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# Instalamos y cargamos las librerías necesarias
library(tidyverse)
library(ggplot2)
library(car)


auto_mpg <- read.csv("auto-mpg.csv")

# Examinar la estructura de los datos
str(auto_mpg)

'data.frame':   398 obs. of  9 variables:
 $ mpg         : num  18 15 18 16 17 15 14 14 14 15 ...
 $ cylinders   : int  8 8 8 8 8 8 8 8 8 8 ...
 $ displacement: num  307 350 318 304 302 429 454 440 455 390 ...
 $ horsepower  : chr  "130" "165" "150" "150" ...
 $ weight      : int  3504 3693 3436 3433 3449 4341 4354 4312 4425 3850 ...
 $ acceleration: num  12 11.5 11 12 10.5 10 9 8.5 10 8.5 ...
 $ model.year  : int  70 70 70 70 70 70 70 70 70 70 ...
 $ origin      : int  1 1 1 1 1 1 1 1 1 1 ...
 $ car.name    : chr  "chevrolet chevelle malibu" "buick skylark 320" "plymouth satellite" "amc rebel sst" ...

# Calcular estadísticas descriptivas de las variables mpg, weight y horsepower
summary(auto_mpg$mpg)

   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
   9.00   17.50   23.00   23.51   29.00   46.60 

summary(auto_mpg$weight)

   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
   1613    2224    2804    2970    3608    5140 

summary(auto_mpg$horsepower)

   Length     Class      Mode 
      398 character character 

# Ajuste del modelo de regresión lineal simple
modelo_simple <- lm(mpg ~ weight, data = auto_mpg)

# Resumen del modelo
summary(modelo_simple)

Call:
lm(formula = mpg ~ weight, data = auto_mpg)

Residuals:
    Min      1Q  Median      3Q     Max 
-12.012  -2.801  -0.351   2.114  16.480 

Coefficients:
              Estimate Std. Error t value Pr(>|t|)    
(Intercept) 46.3173644  0.7952452   58.24   <2e-16 ***
weight      -0.0076766  0.0002575  -29.81   <2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 4.345 on 396 degrees of freedom
Multiple R-squared:  0.6918,    Adjusted R-squared:  0.691 
F-statistic: 888.9 on 1 and 396 DF,  p-value: < 2.2e-16

# Gráficos de diagnóstico del modelo
par(mfrow = c(2, 2))
plot(modelo_simple)

# Gráfico Q-Q
qqPlot(modelo_simple$residuals)

[1] 323 327

# Ajuste del modelo de regresión lineal múltiple
modelo_multiple <- lm(mpg ~ weight + horsepower + acceleration, data = auto_mpg)

# Resumen del modelo
summary(modelo_multiple)

Call:
lm(formula = mpg ~ weight + horsepower + acceleration, data = auto_mpg)

Residuals:
   Min     1Q Median     3Q    Max 
-9.458 -2.023  0.000  1.407 15.062 

