Membangun Regresi Linear Berganda Google Mobility Index dengan Data Set Sembuh Covid-19 di Daerah DKI Jakarta pada Bulan Juli 2021
Nurul Izzah, Prof. Dr. Suhartono, M.Kom
21 Maret 2022
Lembaga : Universitas Islam Negeri Maulana Malik Ibrahim Malang
Jurusan : Teknik Informatika
1. Pengertian Linear Berganda
Regresi Linear Berganda adalah model regresi linear dengan melibatkan lebih dari satu variable bebas atau predictor. Dalam bahasa inggris, istilah ini disebut dengan multiple linear regression.
2. Menampilkan Data Set Sembuh Covid-19
library(readxl)## Warning: package 'readxl' was built under R version 4.1.2datacovidjuli2021 <- read_excel(path = "C:/Users/User/Documents/SEMESTER 2/LINEAR ALGEBRA/data sembuh covid-19 DKI Jakarta Juli 2021.xlsx")
datacovidjuli2021## # A tibble: 31 x 8
## Tanggal Sembuh retail_and_recr~ grocery_and_pha~ parks_percent_c~
## <dttm> <dbl> <dbl> <dbl> <dbl>
## 1 2021-07-01 00:00:00 468461 -42 -5 -67
## 2 2021-07-02 00:00:00 473467 -32 2 -51
## 3 2021-07-03 00:00:00 479150 -34 -1 -53
## 4 2021-07-04 00:00:00 484949 -34 -2 -52
## 5 2021-07-05 00:00:00 491556 -37 -6 -55
## 6 2021-07-06 00:00:00 497492 -31 2 -45
## 7 2021-07-07 00:00:00 501199 -36 2 -56
## 8 2021-07-08 00:00:00 512085 -39 -5 -63
## 9 2021-07-09 00:00:00 526941 -32 -2 -50
## 10 2021-07-10 00:00:00 543867 -35 -6 -55
## # ... with 21 more rows, and 3 more variables:
## # transit_stations_percent_change_from_baseline <dbl>,
## # workplaces_percent_change_from_baseline <dbl>,
## # residential_percent_change_from_baseline <dbl>3. Menampilkan Nilai Minimum (Q1), Median (Q2), dan Maximum (Q3) dengan Fungsi summary()
summary(datacovidjuli2021)## Tanggal Sembuh
## Min. :2021-07-01 00:00:00 Min. :468461
## 1st Qu.:2021-07-08 12:00:00 1st Qu.:519513
## Median :2021-07-16 00:00:00 Median :604060
## Mean :2021-07-16 00:00:00 Mean :614736
## 3rd Qu.:2021-07-23 12:00:00 3rd Qu.:695171
## Max. :2021-07-31 00:00:00 Max. :784668
## retail_and_recreation_percent_change_from_baseline
## Min. :-42.00
## 1st Qu.:-34.00
## Median :-31.00
## Mean :-31.16
## 3rd Qu.:-28.00
## Max. :-22.00
## grocery_and_pharmacy_percent_change_from_baseline
## Min. :-13.000
## 1st Qu.: -5.500
## Median : -2.000
## Mean : -2.161
## 3rd Qu.: 0.000
## Max. : 6.000
## parks_percent_change_from_baseline
## Min. :-67.0
## 1st Qu.:-54.0
## Median :-50.0
## Mean :-50.9
## 3rd Qu.:-47.0
## Max. :-41.0
## transit_stations_percent_change_from_baseline
## Min. :-61.00
## 1st Qu.:-51.00
## Median :-47.00
## Mean :-47.84
## 3rd Qu.:-45.00
## Max. :-39.00
## workplaces_percent_change_from_baseline
## Min. :-73.00
## 1st Qu.:-39.50
## Median :-35.00
## Mean :-34.03
## 3rd Qu.:-23.50
## Max. :-14.00
## residential_percent_change_from_baseline
## Min. : 7.00
## 1st Qu.:11.50
## Median :14.00
## Mean :13.61
## 3rd Qu.:16.00
## Max. :22.004. Membuat Matriks dengan Fungsi pairs()
pairs(datacovidjuli2021)
pairs(datacovidjuli2021, lower.panel=NULL)
5. Visualisasi Data dengan Fungsi plot()
plot(datacovidjuli2021$Sembuh ~ datacovidjuli2021$Tanggal, data = datacovidjuli2021)
Visualisasi Data dimana data sembuh Covid sebagai Variabel Y dan Google Mobility Index sebagai variabel Y
plot(datacovidjuli2021$Sembuh ~ datacovidjuli2021$
retail_and_recreation_percent_change_from_baseline+datacovidjuli2021$
grocery_and_pharmacy_percent_change_from_baseline+datacovidjuli2021$
parks_percent_change_from_baseline+datacovidjuli2021$
transit_stations_percent_change_from_baseline+datacovidjuli2021$
workplaces_percent_change_from_baseline+datacovidjuli2021$
residential_percent_change_from_baseline, data = datacovidjuli2021)
6. Membangun Korelasi antar Variabel
korelasi adalah nilai yang menunjukkan kekuatan dan arah hubungan linier antara dua peubah acak.
