1 Ecuación de regresión lineal múltiple

\[y_i=\beta_0 + \beta_1{\times}x_{i,1} + \beta_2{\times}x_{i,2} + \cdots + \beta_p{\times}x_{i,p} + error_{i}\]

\[error_{i}{\sim}N(0,\sigma_{error}^2)\]

\[\boldsymbol{y}_{(n{\times}1)}=\boldsymbol{X}_{(n{\times}p)}\boldsymbol{\beta}_{(p{\times}1)}+\boldsymbol{error}_{(n{\times}1)}\]

\[\boldsymbol{error}_{(n{\times}1)}{\sim}N(\boldsymbol{0}_{(n{\times}1)},\sigma_{error}^2\boldsymbol{I}_{(n{\times}1)})\]

2 Librería

library(car)
library(broom)
library(tidyverse)
library(ggfortify)
library(mosaic)
library(huxtable)
library(jtools)
library(latex2exp)
library(pubh)
library(sjlabelled)
library(sjPlot)
library(sjmisc)
library(Ecdat)

3 Base de datos

data(birthwt, package = "MASS")

library(tidyverse)
birthwt <- birthwt %>%
  mutate(
    age = as.numeric(age),
    lwt = as.numeric(lwt),
    smoke = factor(smoke, labels = c("Non-smoker", "Smoker")),
    race = factor(race, labels = c("White", "African American", "Other")),
    bwt = as.numeric(bwt)
    ) %>%
  var_labels(
    bwt = 'Birth weight (g)',
    smoke = 'Smoking status',
    race = 'Race'
    )

state: estado
year: año
cpi: índice de precios al consumidor
pop: población estatal
packpc: número de paquetes consumidos per cápita
income: ingresos personales estatales (total, nominal)
tax: promedio de impuestos especiales estatales, federales y locales promedio para el año fiscal
avgprs: precio promedio durante el año fiscal, incluidos los impuestos sobre las ventas
taxs: impuestos especiales promedio para el año fiscal, incluidos los impuestos sobre las ventas

glimpse(birthwt)

## Rows: 189
## Columns: 10
## $ low   <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, …
## $ age   <dbl> 19, 33, 20, 21, 18, 21, 22, 17, 29, 26, 19, 19, 22, 30, 18, 18,…
## $ lwt   <dbl> 182, 155, 105, 108, 107, 124, 118, 103, 123, 113, 95, 150, 95, …
## $ race  <fct> African American, Other, White, White, White, Other, White, Oth…
## $ smoke <fct> Non-smoker, Non-smoker, Smoker, Smoker, Smoker, Non-smoker, Non…
## $ ptl   <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, …
## $ ht    <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, …
## $ ui    <int> 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, …
## $ ftv   <int> 0, 3, 1, 2, 0, 0, 1, 1, 1, 0, 0, 1, 0, 2, 0, 0, 0, 3, 0, 1, 2, …
## $ bwt   <dbl> 2523, 2551, 2557, 2594, 2600, 2622, 2637, 2637, 2663, 2665, 272…

4 Análisis exploratorio

birthwt %>%
  group_by(race, smoke) %>%
  summarise(
    n = n(),
    Mean = mean(bwt, na.rm = TRUE),
    SD = sd(bwt, na.rm = TRUE),
    Median = median(bwt, na.rm = TRUE),
    CV = rel_dis(bwt)
  )

## # A tibble: 6 x 7
## # Groups:   race [3]
##   race             smoke          n  Mean    SD Median    CV
##   <fct>            <fct>      <int> <dbl> <dbl>  <dbl> <dbl>
## 1 White            Non-smoker    44 3429.  710.  3593  0.207
## 2 White            Smoker        52 2827.  626.  2776. 0.222
## 3 African American Non-smoker    16 2854.  621.  2920  0.218
## 4 African American Smoker        10 2504   637.  2381  0.254
## 5 Other            Non-smoker    55 2816.  709.  2807  0.252
## 6 Other            Smoker        12 2757.  810.  3146. 0.294

birthwt %>%
  gen_bst_df(bwt ~ race|smoke)