Coefficients:
                Estimate Std. Error t value Pr(>|t|)    
(Intercept)    4.143e+01  2.496e+00  16.601  < 2e-16 ***
weight        -3.570e-03  6.972e-04  -5.120 5.45e-07 ***
horsepower100 -6.498e+00  1.860e+00  -3.494 0.000546 ***
horsepower102 -6.109e+00  4.058e+00  -1.505 0.133287    
horsepower103 -6.899e+00  4.030e+00  -1.712 0.087938 .  
horsepower105 -4.568e+00  1.974e+00  -2.315 0.021306 *  
horsepower107 -7.971e+00  4.037e+00  -1.974 0.049258 *  
horsepower108 -7.946e+00  4.042e+00  -1.966 0.050226 .  
horsepower110 -5.724e+00  1.875e+00  -3.053 0.002466 ** 
horsepower112 -7.619e+00  2.680e+00  -2.843 0.004771 ** 
horsepower113 -4.210e+00  4.054e+00  -1.038 0.299885    
horsepower115 -3.118e+00  2.337e+00  -1.334 0.183129    
horsepower116 -2.406e+00  4.100e+00  -0.587 0.557653    
horsepower120 -6.390e+00  2.580e+00  -2.477 0.013790 *  
horsepower122 -7.905e+00  4.068e+00  -1.943 0.052943 .  
horsepower125 -5.049e+00  2.781e+00  -1.815 0.070459 .  
horsepower129 -1.053e+01  3.243e+00  -3.246 0.001302 ** 
horsepower130 -8.530e+00  2.588e+00  -3.296 0.001096 ** 
horsepower132  4.618e+00  4.137e+00   1.116 0.265172    
horsepower133 -8.955e+00  4.086e+00  -2.192 0.029177 *  
horsepower135 -5.612e+00  4.166e+00  -1.347 0.178953    
horsepower137 -9.237e+00  4.229e+00  -2.184 0.029713 *  
horsepower138 -7.385e+00  4.255e+00  -1.735 0.083692 .  
horsepower139 -7.072e+00  3.261e+00  -2.168 0.030908 *  
horsepower140 -6.951e+00  2.517e+00  -2.762 0.006100 ** 
horsepower142 -7.746e+00  4.238e+00  -1.828 0.068582 .  
horsepower145 -8.299e+00  2.532e+00  -3.277 0.001171 ** 
horsepower148 -7.301e+00  4.421e+00  -1.652 0.099656 .  
horsepower149 -6.191e+00  4.296e+00  -1.441 0.150583    
horsepower150 -8.971e+00  2.278e+00  -3.938 0.000102 ***
horsepower152 -8.561e+00  4.332e+00  -1.976 0.049060 *  
horsepower153 -9.206e+00  3.399e+00  -2.708 0.007152 ** 
horsepower155 -6.976e+00  3.443e+00  -2.026 0.043647 *  
horsepower158 -9.480e+00  4.362e+00  -2.174 0.030515 *  
horsepower160 -1.124e+01  3.502e+00  -3.211 0.001467 ** 
horsepower165 -9.391e+00  2.826e+00  -3.323 0.001001 ** 
horsepower167 -8.672e+00  4.542e+00  -1.909 0.057163 .  
horsepower170 -8.363e+00  2.922e+00  -2.862 0.004501 ** 
horsepower175 -9.298e+00  2.908e+00  -3.197 0.001535 ** 
horsepower180 -9.403e+00  2.911e+00  -3.230 0.001374 ** 
horsepower190 -9.068e+00  3.195e+00  -2.838 0.004852 ** 
horsepower193 -1.074e+01  4.272e+00  -2.513 0.012498 *  
horsepower198 -8.553e+00  3.716e+00  -2.302 0.022036 *  
horsepower200 -1.191e+01  4.288e+00  -2.778 0.005803 ** 
horsepower208 -1.104e+01  4.533e+00  -2.434 0.015495 *  
horsepower210 -1.128e+01  4.346e+00  -2.596 0.009888 ** 
horsepower215 -9.941e+00  3.325e+00  -2.990 0.003022 ** 
horsepower220 -9.551e+00  4.558e+00  -2.095 0.036981 *  
horsepower225 -1.059e+01  3.229e+00  -3.279 0.001165 ** 
horsepower230 -7.693e+00  4.508e+00  -1.706 0.088978 .  
horsepower46  -3.287e+00  3.136e+00  -1.048 0.295526    
horsepower48   1.558e+01  2.764e+00   5.638 3.96e-08 ***
horsepower49  -7.021e-01  4.067e+00  -0.173 0.863058    
horsepower52   5.098e+00  2.514e+00   2.028 0.043402 *  
horsepower53   2.509e+00  3.075e+00   0.816 0.415233    
horsepower54  -4.282e+00  4.126e+00  -1.038 0.300192    
horsepower58   7.119e+00  3.080e+00   2.311 0.021484 *  
horsepower60   2.329e+00  2.310e+00   1.008 0.314082    
horsepower61   2.654e+00  4.046e+00   0.656 0.512417    
horsepower62   3.504e+00  3.051e+00   1.149 0.251607    
horsepower63   4.608e+00  2.637e+00   1.747 0.081602 .  
horsepower64   8.522e+00  4.031e+00   2.114 0.035312 *  
horsepower65   6.059e+00  1.968e+00   3.079 0.002269 ** 
horsepower66   4.835e+00  4.034e+00   1.198 0.231716    
horsepower67   4.359e+00  1.870e+00   2.331 0.020400 *  
horsepower68   2.555e+00  2.167e+00   1.179 0.239284    
horsepower69   2.783e+00  2.648e+00   1.051 0.294116    
horsepower70   2.700e+00  1.876e+00   1.439 0.151062    
horsepower71  -1.684e-01  2.255e+00  -0.075 0.940527    
horsepower72  -5.034e+00  2.149e+00  -2.343 0.019794 *  
horsepower74   4.338e+00  2.632e+00   1.648 0.100384    
horsepower75  -2.639e-01  1.822e+00  -0.145 0.884963    
horsepower76   2.773e+00  2.399e+00   1.156 0.248619    
horsepower77   1.790e+00  4.055e+00   0.441 0.659284    
horsepower78  -1.576e+00  2.148e+00  -0.734 0.463650    
horsepower79  -1.007e+00  3.037e+00  -0.332 0.740335    
horsepower80  -1.129e-01  2.071e+00  -0.055 0.956556    
horsepower81  -3.113e+00  3.034e+00  -1.026 0.305803    
horsepower82   4.317e+00  4.019e+00   1.074 0.283708    
horsepower83  -9.528e-01  2.402e+00  -0.397 0.691908    
horsepower84   1.153e+00  2.182e+00   0.529 0.597423    
horsepower85  -3.315e+00  1.979e+00  -1.675 0.094941 .  
horsepower86  -4.565e+00  2.260e+00  -2.020 0.044283 *  
horsepower87  -3.540e+00  3.039e+00  -1.165 0.244945    
horsepower88  -2.419e+00  1.748e+00  -1.384 0.167460    
horsepower89  -1.993e+00  4.027e+00  -0.495 0.621022    
horsepower90  -2.885e+00  1.745e+00  -1.654 0.099254 .  
horsepower91  -8.578e+00  4.042e+00  -2.122 0.034655 *  
horsepower92  -6.659e-01  2.165e+00  -0.308 0.758585    
horsepower93  -2.870e+00  4.018e+00  -0.714 0.475602    
horsepower94  -6.653e+00  4.014e+00  -1.658 0.098423 .  
horsepower95  -5.133e+00  1.844e+00  -2.783 0.005720 ** 
horsepower96  -1.427e+00  2.663e+00  -0.536 0.592350    
horsepower97  -6.258e+00  1.991e+00  -3.143 0.001841 ** 
horsepower98  -5.283e+00  3.084e+00  -1.713 0.087766 .  
acceleration  -2.596e-01  1.376e-01  -1.887 0.060105 .  
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 3.715 on 302 degrees of freedom
Multiple R-squared:  0.8281,    Adjusted R-squared:  0.7741 
F-statistic: 15.32 on 95 and 302 DF,  p-value: < 2.2e-16

