library(DataExplorer) 
library(skimr) 
library(corrplot)
library(tidyverse)
library(splines)
library(ISLR)
par(mar = c(3, 3, 3, 3))
attach(Auto) # Data dari library ISLR, mpg = mile.per.gallon, horsepower
## The following object is masked from package:lubridate:
## 
##     origin
## The following object is masked from package:ggplot2:
## 
##     mpg
str(Auto)
## 'data.frame':    392 obs. of  9 variables:
##  $ mpg         : num  18 15 18 16 17 15 14 14 14 15 ...
##  $ cylinders   : num  8 8 8 8 8 8 8 8 8 8 ...
##  $ displacement: num  307 350 318 304 302 429 454 440 455 390 ...
##  $ horsepower  : num  130 165 150 150 140 198 220 215 225 190 ...
##  $ weight      : num  3504 3693 3436 3433 3449 ...
##  $ acceleration: num  12 11.5 11 12 10.5 10 9 8.5 10 8.5 ...
##  $ year        : num  70 70 70 70 70 70 70 70 70 70 ...
##  $ origin      : num  1 1 1 1 1 1 1 1 1 1 ...
##  $ name        : Factor w/ 304 levels "amc ambassador brougham",..: 49 36 231 14 161 141 54 223 241 2 ...
plot_intro(data = Auto, geom_label_args = list(size=2.5)) ##Info data

skim_without_charts(data = Auto)
Data summary
Name Auto
Number of rows 392
Number of columns 9
_______________________
Column type frequency:
factor 1
numeric 8
________________________
Group variables None

Variable type: factor

skim_variable n_missing complete_rate ordered n_unique top_counts
name 0 1 FALSE 301 amc: 5, for: 5, toy: 5, amc: 4

Variable type: numeric

skim_variable n_missing complete_rate mean sd p0 p25 p50 p75 p100
mpg 0 1 23.45 7.81 9 17.00 22.75 29.00 46.6
cylinders 0 1 5.47 1.71 3 4.00 4.00 8.00 8.0
displacement 0 1 194.41 104.64 68 105.00 151.00 275.75 455.0
horsepower 0 1 104.47 38.49 46 75.00 93.50 126.00 230.0
weight 0 1 2977.58 849.40 1613 2225.25 2803.50 3614.75 5140.0
acceleration 0 1 15.54 2.76 8 13.78 15.50 17.02 24.8
year 0 1 75.98 3.68 70 73.00 76.00 79.00 82.0
origin 0 1 1.58 0.81 1 1.00 1.00 2.00 3.0 
plot_scatterplot(data = Auto,by="mpg",
                 geom_point_args = list(color="coral3") 
)

Melihat Hubungan “mpg” dengan “horsepower”

ggplot(Auto,aes(x=horsepower, y=mpg)) +  
  geom_point(alpha=0.55, color="black") +  
  theme_bw()

Regresi Linear

fit.lin <- lm(mpg ~ horsepower ,data =Auto)
coef(summary(fit.lin))
##               Estimate  Std. Error   t value      Pr(>|t|)
## (Intercept) 39.9358610 0.717498656  55.65984 1.220362e-187
## horsepower  -0.1578447 0.006445501 -24.48914  7.031989e-81
ggplot(Auto,aes(x=horsepower, y=mpg)) +   
  geom_point(alpha=0.55, color="black") +  
  stat_smooth(method = "lm",   
              formula = y ~ x,
              lty = 1, col = "blue",se = FALSE)+
  theme_bw()

Regresi Polynomial Ordo 4

fit.pol <- lm(mpg ~ poly(horsepower,4, raw = TRUE) ,data =Auto)
coef(summary(fit.pol))
##                                       Estimate   Std. Error    t value
## (Intercept)                       4.756768e+01 1.195992e+01  3.9772578
## poly(horsepower, 4, raw = TRUE)1 -7.667214e-02 4.312613e-01 -0.1777858
## poly(horsepower, 4, raw = TRUE)2 -4.344641e-03 5.496593e-03 -0.7904242
## poly(horsepower, 4, raw = TRUE)3  3.245115e-05 2.925826e-05  1.1091279
## poly(horsepower, 4, raw = TRUE)4 -6.530363e-08 5.504268e-08 -1.1864180
##                                      Pr(>|t|)
## (Intercept)                      8.321165e-05
## poly(horsepower, 4, raw = TRUE)1 8.589842e-01
## poly(horsepower, 4, raw = TRUE)2 4.297641e-01
## poly(horsepower, 4, raw = TRUE)3 2.680638e-01
## poly(horsepower, 4, raw = TRUE)4 2.361851e-01
ggplot(Auto,aes(x=horsepower, y=mpg)) +   
  geom_point(alpha=0.55, color="black") +  
  stat_smooth(method = "lm",   
              formula = y ~ poly(x,4,raw=TRUE),
              lty = 1, col = "blue",se = FALSE)+
  theme_bw()