Birth weight (g)	LowerCI	UpperCI	Race	Smoking status
3.43e+03	3.21e+03	3.63e+03	White	Non-smoker
2.83e+03	2.67e+03	2.99e+03	White	Smoker
2.85e+03	2.58e+03	3.16e+03	African American	Non-smoker
2.5e+03	2.1e+03	2.86e+03	African American	Smoker
2.82e+03	2.62e+03	3.01e+03	Other	Non-smoker
2.76e+03	2.29e+03	3.15e+03	Other	Smoker

birthwt %>%
  bar_error(bwt ~ race, fill = ~ smoke) %>%
  axis_labs() %>%
  gf_labs(fill = "Smoking status:")

4.1 Análisis de correlación

library(PerformanceAnalytics)
chart.Correlation(birthwt[,c(2,3,10)], histogram = TRUE, pch = 19)

4.2 Análisis de datos faltantes

sapply(birthwt, function(x) sum(is.na(x)))

##   low   age   lwt  race smoke   ptl    ht    ui   ftv   bwt 
##     0     0     0     0     0     0     0     0     0     0

cor.mtest <- function(mat, ...) {
  mat <- as.matrix(mat)
  n <- ncol(mat)
  p.mat<- matrix(NA, n, n)
  diag(p.mat) <- 0
  for (i in 1:(n - 1)) {
    for (j in (i + 1):n) {
      tmp <- cor.test(mat[, i], mat[, j], ...)
      p.mat[i, j] <- p.mat[j, i] <- tmp$p.value
    }
  }
  colnames(p.mat) <- rownames(p.mat) <- colnames(mat)
  p.mat
}

p.mat <- cor.mtest(birthwt[,c(2,3,10)])

library(corrplot)
birthwt.cor <- cor(birthwt[,c(2,3,10)])
corrplot(birthwt.cor, method = "number", type = "upper",
         tl.cex = 0.9, number.cex = 0.6,  order="hclust",  diag = FALSE,
         addCoef.col = "black", tl.col = "black", 
         p.mat = p.mat, sig.level = 0.05, insig = "blank")

5 Partición de la base de datos

set.seed(0123456789)

library(dplyr)
birthwt.train <- sample_frac(tbl = birthwt, replace = FALSE, size = 0.80)
birthwt.test <- anti_join(birthwt, birthwt.train)

6 Ajuste de un modelo lineal a los datos

model_norm <- lm(bwt ~ smoke + race, data = birthwt.train)

6.1 Diagnósticos del modelo lineal

library(ggfortify)
autoplot(model_norm)

6.2 Resúmen del modelo lineal

model_norm %>% augment() %>% as_tibble()