# Gráficos de diagnóstico del modelo
par(mfrow = c(2, 2))
plot(modelo_multiple)

Warning: not plotting observations with leverage one:
  24, 27, 28, 29, 60, 68, 89, 93, 105, 111, 114, 117, 118, 120, 124, 146, 151, 160, 191, 208, 211, 233, 237, 246, 275, 278, 288, 289, 291, 298, 334, 345, 362, 398

# Verificar multicolinealidad usando VIF
vif(modelo_multiple)

                  GVIF Df GVIF^(1/(2*Df))
weight       10.026270  1        3.166429
horsepower   22.889379 93        1.016974
acceleration  4.141248  1        2.035006

# Convertir 'origin' en variables dummy
auto_mpg <- auto_mpg %>%
  mutate(origin = as.factor(origin)) %>%
  mutate(origin_1 = ifelse(origin == 1, 1, 0),
         origin_2 = ifelse(origin == 2, 1, 0),
         origin_3 = ifelse(origin == 3, 1, 0))

# Ajuste del nuevo modelo con variables dummy
modelo_dummy <- lm(mpg ~ weight + horsepower + acceleration + origin_1 + origin_2, data = auto_mpg)

# Resumen del modelo
summary(modelo_dummy)

Call:
lm(formula = mpg ~ weight + horsepower + acceleration + origin_1 + 
    origin_2, data = auto_mpg)

Residuals:
    Min      1Q  Median      3Q     Max 
-11.795  -1.935   0.000   1.327  14.908 

