📚 Laporan Praktikum 2 — Komputasi Statistika B
Program Studi Sarjana Statistika | Departemen Statistika
Fakultas Sains, Teknologi, dan Matematika — Universitas Brawijaya
Asisten: Muhammad Ad’hiya Hartono · M Adika Rosyad Bhakti Putra · Joyce Abigail Gracia Zebua · Ghina Azziqra

📋 BAB I — Studi Kasus

Dataset yang digunakan berasal dari sumber terbuka (Kaggle) berisi data spesifikasi dan harga mobil. Dari dataset tersebut diambil 50 observasi pertama dengan 4 variabel:

price Variabel Dependen (Y)

horsepower X₁ — Tenaga Mesin (hp)

carheight X₂ — Tinggi Mobil (inch)

citympg X₃ — Efisiensi BBM Kota (mpg)

📖 BAB II — Tinjauan Pustaka

Regresi Linier Berganda

Regresi linier berganda adalah metode statistika untuk mengetahui hubungan satu variabel dependen (Y) dengan dua atau lebih variabel independen (X). Model umum:

Ŷ = β₀ + β₁X₁ + β₂X₂ + … + βₖXₖ + ε

Koefisien diestimasi dengan Ordinary Least Squares (OLS), yaitu meminimalkan jumlah kuadrat residual (Gujarati & Porter, 2009).

Uji Signifikansi

Uji F (Simultan) — apakah semua prediktor secara bersama-sama signifikan (p-value < 0,05 → tolak H₀)
Uji t (Parsial) — apakah masing-masing prediktor signifikan secara individual

Uji Asumsi Klasik

Asumsi	Uji	Keputusan
Normalitas	Shapiro-Wilk	p-value > 0,05 → normal
Homoskedastisitas	Breusch-Pagan	p-value > 0,05 → homoskedastis
Non-autokorelasi	Durbin-Watson	p-value > 0,05 → tidak ada autokorelasi
Non-multikolinearitas	VIF	VIF < 10 → tidak ada masalah

🔍 BAB III — Eksplorasi Data

Import & Persiapan Data

# Import data — ganti path sesuai lokasi file CSV Anda
# car_price <- read.csv(file.choose())

# Simulasi data sesuai laporan (50 observasi)
car_price <- data.frame(
  price      = c(13495,16500,16500,13950,17450,15250,17710,18920,23875,17859.17,
                 16430,16925,20970,21105,24565,30760,41315,36880,5151,6295,
                 6575,5572,6377,7957,6229,6692,7609,8558,8921,12964,
                 6479,6855,5399,6529,7129,7295,7295,7895,9095,8845,
                 10295,12945,10345,6785,8916.5,8916.5,11048,32250,35550,36000),
  horsepower = c(111,111,154,102,115,110,110,110,140,160,
                 101,101,121,121,121,182,182,182,48,70,
                 70,68,68,102,68,68,68,102,88,145,
                 58,76,60,76,76,76,76,86,86,86,
                 86,101,100,78,70,70,90,176,176,262),
  carheight  = c(48.8,48.8,52.4,54.3,54.3,53.1,55.7,55.7,55.9,52.0,
                 54.3,54.3,54.3,54.3,55.7,55.7,53.7,56.3,53.2,52.0,
                 52.0,50.8,50.8,50.8,50.6,50.6,50.6,50.6,59.8,50.2,
                 50.8,50.8,52.6,52.6,52.6,54.5,58.3,53.3,53.3,54.1,
                 54.1,54.1,51.0,53.5,52.0,52.0,51.4,52.8,52.8,47.8),
  citympg    = c(21,21,19,24,18,19,19,19,17,16,
                 23,23,21,21,20,16,16,15,47,38,
                 38,37,31,24,31,31,31,24,24,19,
                 49,31,38,30,30,30,30,27,27,27,
                 27,24,25,24,38,38,24,15,15,13)
)

data_mobil <- car_price[1:50, c("price","horsepower","carheight","citympg")]

Tampilan Data

knitr::kable(data_mobil, 
             caption = "Tabel 1. Data 50 Observasi Mobil",
             align = "cccc",
             digits = 2)

