DataSet
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## ✔ ggplot2 3.4.4 ✔ tibble 3.2.1
## ✔ lubridate 1.9.3 ✔ tidyr 1.3.0
## ✔ purrr 1.0.2
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## ℹ Use the conflicted package (<http://conflicted.r-lib.org/>) to force all conflicts to become errorslibrary(lubridate)
set.seed(123)
n = 831
start = ymd("2022-01-01")
end = ymd("2024-04-10")
dates = seq(start, end, by = "day")
promotional = runif(n, min = 1000, max = 5000)
price = rnorm(n, 50, 10)
weather = sample(c('sunny', 'cloudy', 'rainy'), size = n , replace = T)
salestrend = 0.1 * seq(1, n)
seasonal = sin(seq(1, n) * 2 * pi / 365 * 7) * 100
noise = rnorm(n, 0, 100)
revenue = 1000 + salestrend + seasonal + noise
simulate = tibble(Date = dates, Promotional_Spending = promotional, Price = price, Weather = weather, Revenue = revenue)
head (simulate)## # A tibble: 6 × 5
## Date Promotional_Spending Price Weather Revenue
## <date> <dbl> <dbl> <chr> <dbl>
## 1 2022-01-01 2150. 57.5 cloudy 1171.
## 2 2022-01-02 4153. 55.9 cloudy 1056.
## 3 2022-01-03 2636. 51.8 cloudy 1074.
## 4 2022-01-04 4532. 54.0 rainy 1022.
## 5 2022-01-05 4762. 37.0 cloudy 1062.
## 6 2022-01-06 1182. 56.3 rainy 926.Explorations
Weathers
Pertama, kita mengeksplor data untuk melihat maisng-masing variabel yang akan diteliti.
ggplot(simulate, aes(x = Weather)) +
geom_bar(fill = "beige") +
labs(title = "Observasi Cuaca",
x = "Cuaca",
y = "Jumlah")
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## - attr(*, "validate")= logi TRUEDapat Dilihat bahwa ketiganya cenderung terdistribusi sama rata jumlahnya.
Daily Revenue
ggplot(simulate, aes(x = Date, y = Revenue)) +
geom_line(color = "red") +
labs(title = "Daily Trend",
x = "Tanggal",
y = "Revenue") +
theme_minimal()
Monthly Revenue
newdataset = simulate %>%
group_by(month = lubridate::floor_date(Date, 'month')) %>%
summarize(Average= mean(Revenue))
ggplot(newdataset, aes(x = month, y = Average)) +
geom_line(color = "red") +
labs(title = "Monthly Trend",
x = "Bulan",
y = "Revenue") +
theme_minimal()
Secara Bulanan, dapat dilihat bahwa Trwend cenderung naik turunn atau adanya sebuah Seasonal pada Data.
Regression Model
simulate$Weather = as.factor(simulate$Weather)
regmodel = lm(Revenue ~ Promotional_Spending + Price + Weather , data = simulate)
summary(regmodel)##
## Call:
## lm(formula = Revenue ~ Promotional_Spending + Price + Weather,
## data = simulate)
##
## Residuals:
## Min 1Q Median 3Q Max
## -353.07 -87.42 2.86 79.01 337.62
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.054e+03 2.465e+01 42.781 <2e-16 ***
## Promotional_Spending 7.874e-03 3.691e-03 2.133 0.0332 *
## Price -5.408e-01 4.232e-01 -1.278 0.2016
## Weatherrainy -1.845e+01 1.038e+01 -1.777 0.0759 .
## Weathersunny -1.143e+01 1.056e+01 -1.083 0.2791
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 121.9 on 826 degrees of freedom
## Multiple R-squared: 0.01044, Adjusted R-squared: 0.005645
## F-statistic: 2.178 on 4 and 826 DF, p-value: 0.06971##
## Attaching package: 'plotly'## The following object is masked from 'package:ggplot2':
##
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## layoutpredictions = predict(regmodel)
actualplot = plot_ly(x = dates, y = revenue, type = 'scatter', mode = 'lines', name = 'Actual') %>%
add_trace(y =predictions , name ='Predicted') %>%
layout(title ='Regression Model Forecasting',
xaxis = list(title = 'Date'),
yaxis = list(title = 'Revenue'))
actualplotPlot Yang ada menggambarkan bahwa dataset tidak cocok menggunakan data linear. Dibuktikan dengan nilai R-SQuared yang sangatlah rendah. 1.2% saja. Hal ini juga disebabkan oleh penggunaan variabel prediktor yang kurang berpengaruh signifikan terhadap variabel dependen.