Coefficients:
                Estimate Std. Error t value Pr(>|t|)    
(Intercept)    4.212e+01  2.444e+00  17.237  < 2e-16 ***
weight        -2.505e-03  7.138e-04  -3.510 0.000517 ***
horsepower100 -7.221e+00  1.812e+00  -3.985 8.49e-05 ***
horsepower102 -7.607e+00  3.969e+00  -1.917 0.056216 .  
horsepower103 -8.054e+00  3.934e+00  -2.047 0.041485 *  
horsepower105 -5.114e+00  1.918e+00  -2.666 0.008091 ** 
horsepower107 -7.595e+00  3.910e+00  -1.942 0.053035 .  
horsepower108 -1.152e+01  3.980e+00  -2.895 0.004068 ** 
horsepower110 -6.509e+00  1.822e+00  -3.573 0.000412 ***
horsepower112 -8.448e+00  2.609e+00  -3.238 0.001341 ** 
horsepower113 -4.781e+00  3.945e+00  -1.212 0.226522    
horsepower115 -3.568e+00  2.262e+00  -1.577 0.115828    
horsepower116 -5.994e+00  4.035e+00  -1.486 0.138442    
horsepower120 -8.294e+00  2.525e+00  -3.284 0.001143 ** 
horsepower122 -1.138e+01  4.001e+00  -2.844 0.004760 ** 
horsepower125 -6.192e+00  2.701e+00  -2.293 0.022554 *  
horsepower129 -1.121e+01  3.142e+00  -3.567 0.000420 ***
horsepower130 -9.693e+00  2.516e+00  -3.853 0.000143 ***
horsepower132  1.001e+00  4.071e+00   0.246 0.805954    
horsepower133 -1.073e+01  4.003e+00  -2.680 0.007766 ** 
horsepower135 -6.664e+00  4.035e+00  -1.651 0.099691 .  
horsepower137 -1.052e+01  4.098e+00  -2.568 0.010710 *  
horsepower138 -8.600e+00  4.123e+00  -2.086 0.037847 *  
horsepower139 -7.701e+00  3.160e+00  -2.437 0.015373 *  
horsepower140 -8.290e+00  2.451e+00  -3.382 0.000816 ***
horsepower142 -9.050e+00  4.107e+00  -2.203 0.028336 *  
horsepower145 -9.566e+00  2.465e+00  -3.881 0.000128 ***
horsepower148 -9.259e+00  4.293e+00  -2.157 0.031836 *  
horsepower149 -7.791e+00  4.167e+00  -1.870 0.062514 .  
horsepower150 -1.028e+01  2.221e+00  -4.626 5.55e-06 ***
horsepower152 -1.006e+01  4.201e+00  -2.394 0.017259 *  
horsepower153 -1.062e+01  3.301e+00  -3.217 0.001437 ** 
horsepower155 -8.683e+00  3.349e+00  -2.593 0.009981 ** 
horsepower158 -1.113e+01  4.231e+00  -2.631 0.008953 ** 
horsepower160 -1.258e+01  3.399e+00  -3.701 0.000255 ***
horsepower165 -1.057e+01  2.746e+00  -3.849 0.000145 ***
horsepower167 -1.091e+01  4.415e+00  -2.471 0.014038 *  
horsepower170 -1.003e+01  2.847e+00  -3.524 0.000492 ***
horsepower175 -1.099e+01  2.835e+00  -3.876 0.000130 ***
horsepower180 -1.105e+01  2.836e+00  -3.898 0.000120 ***
horsepower190 -1.057e+01  3.106e+00  -3.404 0.000754 ***
horsepower193 -1.270e+01  4.151e+00  -3.059 0.002419 ** 
horsepower198 -1.054e+01  3.616e+00  -2.915 0.003830 ** 
horsepower200 -1.355e+01  4.160e+00  -3.257 0.001254 ** 
horsepower208 -1.301e+01  4.402e+00  -2.954 0.003380 ** 
horsepower210 -1.295e+01  4.216e+00  -3.071 0.002330 ** 
horsepower215 -1.182e+01  3.239e+00  -3.651 0.000309 ***
horsepower220 -1.125e+01  4.422e+00  -2.545 0.011424 *  
horsepower225 -1.206e+01  3.138e+00  -3.842 0.000149 ***
horsepower230 -9.307e+00  4.372e+00  -2.129 0.034091 *  
