MODELOS DE REGRESIÓN SIMPLE

CARGAR DATOS

setwd("/cloud/project")
datos<-read.csv("database.csv", header =TRUE,sep=",",dec=".")

CARGAR LIBRERIAS Y PACKETES

library(e1071)
library(PASWR)

## Loading required package: lattice

library(SmartEDA)
library(plotly)

## Loading required package: ggplot2

## 
## Attaching package: 'plotly'

## The following object is masked from 'package:ggplot2':
## 
##     last_plot

## The following object is masked from 'package:stats':
## 
##     filter

## The following object is masked from 'package:graphics':
## 
##     layout

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)
library(tidyverse)

## ── Attaching core tidyverse packages ──────────────────────── tidyverse 2.0.0 ──
## ✔ forcats   1.0.0     ✔ stringr   1.5.1
## ✔ lubridate 1.9.4     ✔ tibble    3.3.0
## ✔ purrr     1.1.0     ✔ tidyr     1.3.1
## ✔ readr     2.1.5

## ── Conflicts ────────────────────────────────────────── tidyverse_conflicts() ──
## ✖ dplyr::filter() masks plotly::filter(), stats::filter()
## ✖ dplyr::lag()    masks stats::lag()
## ℹ Use the conflicted package (<http://conflicted.r-lib.org/>) to force all conflicts to become errors

VISUALIZAR MI TABLA

str(datos)