Regres Fungsi Tangga

fit.tangga <- lm(mpg ~ cut(horsepower,5) ,data =Auto)
coef(summary(fit.tangga))
##                                Estimate Std. Error   t value      Pr(>|t|)
## (Intercept)                   31.303279  0.4272125  73.27332 5.778755e-229
## cut(horsepower, 5)(82.8,120]  -8.281327  0.5641636 -14.67895  4.299840e-39
## cut(horsepower, 5)(120,156]  -15.242673  0.7210260 -21.14025  1.689525e-66
## cut(horsepower, 5)(156,193]  -17.592168  1.0035874 -17.52928  4.667022e-51
## cut(horsepower, 5)(193,230]  -18.534048  1.3766995 -13.46267  3.743262e-34
ggplot(Auto,aes(x=horsepower, y=mpg)) +   
  geom_point(alpha=0.55, color="black") +  
  stat_smooth(method = "lm",   
              formula = y ~ cut(x,5),
              lty = 1, col = "blue",se = FALSE)+
  theme_bw()

Regresi Splines : Cubic Splines

fit.cb.spline <- lm(mpg ~ bs(horsepower, knots = c(75, 100, 125, 150, 175, 200)),
                 data =Auto)
coef(summary(fit.cb.spline))
##                                                           Estimate Std. Error
## (Intercept)                                              32.943821   1.917611
## bs(horsepower, knots = c(75, 100, 125, 150, 175, 200))1   4.508934   3.196670
## bs(horsepower, knots = c(75, 100, 125, 150, 175, 200))2  -3.019578   2.045188
## bs(horsepower, knots = c(75, 100, 125, 150, 175, 200))3 -13.182880   2.439451
## bs(horsepower, knots = c(75, 100, 125, 150, 175, 200))4 -12.291726   2.359226
## bs(horsepower, knots = c(75, 100, 125, 150, 175, 200))5 -19.767519   2.465359
## bs(horsepower, knots = c(75, 100, 125, 150, 175, 200))6 -18.234179   2.834607
## bs(horsepower, knots = c(75, 100, 125, 150, 175, 200))7 -21.557173   4.361744
## bs(horsepower, knots = c(75, 100, 125, 150, 175, 200))8 -21.567155   4.645299
## bs(horsepower, knots = c(75, 100, 125, 150, 175, 200))9 -17.328495   3.977378
##                                                           t value     Pr(>|t|)
## (Intercept)                                             17.179618 2.014191e-49
## bs(horsepower, knots = c(75, 100, 125, 150, 175, 200))1  1.410510 1.592030e-01
## bs(horsepower, knots = c(75, 100, 125, 150, 175, 200))2 -1.476431 1.406522e-01
## bs(horsepower, knots = c(75, 100, 125, 150, 175, 200))3 -5.404034 1.149367e-07
## bs(horsepower, knots = c(75, 100, 125, 150, 175, 200))4 -5.210066 3.094816e-07
## bs(horsepower, knots = c(75, 100, 125, 150, 175, 200))5 -8.018110 1.324614e-14
## bs(horsepower, knots = c(75, 100, 125, 150, 175, 200))6 -6.432701 3.753133e-10
## bs(horsepower, knots = c(75, 100, 125, 150, 175, 200))7 -4.942329 1.157496e-06
## bs(horsepower, knots = c(75, 100, 125, 150, 175, 200))8 -4.642791 4.734027e-06
## bs(horsepower, knots = c(75, 100, 125, 150, 175, 200))9 -4.356764 1.698392e-05
ggplot(Auto,aes(x=horsepower, y=mpg))+   
  geom_point(alpha=0.55, color="black")+  
  stat_smooth(method = "lm",   
              formula = y ~ bs(x, knots = c(75, 100, 125, 150, 175, 200)),  
              lty = 1, col = "blue",se = FALSE)+
  theme_bw()