horsepower46  -3.371e+00  3.060e+00  -1.102 0.271520    
horsepower48   1.526e+01  2.707e+00   5.638 3.96e-08 ***
horsepower49  -7.778e-01  3.953e+00  -0.197 0.844158    
horsepower52   4.092e+00  2.440e+00   1.677 0.094572 .  
horsepower53   1.695e-01  3.021e+00   0.056 0.955289    
horsepower54  -4.709e+00  4.014e+00  -1.173 0.241602    
horsepower58   5.944e+00  2.989e+00   1.989 0.047627 *  
horsepower60   1.048e+00  2.251e+00   0.465 0.642023    
horsepower61   1.164e-01  3.952e+00   0.029 0.976533    
horsepower62   2.140e+00  2.965e+00   0.722 0.470905    
horsepower63   5.370e+00  2.567e+00   2.092 0.037322 *  
horsepower64   9.568e+00  3.912e+00   2.446 0.015038 *  
horsepower65   4.188e+00  1.954e+00   2.143 0.032933 *  
horsepower66   5.931e+00  3.917e+00   1.514 0.131049    
horsepower67   2.381e+00  1.854e+00   1.284 0.199986    
horsepower68   5.195e-01  2.148e+00   0.242 0.809031    
horsepower69   1.781e+00  2.577e+00   0.691 0.489963    
horsepower70   2.093e+00  1.819e+00   1.150 0.250915    
horsepower71  -6.764e-01  2.226e+00  -0.304 0.761447    
horsepower72  -5.427e+00  2.089e+00  -2.598 0.009827 ** 
horsepower74   3.012e+00  2.570e+00   1.172 0.242178    
horsepower75  -1.877e+00  1.794e+00  -1.046 0.296463    
horsepower76   2.014e+00  2.369e+00   0.850 0.396028    
horsepower77  -4.669e-02  3.976e+00  -0.012 0.990638    
horsepower78  -1.941e+00  2.090e+00  -0.929 0.353779    
horsepower79  -5.356e-01  2.947e+00  -0.182 0.855894    
horsepower80   2.167e-01  2.008e+00   0.108 0.914134    
horsepower81  -3.431e+00  2.937e+00  -1.168 0.243686    
horsepower82   4.509e+00  3.892e+00   1.159 0.247528    
horsepower83  -9.333e-01  2.324e+00  -0.402 0.688325    
horsepower84   1.556e+00  2.124e+00   0.733 0.464290    
horsepower85  -3.319e+00  1.924e+00  -1.725 0.085474 .  
horsepower86  -4.346e+00  2.188e+00  -1.987 0.047868 *  
horsepower87  -4.651e+00  2.987e+00  -1.557 0.120445    
horsepower88  -3.325e+00  1.703e+00  -1.953 0.051771 .  
horsepower89  -1.892e+00  3.899e+00  -0.485 0.627849    
horsepower90  -3.297e+00  1.692e+00  -1.949 0.052261 .  
horsepower91  -9.497e+00  3.941e+00  -2.410 0.016547 *  
horsepower92  -1.527e+00  2.110e+00  -0.723 0.469969    
horsepower93  -5.873e+00  3.939e+00  -1.491 0.136973    
horsepower94  -9.628e+00  3.933e+00  -2.448 0.014942 *  
horsepower95  -6.493e+00  1.807e+00  -3.593 0.000382 ***
horsepower96  -3.461e+00  2.615e+00  -1.323 0.186727    
horsepower97  -8.687e+00  1.998e+00  -4.348 1.88e-05 ***
horsepower98  -6.267e+00  2.994e+00  -2.093 0.037153 *  
acceleration  -2.747e-01  1.330e-01  -2.065 0.039823 *  
origin_1      -3.487e+00  7.273e-01  -4.794 2.58e-06 ***
origin_2      -2.309e+00  7.918e-01  -2.917 0.003807 ** 
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 3.591 on 300 degrees of freedom
Multiple R-squared:  0.8405,    Adjusted R-squared:  0.7889 
F-statistic: 16.29 on 97 and 300 DF,  p-value: < 2.2e-16

