En este ejemplo trabajaremos con el cuarteto de Anscombe, el cual es un cuarteto de conjuntos de datos creados para remarcar la importancia de las graficas en el análisis estadístico. Primero veamos las características de los conjuntos:

library(dplyr)
## 
## Attaching package: 'dplyr'
## The following objects are masked from 'package:stats':
## 
##     filter, lag
## The following objects are masked from 'package:base':
## 
##     intersect, setdiff, setequal, union
library(ggplot2)
str(anscombe)
## 'data.frame':    11 obs. of  8 variables:
##  $ x1: num  10 8 13 9 11 14 6 4 12 7 ...
##  $ x2: num  10 8 13 9 11 14 6 4 12 7 ...
##  $ x3: num  10 8 13 9 11 14 6 4 12 7 ...
##  $ x4: num  8 8 8 8 8 8 8 19 8 8 ...
##  $ y1: num  8.04 6.95 7.58 8.81 8.33 ...
##  $ y2: num  9.14 8.14 8.74 8.77 9.26 8.1 6.13 3.1 9.13 7.26 ...
##  $ y3: num  7.46 6.77 12.74 7.11 7.81 ...
##  $ y4: num  6.58 5.76 7.71 8.84 8.47 7.04 5.25 12.5 5.56 7.91 ...
summary(anscombe)
##        x1             x2             x3             x4           y1        
##  Min.   : 4.0   Min.   : 4.0   Min.   : 4.0   Min.   : 8   Min.   : 4.260  
##  1st Qu.: 6.5   1st Qu.: 6.5   1st Qu.: 6.5   1st Qu.: 8   1st Qu.: 6.315  
##  Median : 9.0   Median : 9.0   Median : 9.0   Median : 8   Median : 7.580  
##  Mean   : 9.0   Mean   : 9.0   Mean   : 9.0   Mean   : 9   Mean   : 7.501  
##  3rd Qu.:11.5   3rd Qu.:11.5   3rd Qu.:11.5   3rd Qu.: 8   3rd Qu.: 8.570  
##  Max.   :14.0   Max.   :14.0   Max.   :14.0   Max.   :19   Max.   :10.840  
##        y2              y3              y4        
##  Min.   :3.100   Min.   : 5.39   Min.   : 5.250  
##  1st Qu.:6.695   1st Qu.: 6.25   1st Qu.: 6.170  
##  Median :8.140   Median : 7.11   Median : 7.040  
##  Mean   :7.501   Mean   : 7.50   Mean   : 7.501  
##  3rd Qu.:8.950   3rd Qu.: 7.98   3rd Qu.: 8.190  
##  Max.   :9.260   Max.   :12.74   Max.   :12.500
var(anscombe)
##        x1     x2     x3     x4        y1        y2       y3        y4
## x1 11.000 11.000 11.000 -5.500  5.501000  5.500000  5.49700 -2.115000
## x2 11.000 11.000 11.000 -5.500  5.501000  5.500000  5.49700 -2.115000
## x3 11.000 11.000 11.000 -5.500  5.501000  5.500000  5.49700 -2.115000
## x4 -5.500 -5.500 -5.500 11.000 -3.565000 -4.841000 -2.32100  5.499000
## y1  5.501  5.501  5.501 -3.565  4.127269  3.095609  1.93343 -2.017731
## y2  5.500  5.500  5.500 -4.841  3.095609  4.127629  2.42524 -1.972351
## y3  5.497  5.497  5.497 -2.321  1.933430  2.425240  4.12262 -0.641000
## y4 -2.115 -2.115 -2.115  5.499 -2.017731 -1.972351 -0.64100  4.123249

Rcuerde que los conjuntos van por pares, es decir, (x1,y1), (x2,y2), (x3,y3) y (x4,y4).

A continuación ajustamos un modelo lineal a cada par

modelo1 <- lm(y1~x1, data = anscombe)
modelo2 <- lm(y2~x2, data = anscombe)
modelo3 <- lm(y3~x3, data = anscombe)
modelo4 <- lm(y4~x4, data = anscombe)
summary(modelo1)
## 
## Call:
## lm(formula = y1 ~ x1, data = anscombe)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -1.92127 -0.45577 -0.04136  0.70941  1.83882 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)   
## (Intercept)   3.0001     1.1247   2.667  0.02573 * 
## x1            0.5001     0.1179   4.241  0.00217 **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.237 on 9 degrees of freedom
## Multiple R-squared:  0.6665, Adjusted R-squared:  0.6295 
## F-statistic: 17.99 on 1 and 9 DF,  p-value: 0.00217
summary(modelo2)
## 
## Call:
## lm(formula = y2 ~ x2, data = anscombe)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -1.9009 -0.7609  0.1291  0.9491  1.2691 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)   
## (Intercept)    3.001      1.125   2.667  0.02576 * 
## x2             0.500      0.118   4.239  0.00218 **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.237 on 9 degrees of freedom
## Multiple R-squared:  0.6662, Adjusted R-squared:  0.6292 
## F-statistic: 17.97 on 1 and 9 DF,  p-value: 0.002179
summary(modelo3)
## 
## Call:
## lm(formula = y3 ~ x3, data = anscombe)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -1.1586 -0.6146 -0.2303  0.1540  3.2411 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)   
## (Intercept)   3.0025     1.1245   2.670  0.02562 * 
## x3            0.4997     0.1179   4.239  0.00218 **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.236 on 9 degrees of freedom
## Multiple R-squared:  0.6663, Adjusted R-squared:  0.6292 
## F-statistic: 17.97 on 1 and 9 DF,  p-value: 0.002176
summary(modelo4)
## 
## Call:
## lm(formula = y4 ~ x4, data = anscombe)
## 
## Residuals:
##    Min     1Q Median     3Q    Max 
## -1.751 -0.831  0.000  0.809  1.839 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)   
## (Intercept)   3.0017     1.1239   2.671  0.02559 * 
## x4            0.4999     0.1178   4.243  0.00216 **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.236 on 9 degrees of freedom
## Multiple R-squared:  0.6667, Adjusted R-squared:  0.6297 
## F-statistic:    18 on 1 and 9 DF,  p-value: 0.002165

¿Qué información se puede extraer del summary?

Finalmente grafiquemos los datos junto con el modelo correspondiente en cada caso

ggplot(anscombe, aes(x1,y1))+ geom_point()+geom_smooth(method = 'lm', formula= y~x)

ggplot(anscombe, aes(x2,y2))+ geom_point()+geom_smooth(method = 'lm', formula= y~x)

ggplot(anscombe, aes(x3,y3))+ geom_point()+geom_smooth(method = 'lm', formula= y~x)

ggplot(anscombe, aes(x4,y4))+ geom_point()+geom_smooth(method = 'lm', formula= y~x)

Existe otro paquete que nos muestra conjutnos creados de manera similar:

library(datasauRus)
ggplot(data=datasaurus_dozen, aes(x=x, y=y, colour=dataset))+geom_point()+facet_wrap(~dataset, ncol=3)