UTS PRAKTIK KOMPUTASI STATISTIK

1. Analisis Dataset MTCARS

# a. Statistik Deskriptif Variabel MPG
summary_mpg <- summary(mtcars$mpg)
cat("Statistik Deskriptif MPG:\n")

## Statistik Deskriptif MPG:

print(summary_mpg)

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   10.40   15.43   19.20   20.09   22.80   33.90

sd_mpg <- sd(mtcars$mpg)
cat("\nStandar Deviasi MPG:", sd_mpg)

## 
## Standar Deviasi MPG: 6.026948

# b. Boxplot MPG berdasarkan Jumlah Silinder
ggplot(mtcars, aes(x = factor(cyl), y = mpg, fill = factor(cyl))) +
  geom_boxplot() +
  labs(title = "Distribusi MPG berdasarkan Jumlah Silinder",
       x = "Jumlah Silinder", 
       y = "Miles per Gallon (MPG)") +
  theme_minimal()

2. Histogram Horsepower dengan Densitas

ggplot(mtcars, aes(x = hp)) +
  geom_histogram(aes(y = ..density..), 
                 bins = 15, 
                 fill = "blue", 
                 alpha = 0.7) +
  geom_density(color = "red") +
  labs(title = "Distribusi Horsepower",
       x = "Horsepower", 
       y = "Densitas") +
  theme_minimal()

## Warning: The dot-dot notation (`..density..`) was deprecated in ggplot2 3.4.0.
## ℹ Please use `after_stat(density)` instead.
## This warning is displayed once every 8 hours.
## Call `lifecycle::last_lifecycle_warnings()` to see where this warning was
## generated.

3. ANOVA pada Dataset Iris

# Melakukan ANOVA untuk Sepal Length antar spesies
anova_result <- aov(Sepal.Length ~ Species, data = iris)
summary(anova_result)

##              Df Sum Sq Mean Sq F value Pr(>F)    
## Species       2  63.21  31.606   119.3 <2e-16 ***
## Residuals   147  38.96   0.265                   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

4. T-Test Panjang Petal Iris

# Uji t-test untuk Petal Length antara setosa dan versicolor
t_test_result <- t.test(Petal.Length ~ Species, 
                        data = subset(iris, Species %in% c("setosa", "versicolor")))
print(t_test_result)

## 
##  Welch Two Sample t-test
## 
## data:  Petal.Length by Species
## t = -39.493, df = 62.14, p-value < 2.2e-16
## alternative hypothesis: true difference in means between group setosa and group versicolor is not equal to 0
## 95 percent confidence interval:
##  -2.939618 -2.656382
## sample estimates:
##     mean in group setosa mean in group versicolor 
##                    1.462                    4.260

5. Regresi Linear Sederhana MTCARS

# Model Regresi MPG berdasarkan Berat (WT)
model <- lm(mpg ~ wt, data = mtcars)

# a. Ringkasan Model
summary(model)

## 
## Call:
## lm(formula = mpg ~ wt, data = mtcars)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -4.5432 -2.3647 -0.1252  1.4096  6.8727 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  37.2851     1.8776  19.858  < 2e-16 ***
## wt           -5.3445     0.5591  -9.559 1.29e-10 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 3.046 on 30 degrees of freedom
## Multiple R-squared:  0.7528, Adjusted R-squared:  0.7446 
## F-statistic: 91.38 on 1 and 30 DF,  p-value: 1.294e-10

# b. Scatter Plot dengan Garis Regresi
ggplot(mtcars, aes(x = wt, y = mpg)) +
  geom_point(color = "blue") +
  geom_smooth(method = "lm", color = "red") +
  labs(title = "Regresi Linear: MPG vs Berat",
       x = "Berat (1000 lbs)", 
       y = "Miles per Gallon") +
  theme_minimal()

## `geom_smooth()` using formula = 'y ~ x'

# Mengambil koefisien regresi dari model
coefficients <- summary(model)$coefficients
cat("Koefisien Regresi:\n")

## Koefisien Regresi:

print(coefficients)

##              Estimate Std. Error   t value     Pr(>|t|)
## (Intercept) 37.285126   1.877627 19.857575 8.241799e-19
## wt          -5.344472   0.559101 -9.559044 1.293959e-10

# Mengambil nilai R-squared
r_squared <- summary(model)$r.squared
cat("\nNilai R-squared:", r_squared)

## 
## Nilai R-squared: 0.7528328