## 'data.frame':    38113 obs. of  81 variables:
##  $ Vehicle.ID                         : int  26587 27705 26561 27681 27550 28426 27549 28425 27593 28455 ...
##  $ Year                               : int  1984 1984 1984 1984 1984 1984 1984 1984 1984 1984 ...
##  $ Make                               : chr  "Alfa Romeo" "Alfa Romeo" "Alfa Romeo" "Alfa Romeo" ...
##  $ Model                              : chr  "GT V6 2.5" "GT V6 2.5" "Spider Veloce 2000" "Spider Veloce 2000" ...
##  $ Class                              : chr  "Minicompact Cars" "Minicompact Cars" "Two Seaters" "Two Seaters" ...
##  $ Drive                              : chr  "" "" "" "" ...
##  $ Transmission                       : chr  "Manual 5-Speed" "Manual 5-Speed" "Manual 5-Speed" "Manual 5-Speed" ...
##  $ Transmission.Descriptor            : chr  "" "" "" "" ...
##  $ Engine.Index                       : int  9001 9005 9002 9006 1830 1880 1831 1881 1524 1574 ...
##  $ Engine.Descriptor                  : chr  "(FFS)" "(FFS) CA model" "(FFS)" "(FFS) CA model" ...
##  $ Engine.Cylinders                   : int  6 6 4 4 4 4 6 6 6 6 ...
##  $ Engine.Displacement                : num  2.5 2.5 2 2 2.5 2.5 4.2 4.2 4.2 4.2 ...
##  $ Turbocharger                       : logi  NA NA NA NA NA NA ...
##  $ Supercharger                       : chr  "" "" "" "" ...
##  $ Fuel.Type                          : chr  "Regular" "Regular" "Regular" "Regular" ...
##  $ Fuel.Type.1                        : chr  "Regular Gasoline" "Regular Gasoline" "Regular Gasoline" "Regular Gasoline" ...
##  $ Fuel.Type.2                        : chr  "" "" "" "" ...
##  $ City.MPG..FT1.                     : int  17 17 18 18 18 18 13 13 15 15 ...
##  $ Unrounded.City.MPG..FT1.           : num  0 0 0 0 0 0 0 0 0 0 ...
##  $ City.MPG..FT2.                     : int  0 0 0 0 0 0 0 0 0 0 ...
##  $ Unrounded.City.MPG..FT2.           : num  0 0 0 0 0 0 0 0 0 0 ...
##  $ City.Gasoline.Consumption..CD.     : num  0 0 0 0 0 0 0 0 0 0 ...
##  $ City.Electricity.Consumption       : num  0 0 0 0 0 0 0 0 0 0 ...
##  $ City.Utility.Factor                : num  0 0 0 0 0 0 0 0 0 0 ...
##  $ Highway.MPG..FT1.                  : int  24 24 25 25 17 17 13 13 20 19 ...
##  $ Unrounded.Highway.MPG..FT1.        : num  0 0 0 0 0 0 0 0 0 0 ...
##  $ Highway.MPG..FT2.                  : int  0 0 0 0 0 0 0 0 0 0 ...
##  $ Unrounded.Highway.MPG..FT2.        : num  0 0 0 0 0 0 0 0 0 0 ...
##  $ Highway.Gasoline.Consumption..CD.  : num  0 0 0 0 0 0 0 0 0 0 ...
##  $ Highway.Electricity.Consumption    : num  0 0 0 0 0 0 0 0 0 0 ...
##  $ Highway.Utility.Factor             : num  0 0 0 0 0 0 0 0 0 0 ...
##  $ Unadjusted.City.MPG..FT1.          : num  21 21 23 23 22 22 16 16 19 19 ...
##  $ Unadjusted.Highway.MPG..FT1.       : num  34 34 35 35 24 24 18 18 27 26 ...
##  $ Unadjusted.City.MPG..FT2.          : num  0 0 0 0 0 0 0 0 0 0 ...
##  $ Unadjusted.Highway.MPG..FT2.       : num  0 0 0 0 0 0 0 0 0 0 ...
##  $ Combined.MPG..FT1.                 : int  20 20 21 21 17 17 13 13 17 17 ...
##  $ Unrounded.Combined.MPG..FT1.       : num  0 0 0 0 0 0 0 0 0 0 ...
##  $ Combined.MPG..FT2.                 : int  0 0 0 0 0 0 0 0 0 0 ...
##  $ Unrounded.Combined.MPG..FT2.       : num  0 0 0 0 0 0 0 0 0 0 ...
##  $ Combined.Electricity.Consumption   : num  0 0 0 0 0 0 0 0 0 0 ...
##  $ Combined.Gasoline.Consumption..CD. : num  0 0 0 0 0 0 0 0 0 0 ...
##  $ Combined.Utility.Factor            : num  0 0 0 0 0 0 0 0 0 0 ...
##  $ Annual.Fuel.Cost..FT1.             : int  1750 1750 1650 1650 2050 2050 2700 2700 2050 2050 ...
##  $ Annual.Fuel.Cost..FT2.             : int  0 0 0 0 0 0 0 0 0 0 ...
##  $ Gas.Guzzler.Tax                    : chr  "" "" "" "" ...
##  $ Save.or.Spend..5.Year.             : int  -2000 -2000 -1500 -1500 -3500 -3500 -6750 -6750 -3500 -3500 ...
##  $ Annual.Consumption.in.Barrels..FT1.: num  16.5 16.5 15.7 15.7 19.4 ...
##  $ Annual.Consumption.in.Barrels..FT2.: num  0 0 0 0 0 0 0 0 0 0 ...
##  $ Tailpipe.CO2..FT1.                 : int  -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 ...
##  $ Tailpipe.CO2.in.Grams.Mile..FT1.   : num  444 444 423 423 523 ...
##  $ Tailpipe.CO2..FT2.                 : int  -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 ...
##  $ Tailpipe.CO2.in.Grams.Mile..FT2.   : num  0 0 0 0 0 0 0 0 0 0 ...
##  $ Fuel.Economy.Score                 : int  -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 ...
##  $ GHG.Score                          : int  -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 ...
##  $ GHG.Score..Alt.Fuel.               : int  -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 ...
##  $ My.MPG.Data                        : chr  "N" "N" "N" "N" ...
##  $ X2D.Passenger.Volume               : int  74 74 0 0 0 0 0 0 0 0 ...
##  $ X2D.Luggage.Volume                 : int  7 7 0 0 0 0 0 0 0 0 ...
##  $ X4D.Passenger.Volume               : int  0 0 0 0 0 0 0 0 0 0 ...
##  $ X4D.Luggage.Volume                 : int  0 0 0 0 0 0 0 0 0 0 ...
##  $ Hatchback.Passenger.Volume         : int  0 0 0 0 0 0 0 0 0 0 ...
##  $ Hatchback.Luggage.Volume           : int  0 0 0 0 0 0 0 0 0 0 ...
##  $ Start.Stop.Technology              : chr  "" "" "" "" ...
##  $ Alternative.Fuel.Technology        : chr  "" "" "" "" ...
##  $ Electric.Motor                     : chr  "" "" "" "" ...
##  $ Manufacturer.Code                  : chr  "" "" "" "" ...
##  $ Gasoline.Electricity.Blended..CD.  : chr  "False" "False" "False" "False" ...
##  $ Vehicle.Charger                    : chr  "" "" "" "" ...
##  $ Alternate.Charger                  : chr  "" "" "" "" ...
##  $ Hours.to.Charge..120V.             : int  0 0 0 0 0 0 0 0 0 0 ...
##  $ Hours.to.Charge..240V.             : num  0 0 0 0 0 0 0 0 0 0 ...
##  $ Hours.to.Charge..AC.240V.          : num  0 0 0 0 0 0 0 0 0 0 ...
##  $ Composite.City.MPG                 : int  0 0 0 0 0 0 0 0 0 0 ...
##  $ Composite.Highway.MPG              : int  0 0 0 0 0 0 0 0 0 0 ...
##  $ Composite.Combined.MPG             : int  0 0 0 0 0 0 0 0 0 0 ...
##  $ Range..FT1.                        : int  0 0 0 0 0 0 0 0 0 0 ...
##  $ City.Range..FT1.                   : num  0 0 0 0 0 0 0 0 0 0 ...
##  $ Highway.Range..FT1.                : num  0 0 0 0 0 0 0 0 0 0 ...
##  $ Range..FT2.                        : chr  "" "" "" "" ...
##  $ City.Range..FT2.                   : num  0 0 0 0 0 0 0 0 0 0 ...
##  $ Highway.Range..FT2.                : num  0 0 0 0 0 0 0 0 0 0 ...