Regresi Splines : Natural Cubic Splines

fit.ncb.spline <- lm(mpg ~ ns(horsepower, knots = c(75, 100, 125, 150, 175, 200)),
                  data =Auto)
coef(summary(fit.ncb.spline))
##                                                          Estimate Std. Error
## (Intercept)                                              35.50748   1.312311
## ns(horsepower, knots = c(75, 100, 125, 150, 175, 200))1 -16.97462   1.310943
## ns(horsepower, knots = c(75, 100, 125, 150, 175, 200))2 -13.82750   2.190621
## ns(horsepower, knots = c(75, 100, 125, 150, 175, 200))3 -22.94357   1.790913
## ns(horsepower, knots = c(75, 100, 125, 150, 175, 200))4 -20.12330   2.392789
## ns(horsepower, knots = c(75, 100, 125, 150, 175, 200))5 -24.40386   2.873859
## ns(horsepower, knots = c(75, 100, 125, 150, 175, 200))6 -25.43013   3.270841
## ns(horsepower, knots = c(75, 100, 125, 150, 175, 200))7 -18.96067   2.420874
##                                                            t value     Pr(>|t|)
## (Intercept)                                              27.057217 5.414910e-91
## ns(horsepower, knots = c(75, 100, 125, 150, 175, 200))1 -12.948402 4.529701e-32
## ns(horsepower, knots = c(75, 100, 125, 150, 175, 200))2  -6.312135 7.601502e-10
## ns(horsepower, knots = c(75, 100, 125, 150, 175, 200))3 -12.811099 1.568816e-31
## ns(horsepower, knots = c(75, 100, 125, 150, 175, 200))4  -8.409977 8.146755e-16
## ns(horsepower, knots = c(75, 100, 125, 150, 175, 200))5  -8.491669 4.515988e-16
## ns(horsepower, knots = c(75, 100, 125, 150, 175, 200))6  -7.774797 7.013088e-14
## ns(horsepower, knots = c(75, 100, 125, 150, 175, 200))7  -7.832159 4.736510e-14
ggplot(Auto,aes(x=horsepower, y=mpg))+   
  geom_point(alpha=0.55, color="black")+  
  stat_smooth(method = "lm",   
              formula = y ~ ns(x, knots = c(75, 100, 125, 150, 175, 200)),  
              lty = 1, col = "blue",se = FALSE)+
  theme_bw()

Plot Gabungan Splines

ggplot(Auto,aes(x=horsepower, y=mpg))+   
  geom_point(alpha=0.55, color="black")+  
  stat_smooth(method = "lm",   
              formula = y ~ bs(x, knots = c(75, 100, 125, 150, 175, 200)),  
              lty = 1, aes(col = "Cubic Spline"),se = F)+
  stat_smooth(method = "lm",   
              formula = y ~ ns(x, knots = c(75, 100, 125, 150, 175, 200)),  
              lty = 1, aes(col = "Natural Cubic Spline"),se = F)+
              labs(color="Tipe Spline")

              scale_color_manual(values = c("Natural Cubic Spline"="red",
              "Cubic Spline"="blue"))
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##  $ legend.position                 : chr "right"
##  $ legend.position.inside          : NULL
##  $ legend.direction                : NULL
##  $ legend.byrow                    : NULL
##  $ legend.justification            : chr "center"
##  $ legend.justification.top        : NULL
##  $ legend.justification.bottom     : NULL
##  $ legend.justification.left       : NULL
##  $ legend.justification.right      : NULL
##  $ legend.justification.inside     : NULL
##  $ legend.location                 : NULL
##  $ legend.box                      : NULL
##  $ legend.box.just                 : NULL
##  $ legend.box.margin               : 'margin' num [1:4] 0cm 0cm 0cm 0cm
##   ..- attr(*, "unit")= int 1
##  $ legend.box.background           : list()
##   ..- attr(*, "class")= chr [1:2] "element_blank" "element"
##  $ legend.box.spacing              : 'simpleUnit' num 11points
##   ..- attr(*, "unit")= int 8
##   [list output truncated]
##  - attr(*, "class")= chr [1:2] "theme" "gg"
##  - attr(*, "complete")= logi TRUE
##  - attr(*, "validate")= logi TRUE

Perbandingan Model Berdasarkan Nilai MSE

MSE = function(y.duga,y.aktual){  
                mean((y.duga - y.aktual)^2)  
}

data.frame(Reg.Linear = MSE(predict(fit.lin),Auto$mpg), 
           Polynomial = MSE(predict(fit.pol),Auto$mpg), 
           Fgs.Tangga = MSE(predict(fit.tangga),Auto$mpg), 
           Cbc.Spline = MSE(predict(fit.cb.spline),Auto$mpg), 
           NCb.Spline = MSE(predict(fit.ncb.spline),Auto$mpg))
##   Reg.Linear Polynomial Fgs.Tangga Cbc.Spline NCb.Spline
## 1   23.94366   18.87633   21.98227   17.95169   18.11617