Import Data
library (readr)
## Warning: package 'readr' was built under R version 4.5.3
path <- "C:\\Users\\ASUS\\Downloads\\Data Cleaning - Rumah 123.csv"
# 1. Baca mentah per baris (aman dari masalah encoding)
baris <- readLines(path, encoding = "latin1", warn = FALSE)
# 2. Buang tanda kutip yang membungkus satu baris penuh
baris <- gsub('"', "", baris)
# 3. Deteksi pemisah otomatis dari baris header
pemisah <- if (grepl(";", baris[1])) ";" else if (grepl("\t", baris[1])) "\t" else ","
# 4. Pecah jadi kolom, nama kolom dipertahankan
data <- read.table(
text = paste(baris, collapse = "\n"),
sep = pemisah, header = TRUE, quote = "",
check.names = FALSE, strip.white = TRUE,
stringsAsFactors = FALSE, fill = TRUE
)
# 5. Ubah kolom yang isinya angka jadi numerik
data[] <- lapply(data, type.convert, as.is = TRUE)
library(dplyr)
##
## Attaching package: 'dplyr'
## The following objects are masked from 'package:stats':
##
## filter, lag
## The following objects are masked from 'package:base':
##
## intersect, setdiff, setequal, union
data <- data %>% rename(Harga = `Harga (Miliar)`)
data <- data %>% rename(`Luas Tanah` = `Luas Tanah (m²)`)
data <- data %>% rename(`Luas Bangunan` = `Luas Bangunan (m²)`)
data <- data %>% rename(`Cicilan` = `Cicilan (Jutaan per Bulan)`)
str(data)
## 'data.frame': 1015 obs. of 10 variables:
## $ Kamar Tidur : int 2 2 2 2 2 2 2 2 2 2 ...
## $ Kamar Mandi : int 1 1 1 1 1 1 1 1 1 1 ...
## $ Luas Tanah : int 65 50 72 72 60 60 58 75 60 72 ...
## $ Garasi : int 0 1 0 0 1 1 0 0 0 0 ...
## $ Luas Bangunan : int 35 30 50 50 45 32 45 60 45 36 ...
## $ Jenis Bangunan: chr "Rumah" "Rumah" "Rumah" "Rumah" ...
## $ Harga : num 0.3 0.353 0.36 0.36 0.43 0.45 0.47 0.47 0.47 0.48 ...
## $ Cicilan : num 1 1 1 1 1 1 1 1 1 1 ...
## $ Kec : chr "Grand Wisata" "Jati Asih" "Grand Wisata" "Bekasi" ...
## $ Kab/Kota : chr "Bekasi" "Bekasi" "Bekasi" "Bekasi" ...
head(data)
## Kamar Tidur Kamar Mandi Luas Tanah Garasi Luas Bangunan Jenis Bangunan Harga
## 1 2 1 65 0 35 Rumah 0.300
## 2 2 1 50 1 30 Rumah 0.353
## 3 2 1 72 0 50 Rumah 0.360
## 4 2 1 72 0 50 Rumah 0.360
## 5 2 1 60 1 45 Rumah 0.430
## 6 2 1 60 1 32 Rumah 0.450
## Cicilan Kec Kab/Kota
## 1 1 Grand Wisata Bekasi
## 2 1 Jati Asih Bekasi
## 3 1 Grand Wisata Bekasi
## 4 1 Bekasi Bekasi
## 5 1 Bekasi Utara Bekasi
## 6 1 Cibitung Bekasi
Regresi Harga Rumah dengan 6 Peubah Prediktor
Model Regresi Awal
library(dplyr)
library(lmtest)
## Warning: package 'lmtest' was built under R version 4.5.3
## Loading required package: zoo
## Warning: package 'zoo' was built under R version 4.5.3
##
## Attaching package: 'zoo'
## The following objects are masked from 'package:base':
##
## as.Date, as.Date.numeric
library(car)
## Warning: package 'car' was built under R version 4.5.3
## Loading required package: carData
## Warning: package 'carData' was built under R version 4.5.3
##
## Attaching package: 'car'
## The following object is masked from 'package:dplyr':
##
## recode
model <- lm(Harga ~ `Kamar Tidur`+`Kamar Mandi`+`Luas Tanah`+`Garasi`+`Luas Bangunan`+`Cicilan`, data = data)
summary(model)
##
## Call:
## lm(formula = Harga ~ `Kamar Tidur` + `Kamar Mandi` + `Luas Tanah` +
## Garasi + `Luas Bangunan` + Cicilan, data = data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -107.13 -23.07 -10.37 -5.94 721.26
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 8.11031 7.27568 1.115 0.2652
