Analisis Regresi Profit Cafe Mocha
Jennifer Elysia N. M0723047
1. Pendahuluan
Produk Caffe Mocha adalah salah satu minuman kopi unggulan dalam industri retail yang bersaing ketat. Untuk memahami faktor-faktor yang memengaruhi profit penjualannya, analisis regresi linear berganda digunakan.
Analisis ini melibatkan berbagai uji statistik: - Model
Regresi Linear Berganda untuk menilai pengaruh simultan
beberapa variabel prediktor (Sales, Market,
State) terhadap Profit. - Uji
ANOVA untuk melihat apakah model secara keseluruhan signifikan.
- Goodness of Fit (Adjusted R-squared) untuk mengukur
seberapa baik model menjelaskan variabilitas data. - Uji
Multikolinearitas (VIF) memastikan tidak ada hubungan antar
prediktor yang merusak model. - Visualisasi mendukung
pemahaman hubungan antar variabel secara visual.
2. Import Data
excel_sheets("C:/Users/AS/Documents/Copy of 3. CM1 - Coffee Chain Datasets Esspresso.xlsx")## [1] "data" "deskripsi"df <- read_excel("C:/Users/AS/Documents/Copy of 3. CM1 - Coffee Chain Datasets Esspresso.xlsx", sheet = "data")
coffee_data <- read_excel("C:/Users/AS/Documents/Copy of 3. CM1 - Coffee Chain Datasets Esspresso.xlsx", sheet = "data")
mocha_data <- coffee_data %>%
filter(Product == "Caffe Mocha")
mocha_data$Market <- as.factor(mocha_data$Market)
mocha_data$State <- as.factor(mocha_data$State)
kable(head(mocha_data))| Area Code | Date | Market | Market Size | Product | Product Line | Product Type | State | Type | Budget COGS | Budget Margin | Budget Profit | Budget Sales | COGS | Inventory | Margin | Marketing | Profit | Sales | Total Expenses |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 303 | 2012-01-01 | Central | Major Market | Caffe Mocha | Beans | Espresso | Colorado | Regular | 60 | 90 | 70 | 150 | 54 | 456 | 80 | 15 | 54 | 134 | 26 |
| 309 | 2012-01-01 | Central | Major Market | Caffe Mocha | Beans | Espresso | Illinois | Regular | 270 | 370 | 260 | 640 | 234 | 1310 | 312 | 77 | 203 | 546 | 109 |
| 563 | 2012-01-01 | Central | Small Market | Caffe Mocha | Beans | Espresso | Iowa | Regular | 10 | 40 | 30 | 50 | 17 | 777 | 26 | 4 | 11 | 43 | 15 |
| 573 | 2012-01-01 | Central | Small Market | Caffe Mocha | Beans | Espresso | Missouri | Regular | 50 | 90 | 70 | 140 | 50 | 821 | 73 | 14 | 48 | 123 | 25 |
| 614 | 2012-01-01 | Central | Major Market | Caffe Mocha | Beans | Espresso | Ohio | Regular | 190 | 210 | 140 | 400 | 170 | 1091 | 171 | 47 | 99 | 341 | 72 |
| 414 | 2012-01-01 | Central | Small Market | Caffe Mocha | Beans | Espresso | Wisconsin | Regular | 80 | 90 | 50 | 170 | 69 | 965 | 81 | 21 | 38 | 150 | 43 |
3. Model Regresi Linear
model_mocha <- lm(Profit ~ Sales + Market + State, data = mocha_data)
summary(model_mocha)##
## Call:
## lm(formula = Profit ~ Sales + Market + State, data = mocha_data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -131.331 -7.341 -0.037 6.261 96.747
##
## Coefficients: (3 not defined because of singularities)
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -29.73327 7.39860 -4.019 6.84e-05 ***
## Sales 0.50488 0.03505 14.405 < 2e-16 ***
## MarketEast -269.81129 6.89278 -39.144 < 2e-16 ***
## MarketSouth 35.13966 6.67693 5.263 2.18e-07 ***
## MarketWest -95.14270 7.68837 -12.375 < 2e-16 ***
## StateColorado 29.58169 5.81538 5.087 5.32e-07 ***
## StateConnecticut 226.10451 6.37887 35.446 < 2e-16 ***
## StateFlorida 199.72059 8.47700 23.560 < 2e-16 ***
## StateIllinois -3.59029 16.23132 -0.221 0.825039
## StateIowa 20.54065 7.22637 2.842 0.004676 **
## StateLouisiana -17.94675 7.28102 -2.465 0.014072 *
## StateMassachusetts 228.18289 6.02216 37.891 < 2e-16 ***
## StateMissouri 24.06021 6.19777 3.882 0.000119 ***
## StateNevada 115.02603 11.09301 10.369 < 2e-16 ***
## StateNew Hampshire 233.87262 6.01770 38.864 < 2e-16 ***
## StateNew Mexico -70.82833 7.92870 -8.933 < 2e-16 ***
## StateNew York NA NA NA NA
## StateOhio -22.97695 7.79222 -2.949 0.003354 **
## StateOklahoma -14.10521 9.45156 -1.492 0.136290
## StateOregon 93.70371 8.85204 10.586 < 2e-16 ***
## StateTexas NA NA NA NA
## StateUtah 110.00329 8.23356 13.360 < 2e-16 ***
## StateWashington 78.01834 8.75077 8.916 < 2e-16 ***
## StateWisconsin NA NA NA NA
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 20.03 on 459 degrees of freedom
## Multiple R-squared: 0.9595, Adjusted R-squared: 0.9578
## F-statistic: 544.3 on 20 and 459 DF, p-value: < 2.2e-16Disini dapat diketahui bahwa Sales signifikan dan
positif → semakin tinggi penjualan artinya semakin tinggi profit.