Tabel 1. Data 50 Observasi Mobil
price	horsepower	carheight	citympg
13495.00	111	48.8	21
16500.00	111	48.8	21
16500.00	154	52.4	19
13950.00	102	54.3	24
17450.00	115	54.3	18
15250.00	110	53.1	19
17710.00	110	55.7	19
18920.00	110	55.7	19
23875.00	140	55.9	17
17859.17	160	52.0	16
16430.00	101	54.3	23
16925.00	101	54.3	23
20970.00	121	54.3	21
21105.00	121	54.3	21
24565.00	121	55.7	20
30760.00	182	55.7	16
41315.00	182	53.7	16
36880.00	182	56.3	15
5151.00	48	53.2	47
6295.00	70	52.0	38
6575.00	70	52.0	38
5572.00	68	50.8	37
6377.00	68	50.8	31
7957.00	102	50.8	24
6229.00	68	50.6	31
6692.00	68	50.6	31
7609.00	68	50.6	31
8558.00	102	50.6	24
8921.00	88	59.8	24
12964.00	145	50.2	19
6479.00	58	50.8	49
6855.00	76	50.8	31
5399.00	60	52.6	38
6529.00	76	52.6	30
7129.00	76	52.6	30
7295.00	76	54.5	30
7295.00	76	58.3	30
7895.00	86	53.3	27
9095.00	86	53.3	27
8845.00	86	54.1	27
10295.00	86	54.1	27
12945.00	101	54.1	24
10345.00	100	51.0	25
6785.00	78	53.5	24
8916.50	70	52.0	38
8916.50	70	52.0	38
11048.00	90	51.4	24
32250.00	176	52.8	15
35550.00	176	52.8	15
36000.00	262	47.8	13

Statistik Deskriptif

summary(data_mobil)

##      price         horsepower      carheight        citympg     
##  Min.   : 5151   Min.   : 48.0   Min.   :47.80   Min.   :13.00  
##  1st Qu.: 7170   1st Qu.: 76.0   1st Qu.:50.85   1st Qu.:19.00  
##  Median :10320   Median :100.5   Median :52.80   Median :24.00  
##  Mean   :14305   Mean   :105.3   Mean   :52.92   Mean   :25.70  
##  3rd Qu.:17645   3rd Qu.:119.5   3rd Qu.:54.30   3rd Qu.:30.75  
##  Max.   :41315   Max.   :262.0   Max.   :59.80   Max.   :49.00

💰 Price

Min: $5.151

Median: $10.320

Mean: $14.305

Max: $41.315

⚙️ Horsepower

Min: 48

Median: 100,5

Mean: 105,3

Max: 262

📐 Car Height

Min: 47,80

Median: 52,80

Mean: 52,92

Max: 59,80

⛽ City MPG

Min: 13

Median: 24

Mean: 25,7

Max: 49

Scatter Plot Eksplorasi

library(ggplot2)

ggplot(data_mobil, aes(x = horsepower, y = price)) +
  geom_point(color = "#e8658a", size = 3, alpha = 0.8, shape = 19) +
  geom_smooth(method = "lm", se = TRUE,
              color = "#8b3a52", fill = "#ffd6e7", alpha = 0.35, linewidth = 1.2) +
  labs(title    = "Horsepower vs Price",
       subtitle = "Hubungan positif kuat antara tenaga mesin dan harga",
       x = "Horsepower (hp)", y = "Price (USD)") +
  scale_y_continuous(labels = scales::comma) +
  theme_pink()

Gambar 1. Scatter Plot Horsepower vs Price

ggplot(data_mobil, aes(x = carheight, y = price)) +
  geom_point(color = "#c94c70", size = 3, alpha = 0.8, shape = 19) +
  geom_smooth(method = "lm", se = TRUE,
              color = "#8b3a52", fill = "#ffd6e7", alpha = 0.35, linewidth = 1.2) +
  labs(title    = "Car Height vs Price",
       subtitle = "Hubungan yang lemah dan tersebar acak",
       x = "Car Height (inch)", y = "Price (USD)") +
  scale_y_continuous(labels = scales::comma) +
  theme_pink()

Gambar 2. Scatter Plot Car Height vs Price

ggplot(data_mobil, aes(x = citympg, y = price)) +
  geom_point(color = "#b5657a", size = 3, alpha = 0.8, shape = 19) +
  geom_smooth(method = "lm", se = TRUE,
              color = "#8b3a52", fill = "#ffd6e7", alpha = 0.35, linewidth = 1.2) +
  labs(title    = "City MPG vs Price",
       subtitle = "Hubungan negatif — semakin irit, harga cenderung lebih rendah",
       x = "City MPG (mpg)", y = "Price (USD)") +
  scale_y_continuous(labels = scales::comma) +
  theme_pink()

Gambar 3. Scatter Plot City MPG vs Price

💡 Interpretasi Eksplorasi Visual:
- Horsepower → hubungan linear positif kuat dengan harga mobil
- City MPG → hubungan linear negatif yang cukup jelas
- Car Height → menyebar acak, hubungan lemah terhadap harga

📐 BAB IV — Membangun Model Regresi Linier Berganda

Bentuk Model

Ŷ = β₀ + β₁X₁ + β₂X₂ + β₃X₃

di mana Y = price, X₁ = horsepower, X₂ = carheight, X₃ = citympg

Estimasi Model

model_regresi <- lm(price ~ horsepower + carheight + citympg,
                    data = data_mobil)
model_regresi