bwt	smoke	race	.fitted	.resid	.std.resid	.hat	.sigma	.cooksd
3.94e+03	Non-smoker	Other	2.91e+03	1.03e+03	1.69	0.0208	611	0.0152
3.27e+03	Non-smoker	Other	2.91e+03	364	0.597	0.0208	617	0.00189
3.77e+03	Non-smoker	Other	2.91e+03	860	1.41	0.0208	613	0.0106
2.77e+03	Smoker	White	2.91e+03	-139	-0.229	0.019	617	0.000253
3.06e+03	Non-smoker	White	3.34e+03	-276	-0.454	0.0221	617	0.00116
3.06e+03	Smoker	White	2.91e+03	154	0.252	0.019	617	0.000307
3.57e+03	Smoker	Other	2.48e+03	1.09e+03	1.81	0.0394	611	0.0336
2.3e+03	Non-smoker	Other	2.91e+03	-609	-1	0.0208	615	0.00532
2.73e+03	Non-smoker	Other	2.91e+03	-177	-0.291	0.0208	617	0.000451
2.95e+03	Smoker	White	2.91e+03	39.6	0.065	0.019	618	2.04e-05
2.66e+03	Smoker	White	2.91e+03	-245	-0.403	0.019	617	0.000784
2.47e+03	Smoker	White	2.91e+03	-442	-0.726	0.019	616	0.00255
2.66e+03	Smoker	White	2.91e+03	-243	-0.399	0.019	617	0.000771
2.08e+03	Smoker	White	2.91e+03	-824	-1.35	0.019	614	0.00885
2.84e+03	Non-smoker	Other	2.91e+03	-75.5	-0.124	0.0208	617	8.15e-05
2.06e+03	Non-smoker	Other	2.91e+03	-855	-1.4	0.0208	613	0.0105
2.92e+03	Smoker	White	2.91e+03	13.6	0.0223	0.019	618	2.41e-06
3.2e+03	Non-smoker	Other	2.91e+03	293	0.48	0.0208	617	0.00122
1.89e+03	Non-smoker	Other	2.91e+03	-1.02e+03	-1.67	0.0208	612	0.0148
2.41e+03	Smoker	White	2.91e+03	-494	-0.811	0.019	616	0.00318
3.32e+03	Non-smoker	African American	3.02e+03	298	0.498	0.0506	617	0.0033
2.75e+03	Non-smoker	Other	2.91e+03	-159	-0.262	0.0208	617	0.000364
3.06e+03	Smoker	White	2.91e+03	154	0.252	0.019	617	0.000307
1.59e+03	Non-smoker	Other	2.91e+03	-1.32e+03	-2.17	0.0208	608	0.025
4.05e+03	Non-smoker	White	3.34e+03	716	1.18	0.0221	615	0.00783
3.86e+03	Smoker	White	2.91e+03	948	1.55	0.019	612	0.0117
2.44e+03	Non-smoker	African American	3.02e+03	-581	-0.968	0.0506	616	0.0125
2.5e+03	Non-smoker	African American	3.02e+03	-524	-0.873	0.0506	616	0.0102
3.94e+03	Smoker	White	2.91e+03	1.03e+03	1.69	0.019	611	0.0139
2.82e+03	Smoker	White	2.91e+03	-87.4	-0.143	0.019	617	9.94e-05
3.63e+03	Smoker	White	2.91e+03	721	1.18	0.019	615	0.00676
1.47e+03	Non-smoker	Other	2.91e+03	-1.44e+03	-2.36	0.0208	606	0.0295
2.47e+03	Smoker	Other	2.48e+03	-14.7	-0.0244	0.0394	618	6.12e-06
3.94e+03	Non-smoker	White	3.34e+03	603	0.991	0.0221	615	0.00555
3.76e+03	Smoker	White	2.91e+03	848	1.39	0.019	613	0.00936
3.1e+03	Non-smoker	Other	2.91e+03	194	0.318	0.0208	617	0.000536
3.09e+03	Non-smoker	White	3.34e+03	-248	-0.408	0.0221	617	0.00094
3.32e+03	Smoker	Other	2.48e+03	840	1.39	0.0394	613	0.0199
4.59e+03	Non-smoker	White	3.34e+03	1.25e+03	2.06	0.0221	609	0.0241
3.33e+03	Smoker	Other	2.48e+03	850	1.41	0.0394	613	0.0204
2.12e+03	Smoker	Other	2.48e+03	-356	-0.59	0.0394	617	0.00357
2.13e+03	Smoker	African American	2.59e+03	-463	-0.774	0.0561	616	0.00891
2.37e+03	Smoker	African American	2.59e+03	-222	-0.371	0.0561	617	0.00205
3.54e+03	Non-smoker	Other	2.91e+03	634	1.04	0.0208	615	0.00574
2.32e+03	Non-smoker	Other	2.91e+03	-585	-0.961	0.0208	616	0.0049
2.08e+03	Smoker	White	2.91e+03	-824	-1.35	0.019	614	0.00885
2.45e+03	Non-smoker	Other	2.91e+03	-460	-0.756	0.0208	616	0.00303
3.15e+03	Smoker	White	2.91e+03	239	0.391	0.019	617	0.000741
3.03e+03	Smoker	White	2.91e+03	125	0.204	0.019	617	0.000202
2.5e+03	Smoker	Other	2.48e+03	14.3	0.0236	0.0394	618	5.73e-06