Beberapa State dan Market juga signifikan →
profit dipengaruhi oleh lokasi geografis.
4. Uji Signifikansi Model (ANOVA)
anova(model_mocha)## Analysis of Variance Table
##
## Response: Profit
## Df Sum Sq Mean Sq F value Pr(>F)
## Sales 1 2263731 2263731 5640.27 < 2.2e-16 ***
## Market 3 828296 276099 687.92 < 2.2e-16 ***
## State 16 1276850 79803 198.84 < 2.2e-16 ***
## Residuals 459 184220 401
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1Uji ANOVA menunjukkan bahwa model secara keseluruhan
signifikan. Ini berarti setidaknya satu variabel dalam model
memiliki pengaruh nyata terhadap Profit.
5. Goodness of Fit
summary(model_mocha)$adj.r.squared## [1] 0.9577766Nilai Adjusted R-squared yang tinggi (misalnya > 0.95) menunjukkan bahwa model mampu menjelaskan sebagian besar variasi dari profit. Pada uji ini didapatkan nilai R-Squared sebesar 0.9577766.
6. Uji Multikolinearitas (VIF)
alias(model_mocha)## Model :
## Profit ~ Sales + Market + State
##
## Complete :
## (Intercept) Sales MarketEast MarketSouth MarketWest
## StateNew York 0 0 1 0 0
## StateTexas 0 0 0 1 0
## StateWisconsin 1 0 -1 -1 -1
## StateColorado StateConnecticut StateFlorida StateIllinois
## StateNew York 0 -1 -1 0
## StateTexas 0 0 0 0
## StateWisconsin -1 0 0 -1
## StateIowa StateLouisiana StateMassachusetts StateMissouri
## StateNew York 0 0 -1 0
## StateTexas 0 -1 0 0
## StateWisconsin -1 0 0 -1
## StateNevada StateNew Hampshire StateNew Mexico StateOhio
## StateNew York 0 -1 0 0
## StateTexas 0 0 -1 0
## StateWisconsin 0 0 0 -1
## StateOklahoma StateOregon StateUtah StateWashington
## StateNew York 0 0 0 0
## StateTexas -1 0 0 0
## StateWisconsin 0 0 0 0model_mocha <- lm(Profit ~ Sales + State, data = mocha_data)
vif(model_mocha)## GVIF Df GVIF^(1/(2*Df))
## Sales 24.65483 1 4.965363
## State 24.65483 19 1.088000Karena Market menyebabkan aliasing, model
disederhanakan. Nilai VIF < 5 menunjukkan tidak ada
multikolinearitas, sehingga koefisien regresi dapat
dipercaya.
7. Visualisasi Hubungan Sales dan Profit
ggplot(mocha_data, aes(x = Sales, y = Profit, color = Market)) +
geom_point() +
geom_smooth(method = "lm", se = FALSE) +
labs(title = "Hubungan Sales dan Profit Cafe Mocha", x = "Sales", y = "Profit") +
theme_minimal()## `geom_smooth()` using formula = 'y ~ x'
Terdapat hubungan linear positif antara Sales dan
Profit, memperkuat hasil regresi yang ditemukan
sebelumnya.
8. Kesimpulan
Berdasarkan hasil analisis: - Sales dan
State berpengaruh signifikan terhadap Profit.
- Model menunjukkan performa sangat baik dengan Adjusted R-squared
tinggi. - Tidak ada multikolinearitas. - Visualisasi mendukung hubungan
positif antar variabel.
Model ini valid digunakan sebagai dasar strategi peningkatan profit Cafe Mocha berdasarkan lokasi dan tingkat penjualan.