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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 adalah 42.98 km.

Tugas Individu

Model Regresi

\[y = \beta_0 + \beta_1 X_1 + \varepsilon\]

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
beta_0 = round(model$coefficients[1], 4)
beta_1 = round(model$coefficients[2], 4)
coef(model)
## (Intercept)       speed 
##  -17.579095    3.932409

Interpretasi model Nilai beta0 adalah -17.5791.
Nilai beta1 adalah 3.9324.

Setiap peningkatan 1 satuan X1 (speed), meningkatkan Y (dist) sebanyak 3.9324.

Model akhir \[ y = -17.5791 + 3.9324 X_1 + \varepsilon \] ## Uji Asumsi Model Regresi

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

Berdasarkan output di atas, nilai p-value = 0.3707773 > \(\alpha = 0.05\). Oleh karena itu, dapat disimpulkan bahwa asumsi normalitas residual terpenuhi pada taraf signifikansi \(\alpha = 0.05\)

library(lmtest)
(uji_dw = dwtest(model))
## 
##  Durbin-Watson test
## 
## data:  model
## DW = 1.6762, p-value = 0.09522
## alternative hypothesis: true autocorrelation is greater than 0
pval_dw = uji_dw$p.value

Berdasarkan output di atas, nilai p-value = 0.0952171 > \(\alpha = 0.05\). Oleh karena itu, dapat disimpulkan bahwa asumsi autokorelasi terpenuhi pada taraf signifikansi \(\alpha = 0.05\)

Plot Regresi

Scatterplot Jarak vs Kecepatan

Scatterplot Jarak vs Kecepatan