a. Korelasi Variabel y dengan x1
cor(datacovidjuli2021$Sembuh,datacovidjuli2021$
retail_and_recreation_percent_change_from_baseline)## [1] 0.7820109b. Korelasi Variabel y dengan x2
cor(datacovidjuli2021$Sembuh,datacovidjuli2021$
grocery_and_pharmacy_percent_change_from_baseline)## [1] 0.2624391c. Korelasi Variabel y dengan x3
cor(datacovidjuli2021$Sembuh,datacovidjuli2021$
parks_percent_change_from_baseline)## [1] 0.5192907d. Korelasi Variabel y dengan x4
cor(datacovidjuli2021$Sembuh,datacovidjuli2021$
transit_stations_percent_change_from_baseline)## [1] 0.6064333e. Korelasi variabel y dengan x5
cor(datacovidjuli2021$Sembuh,datacovidjuli2021$
workplaces_percent_change_from_baseline)## [1] 0.2220271f. Korelasi variabel y dengan x6
cor(datacovidjuli2021$Sembuh,datacovidjuli2021$
residential_percent_change_from_baseline)## [1] -0.41064197. Menggunakan Permodelan dari Data Sembuh Covid-19
model <- lm(datacovidjuli2021$Sembuh ~ datacovidjuli2021$Tanggal, data = datacovidjuli2021)summary(model)##
## Call:
## lm(formula = datacovidjuli2021$Sembuh ~ datacovidjuli2021$Tanggal,
## data = datacovidjuli2021)
##
## Residuals:
## Min 1Q Median 3Q Max
## -13716 -7964 -894 8517 20479
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -2.086e+08 3.553e+06 -58.73 <2e-16 ***
## datacovidjuli2021$Tanggal 1.287e-01 2.184e-03 58.90 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 9399 on 29 degrees of freedom
## Multiple R-squared: 0.9917, Adjusted R-squared: 0.9914
## F-statistic: 3469 on 1 and 29 DF, p-value: < 2.2e-168. Menggunakan Fungsi anova()
anova(model)## Analysis of Variance Table
##
## Response: datacovidjuli2021$Sembuh
## Df Sum Sq Mean Sq F value Pr(>F)
## datacovidjuli2021$Tanggal 1 3.0649e+11 3.0649e+11 3469.3 < 2.2e-16 ***
## Residuals 29 2.5620e+09 8.8345e+07
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 19. Membuat plot() Model dari Data Real dan Prediksi
plot(datacovidjuli2021$Sembuh ~ datacovidjuli2021$
Tanggal,
data = datacovidjuli2021, col = "navy", pch = 20, cex = 1.5,
main = "Data Sembuh Covid-19 di DKI Jakarta dan Google Mobility Index")
abline(model) #Add a regression line
plot(cooks.distance(model), pch = 16, col = "navy") #Plot the Cooks Distances.
plot(model)
10. Penggunaan AIC dan BIC
a. AIC
AIC(model)## [1] 659.1062b. BIC
BIC(model)## [1] 663.408111. Memunculkan Nilai Prediksi dan Visualisasi
head(predict(model), n = 11)## 1 2 3 4 5 6 7 8
## 447982.5 459099.4 470216.2 481333.1 492450.0 503566.8 514683.7 525800.6
## 9 10 11
## 536917.4 548034.3 559151.2plot(head(predict(model), n = 10))
12. Menampilkan Nilai Residuals
head(resid(model), n = 11)## 1 2 3 4 5 6
## 20478.5081 14367.6419 8933.7758 3615.9097 -893.9565 -6074.8226
## 7 8 9 10 11
## -13484.6887 -13715.5548 -9976.4210 -4167.2871 5285.8468coef(model)## (Intercept) datacovidjuli2021$Tanggal
## -2.086492e+08 1.286674e-0113. Menambahkan Data Residuals dan Data Predicted dengan Tabel
a. Data Residuals
datacovidjuli2021$residuals <- model$residualsb. Data Pedicted
datacovidjuli2021$predicted <- model$fitted.values
datacovidjuli2021## # A tibble: 31 x 10
## Tanggal Sembuh retail_and_recr~ grocery_and_pha~ parks_percent_c~
## <dttm> <dbl> <dbl> <dbl> <dbl>
## 1 2021-07-01 00:00:00 468461 -42 -5 -67
## 2 2021-07-02 00:00:00 473467 -32 2 -51
## 3 2021-07-03 00:00:00 479150 -34 -1 -53
## 4 2021-07-04 00:00:00 484949 -34 -2 -52
## 5 2021-07-05 00:00:00 491556 -37 -6 -55
## 6 2021-07-06 00:00:00 497492 -31 2 -45
## 7 2021-07-07 00:00:00 501199 -36 2 -56
## 8 2021-07-08 00:00:00 512085 -39 -5 -63
## 9 2021-07-09 00:00:00 526941 -32 -2 -50
## 10 2021-07-10 00:00:00 543867 -35 -6 -55
## # ... with 21 more rows, and 5 more variables:
## # transit_stations_percent_change_from_baseline <dbl>,
## # workplaces_percent_change_from_baseline <dbl>,
## # residential_percent_change_from_baseline <dbl>, residuals <dbl>,
## # predicted <dbl>14. Menambahkan Fungsi scatter.smooth(), boxplot(), dan plot() untuk Visualisasi
scatter.smooth(x=datacovidjuli2021$Tanggal, y=datacovidjuli2021$Sembuh,