## 
## Call:
## lm(formula = price ~ horsepower + carheight + citympg, data = data_mobil)
## 
## Coefficients:
## (Intercept)   horsepower    carheight      citympg  
##   -51922.13       214.87       785.07        80.14

Persamaan Model yang Diperoleh:
Ŷ = −51922,13 + 214,87 X₁ + 785,07 X₂ + 80,14 X₃

📌 Interpretasi Koefisien:

Intercept (−51.922,13) — Jika semua prediktor bernilai nol, estimasi harga mobil adalah −$51.922,13 (tidak bermakna secara praktis karena di luar rentang data).
Horsepower (+214,87) — Setiap kenaikan 1 hp, harga mobil naik $214,87 (ceteris paribus).
Car Height (+785,07) — Setiap kenaikan 1 inch tinggi, harga naik $785,07 (ceteris paribus).
City MPG (+80,14) — Setiap kenaikan 1 mpg, harga naik $80,14 (ceteris paribus).

🧪 BAB V — Uji Signifikansi Model

summary(model_regresi)

## 
## Call:
## lm(formula = price ~ horsepower + carheight + citympg, data = data_mobil)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -7327.8 -1550.5   208.1  1949.1 10690.7 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept) -51922.13   15219.81  -3.411  0.00136 ** 
## horsepower     214.87      22.60   9.506 1.99e-12 ***
## carheight      785.07     240.98   3.258  0.00211 ** 
## citympg         80.14     117.37   0.683  0.49820    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 3728 on 46 degrees of freedom
## Multiple R-squared:  0.8548, Adjusted R-squared:  0.8453 
## F-statistic: 90.23 on 3 and 46 DF,  p-value: < 2.2e-16

Uji F (Simultan)

F-statistic	90,23
p-value	< 2,2 × 10⁻¹⁶
Keputusan	Tolak H₀

✅ Karena p-value < α (0,05), ketiga variabel secara bersama-sama berpengaruh signifikan terhadap harga mobil.

Uji t (Parsial)

Variabel	Koefisien	p-value	Keputusan
Horsepower (X₁)	214,87	1,99 × 10⁻¹²	Signifikan ✓
Car Height (X₂)	785,07	0,00211	Signifikan ✓
City MPG (X₃)	80,14	0,49820	Tidak Signifikan ✗

📊 Kebaikan Model — R-Squared:
- Multiple R² = 0,8548
- Adjusted R² = 0,8453
→ Model mampu menjelaskan 84,53% variasi harga mobil. Sisanya 15,47% oleh faktor lain di luar model.

✅ BAB VI — Uji Asumsi Regresi

1. Normalitas Sisaan

shapiro.test(residuals(model_regresi))

## 
##  Shapiro-Wilk normality test
## 
## data:  residuals(model_regresi)
## W = 0.95939, p-value = 0.08383

# QQ Plot cantik
residuals_df <- data.frame(residuals = residuals(model_regresi))

ggplot(residuals_df, aes(sample = residuals)) +
  stat_qq(color = "#e8658a", size = 2.5, alpha = 0.8) +
  stat_qq_line(color = "#8b3a52", linewidth = 1.2, linetype = "dashed") +
  labs(title    = "Normal Q-Q Plot Residual",
       subtitle = "Titik mengikuti garis → residual mendekati normal",
       x = "Theoretical Quantiles", y = "Sample Quantiles") +
  theme_pink()

Gambar 4. Q-Q Plot Residual

W	0,95939
p-value	0,08383
Keputusan	Terima H₀

✓ TERPENUHI Karena p-value (0,084) > 0,05 → residual berdistribusi normal.

2. Homoskedastisitas

library(lmtest)
bptest(model_regresi)

## 
##  studentized Breusch-Pagan test
## 
## data:  model_regresi
## BP = 18.505, df = 3, p-value = 0.0003459

fitted_df <- data.frame(
  fitted    = fitted(model_regresi),
  residuals = residuals(model_regresi)
)

ggplot(fitted_df, aes(x = fitted, y = residuals)) +
  geom_point(color = "#e8658a", size = 2.5, alpha = 0.8) +
  geom_hline(yintercept = 0, color = "#8b3a52",
             linewidth = 1.1, linetype = "dashed") +
  geom_smooth(se = FALSE, color = "#c94c70",
              linewidth = 0.9, method = "loess") +
  labs(title    = "Residuals vs Fitted Values",
       subtitle = "Pola mengembang → indikasi heteroskedastisitas",
       x = "Fitted Values", y = "Residuals") +
  scale_x_continuous(labels = scales::comma) +
  theme_pink()

Gambar 5. Plot Fitted vs Residuals

BP	18,505
p-value	0,0003459
Keputusan	Tolak H₀

✗ TIDAK TERPENUHI Karena p-value (0,0003) < 0,05 → terdapat heteroskedastisitas.
> 💡 Solusi: transformasi variabel atau metode Weighted Least Squares (WLS).

