# ===============================
# 1. INPUT DATA BISNIS
# ===============================
data_bisnis <- data.frame(
Sales = c(520, 610, 580, 450, 700, 640, 500, 720, 680, 560, 590, 630),
Promotion = c(50, 65, 60, 40, 80, 70, 45, 85, 75, 55, 58, 68),
Staff = c(20, 25, 23, 18, 30, 27, 19, 32, 29, 22, 24, 26),
StoreSize = c(200, 250, 230, 180, 300, 270, 190, 320, 290, 210, 240, 260),
CustomerSat = c(78, 85, 82, 70, 90, 88, 75, 92, 89, 80, 83, 87),
Loyalty = c(72, 80, 78, 65, 88, 84, 70, 90, 86, 75, 79, 83)
)
data_bisnis
## Sales Promotion Staff StoreSize CustomerSat Loyalty
## 1 520 50 20 200 78 72
## 2 610 65 25 250 85 80
## 3 580 60 23 230 82 78
## 4 450 40 18 180 70 65
## 5 700 80 30 300 90 88
## 6 640 70 27 270 88 84
## 7 500 45 19 190 75 70
## 8 720 85 32 320 92 90
## 9 680 75 29 290 89 86
## 10 560 55 22 210 80 75
## 11 590 58 24 240 83 79
## 12 630 68 26 260 87 83
# Korelasi Bivariat #
cor(data_bisnis$Promotion, data_bisnis$Sales)
## [1] 0.994136
cor.test(data_bisnis$Promotion, data_bisnis$Sales)
##
## Pearson's product-moment correlation
##
## data: data_bisnis$Promotion and data_bisnis$Sales
## t = 29.072, df = 10, p-value = 5.407e-11
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## 0.9785095 0.9984090
## sample estimates:
## cor
## 0.994136
# ======Interpretasi=========
# -) Jika r mendekati 1 → promosi dan penjualan bergerak searah
# -) Lihat p-value untuk signifikansi
# Korelasi Berganda #
model <- lm(Sales ~ Promotion + Staff + StoreSize, data = data_bisnis)
summary(model)
##
## Call:
## lm(formula = Sales ~ Promotion + Staff + StoreSize, data = data_bisnis)
##
## Residuals:
## Min 1Q Median 3Q Max
## -17.1250 -0.6046 0.0464 3.0067 14.7174
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 201.2062 31.5305 6.381 0.000213 ***
## Promotion 4.1824 1.9244 2.173 0.061495 .
## Staff 13.7017 12.4941 1.097 0.304703
## StoreSize -0.8223 1.0305 -0.798 0.447930
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 9.659 on 8 degrees of freedom
## Multiple R-squared: 0.99, Adjusted R-squared: 0.9862
## F-statistic: 263 on 3 and 8 DF, p-value: 2.487e-08
# Ambil R^2
R2 <- summary(model)$r.squared
R <- sqrt(R2)
R2
## [1] 0.9899639
R
## [1] 0.9949693
# ======Interpretasi=========
# R² menunjukkan berapa persen variasi Sales dijelaskan oleh ketiga variabel
# Korelasi Parsial #
# Case: Apakah Promotion tetap berpengaruh terhadap Sales setelah dikontrol Staff dan StoreSize?
library(ppcor)
## Loading required package: MASS
pcor.test(
data_bisnis$Promotion,
data_bisnis$Sales,
data_bisnis[, c("Staff", "StoreSize")]
)
## estimate p.value statistic n gp Method
## 1 0.6092977 0.06149483 2.173369 12 2 pearson
# ======Interpretasi=========
# R² menunjukkan berapa persen variasi Sales dijelaskan oleh ketiga variabel
# Korelasi Kanonik #
# Kelompok 1 (Operasional):Promotion,Staff,StoreSize
# Kelompok 2 (Outcome): Sales,CustomerSat,Loyalty
# Standarisasi dulu
X <- scale(data_bisnis[, c("Promotion", "Staff", "StoreSize")])
Y <- scale(data_bisnis[, c("Sales", "CustomerSat", "Loyalty")])
cc <- cancor(X, Y)
# Nilai canonical correlation
cc$cor
## [1] 0.9959211 0.5134494 0.3985442
# Koefisien pembentuk kombinasi
cc$xcoef
## [,1] [,2] [,3]
## Promotion -0.1570032 2.0713305 -1.819253
## Staff -0.3103713 0.7337338 5.688635
## StoreSize 0.1659745 -2.8189990 -3.885821
cc$ycoef
## [,1] [,2] [,3]
## Sales -0.400158282 1.998564 3.5166710
## CustomerSat 0.094027878 3.175984 -0.3855181
## Loyalty 0.006076517 -5.147160 -3.1583887
# ======Interpretasi=========
# -)Canonical correlation pertama menunjukkan seberapa kuat hubungan sistem operasional
# dengan sistem outcome bisnis.
# -)Jika misalnya hasilnya 0.85 → hubungan antar sistem sangat kuat.