3.8e+03	Non-smoker	White	3.34e+03	461	0.757	0.0221	616	0.00324
3.91e+03	Non-smoker	White	3.34e+03	574	0.943	0.0221	616	0.00503
1.73e+03	Non-smoker	Other	2.91e+03	-1.18e+03	-1.94	0.0208	610	0.02
2.28e+03	Non-smoker	Other	2.91e+03	-628	-1.03	0.0208	615	0.00565
2.35e+03	Non-smoker	White	3.34e+03	-985	-1.62	0.0221	612	0.0148
3.77e+03	Non-smoker	Other	2.91e+03	860	1.41	0.0208	613	0.0106
2.84e+03	Non-smoker	White	3.34e+03	-502	-0.825	0.0221	616	0.00385
2.59e+03	Smoker	White	2.91e+03	-314	-0.516	0.019	617	0.00129
2.3e+03	Smoker	White	2.91e+03	-612	-1	0.019	615	0.00488
1.82e+03	Smoker	White	2.91e+03	-1.09e+03	-1.79	0.019	611	0.0155
2.42e+03	Smoker	White	2.91e+03	-484	-0.795	0.019	616	0.00306
3.4e+03	Non-smoker	African American	3.02e+03	383	0.639	0.0506	617	0.00544
3.2e+03	Smoker	Other	2.48e+03	722	1.2	0.0394	615	0.0147
3.86e+03	Non-smoker	African American	3.02e+03	841	1.4	0.0506	613	0.0262
2.72e+03	Non-smoker	Other	2.91e+03	-188	-0.309	0.0208	617	0.000508
3.42e+03	Non-smoker	White	3.34e+03	77.9	0.128	0.0221	617	9.26e-05
4e+03	Non-smoker	White	3.34e+03	659	1.08	0.0221	615	0.00663
2.47e+03	Smoker	White	2.91e+03	-442	-0.726	0.019	616	0.00255
1.88e+03	Smoker	White	2.91e+03	-1.02e+03	-1.68	0.019	612	0.0136
3.65e+03	Smoker	White	2.91e+03	743	1.22	0.019	614	0.00718
3.7e+03	Non-smoker	White	3.34e+03	361	0.593	0.0221	617	0.00199
3.3e+03	Smoker	Other	2.48e+03	822	1.36	0.0394	614	0.0191
2.56e+03	Smoker	White	2.91e+03	-351	-0.576	0.019	617	0.00161
2.06e+03	Non-smoker	Other	2.91e+03	-855	-1.4	0.0208	613	0.0105
3.37e+03	Non-smoker	African American	3.02e+03	355	0.593	0.0506	617	0.00468
2.24e+03	Non-smoker	Other	2.91e+03	-670	-1.1	0.0208	615	0.00643
3.22e+03	Non-smoker	Other	2.91e+03	315	0.516	0.0208	617	0.00142
3.54e+03	Non-smoker	Other	2.91e+03	634	1.04	0.0208	615	0.00574
3.61e+03	Non-smoker	White	3.34e+03	276	0.453	0.0221	617	0.00116
2.55e+03	Non-smoker	Other	2.91e+03	-359	-0.59	0.0208	617	0.00185
3.65e+03	Non-smoker	White	3.34e+03	313	0.514	0.0221	617	0.0015
3.46e+03	Non-smoker	White	3.34e+03	121	0.199	0.0221	617	0.000223
2.91e+03	Smoker	White	2.91e+03	-2.39	-0.00392	0.019	618	7.42e-08
3.09e+03	Non-smoker	Other	2.91e+03	180	0.295	0.0208	617	0.000461
3.23e+03	Non-smoker	Other	2.91e+03	322	0.528	0.0208	617	0.00148
4.11e+03	Non-smoker	White	3.34e+03	773	1.27	0.0221	614	0.00912
2.88e+03	Non-smoker	White	3.34e+03	-461	-0.758	0.0221	616	0.00325
1.94e+03	Smoker	White	2.91e+03	-972	-1.6	0.019	612	0.0123
2.38e+03	Non-smoker	Other	2.91e+03	-529	-0.869	0.0208	616	0.00401
1.7e+03	Non-smoker	African American	3.02e+03	-1.32e+03	-2.2	0.0506	607	0.0643
1.9e+03	Non-smoker	Other	2.91e+03	-1.01e+03	-1.66	0.0208	612	0.0146
2.78e+03	Non-smoker	African American	3.02e+03	-241	-0.401	0.0506	617	0.00214
2.35e+03	Smoker	White	2.91e+03	-555	-0.911	0.019	616	0.00402
2.62e+03	Non-smoker	Other	2.91e+03	-288	-0.474	0.0208	617	0.00119
4.17e+03	Non-smoker	White	3.34e+03	829	1.36	0.0221	614	0.0105
2.75e+03	Non-smoker	Other	2.91e+03	-160	-0.264	0.0208	617	0.000368
3.65e+03	Non-smoker	White	3.34e+03	313	0.514	0.0221	617	0.0015
3.2e+03	Non-smoker	Other	2.91e+03	293	0.48	0.0208	617	0.00122
3.88e+03	Smoker	White	2.91e+03	976	1.6	0.019	612	0.0124
3.08e+03	Non-smoker	White	3.34e+03	-258	-0.424	0.0221	617	0.00102
3.61e+03	Non-smoker	White	3.34e+03	276	0.453	0.0221	617	0.00116
