Deskripsi Data

Rata-rata Kecepatan Mobil adalah 15.4 km/jam
Rata-rata Jarak Tempuh Mobil adalah 42.98 km/jam

Plot Speed vs Jarak

Scatterplot Kecepatan vs Jarak

Scatterplot Kecepatan vs Jarak 

summary(cars)
##      speed           dist       
##  Min.   : 4.0   Min.   :  2.00  
##  1st Qu.:12.0   1st Qu.: 26.00  
##  Median :15.0   Median : 36.00  
##  Mean   :15.4   Mean   : 42.98  
##  3rd Qu.:19.0   3rd Qu.: 56.00  
##  Max.   :25.0   Max.   :120.00

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Rata-rata Kecepatan Mobil adalah 15.4 km/jam
Rata-rata Jarak Tempuh Mobil adalah 42.98 km/jam

Model Regresi

Persamaan Model Regresi: \[ y = \beta_0 + \beta_1 X_1 + \beta_2 X_2 + \epsilon \]

model <- lm(dist ~ speed, data = cars)
summary(model)
## 
## Call:
## lm(formula = dist ~ speed, data = cars)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -29.069  -9.525  -2.272   9.215  43.201 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) -17.5791     6.7584  -2.601   0.0123 *  
## speed         3.9324     0.4155   9.464 1.49e-12 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 15.38 on 48 degrees of freedom
## Multiple R-squared:  0.6511, Adjusted R-squared:  0.6438 
## F-statistic: 89.57 on 1 and 48 DF,  p-value: 1.49e-12
coef(model)
## (Intercept)       speed 
##  -17.579095    3.932409

Model akhir:

\[ \widehat{Y} = -17.579 + 3.932\,X_1 \]

Interpretasi

Setiap kenaikan 1 satuan speed diperkirakan meningkatkan dist sebesar 3.932 satuan.

Uji Asumsi model Regresi

#Uji Normalitas Residual
error = model$residuals
uji_ks=ks.test(error,"pnorm",mean(error),sqrt(var(error)))
uji_ks
## 
##  Asymptotic one-sample Kolmogorov-Smirnov test
## 
## data:  error
## D = 0.12957, p-value = 0.3708
## alternative hypothesis: two-sided

Interpretasi:
Nilai p-value uji Kolmogorov–Smirnov adalah 0.3708.
Dengan α = 0.05, keputusan gagal menolak H0, sehingga residual dapat dianggap berdistribusi normal.

library(lmtest)
## Loading required package: zoo
## 
## Attaching package: 'zoo'
## The following objects are masked from 'package:base':
## 
##     as.Date, as.Date.numeric
uji_dw <- dwtest(model)
uji_dw
## 
##  Durbin-Watson test
## 
## data:  model
## DW = 1.6762, p-value = 0.09522
## alternative hypothesis: true autocorrelation is greater than 0

Interpretasi

Nilai p-value uji Durbin–Watson adalah 0.0952.
Dengan α = 0.05, keputusan gagal menolak H0, sehingga residual tidak menunjukkan autokorelasi yang signifikan.