Effect of Network Latency and Concurrent Users on Web Application Server Response Time

# Contoh kode R: Multiple Linear Regression with Classical Assumption Tests
suppressPackageStartupMessages({
  library(ggplot2)
  library(patchwork)
  library(lmtest)
  library(car)
})
set.seed(42)
# ---- Gaya grafik ----
pal <- c("#1f6feb", "#e8590c", "#2f9e44", "#ae3ec9", "#f59f00")
warna <- list(bg = "#f4f6fa", panel = "#ffffff", teks = "#1f2933", redup = "#5f6b78", grid = "#e3e8ee", bar = "#1d3557")
tata <- 1
theme_set(theme_minimal(base_size = 11) + theme(legend.position = "bottom"))

# ---- Data sintetis ----
n <- 200
d <- data.frame(network_latency = rnorm(n, 50, 10),
                concurrent_users = rnorm(n, 30, 6))
z1 <- as.numeric(scale(d$network_latency))
z2 <- as.numeric(scale(d$concurrent_users))
b1 <- runif(1, 0.45, 0.85)
b2 <- runif(1, 0.15, 0.5) * sample(c(-1, 1), 1)
d$server_response_time <- 100 + 15 * (b1 * z1 + b2 * z2 + rnorm(n, 0, runif(1, 0.45, 0.8)))
write.csv(d, "data_contoh.csv", row.names = FALSE)

# ---- Analisis: regresi linear berganda (OLS) ----
fit <- lm(server_response_time ~ network_latency + concurrent_users, data = d)
s <- summary(fit)
print(s)

# ---- Uji asumsi klasik ----
sw <- shapiro.test(residuals(fit))   # normalitas residual
bp <- lmtest::bptest(fit)            # heteroskedastisitas (Breusch-Pagan)
dw <- lmtest::dwtest(fit)            # autokorelasi (Durbin-Watson)
vf <- car::vif(fit)                  # multikolinearitas
print(sw); print(bp); print(dw); print(vf)


# ---- Grafik ----
d$prediksi <- fitted(fit)
d$residual <- residuals(fit)
p1 <- ggplot(d, aes(network_latency, server_response_time)) +
  geom_point(colour = pal[1], alpha = 0.55, size = 1.8) +
  geom_smooth(method = "lm", formula = y ~ x, colour = pal[2], fill = pal[2], alpha = 0.18, linewidth = 1.1) +
  labs(title = "Partial relationship with OLS fit", x = "network_latency", y = "server_response_time")
p2 <- ggplot(d, aes(prediksi, residual)) +
  geom_hline(yintercept = 0, linetype = "dashed", colour = warna$redup) +
  geom_point(colour = pal[3], alpha = 0.6, size = 1.5) +
  geom_smooth(method = "loess", formula = y ~ x, se = FALSE, colour = pal[2], linewidth = 0.8) +
  labs(title = "Residuals vs fitted", x = "Fitted value", y = "Residual")
p3 <- ggplot(d, aes(sample = residual)) +
  stat_qq(colour = pal[1], alpha = 0.6, size = 1.3) +
  stat_qq_line(colour = pal[2], linewidth = 0.9) +
  labs(title = "Normal Q-Q of residuals", x = "Theoretical quantile", y = "Sample quantile")
p_hasil <- if (tata == 1) p1 | (p2 / p3) else p1 / (p2 | p3)

print(p_hasil)