## `Kamar Tidur` 3.53056 2.78285 1.269 0.2048
## `Kamar Mandi` -3.65197 1.91042 -1.912 0.0562 .
## `Luas Tanah` -0.07156 0.01824 -3.924 9.29e-05 ***
## Garasi 14.11149 2.43642 5.792 9.29e-09 ***
## `Luas Bangunan` 0.06055 0.01496 4.047 5.59e-05 ***
## Cicilan 0.02163 0.05331 0.406 0.6851
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 75.37 on 1008 degrees of freedom
## Multiple R-squared: 0.05407, Adjusted R-squared: 0.04844
## F-statistic: 9.603 on 6 and 1008 DF, p-value: 2.728e-10
t.test(model$residuals,mu = 0,conf.level=0.95)
##
## One Sample t-test
##
## data: model$residuals
## t = -5.6503e-15, df = 1014, p-value = 1
## alternative hypothesis: true mean is not equal to 0
## 95 percent confidence interval:
## -4.628822 4.628822
## sample estimates:
## mean of x
## -1.332836e-14
bptest(model)
##
## studentized Breusch-Pagan test
##
## data: model
## BP = 19.085, df = 6, p-value = 0.004023
ks.test(model$residuals, "pnorm", mean(model$residuals), sd(model$residuals))
## Warning in ks.test.default(model$residuals, "pnorm", mean(model$residuals), :
## ties should not be present for the one-sample Kolmogorov-Smirnov test
##
## Asymptotic one-sample Kolmogorov-Smirnov test
##
## data: model$residuals
## D = 0.39977, p-value < 2.2e-16
## alternative hypothesis: two-sided
shapiro.test(model$residuals)
##
## Shapiro-Wilk normality test
##
## data: model$residuals
## W = 0.38035, p-value < 2.2e-16
dwtest(model)
##
## Durbin-Watson test
##
## data: model
## DW = 1.4786, p-value < 2.2e-16
## alternative hypothesis: true autocorrelation is greater than 0
vif(model)
## `Kamar Tidur` `Kamar Mandi` `Luas Tanah` Garasi `Luas Bangunan`
## 1.611145 3.902717 4.920269 1.289932 8.420083
## Cicilan
## 1.077082
Penanganan Autokorelasi dengan Transformasi Boxcox
library(MASS)
##
## Attaching package: 'MASS'
## The following object is masked from 'package:dplyr':
##
## select
boxcox_result <- boxcox(model)
lambda_optimal <- boxcox_result$x[which.max(boxcox_result$y)]
if (lambda_optimal != 0) {
data$Harga_transformed <- (data$Harga^lambda_optimal - 1) / lambda_optimal
} else {
data$Harga_transformed <- log(data$Harga)
}
model2 <- lm(Harga_transformed ~ `Kamar Tidur` + `Kamar Mandi` + `Luas Tanah`+`Luas Bangunan` + `Garasi` + `Jenis Bangunan` + `Cicilan`, data = data)
summary(model2)
##
## Call:
## lm(formula = Harga_transformed ~ `Kamar Tidur` + `Kamar Mandi` +
## `Luas Tanah` + `Luas Bangunan` + Garasi + `Jenis Bangunan` +
## Cicilan, data = data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -4.0901 -0.3811 -0.0069 0.3237 3.0137
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -3.869e-01 1.784e-01 -2.169 0.030332 *
## `Kamar Tidur` 3.387e-01 2.548e-02 13.295 < 2e-16 ***
## `Kamar Mandi` 7.587e-02 1.793e-02 4.233 2.52e-05 ***
## `Luas Tanah` 8.368e-05 1.769e-04 0.473 0.636305
## `Luas Bangunan` -1.081e-04 1.474e-04 -0.734 0.463362
## Garasi 1.723e-01 2.208e-02 7.805 1.49e-14 ***
## `Jenis Bangunan`Gudang 8.120e-01 5.170e-01 1.571 0.116603
## `Jenis Bangunan`Kantor -2.061e+00 4.852e-01 -4.247 2.37e-05 ***
## `Jenis Bangunan`Ruang Usaha 2.294e+00 5.106e-01 4.493 7.85e-06 ***
## `Jenis Bangunan`Ruko 1.049e+00 2.910e-01 3.605 0.000328 ***
## `Jenis Bangunan`Rumah -5.904e-01 1.750e-01 -3.373 0.000771 ***
## Cicilan -2.478e-04 5.020e-04 -0.494 0.621601
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.6687 on 1003 degrees of freedom