main="Tanggal ~ Sembuh")
boxplot(datacovidjuli2021$Sembuh, main="Sembuh",
boxplot.stats(datacovidjuli2021$Sembuh)$out)
plot(density(datacovidjuli2021$Sembuh), main="Google Mobility Index: Sembuh",
ylab="Frequency")
coefs <- coef(model)
plot(Sembuh ~ Tanggal, data = datacovidjuli2021)
abline(coefs)
text(x = 12, y = 10, paste('expression = ', round(coefs[1], 2), '+',
round(coefs[2], 2), '*Sembuh'))
15. Menguji Korelasi antar Variabel
a. Menguji Korelasi variabel y dengan x1
cor.test(datacovidjuli2021$
retail_and_recreation_percent_change_from_baseline,
datacovidjuli2021$Sembuh)##
## Pearson's product-moment correlation
##
## data: datacovidjuli2021$retail_and_recreation_percent_change_from_baseline and datacovidjuli2021$Sembuh
## t = 6.7568, df = 29, p-value = 2.045e-07
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## 0.5916026 0.8897917
## sample estimates:
## cor
## 0.7820109b. Menguji Korelasi variabel y dengan x2
cor.test(datacovidjuli2021$
grocery_and_pharmacy_percent_change_from_baseline,
datacovidjuli2021$Sembuh)##
## Pearson's product-moment correlation
##
## data: datacovidjuli2021$grocery_and_pharmacy_percent_change_from_baseline and datacovidjuli2021$Sembuh
## t = 1.4646, df = 29, p-value = 0.1538
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.1013233 0.5643032
## sample estimates:
## cor
## 0.2624391c. Menguji Korelasi variabel y dengan x3
cor.test(datacovidjuli2021$
parks_percent_change_from_baseline,
datacovidjuli2021$Sembuh)##
## Pearson's product-moment correlation
##
## data: datacovidjuli2021$parks_percent_change_from_baseline and datacovidjuli2021$Sembuh
## t = 3.2723, df = 29, p-value = 0.002757
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## 0.2021467 0.7378604
## sample estimates:
## cor
## 0.5192907d. Menguji Korelasi variabel y dengan x4
cor.test(datacovidjuli2021$
transit_stations_percent_change_from_baseline,
datacovidjuli2021$Sembuh)##
## Pearson's product-moment correlation
##
## data: datacovidjuli2021$transit_stations_percent_change_from_baseline and datacovidjuli2021$Sembuh
## t = 4.1072, df = 29, p-value = 0.0002988
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## 0.3210902 0.7908358
## sample estimates:
## cor
## 0.6064333e. Menguji Korelasi variabel y dengan x5
cor.test(datacovidjuli2021$
workplaces_percent_change_from_baseline,
datacovidjuli2021$Sembuh)##
## Pearson's product-moment correlation
##
## data: datacovidjuli2021$workplaces_percent_change_from_baseline and datacovidjuli2021$Sembuh
## t = 1.2263, df = 29, p-value = 0.23
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.1436114 0.5343298
## sample estimates:
## cor
## 0.2220271f. Menguji Korelasi variabel y dengan x6
cor.test(datacovidjuli2021$
residential_percent_change_from_baseline,
datacovidjuli2021$Sembuh)##
## Pearson's product-moment correlation
##
## data: datacovidjuli2021$residential_percent_change_from_baseline and datacovidjuli2021$Sembuh
## t = -2.4253, df = 29, p-value = 0.02175
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.66781095 -0.06588915
## sample estimates:
## cor
## -0.4106419Sumber:
https://rpubs.com/suhartono-uinmaliki/877449
summary(cars)## speed dist
## Min. : 4.0 Min. : 2.00
## 1st Qu.:12.0 1st Qu.: 26.00
## Median :15.0 Median : 36.00
## Mean :15.4 Mean : 42.98
## 3rd Qu.:19.0 3rd Qu.: 56.00
## Max. :25.0 Max. :120.00