Model regresi linear

Latihan Pertanyaan Wawancara Statistik di R

Zuzanna Chmielewska

Actuary

Model regresi linear

Model regresi linear

Model regresi linear

$$ y_i = \beta_0 + \beta_1 \cdot x_{i1} + ... + \beta_p \cdot x_{ip} + e_{i}$$ where:

• $y_i$ - variabel dependen,
• $x_{ij}$ - variabel independen,
• $\beta_{j}$ - parameter,
• $e_i$ - galat.

Fungsi prediktor linear

$$ \hat{y_i} = \beta_0 + \beta_1 \cdot x_{i1} + ... + \beta_p \cdot x_{ip}$$

$$ \hat{y_i} = \beta_0 + \beta_1 \cdot x_{i} $$

$$ \hat{y_i} = \beta_0 + \beta_1 \cdot x_{i} $$

$$ \hat{y_i} = \beta_0 + \beta_1 \cdot x_{i} $$

$$ \hat{y_i} = \beta_0 + \beta_1 \cdot x_{i} $$

Transformasi log

Contoh: $$ \hat{y_i} = \beta_0 + \beta_1 \cdot ln(x_{i1}) + ... + \beta_p \cdot x_{ip}$$

$$ ln(\hat{y_i}) = \beta_0 + \beta_1 \cdot x_{i1} + ... + \beta_p \cdot x_{ip}$$

Asumsi

• Hubungan linear
• Galat berdistribusi normal
• Galat homoskedastik
• Observasi independen

Model linear di R

model <- lm(dist ~ speed, data = cars)

print(model)

Call:
lm(formula = dist ~ speed, data = cars)

Coefficients:
(Intercept)        speed  
    -17.579        3.932

Model linear di R

model <- lm(dist ~ speed, data = cars)
new_car <- data.frame(speed = 17.5)

predict(model, newdata = new_car)

       1 
51.23806

Plot diagnostik

model <- lm(dist ~ speed, data = cars)
plot(model)

Ringkasan

• model regresi linear
• fungsi prediktor linear
• lm() di R
• plot diagnostik

Ayo berlatih!

Latihan Pertanyaan Wawancara Statistik di R