VERIFICAR LA POSICIÓN DE MI VARIABLE

which(names(datos)== "Annual.Fuel.Cost..FT1.")

## [1] 43

which(names(datos)== "Engine.Displacement")

## [1] 12

which(names(datos)== "City.MPG..FT1.")

## [1] 18

which(names(datos)== "Highway.MPG..FT1.")

## [1] 25

which(names(datos)== "Combined.MPG..FT1.")

## [1] 36

which(names(datos)== "Unadjusted.City.MPG..FT1.")

## [1] 32

which(names(datos)== "Unadjusted.Highway.MPG..FT1.")

## [1] 33

EXTRAER DATOS

DatCostAnuCmbFT1<-datos[ ,43]
DatDesplazamientoMotor<-datos[ ,12]
DatCiudadmpgFT1<-datos[ ,18]
DatCarreterampgFT1<-datos[ ,25]
DatCombustibleCombmpgFT1<-datos[ ,36]
DatCorrCiudadmpgFT1<-datos[ ,32]
DatCorrCarreterampgFT1<-datos[ ,33]

RESUMEN DE ESTADÍSTICA DESCRIPÍVA DE CADA VARIABLE

summary(DatCostAnuCmbFT1)

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##     500    1600    1950    1971    2350    6050

summary(DatDesplazamientoMotor)

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max.    NA's 
##   0.000   2.200   3.000   3.318   4.300   8.400     134

summary(DatCiudadmpgFT1)

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##    6.00   15.00   17.00   17.98   20.00  150.00

summary(DatCarreterampgFT1)

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##    9.00   20.00   24.00   24.08   27.00  122.00

summary(DatCombustibleCombmpgFT1)