Time Series
ACF (Autocorrelation Function) disajikan pada grafik ACF, sumbu horizontal mewakili lag (waktu antara pengamatan), sedangkan sumbu vertikal menunjukkan nilai korelasi antara observasi yang dipisahkan oleh lag tersebut. Puncak-puncak yang signifikan di atas interval abu-abu menunjukkan autocorrelation yang signifikan pada lag-lag tersebut. Dengan menganalisis plot ACF, kita dapat mengidentifikasi pola-pola musiman, tren
Auto-Correlation
simulate$Date <- as.Date(simulate$Date)
ts_data <- ts(simulate$Revenue, start = c(year(simulate$Date[1]), month(simulate$Date[1])), frequency = 12)
acf(ts_data)
plot(acf(ts_data), main = "Autocorrelation Function (ACF)")
Pada grafik diatas, terjadi Autokorelasi diluar batas toleransi autokorelasi yang berarti adanya Seasonal atau Trend yangterjadi pada Data (Data tidak menunjukkan Stasioneritas)
ARIMA Model
## Registered S3 method overwritten by 'quantmod':
## method from
## as.zoo.data.frame zoosimulate$Date <- as.Date(simulate$Date)
ts_data <- ts(simulate$Revenue, start = c(year(simulate$Date[1]), month(simulate$Date[1])), frequency = 12)
arima_model <- auto.arima(ts_data)
summary(arima_model)## Series: ts_data
## ARIMA(2,1,2)
##
## Coefficients:
## ar1 ar2 ma1 ma2
## 0.8409 -0.0523 -1.6604 0.7353
## s.e. 0.0834 0.0448 0.0752 0.0636
##
## sigma^2 = 11965: log likelihood = -5073
## AIC=10156.01 AICc=10156.08 BIC=10179.62
##
## Training set error measures:
## ME RMSE MAE MPE MAPE MASE
## Training set -0.3706182 109.0548 87.14948 -0.9728241 8.543867 0.6587493
## ACF1
## Training set -0.001315256Menggunakan model time Series ARIMA hasil prediksi menghasilkan Eror Rate hanya 8,54% saja dibandingkan dengan R-Squared Model Regresi Linear.
Forecasting
forecast_arima <- forecast(arima_model)
plot_time_series <- plot_ly(x = ~time(ts_data), y = ~as.numeric(ts_data), type = 'scatter', mode = 'lines', name = 'Actual') %>%
add_trace(x = time(forecast_arima$mean), y = forecast_arima$mean, mode = 'lines', name = 'Predicted (ARIMA)') %>%
layout(title = 'Actual vs. ARIMA Forecast',
xaxis = list(title = 'Time'),
yaxis = list(title = 'Sales Revenue'))
plot_time_seriesDecompositioon
##
## Attaching package: 'reshape2'## The following object is masked from 'package:tidyr':
##
## smithsdecomposed <- decompose(ts_data)
trend <- decomposed$trend
seasonal <- decomposed$seasonal
cycle <- decomposed$random
decomposition_data <- data.frame(Date = time(ts_data), Trend = trend, Seasonal = seasonal, Cycle = cycle)
melted_data <- melt(decomposition_data, id.vars = "Date")
head(melted_data)## Date variable value
## 1 2022.000 Trend NA
## 2 2022.083 Trend NA
## 3 2022.167 Trend NA
## 4 2022.250 Trend NA
## 5 2022.333 Trend NA
## 6 2022.417 Trend NAmelted_data = na.omit(melted_data)
ggplot(melted_data, aes(x = Date, y = value, color = variable)) +
geom_line() +
facet_wrap(~ variable, scales = "free_y", nrow = 3) +
labs(title = "Decomposition of Time Series Data",
x = "Date",
y = "Value") +
theme_minimal()
Summary
regression_forecast_values <- predict(regmodel, newdata = simulate)
regression_mape <- (mean((abs(simulate$Revenue - regression_forecast_values)/simulate$Revenue)))
arima_forecast_values <- forecast_arima$mean[1:length(ts_data)]
arima_mape <- mean((abs(as.vector(ts_data) - arima_forecast_values) / as.vector(ts_data)), na.rm = TRUE)
cat("MAPE untuk model regresi:", regression_mape, "\n")## MAPE untuk model regresi: 0.09618761## MAPE untuk model ARIMA: 0.0740447Dalam hasil evaluasi model, MAPE (Mean Absolute Percentage Error) digunakan sebagai metrik untuk mengevaluasi kedua model, yaitu model regresi dan model ARIMA, dalam forecasting nilai sales revenue di masa depan. Nilai MAPE yang lebih rendah menunjukkan tingkat kesalahan yang lebih kecil dalam prediksi. Dalam hal ini, model regresi linear memiliki MAPE lebih besar dengan signifikansi yang rendah sehingga model dapayt dikatakan tidak kompeten, sedangkan model ARIMA memiliki MAPE sebesar 7.5% . Dari hasil tersebut, dapat disimpulkan bahwa model regresi memilikitidak valid dalam menghadapi trend dan seasonal dengan model ARIMA, sehingga dapat dianggap lebih baik ARIMA dalam memprediksi sales revenue di masa depan.