = 0, col = "red") +
facet_wrap(. ~ Cristal)
Tests estadÃsticos
# Tests de hipótesis
ols_test_normality(fit.M1)## Warning in ks.test(y, "pnorm", mean(y), sd(y)): ties should not be present for
## the Kolmogorov-Smirnov test## -----------------------------------------------
## Test Statistic pvalue
## -----------------------------------------------
## Shapiro-Wilk 0.9859 0.7148
## Kolmogorov-Smirnov 0.073 0.9061
## Cramer-von Mises 6.6198 0.0000
## Anderson-Darling 0.2631 0.6893
## -----------------------------------------------leveneTest(.stdresid ~ Cristal, data = diagnostico)## Levene's Test for Homogeneity of Variance (center = median)
## Df F value Pr(>F)
## group 3 0.2962 0.828
## 56# Influencia
ols_plot_cooksd_chart(fit.M1)
Predicción
plot_model(fit.M1, "pred", terms = c("TempExt", "Cristal"),
title ="Predicción de la media")
Ejercicio 13 polinomico
Estimación
fit.M1 <- lm(Calor ~ (TempExt + I(TempExt^2) + I(TempExt^3) + I(TempExt^4))*Cristal, data = ejer13)
ols_step_backward_p(fit.M1, prem = 0.05)##
##
## Elimination Summary
## -------------------------------------------------------------------------------------
## Variable Adj.
## Step Removed R-Square R-Square C(p) AIC RMSE
## -------------------------------------------------------------------------------------
## 1 I(TempExt^4) 0.9889 0.9836 -2.0000 107.2356 0.5104
## 2 I(TempExt^4):Cristal 0.9886 0.9847 -2.9606 100.7747 0.4929
## 3 TempExt:Cristal 0.9883 0.9853 -3.6766 96.6232 0.4843
## 4 I(TempExt^3):Cristal 0.9881 0.9859 -4.9205 91.6856 0.4738
## 5 I(TempExt^2):Cristal 0.988 0.9866 -6.5742 86.1661 0.4620
## -------------------------------------------------------------------------------------fit.M1 <- lm(Calor ~ TempExt + I(TempExt^2) + I(TempExt^3) + Cristal, data = ejer13)
# Parámetros estimados
tab_model(fit.M1,
show.r2 = FALSE,
show.p = FALSE)| Â | Calor | |
|---|---|---|
| Predictors | Estimates | CI |
| (Intercept) | 20.87 | 17.16 – 24.59 |
| TempExt | -0.87 | -1.19 – -0.55 |
| TempExt^2 | 0.02 | 0.01 – 0.03 |
| TempExt^3 | -0.00 | -0.00 – -0.00 |
| Cristal [B] | 4.07 | 3.73 – 4.41 |
| Cristal [C] | 6.87 | 6.53 – 7.21 |
| Cristal [D] | 9.01 | 8.67 – 9.35 |
| Observations | 60 | |
Diagnóstico
Análisis gráfico
# Valores de diagnóstico
diagnostico <- fortify(fit.M1)
# Gráfico
ggplot(diagnostico,aes(x = TempExt, y = .stdresid, colour = Cristal)) +
geom_point() +
geom_hline(yintercept = 0, col = "red") +
facet_wrap(. ~ Cristal)
Tests estadÃsticos
# Tests de hipótesis
ols_test_normality(fit.M1)## Warning in ks.test(y, "pnorm", mean(y), sd(y)): ties should not be present for
## the Kolmogorov-Smirnov test## -----------------------------------------------
## Test Statistic pvalue
## -----------------------------------------------
## Shapiro-Wilk 0.9224 0.0010
## Kolmogorov-Smirnov 0.0981 0.6107
## Cramer-von Mises 8.2567 0.0000
## Anderson-Darling 0.6036 0.1119
## -----------------------------------------------leveneTest(.stdresid ~ Cristal, data = diagnostico)## Levene's Test for Homogeneity of Variance (center = median)
## Df F value Pr(>F)
## group 3 0.4903 0.6904
## 56# Influencia
ols_plot_cooksd_chart(fit.M1)
Predicción
plot_model(fit.M1, "pred", terms = c("TempExt", "Cristal"),
title ="Predicción de la media")