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##    7.00   17.00   19.00   20.22   23.00  136.00

summary(DatCorrCiudadmpgFT1)

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##    0.00   18.00   21.05   22.65   25.20  224.80

summary(DatCorrCarreterampgFT1)

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##    0.00   27.12   33.00   33.68   38.20  182.70

REGRESIÓN SIMPLE (BIVARIADA)

Engine Displacement y Combined MPG (FT1)

cor(datos[ , c(43,36)])

##                        Annual.Fuel.Cost..FT1. Combined.MPG..FT1.
## Annual.Fuel.Cost..FT1.              1.0000000         -0.7448504
## Combined.MPG..FT1.                 -0.7448504          1.0000000

Annual Fuel Cost (FT1) y City MPG (FT1)

cor(datos[ , c(43,18)])

##                        Annual.Fuel.Cost..FT1. City.MPG..FT1.
## Annual.Fuel.Cost..FT1.              1.0000000     -0.6920496
## City.MPG..FT1.                     -0.6920496      1.0000000

City.MPG..FT1. Y Highway.MPG..FT1.

cor(datos[ , c(18,25)])

##                   City.MPG..FT1. Highway.MPG..FT1.
## City.MPG..FT1.         1.0000000         0.9317386
## Highway.MPG..FT1.      0.9317386         1.0000000

MODELO N1 (Lineal) SIN DEPURAR

Cargar datos

datos<-read.csv("database.csv", header =TRUE,sep=",",dec=".")

Diagrama de dispersion

plot(datos$Annual.Fuel.Cost..FT1.,datos$Engine.Displacement)

x<-datos$Engine.Displacement
y<-datos$Annual.Fuel.Cost..FT1.
plot(x,y)

##circulo de la regresión

regresionLineal<- lm(y~x, na.action = na.omit)
regresionLineal

## 
## Call:
## lm(formula = y ~ x, na.action = na.omit)
## 
## Coefficients:
## (Intercept)            x  
##       977.5        300.6

Resumen del modelo de regresión

summary(regresionLineal)

## 
## Call:
## lm(formula = y ~ x, na.action = na.omit)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -1181.2  -209.7   -29.7   171.2  3509.3 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  977.530      4.515   216.5   <2e-16 ***
## x            300.617      1.259   238.8   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 334.2 on 37977 degrees of freedom
##   (134 observations deleted due to missingness)
## Multiple R-squared:  0.6002, Adjusted R-squared:  0.6002 
## F-statistic: 5.701e+04 on 1 and 37977 DF,  p-value: < 2.2e-16

Gráfica de regresión lineal

plot(x,y,col=4,pch=7,main="Regresión Lineal",
     xlab="Volúmen del motor",ylab="Costo Anual del Combustible Primario")
abline(regresionLineal,col="green")

Test de bondad

R <- cor(x, y, use = "complete.obs")
R2<- R^2*100

MODELO LINEAL DEPURADO

Generar y asiganr X , Y

plot(datos$Annual.Fuel.Cost..FT1.,datos$Engine.Displacement)

x<-datos$Engine.Displacement
y<-datos$Annual.Fuel.Cost..FT1.
plot(x,y)

datos <- data.frame(x = x, y = y)

Agrupar por x y obtener promedio de y

promedios_xy <- datos %>%
  group_by(x) %>%
  summarise(y_prom = mean(y, na.rm = TRUE))

Ajustar modelo con los puntos promediados

modelo_prom <- lm(y_prom ~ x, data = promedios_xy)
summary(modelo_prom)

## 
## Call:
## lm(formula = y_prom ~ x, data = promedios_xy)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -831.32 -135.18   -7.16  162.08  708.73 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)   957.73      69.25   13.83   <2e-16 ***
## x             310.71      15.31   20.30   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 257.1 on 64 degrees of freedom
##   (1 observation deleted due to missingness)
## Multiple R-squared:  0.8655, Adjusted R-squared:  0.8634 
## F-statistic:   412 on 1 and 64 DF,  p-value: < 2.2e-16