# Gráficos de diagnóstico del modelo
par(mfrow = c(2, 2))
plot(modelo_dummy)

Warning: not plotting observations with leverage one:
  24, 27, 28, 29, 60, 68, 89, 93, 105, 111, 114, 117, 118, 120, 124, 146, 151, 160, 191, 208, 211, 233, 237, 246, 275, 278, 288, 289, 291, 298, 334, 345, 362, 398

# Ajuste del modelo libre con una combinación de variables
modelo_libre <- lm(mpg ~ weight + horsepower + acceleration + cylinders, data = auto_mpg)

# Resumen del modelo
summary(modelo_libre)

Call:
lm(formula = mpg ~ weight + horsepower + acceleration + cylinders, 
    data = auto_mpg)

Residuals:
    Min      1Q  Median      3Q     Max 
-10.335  -2.042   0.000   1.377  15.445 

Coefficients:
                Estimate Std. Error t value Pr(>|t|)    
(Intercept)    4.306e+01  2.585e+00  16.657  < 2e-16 ***
weight        -2.687e-03  7.981e-04  -3.366  0.00086 ***
horsepower100 -6.061e+00  1.858e+00  -3.262  0.00123 ** 
horsepower102 -6.985e+00  4.051e+00  -1.724  0.08571 .  
horsepower103 -6.722e+00  4.005e+00  -1.679  0.09428 .  
horsepower105 -4.213e+00  1.967e+00  -2.141  0.03305 *  
horsepower107 -6.771e+00  4.047e+00  -1.673  0.09533 .  
horsepower108 -7.106e+00  4.034e+00  -1.762  0.07915 .  
horsepower110 -5.225e+00  1.876e+00  -2.785  0.00569 ** 
horsepower112 -7.770e+00  2.663e+00  -2.918  0.00379 ** 
horsepower113 -4.374e+00  4.028e+00  -1.086  0.27839    
horsepower115 -2.828e+00  2.325e+00  -1.216  0.22490    
horsepower116 -1.628e+00  4.088e+00  -0.398  0.69080    
horsepower120 -5.717e+00  2.581e+00  -2.215  0.02750 *  
horsepower122 -7.016e+00  4.061e+00  -1.728  0.08510 .  
horsepower125 -3.741e+00  2.825e+00  -1.324  0.18648    
horsepower129 -8.701e+00  3.325e+00  -2.617  0.00933 ** 
horsepower130 -7.074e+00  2.653e+00  -2.667  0.00807 ** 
horsepower132  5.351e+00  4.123e+00   1.298  0.19532    
horsepower133 -8.529e+00  4.064e+00  -2.099  0.03669 *  
horsepower135 -4.047e+00  4.198e+00  -0.964  0.33585    
horsepower137 -7.880e+00  4.245e+00  -1.856  0.06440 .  
horsepower138 -5.991e+00  4.274e+00  -1.402  0.16201    
horsepower139 -5.214e+00  3.346e+00  -1.558  0.12022    
horsepower140 -5.650e+00  2.568e+00  -2.200  0.02857 *  
horsepower142 -6.406e+00  4.253e+00  -1.506  0.13309    
horsepower145 -6.951e+00  2.588e+00  -2.686  0.00763 ** 
horsepower148 -6.518e+00  4.406e+00  -1.479  0.14010    
horsepower149 -5.093e+00  4.296e+00  -1.185  0.23679    
horsepower150 -7.658e+00  2.339e+00  -3.274  0.00118 ** 
horsepower152 -7.409e+00  4.335e+00  -1.709  0.08848 .  
horsepower153 -7.975e+00  3.422e+00  -2.330  0.02044 *  
horsepower155 -5.972e+00  3.451e+00  -1.731  0.08452 .  
horsepower158 -8.453e+00  4.358e+00  -1.940  0.05335 .  
horsepower160 -9.994e+00  3.525e+00  -2.835  0.00489 ** 
horsepower165 -8.365e+00  2.845e+00  -2.940  0.00354 ** 
horsepower167 -8.139e+00  4.519e+00  -1.801  0.07267 .  
horsepower170 -7.375e+00  2.936e+00  -2.512  0.01254 *  
horsepower175 -8.321e+00  2.923e+00  -2.847  0.00471 ** 
horsepower180 -8.400e+00  2.927e+00  -2.870  0.00440 ** 
horsepower190 -7.955e+00  3.214e+00  -2.475  0.01387 *  
horsepower193 -9.866e+00  4.262e+00  -2.315  0.02131 *  
horsepower198 -7.844e+00  3.705e+00  -2.117  0.03509 *  
horsepower200 -1.084e+01  4.288e+00  -2.528  0.01200 *  
horsepower208 -1.031e+01  4.516e+00  -2.283  0.02315 *  
horsepower210 -1.026e+01  4.342e+00  -2.362  0.01881 *  