## Multiple R-squared: 0.4109, Adjusted R-squared: 0.4045
## F-statistic: 63.61 on 11 and 1003 DF, p-value: < 2.2e-16
t.test(model2$residuals,mu = 0,conf.level=0.95)
##
## One Sample t-test
##
## data: model2$residuals
## t = -1.5525e-15, df = 1014, p-value = 1
## alternative hypothesis: true mean is not equal to 0
## 95 percent confidence interval:
## -0.0409618 0.0409618
## sample estimates:
## mean of x
## -3.240772e-17
bptest(model2)
##
## studentized Breusch-Pagan test
##
## data: model2
## BP = 78.473, df = 11, p-value = 2.911e-12
ks.test(model2$residuals, "pnorm", mean(model2$residuals), sd(model2$residuals))
## Warning in ks.test.default(model2$residuals, "pnorm", mean(model2$residuals), :
## ties should not be present for the one-sample Kolmogorov-Smirnov test
##
## Asymptotic one-sample Kolmogorov-Smirnov test
##
## data: model2$residuals
## D = 0.065591, p-value = 0.0003222
## alternative hypothesis: two-sided
shapiro.test(model2$residuals)
##
## Shapiro-Wilk normality test
##
## data: model2$residuals
## W = 0.95445, p-value < 2.2e-16
dwtest(model2)
##
## Durbin-Watson test
##
## data: model2
## DW = 1.2044, p-value < 2.2e-16
## alternative hypothesis: true autocorrelation is greater than 0
vif(model2)
## GVIF Df GVIF^(1/(2*Df))
## `Kamar Tidur` 1.715685 1 1.309842
## `Kamar Mandi` 4.365903 1 2.089474
## `Luas Tanah` 5.883165 1 2.425524
## `Luas Bangunan` 10.381453 1 3.222026
## Garasi 1.346276 1 1.160291
## `Jenis Bangunan` 2.864944 5 1.110994
## Cicilan 1.213280 1 1.101490
Log
model3 <- lm(log(Harga) ~ `Kamar Tidur` + `Kamar Mandi`+`Luas Bangunan` + `Luas Tanah` + `Garasi` + `Cicilan`, data = data)
summary(model3)
##
## Call:
## lm(formula = log(Harga) ~ `Kamar Tidur` + `Kamar Mandi` + `Luas Bangunan` +
## `Luas Tanah` + Garasi + Cicilan, data = data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -3.9960 -0.6779 -0.2424 0.2199 6.8021
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.8654437 0.1298035 -6.667 4.28e-11 ***
## `Kamar Tidur` 0.4114271 0.0496481 8.287 3.68e-16 ***
## `Kamar Mandi` 0.0196005 0.0340833 0.575 0.5654
## `Luas Bangunan` 0.0005701 0.0002670 2.136 0.0329 *
## `Luas Tanah` -0.0005035 0.0003253 -1.547 0.1221
## Garasi 0.3994598 0.0434675 9.190 < 2e-16 ***
## Cicilan 0.0024311 0.0009512 2.556 0.0107 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.345 on 1008 degrees of freedom
## Multiple R-squared: 0.2809, Adjusted R-squared: 0.2767
## F-statistic: 65.64 on 6 and 1008 DF, p-value: < 2.2e-16
t.test(model3$residuals,mu = 0,conf.level=0.95)
##
## One Sample t-test
##
## data: model3$residuals
## t = -6.8585e-16, df = 1014, p-value = 1
## alternative hypothesis: true mean is not equal to 0
## 95 percent confidence interval:
## -0.08258154 0.08258154
## sample estimates:
## mean of x
## -2.886315e-17
dwtest(model3)
##
## Durbin-Watson test
##
## data: model3
## DW = 0.85921, p-value < 2.2e-16
## alternative hypothesis: true autocorrelation is greater than 0
bptest(model3)
##
## studentized Breusch-Pagan test
##
## data: model3
## BP = 63.89, df = 6, p-value = 7.27e-12
ks.test(model3$residuals, "pnorm", mean(model3$residuals), sd(model3$residuals))
## Warning in ks.test.default(model3$residuals, "pnorm", mean(model3$residuals), :
## ties should not be present for the one-sample Kolmogorov-Smirnov test
##
## Asymptotic one-sample Kolmogorov-Smirnov test
##
## data: model3$residuals
## D = 0.19342, p-value < 2.2e-16
## alternative hypothesis: two-sided
shapiro.test(model3$residuals)