Gráfica con puntos promediados y línea de regresión

plot(x, y, col = rgb(0, 0, 1, alpha = 0.1), pch = 16,
     main = "Regresión lineal con promedios por X",
     xlab = "Volúmen del motor", ylab = "Costo anual del combustible")

points(promedios_xy$x, promedios_xy$y_prom, col = "red", pch = 19)
abline(modelo_prom, col = "blue", lwd = 2)

Test de bondad

Rm <- cor(promedios_xy$x, promedios_xy$y_prom, use = "complete.obs")
Rm

## [1] 0.9303469

Rm2<- Rm^2*100
Rm2

## [1] 86.55453

Cargar los datos

setwd("/cloud/project")
datos<-read.csv("database.csv", header =TRUE,sep=",",dec=".")

MODELO N2 (POTENCIAL)

Diagrama de dispersion

plot(datos$Annual.Fuel.Cost..FT1.,datos$Combined.MPG..FT1.)

x<-datos$Combined.MPG..FT1.
y<-datos$Annual.Fuel.Cost..FT1.
summary(x)

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##    7.00   17.00   19.00   20.22   23.00  136.00

summary(y)

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##     500    1600    1950    1971    2350    6050

plot(x,y)

x1<-log(x)
y1<-log(y)

Circulo de la regresión

regresionPotencial<- lm(y1~x1, na.action = na.omit)
regresionPotencial

## 
## Call:
## lm(formula = y1 ~ x1, na.action = na.omit)
## 
## Coefficients:
## (Intercept)           x1  
##     10.4313      -0.9706

summary(regresionPotencial)

## 
## Call:
## lm(formula = y1 ~ x1, na.action = na.omit)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.19389 -0.05617 -0.05022  0.11857  0.57043 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 10.431254   0.005239  1991.2   <2e-16 ***
## x1          -0.970617   0.001758  -552.1   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.09039 on 38111 degrees of freedom
## Multiple R-squared:  0.8889, Adjusted R-squared:  0.8889 
## F-statistic: 3.049e+05 on 1 and 38111 DF,  p-value: < 2.2e-16

Extraer coeficientes de la información contenida en summary

beta0<-regresionPotencial$coefficients[1]
beta1<-regresionPotencial$coefficients[2]
b<-beta1
a<-exp(beta0)

Gráfica Modelo Potencial

plot(x,y,col=5,pch=7,main = "Regresión Potencial",
     xlab="Combustible Primario Combinado en MPG",ylab="Costo Anual del Combustible Primario")
curve(a*x^b,from=0, to=100,add=TRUE,col="yellow")

Test de bondad

R <- cor(x1, y1, use = "complete.obs")
R

## [1] -0.9428029

R2<- R^2*100
R2

## [1] 88.88773

Regresion simple 1

GRUPO 5

2025-07-21

MODELOS DE REGRESIÓN SIMPLE

CARGAR DATOS

CARGAR LIBRERIAS Y PACKETES

VISUALIZAR MI TABLA

VERIFICAR LA POSICIÓN DE MI VARIABLE

EXTRAER DATOS

RESUMEN DE ESTADÍSTICA DESCRIPÍVA DE CADA VARIABLE

REGRESIÓN SIMPLE (BIVARIADA)

MODELO N1 (Lineal) SIN DEPURAR

Cargar datos

Diagrama de dispersion

Resumen del modelo de regresión

Gráfica de regresión lineal

Test de bondad

MODELO LINEAL DEPURADO

Generar y asiganr X , Y

Agrupar por x y obtener promedio de y

Ajustar modelo con los puntos promediados

Gráfica con puntos promediados y línea de regresión

Test de bondad

Cargar los datos

MODELO N2 (POTENCIAL)

Diagrama de dispersion

Circulo de la regresión

Extraer coeficientes de la información contenida en summary

Gráfica Modelo Potencial

Test de bondad