U1A10

Regresion lineal simple parte 2

• Este ejemplo se hara con datos de Arboles de cerezas negras "black cherry"

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

head(trees)

##   Girth Height Volume
## 1   8.3     70   10.3
## 2   8.6     65   10.3
## 3   8.8     63   10.2
## 4  10.5     72   16.4
## 5  10.7     81   18.8
## 6  10.8     83   19.7

• Primer vistazo a los datos

glimpse(trees)

## Rows: 31
## Columns: 3
## $ Girth  <dbl> 8.3, 8.6, 8.8, 10.5, 10.7, 10.8, 11.0, 11.0, 11.1, 11.2, 11....
## $ Height <dbl> 70, 65, 63, 72, 81, 83, 66, 75, 80, 75, 79, 76, 76, 69, 75, ...
## $ Volume <dbl> 10.3, 10.3, 10.2, 16.4, 18.8, 19.7, 15.6, 18.2, 22.6, 19.9, ...

• Resumen de posicion central

summary(trees)

##      Girth           Height       Volume     
##  Min.   : 8.30   Min.   :63   Min.   :10.20  
##  1st Qu.:11.05   1st Qu.:72   1st Qu.:19.40  
##  Median :12.90   Median :76   Median :24.20  
##  Mean   :13.25   Mean   :76   Mean   :30.17  
##  3rd Qu.:15.25   3rd Qu.:80   3rd Qu.:37.30  
##  Max.   :20.60   Max.   :87   Max.   :77.00

• Matriz de diagramas de dispersion

pairs(trees)

• Matriz de coeficientes de correlacion lineal

cor(trees)

##            Girth    Height    Volume
## Girth  1.0000000 0.5192801 0.9671194
## Height 0.5192801 1.0000000 0.5982497
## Volume 0.9671194 0.5982497 1.0000000

• Prueba de correlacion de pearson

cor.test(x = trees$Girth, y = trees$Volume, method = "pearson", digits= 3)

## 
##  Pearson's product-moment correlation
## 
## data:  trees$Girth and trees$Volume
## t = 20.478, df = 29, p-value < 2.2e-16
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  0.9322519 0.9841887
## sample estimates:
##       cor 
## 0.9671194

library(GGally)

## Loading required package: ggplot2

## Registered S3 method overwritten by 'GGally':
##   method from   
##   +.gg   ggplot2

ggpairs(trees, lower = list( continuous = "smooth"), diag = list(continuous = "bar"), axisLabels = "none")

## Warning in check_and_set_ggpairs_defaults("diag", diag, continuous =
## "densityDiag", : Changing diag$continuous from 'bar' to 'barDiag'

## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.

## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.

Conclusiones

De lo hasta ahora analizado, podemos concluir que:

1. Observando los diagramas de dispersion notamos que: la variable de diametro (girth) y volumen (volume) estan relacionadas.

2. El coeficiente de correlacion de pearson es bastante alto (r =0.9671194) y tenemos un valor de P significativo (p-value < 2.2e-16). Esto significa que hay una intensa correlacion entre ambas variables.