3. Non-Autokorelasi

dwtest(model_regresi)

## 
##  Durbin-Watson test
## 
## data:  model_regresi
## DW = 1.612, p-value = 0.052
## alternative hypothesis: true autocorrelation is greater than 0

DW	1,612
p-value	0,052
Keputusan	Terima H₀

✓ TERPENUHI Karena p-value (0,052) > 0,05 → tidak terjadi autokorelasi.

4. Non-Multikolinearitas

library(car)
vif(model_regresi)

## horsepower  carheight    citympg 
##   3.234877   1.125351   3.374615

vif_values <- c(horsepower = 3.234877, carheight = 1.125351, citympg = 3.374615)
vif_df <- data.frame(
  variabel = names(vif_values),
  vif      = vif_values
)

ggplot(vif_df, aes(x = reorder(variabel, vif), y = vif, fill = variabel)) +
  geom_col(width = 0.55, show.legend = FALSE,
           color = "#c94c70", linewidth = 0.6) +
  geom_hline(yintercept = 10, color = "#721c24",
             linetype = "dashed", linewidth = 1) +
  geom_text(aes(label = round(vif, 2)), hjust = -0.2,
            color = "#8b3a52", fontface = "bold", size = 4.5) +
  scale_fill_manual(values = c("#ffb3d1","#e8658a","#c94c70")) +
  scale_y_continuous(limits = c(0, 12)) +
  coord_flip() +
  labs(title    = "Variance Inflation Factor (VIF)",
       subtitle = "Semua VIF jauh di bawah ambang batas 10",
       x = NULL, y = "Nilai VIF") +
  annotate("text", x = 0.6, y = 10.3, label = "Batas VIF = 10",
           color = "#721c24", size = 3.5, fontface = "italic") +
  theme_pink()

Gambar 6. Visualisasi Nilai VIF

Variabel	VIF	Status
Horsepower	3,235	Aman ✓
Car Height	1,125	Aman ✓
City MPG	3,375	Aman ✓

✓ TERPENUHI Seluruh VIF < 10 → tidak ada multikolinearitas.

📝 BAB VII — Kesimpulan

1. Eksplorasi Data
Horsepower memiliki hubungan linear positif kuat dengan price; City MPG memiliki hubungan negatif; Car Height menunjukkan hubungan yang lemah.

2. Model Regresi
Ŷ = −51.922,13 + 214,87X₁ + 785,07X₂ + 80,14X₃
Horsepower dan carheight memberikan pengaruh positif terhadap harga.

3. Uji Signifikansi
- Uji F: ketiga prediktor signifikan secara serentak (p < 2,2×10⁻¹⁶)
- Uji t: hanya horsepower dan carheight yang signifikan secara parsial; citympg tidak signifikan (p = 0,498)
- Adjusted R² = 0,8453 → model menjelaskan 84,53% variasi harga

4. Uji Asumsi

Asumsi	Hasil	Status
Normalitas	p = 0,084 > 0,05	✓ Terpenuhi
Homoskedastisitas	p = 0,0003 < 0,05	✗ Tidak Terpenuhi
Non-autokorelasi	p = 0,052 > 0,05	✓ Terpenuhi
Non-multikolinearitas	VIF < 10	✓ Terpenuhi

⚠️ Model perlu perbaikan pada asumsi heteroskedastisitas melalui transformasi variabel atau metode Weighted Least Squares (WLS).

📚 Daftar Pustaka

Gujarati, D. N., & Porter, D. C. (2009). Basic Econometrics (5th ed.). McGraw-Hill.
Hair, J. F., Black, W. C., Babin, B. J., & Anderson, R. E. (2019). Multivariate Data Analysis (8th ed.). Cengage Learning.
Montgomery, D. C., Peck, E. A., & Vining, G. G. (2021). Introduction to Linear Regression Analysis (6th ed.). John Wiley & Sons.
Razali, N. M., & Wah, Y. B. (2011). Power comparisons of Shapiro-Wilk, Kolmogorov-Smirnov, Lilliefors and Anderson-Darling tests. Journal of Statistical Modeling and Analytics, 2(12), 21–33.

🚗 Pemodelan Harga Mobil (Price) Menggunakan Regresi Linier Berganda

dengan Variabel Horsepower, Car Height, dan City MPG

Diva Ladika Ayumi — 245090507111064

28 May 2026