##
## Shapiro-Wilk normality test
##
## data: model3$residuals
## W = 0.7839, p-value < 2.2e-16
vif(model3)
## `Kamar Tidur` `Kamar Mandi` `Luas Bangunan` `Luas Tanah` Garasi
## 1.611145 3.902717 8.420083 4.920269 1.289932
## Cicilan
## 1.077082
Sqrt
model4 <- lm(sqrt(Harga) ~ `Kamar Tidur` + `Kamar Mandi`+`Luas Bangunan` + `Luas Tanah` + `Garasi` + `Cicilan`, data = data)
summary(model4)
##
## Call:
## lm(formula = sqrt(Harga) ~ `Kamar Tidur` + `Kamar Mandi` + `Luas Bangunan` +
## `Luas Tanah` + Garasi + Cicilan, data = data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -6.6439 -1.3599 -0.6169 -0.2378 23.7160
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.7290037 0.3479507 2.095 0.03641 *
## `Kamar Tidur` 0.4077571 0.1330866 3.064 0.00224 **
## `Kamar Mandi` -0.1279939 0.0913635 -1.401 0.16154
## `Luas Bangunan` 0.0031224 0.0007156 4.363 1.41e-05 ***
## `Luas Tanah` -0.0034230 0.0008721 -3.925 9.27e-05 ***
## Garasi 0.8885750 0.1165187 7.626 5.58e-14 ***
## Cicilan 0.0042834 0.0025497 1.680 0.09327 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 3.605 on 1008 degrees of freedom
## Multiple R-squared: 0.1237, Adjusted R-squared: 0.1185
## F-statistic: 23.72 on 6 and 1008 DF, p-value: < 2.2e-16
t.test(model4$residuals,mu = 0,conf.level=0.95)
##
## One Sample t-test
##
## data: model4$residuals
## t = -6.5295e-15, df = 1014, p-value = 1
## alternative hypothesis: true mean is not equal to 0
## 95 percent confidence interval:
## -0.2213678 0.2213678
## sample estimates:
## mean of x
## -7.365938e-16
dwtest(model4)
##
## Durbin-Watson test
##
## data: model4
## DW = 1.0664, p-value < 2.2e-16
## alternative hypothesis: true autocorrelation is greater than 0
bptest(model4)
##
## studentized Breusch-Pagan test
##
## data: model4
## BP = 34.599, df = 6, p-value = 5.154e-06
ks.test(model4$residuals, "pnorm", mean(model4$residuals), sd(model4$residuals))
## Warning in ks.test.default(model4$residuals, "pnorm", mean(model4$residuals), :
## ties should not be present for the one-sample Kolmogorov-Smirnov test
##
## Asymptotic one-sample Kolmogorov-Smirnov test
##
## data: model4$residuals
## D = 0.34181, p-value < 2.2e-16
## alternative hypothesis: two-sided
shapiro.test(model4$residuals)
##
## Shapiro-Wilk normality test
##
## data: model4$residuals
## W = 0.51364, p-value < 2.2e-16
vif(model4)
## `Kamar Tidur` `Kamar Mandi` `Luas Bangunan` `Luas Tanah` Garasi
## 1.611145 3.902717 8.420083 4.920269 1.289932
## Cicilan
## 1.077082
Reciprocal
model5 <- lm(1/Harga ~ `Kamar Tidur` + `Kamar Mandi` + `Luas Tanah` + `Luas Bangunan`+`Garasi` + `Cicilan`, data = data)
summary(model5)
##
## Call:
## lm(formula = 1/Harga ~ `Kamar Tidur` + `Kamar Mandi` + `Luas Tanah` +
## `Luas Bangunan` + Garasi + Cicilan, data = data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.7923 -0.3720 -0.1098 0.2512 9.0595
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.8672569 0.0649066 28.768 < 2e-16 ***
## `Kamar Tidur` -0.2747095 0.0248259 -11.065 < 2e-16 ***
## `Kamar Mandi` -0.0549269 0.0170429 -3.223 0.001310 **
## `Luas Tanah` -0.0004329 0.0001627 -2.661 0.007910 **
## `Luas Bangunan` 0.0003970 0.0001335 2.974 0.003009 **
## Garasi -0.0861586 0.0217354 -3.964 7.89e-05 ***
## Cicilan 0.0017050 0.0004756 3.585 0.000353 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.6724 on 1008 degrees of freedom
## Multiple R-squared: 0.2539, Adjusted R-squared: 0.2494
## F-statistic: 57.17 on 6 and 1008 DF, p-value: < 2.2e-16
t.test(model5$residuals,mu = 0,conf.level=0.95)