horsepower215 -9.138e+00  3.323e+00  -2.750  0.00632 ** 
horsepower220 -8.638e+00  4.547e+00  -1.899  0.05845 .  
horsepower225 -9.455e+00  3.248e+00  -2.911  0.00387 ** 
horsepower230 -6.697e+00  4.501e+00  -1.488  0.13786    
horsepower46  -2.898e+00  3.121e+00  -0.929  0.35388    
horsepower48   1.580e+01  2.748e+00   5.751 2.17e-08 ***
horsepower49  -3.290e-01  4.044e+00  -0.081  0.93522    
horsepower52   5.434e+00  2.502e+00   2.172  0.03062 *  
horsepower53   2.883e+00  3.060e+00   0.942  0.34683    
horsepower54  -4.129e+00  4.100e+00  -1.007  0.31475    
horsepower58   7.506e+00  3.065e+00   2.449  0.01489 *  
horsepower60   2.638e+00  2.299e+00   1.147  0.25221    
horsepower61   2.891e+00  4.021e+00   0.719  0.47267    
horsepower62   3.709e+00  3.032e+00   1.223  0.22227    
horsepower63   4.628e+00  2.620e+00   1.766  0.07838 .  
horsepower64   8.793e+00  4.006e+00   2.195  0.02894 *  
horsepower65   6.260e+00  1.957e+00   3.198  0.00153 ** 
horsepower66   5.111e+00  4.010e+00   1.275  0.20343    
horsepower67   4.451e+00  1.858e+00   2.396  0.01720 *  
horsepower68   2.695e+00  2.154e+00   1.251  0.21176    
horsepower69   2.980e+00  2.633e+00   1.132  0.25860    
horsepower70   2.810e+00  1.864e+00   1.507  0.13275    
horsepower71  -2.084e-01  2.240e+00  -0.093  0.92595    
horsepower72  -4.932e+00  2.135e+00  -2.310  0.02157 *  
horsepower74   4.248e+00  2.615e+00   1.624  0.10538    
horsepower75  -3.489e-01  1.811e+00  -0.193  0.84733    
horsepower76   2.911e+00  2.384e+00   1.221  0.22315    
horsepower77   1.477e+00  4.031e+00   0.366  0.71433    
horsepower78  -1.570e+00  2.134e+00  -0.736  0.46249    
horsepower79  -1.181e+00  3.018e+00  -0.391  0.69578    
horsepower80  -3.011e-01  2.059e+00  -0.146  0.88384    
horsepower81  -2.705e+00  3.020e+00  -0.896  0.37109    
horsepower82   3.934e+00  3.997e+00   0.984  0.32584    
horsepower83  -1.049e+00  2.387e+00  -0.439  0.66062    
horsepower84   8.522e-01  2.172e+00   0.392  0.69506    
horsepower85  -2.887e+00  1.976e+00  -1.461  0.14502    
horsepower86  -4.801e+00  2.248e+00  -2.136  0.03352 *  
horsepower87  -4.044e+00  3.028e+00  -1.336  0.18267    
horsepower88  -2.523e+00  1.737e+00  -1.452  0.14749    
horsepower89  -2.517e+00  4.008e+00  -0.628  0.53050    
horsepower90  -2.808e+00  1.734e+00  -1.620  0.10632    
horsepower91  -9.004e+00  4.021e+00  -2.239  0.02586 *  
horsepower92  -1.031e+00  2.157e+00  -0.478  0.63290    
horsepower93  -3.082e+00  3.993e+00  -0.772  0.44088    
horsepower94  -6.824e+00  3.988e+00  -1.711  0.08813 .  
horsepower95  -4.928e+00  1.835e+00  -2.686  0.00763 ** 
horsepower96  -1.821e+00  2.652e+00  -0.687  0.49279    
horsepower97  -6.223e+00  1.978e+00  -3.145  0.00182 ** 
horsepower98  -5.438e+00  3.065e+00  -1.774  0.07707 .  
acceleration  -2.902e-01  1.374e-01  -2.112  0.03550 *  
cylinders     -7.641e-01  3.431e-01  -2.227  0.02668 *  
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 3.691 on 301 degrees of freedom
Multiple R-squared:  0.8309,    Adjusted R-squared:  0.777 
F-statistic: 15.41 on 96 and 301 DF,  p-value: < 2.2e-16

# Gráficos de diagnóstico del modelo
par(mfrow = c(2, 2))
plot(modelo_libre)

Warning: not plotting observations with leverage one:
  24, 27, 28, 29, 60, 68, 89, 93, 105, 111, 114, 117, 118, 120, 124, 146, 151, 160, 191, 208, 211, 233, 237, 246, 275, 278, 288, 289, 291, 298, 334, 345, 362, 398