Latihan1

Deskripsi Data

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

Rata-Rata Kecepatan Mobil adalah 15.4 km/jam.

Rata-Rata Jarak Tempuh Mobil adalah 42.98 km/jam.

Model Regresi

Persamaan model regresi:

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

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

b0 <- coef(model)[1]
b1 <- coef(model)[2]

Interpretasi model:

Model Akhir: \[ y = -17.579 + 3.932 X_1 \] ## Uji Asumsi Model Regresi

#Uji Asumsi Residual
error = model$residuals
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

library(lmtest)
dwtest(model)

## 
##  Durbin-Watson test
## 
## data:  model
## DW = 1.6762, p-value = 0.09522
## alternative hypothesis: true autocorrelation is greater than 0

Plots speed vs dist

Scatter plot dari dist berdasarkan speed:

Scatterplot Jarak vs Kecepatan