3.57e+03	Non-smoker	Other	2.91e+03	662	1.09	0.0208	615	0.00626
2.22e+03	Smoker	White	2.91e+03	-683	-1.12	0.019	615	0.00608
2.08e+03	Non-smoker	White	3.34e+03	-1.26e+03	-2.06	0.0221	609	0.0241
3.06e+03	Non-smoker	White	3.34e+03	-276	-0.454	0.0221	617	0.00116
2.88e+03	Non-smoker	Other	2.91e+03	-33.5	-0.055	0.0208	618	1.6e-05
2.92e+03	Non-smoker	White	3.34e+03	-418	-0.687	0.0221	617	0.00267
1.79e+03	Smoker	White	2.91e+03	-1.12e+03	-1.83	0.019	610	0.0163
1.93e+03	Smoker	White	2.91e+03	-980	-1.61	0.019	612	0.0125
3.23e+03	Non-smoker	White	3.34e+03	-104	-0.171	0.0221	617	0.000166
2.21e+03	Smoker	Other	2.48e+03	-270	-0.447	0.0394	617	0.00205
3.22e+03	Non-smoker	Other	2.91e+03	315	0.516	0.0208	617	0.00142
3.26e+03	Smoker	Other	2.48e+03	779	1.29	0.0394	614	0.0171
2.1e+03	Non-smoker	White	3.34e+03	-1.24e+03	-2.03	0.0221	609	0.0234
3.86e+03	Non-smoker	White	3.34e+03	522	0.858	0.0221	616	0.00416
2.95e+03	Smoker	African American	2.59e+03	359	0.601	0.0561	617	0.00537
4.15e+03	Non-smoker	White	3.34e+03	815	1.34	0.0221	614	0.0101
2.98e+03	Non-smoker	African American	3.02e+03	-41.6	-0.0694	0.0506	618	6.42e-05
2.6e+03	Smoker	White	2.91e+03	-308	-0.506	0.019	617	0.00124
2.38e+03	Smoker	African American	2.59e+03	-208	-0.348	0.0561	617	0.0018
3e+03	Smoker	White	2.91e+03	96.6	0.158	0.019	617	0.000122
3.1e+03	Non-smoker	White	3.34e+03	-238	-0.391	0.0221	617	0.000866
3.79e+03	Non-smoker	African American	3.02e+03	771	1.29	0.0506	614	0.022
2.92e+03	Smoker	African American	2.59e+03	331	0.554	0.0561	617	0.00456
3.32e+03	Smoker	White	2.91e+03	409	0.67	0.019	617	0.00217
2.98e+03	Smoker	White	2.91e+03	68.6	0.113	0.019	618	6.13e-05
4.17e+03	Non-smoker	White	3.34e+03	836	1.37	0.0221	614	0.0107
3.43e+03	Smoker	White	2.91e+03	522	0.856	0.019	616	0.00354
3.73e+03	Non-smoker	White	3.34e+03	390	0.641	0.0221	617	0.00232
2.3e+03	Smoker	African American	2.59e+03	-293	-0.49	0.0561	617	0.00357
3.47e+03	Non-smoker	White	3.34e+03	135	0.222	0.0221	617	0.000278
2.38e+03	Smoker	African American	2.59e+03	-208	-0.348	0.0561	617	0.0018
3.06e+03	Non-smoker	African American	3.02e+03	43.4	0.0723	0.0506	618	6.97e-05
2.52e+03	Non-smoker	African American	3.02e+03	-496	-0.827	0.0506	616	0.0091
2.64e+03	Non-smoker	Other	2.91e+03	-273	-0.449	0.0208	617	0.00107
3.77e+03	Non-smoker	White	3.34e+03	432	0.71	0.0221	616	0.00285
2.86e+03	Non-smoker	Other	2.91e+03	-47.5	-0.078	0.0208	618	3.23e-05
3.37e+03	Smoker	White	2.91e+03	466	0.764	0.019	616	0.00282
2.92e+03	Non-smoker	African American	3.02e+03	-98.6	-0.164	0.0506	617	0.00036
3.44e+03	Smoker	African American	2.59e+03	855	1.43	0.0561	613	0.0304
2.41e+03	Smoker	White	2.91e+03	-498	-0.818	0.019	616	0.00323
2.78e+03	Smoker	White	2.91e+03	-126	-0.207	0.019	617	0.000208
3.18e+03	Non-smoker	Other	2.91e+03	265	0.434	0.0208	617	0.001
2.41e+03	Smoker	White	2.91e+03	-498	-0.818	0.019	616	0.00323
3.27e+03	Non-smoker	Other	2.91e+03	364	0.597	0.0208	617	0.00189
3.64e+03	Smoker	White	2.91e+03	729	1.2	0.019	615	0.00691
3.83e+03	Non-smoker	White	3.34e+03	489	0.803	0.0221	616	0.00365
3.88e+03	Non-smoker	Other	2.91e+03	974	1.6	0.0208	612	0.0136
3.04e+03	Smoker	African American	2.59e+03	453	0.758	0.0561	616	0.00854
2.81e+03	Non-smoker	Other	2.91e+03	-103	-0.17	0.0208	617	0.000153
3.46e+03	Non-smoker	White	3.34e+03	122	0.2	0.0221	617	0.000227

