Base de datos

La base de datos a trabajar contiene la eficiencia modelos de vehiculos en Millas por Galón y características de los vehiculos:

mpg cyl disp hp drat wt qsec vs am gear carb
Mazda RX4 21.0 6 160.0 110 3.90 2.620 16.46 0 1 4 4
Mazda RX4 Wag 21.0 6 160.0 110 3.90 2.875 17.02 0 1 4 4
Datsun 710 22.8 4 108.0 93 3.85 2.320 18.61 1 1 4 1
Hornet 4 Drive 21.4 6 258.0 110 3.08 3.215 19.44 1 0 3 1
Hornet Sportabout 18.7 8 360.0 175 3.15 3.440 17.02 0 0 3 2
Valiant 18.1 6 225.0 105 2.76 3.460 20.22 1 0 3 1
Duster 360 14.3 8 360.0 245 3.21 3.570 15.84 0 0 3 4
Merc 240D 24.4 4 146.7 62 3.69 3.190 20.00 1 0 4 2
Merc 230 22.8 4 140.8 95 3.92 3.150 22.90 1 0 4 2
Merc 280 19.2 6 167.6 123 3.92 3.440 18.30 1 0 4 4
Merc 280C 17.8 6 167.6 123 3.92 3.440 18.90 1 0 4 4
Merc 450SE 16.4 8 275.8 180 3.07 4.070 17.40 0 0 3 3
Merc 450SL 17.3 8 275.8 180 3.07 3.730 17.60 0 0 3 3
Merc 450SLC 15.2 8 275.8 180 3.07 3.780 18.00 0 0 3 3
Cadillac Fleetwood 10.4 8 472.0 205 2.93 5.250 17.98 0 0 3 4
Lincoln Continental 10.4 8 460.0 215 3.00 5.424 17.82 0 0 3 4
Chrysler Imperial 14.7 8 440.0 230 3.23 5.345 17.42 0 0 3 4
Fiat 128 32.4 4 78.7 66 4.08 2.200 19.47 1 1 4 1
Honda Civic 30.4 4 75.7 52 4.93 1.615 18.52 1 1 4 2
Toyota Corolla 33.9 4 71.1 65 4.22 1.835 19.90 1 1 4 1
Toyota Corona 21.5 4 120.1 97 3.70 2.465 20.01 1 0 3 1
Dodge Challenger 15.5 8 318.0 150 2.76 3.520 16.87 0 0 3 2
AMC Javelin 15.2 8 304.0 150 3.15 3.435 17.30 0 0 3 2
Camaro Z28 13.3 8 350.0 245 3.73 3.840 15.41 0 0 3 4
Pontiac Firebird 19.2 8 400.0 175 3.08 3.845 17.05 0 0 3 2
Fiat X1-9 27.3 4 79.0 66 4.08 1.935 18.90 1 1 4 1
Porsche 914-2 26.0 4 120.3 91 4.43 2.140 16.70 0 1 5 2
Lotus Europa 30.4 4 95.1 113 3.77 1.513 16.90 1 1 5 2
Ford Pantera L 15.8 8 351.0 264 4.22 3.170 14.50 0 1 5 4
Ferrari Dino 19.7 6 145.0 175 3.62 2.770 15.50 0 1 5 6
Maserati Bora 15.0 8 301.0 335 3.54 3.570 14.60 0 1 5 8
Volvo 142E 21.4 4 121.0 109 4.11 2.780 18.60 1 1 4 2

Un ejemplo básico de ajuste de modelo:

Generamos una regresión lineal en la cual explicamos la eficiencia del vehiculo basados en el peso del vehiculo

Modelo1 <- lm(mpg ~ wt, data = mtcars)
summary(Modelo1)
## 
## Call:
## lm(formula = mpg ~ wt, data = mtcars)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -4.5432 -2.3647 -0.1252  1.4096  6.8727 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  37.2851     1.8776  19.858  < 2e-16 ***
## wt           -5.3445     0.5591  -9.559 1.29e-10 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 3.046 on 30 degrees of freedom
## Multiple R-squared:  0.7528, Adjusted R-squared:  0.7446 
## F-statistic: 91.38 on 1 and 30 DF,  p-value: 1.294e-10

Gráfica de la relación

Ahora selección de las variables que explican mejor la eficiencia

Generamos un modelo global que contiene todas las variable

Modelo_Global <- lm(mpg ~., data = mtcars)
options(na.action = "na.fail")

dd <- dredge(Modelo_Global)
subset(dd, delta < 2)
## Global model call: lm(formula = mpg ~ ., data = mtcars)
## ---
## Model selection table 
##     (Intrc)    am    carb     cyl       hp   qsec     wt df  logLik  AICc
## 642   9.618 2.936                          1.2260 -3.917  5 -72.060 156.4
## 517  39.690               -1.5080                 -3.191  4 -74.005 157.5
## 706  17.440 2.926                 -0.01765 0.8106 -3.238  6 -71.164 157.7
## 581  38.750               -0.9416 -0.01804        -3.167  5 -72.738 157.8
## 644  12.900 3.511 -0.4886                  1.0190 -3.434  6 -71.282 157.9
## 519  39.600       -0.4858 -1.2900                 -3.159  5 -72.809 157.9
## 577  37.230                       -0.03177        -3.878  4 -74.326 158.1
## 641  19.750                                0.9292 -5.048  4 -74.360 158.2
##     delta weight
## 642  0.00  0.227
## 517  1.06  0.133
## 706  1.26  0.121
## 581  1.36  0.115
## 644  1.50  0.107
## 519  1.50  0.107
## 577  1.71  0.097
## 641  1.77  0.093
## Models ranked by AICc(x)

Ahora estudio el mejor modelo

Mejor_Modelo <- lm(mpg ~ qsec + am + wt, data = mtcars)
summary(Mejor_Modelo)
## 
## Call:
## lm(formula = mpg ~ qsec + am + wt, data = mtcars)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -3.4811 -1.5555 -0.7257  1.4110  4.6610 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)   9.6178     6.9596   1.382 0.177915    
## qsec          1.2259     0.2887   4.247 0.000216 ***
## am            2.9358     1.4109   2.081 0.046716 *  
## wt           -3.9165     0.7112  -5.507 6.95e-06 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 2.459 on 28 degrees of freedom
## Multiple R-squared:  0.8497, Adjusted R-squared:  0.8336 
## F-statistic: 52.75 on 3 and 28 DF,  p-value: 1.21e-11
ggplot(mtcars, aes(x = mpg, y = wt)) + geom_point(aes(color = qsec))  + facet_grid(am ~ .) + geom_smooth(method = "lm")