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data <- read.csv("C:/Users/WINDOWS/Downloads/semester 6/komputasi lanjut/before uts/advertising.csv")
summary(data)
##        TV             Radio          Newspaper          Sales      
##  Min.   :  0.70   Min.   : 0.000   Min.   :  0.30   Min.   : 1.60  
##  1st Qu.: 74.38   1st Qu.: 9.975   1st Qu.: 12.75   1st Qu.:11.00  
##  Median :149.75   Median :22.900   Median : 25.75   Median :16.00  
##  Mean   :147.04   Mean   :23.264   Mean   : 30.55   Mean   :15.13  
##  3rd Qu.:218.82   3rd Qu.:36.525   3rd Qu.: 45.10   3rd Qu.:19.05  
##  Max.   :296.40   Max.   :49.600   Max.   :114.00   Max.   :27.00

Rata-rata biaya iklan TV: 147.04

Rata-rata biaya iklan Radio: 23.26

Rata-rata biaya iklan Koran (Newspaper): 30.55

Rata-rata Penjualan (Sales): 15.13

Model Regresi Linear Berganda

Persamaan model regresi: \[ y=\beta_0 +\beta_1X_1+ \beta_2 X_2 + \beta_3 X_3+ \epsilon \] Dimana: (Y) = Sales (X1) = TV (X2) = Radio (X3) = Newspaper

model <- lm(Sales ~ TV + Radio +  Newspaper, data=data)
summary(model)
## 
## Call:
## lm(formula = Sales ~ TV + Radio + Newspaper, data = data)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -7.3034 -0.8244 -0.0008  0.8976  3.7473 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 4.6251241  0.3075012  15.041   <2e-16 ***
## TV          0.0544458  0.0013752  39.592   <2e-16 ***
## Radio       0.1070012  0.0084896  12.604   <2e-16 ***
## Newspaper   0.0003357  0.0057881   0.058    0.954    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.662 on 196 degrees of freedom
## Multiple R-squared:  0.9026, Adjusted R-squared:  0.9011 
## F-statistic: 605.4 on 3 and 196 DF,  p-value: < 2.2e-16

Persamaan Regresi

Y = 4.625 + 0.054 TV + 0.107 Radio + 0 Newspaper

Koefisien Determinasi

Nilai R-squared dari model adalah:

0.903

Artinya sebesar 90.26% variasi Sales dapat dijelaskan oleh variabel TV, Radio, dan Newspaper.

Uji F (Simultan)

Uji F digunakan untuk mengetahui apakah variabel independen secara bersama-sama berpengaruh terhadap variabel dependen.

anova(model)
## Analysis of Variance Table
## 
## Response: Sales
##            Df Sum Sq Mean Sq   F value Pr(>F)    
## TV          1 4512.4  4512.4 1634.2115 <2e-16 ***
## Radio       1  502.3   502.3  181.9255 <2e-16 ***
## Newspaper   1    0.0     0.0    0.0034 0.9538    
## Residuals 196  541.2     2.8                     
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Uji t (Parsial)

Uji t digunakan untuk mengetahui pengaruh masing-masing variabel independen terhadap variabel dependen.

summary(model)$coefficients
##                 Estimate  Std. Error     t value     Pr(>|t|)
## (Intercept) 4.6251240788 0.307501165 15.04099695 1.682677e-34
## TV          0.0544457803 0.001375188 39.59152448 1.892945e-95
## Radio       0.1070012282 0.008489563 12.60385655 4.602097e-27
## Newspaper   0.0003356579 0.005788056  0.05799148 9.538145e-01

Uji Asumsi Klasik

Uji Normalitas Residual

error <- residuals(model)

ks.test(error,"pnorm",mean(error),sd(error))
## 
##  Asymptotic one-sample Kolmogorov-Smirnov test
## 
## data:  error
## D = 0.082313, p-value = 0.133
## alternative hypothesis: two-sided

Visualisasi normalitas:

qqnorm(error)
qqline(error, col="red")

Uji Heteroskedastisitas

library(lmtest)
## Warning: package 'lmtest' was built under R version 4.5.2
## Loading required package: zoo
## Warning: package 'zoo' was built under R version 4.5.2
## 
## Attaching package: 'zoo'
## The following objects are masked from 'package:base':
## 
##     as.Date, as.Date.numeric
bptest(model)
## 
##  studentized Breusch-Pagan test
## 
## data:  model
## BP = 3.9785, df = 3, p-value = 0.2638

Visualisasi residual:

plot(model$fitted.values, residuals(model),
     xlab="Nilai Prediksi",
     ylab="Residual",
     main="Plot Residual")

abline(h=0, col="red")

Uji Autokorelasi

dwtest(model)
## 
##  Durbin-Watson test
## 
## data:  model
## DW = 2.2506, p-value = 0.9625
## alternative hypothesis: true autocorrelation is greater than 0

Visualisasi Hubungan Variabel

TV vs Sales

plot(data$TV, data$Sales,
     main="Hubungan Iklan TV dan Sales",
     xlab="TV Advertising",
     ylab="Sales",
     pch=19)

abline(lm(Sales ~ TV, data=data), col="red")

Radio vs Sales

plot(data$Radio, data$Sales,
     main="Hubungan Iklan Radio dan Sales",
     xlab="Radio Advertising",
     ylab="Sales",
     pch=19)

abline(lm(Sales ~ Radio, data=data), col="blue")

Newspaper vs Sales

plot(data$Newspaper, data$Sales,
     main="Hubungan Iklan Newspaper dan Sales",
     xlab="Newspaper Advertising",
     ylab="Sales",
     pch=19)

abline(lm(Sales ~ Newspaper, data=data), col="green")

Diagnostic Plot Model

par(mfrow=c(2,2))
plot(model)