6.3 Coeficientes del modelo

model_norm %>% tidy()

term	estimate	std.error	statistic	p.value
(Intercept)	3.34e+03	91.5	36.5	1.58e-75
smokeSmoker	-430	108	-3.99	0.000104
raceAfrican American	-320	149	-2.14	0.0341
raceOther	-428	117	-3.65	0.000367

6.3.1 Intervalos de confianza

model_norm %>% confint() %>% as_tibble()

2.5 %	97.5 %
3.16e+03	3.52e+03
-643	-217
-615	-24.3
-659	-196

model_norm %>% 
  glm_coef(labels = model_labels(model_norm))

Parameter	Coefficient	Pr(>\|t\|)
Constant	3338.12 (3157.2, 3519.04)	< 0.001
Smoking status: Smoker	-429.74 (-642.58, -216.9)	< 0.001
Race: African American	-319.5 (-614.66, -24.35)	0.034
Race: Other	-427.65 (-659.34, -195.95)	< 0.001

model_norm %>%
  glm_coef(se_rob = TRUE, labels = model_labels(model_norm))

Parameter	Coefficient	Pr(>\|t\|)
Constant	3338.12 (3157.12, 3519.13)	< 0.001
Smoking status: Smoker	-429.74 (-644.83, -214.65)	< 0.001
Race: African American	-319.5 (-587.4, -51.61)	0.02
Race: Other	-427.65 (-671.48, -183.81)	< 0.001

model_norm %>%
  plot_model("pred", terms = ~race|smoke, dot.size = 1.5, title = "")

emmip(model_norm, smoke ~ race) %>%
  gf_labs(y = get_label(birthwt$bwt), x = "", col = "Smoking status")

6.4 Multicollinealidad del modelo

library(regclass)
model_norm %>% VIF() %>% as_tibble()

GVIF	Df	GVIF^(1/(2*Df))
1.12	1	1.06
1.12	2	1.03

6.5 Residuales del modelo ajustado

p1 <- ggplot(birthwt.train, aes(birthwt.train[,2], residuals(model_norm))) +
    geom_point() + geom_smooth(color = "blue")
p2 <- ggplot(birthwt.train, aes(birthwt.train[,3], residuals(model_norm))) +
  geom_point() + geom_smooth(color = "blue")
p3 <- ggplot(birthwt.train, aes(birthwt.train[,10], residuals(model_norm))) +
  geom_point() + geom_smooth(color = "blue")

library(pdp)
grid.arrange(p1, p2, p3)

6.6 Datos arípicos

library(olsrr)
model_norm %>% ols_plot_cooksd_bar()

6.7 Reajustando el modelo de regresión lineal

6.7.1 Algoritmo paso a paso

model_norm %>% 
  Anova() %>% 
  tidy()

term	sumsq	df	statistic	p.value
smoke	6.03e+06	1	15.9	0.000104
race	5.46e+06	2	7.21	0.00103
Residuals	5.57e+07	147

model_norm %>% 
  tidy()

term	estimate	std.error	statistic	p.value
(Intercept)	3.34e+03	91.5	36.5	1.58e-75
smokeSmoker	-430	108	-3.99	0.000104
raceAfrican American	-320	149	-2.14	0.0341
raceOther	-428	117	-3.65	0.000367

model_norm %>% 
  glm_coef(labels = model_labels(model_norm))

Parameter	Coefficient	Pr(>\|t\|)
Constant	3338.12 (3157.2, 3519.04)	< 0.001
Smoking status: Smoker	-429.74 (-642.58, -216.9)	< 0.001
Race: African American	-319.5 (-614.66, -24.35)	0.034
Race: Other	-427.65 (-659.34, -195.95)	< 0.001

model_norm %>%
  glm_coef(se_rob = TRUE, labels = model_labels(model_norm))

Parameter	Coefficient	Pr(>\|t\|)
Constant	3338.12 (3157.12, 3519.13)	< 0.001
Smoking status: Smoker	-429.74 (-644.83, -214.65)	< 0.001
Race: African American	-319.5 (-587.4, -51.61)	0.02
Race: Other	-427.65 (-671.48, -183.81)	< 0.001

6.8 Criterios de ajuste del modelo líneal

model_norm %>% glance()

r.squared	adj.r.squared	sigma	statistic	p.value	df	logLik	AIC	BIC	deviance	df.residual	nobs
0.136	0.119	615	7.73	7.88e-05	3	-1.18e+03	2.37e+03	2.39e+03	5.57e+07	147	151

library(MASS)
model_norm_AIC <- stepAIC(model_norm, trace = 0)

model_norm_AIC %>% 
  Anova() %>% 
  tidy()

term	sumsq	df	statistic	p.value
smoke	6.03e+06	1	15.9	0.000104
race	5.46e+06	2	7.21	0.00103
Residuals	5.57e+07	147

model_norm_AIC %>% glance()

r.squared	adj.r.squared	sigma	statistic	p.value	df	logLik	AIC	BIC	deviance	df.residual	nobs
0.136	0.119	615	7.73	7.88e-05	3	-1.18e+03	2.37e+03	2.39e+03	5.57e+07	147	151

6.9 Análisis de varianza

model_norm %>% Anova() %>% tidy()

term	sumsq	df	statistic	p.value
smoke	6.03e+06	1	15.9	0.000104
race	5.46e+06	2	7.21	0.00103
Residuals	5.57e+07	147

6.10 Comparación de criterios

AIC(model_norm, model_norm_AIC)

df	AIC
5	2.37e+03
5	2.37e+03

6.11 Importancia relativa decada variable

#library(relaimpo)
#calc.relimp(model_norm_AIC, type = c("lmg", "last", "first", "pratt", "betasq"), rela = T)

#boot <- boot.relimp(model_norm, b = 1000, type = c("lmg", "last", "first", "pratt"), 
#                    rank = TRUE, diff = TRUE, rela = TRUE)
#booteval.relimp(boot)

#plot(booteval.relimp(boot,sort=TRUE))

Regresión lineal múltiple

M Sc. Mario Gregorio Saavedra Rodríguez

14/11/2019