##
## One Sample t-test
##
## data: model5$residuals
## t = 2.1145e-15, df = 1014, p-value = 1
## alternative hypothesis: true mean is not equal to 0
## 95 percent confidence interval:
## -0.04129388 0.04129388
## sample estimates:
## mean of x
## 4.449705e-17
dwtest(model5)
##
## Durbin-Watson test
##
## data: model5
## DW = 1.3707, p-value < 2.2e-16
## alternative hypothesis: true autocorrelation is greater than 0
bptest(model5)
##
## studentized Breusch-Pagan test
##
## data: model5
## BP = 2.9529, df = 6, p-value = 0.8147
ks.test(model5$residuals, "pnorm", mean(model5$residuals), sd(model5$residuals))
## Warning in ks.test.default(model5$residuals, "pnorm", mean(model5$residuals), :
## ties should not be present for the one-sample Kolmogorov-Smirnov test
##
## Asymptotic one-sample Kolmogorov-Smirnov test
##
## data: model5$residuals
## D = 0.11148, p-value = 2.211e-11
## alternative hypothesis: two-sided
shapiro.test(model5$residuals)
##
## Shapiro-Wilk normality test
##
## data: model5$residuals
## W = 0.77976, p-value < 2.2e-16
vif(model5)
## `Kamar Tidur` `Kamar Mandi` `Luas Tanah` `Luas Bangunan` Garasi
## 1.611145 3.902717 4.920269 8.420083 1.289932
## Cicilan
## 1.077082
Kuadrat
model6 <- lm(I(Harga^2) ~ `Kamar Tidur` + `Kamar Mandi` + `Luas Tanah` + `Garasi` + `Luas Bangunan` + `Cicilan`, data = data)
summary(model6)
##
## Call:
## lm(formula = I(Harga^2) ~ `Kamar Tidur` + `Kamar Mandi` + `Luas Tanah` +
## Garasi + `Luas Bangunan` + Cicilan, data = data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -37887 -8566 -4097 -2438 573655
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 4301.444 3672.522 1.171 0.24177
## `Kamar Tidur` 985.926 1404.692 0.702 0.48292
## `Kamar Mandi` -1774.895 964.316 -1.841 0.06598 .
## `Luas Tanah` -25.248 9.205 -2.743 0.00620 **
## Garasi 4912.488 1229.822 3.994 6.96e-05 ***
## `Luas Bangunan` 20.547 7.553 2.720 0.00663 **
## Cicilan -3.298 26.912 -0.123 0.90249
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 38050 on 1008 degrees of freedom
## Multiple R-squared: 0.02087, Adjusted R-squared: 0.01505
## F-statistic: 3.582 on 6 and 1008 DF, p-value: 0.001616
t.test(model6$residuals,mu = 0,conf.level=0.95)
##
## One Sample t-test
##
## data: model6$residuals
## t = 1.6557e-15, df = 1014, p-value = 1
## alternative hypothesis: true mean is not equal to 0
## 95 percent confidence interval:
## -2336.475 2336.475
## sample estimates:
## mean of x
## 1.971401e-12
dwtest(model6)
##
## Durbin-Watson test
##
## data: model6
## DW = 1.9168, p-value = 0.08873
## alternative hypothesis: true autocorrelation is greater than 0
bptest(model6)
##
## studentized Breusch-Pagan test
##
## data: model6
## BP = 8.0494, df = 6, p-value = 0.2345
ks.test(model6$residuals, "pnorm", mean(model6$residuals), sd(model6$residuals))
## Warning in ks.test.default(model6$residuals, "pnorm", mean(model6$residuals), :
## ties should not be present for the one-sample Kolmogorov-Smirnov test
##
## Asymptotic one-sample Kolmogorov-Smirnov test
##
## data: model6$residuals
## D = 0.42272, p-value < 2.2e-16
## alternative hypothesis: two-sided
shapiro.test(model6$residuals)
##
## Shapiro-Wilk normality test
##
## data: model6$residuals
## W = 0.24236, p-value < 2.2e-16
vif(model6)
## `Kamar Tidur` `Kamar Mandi` `Luas Tanah` Garasi `Luas Bangunan`
## 1.611145 3.902717 4.920269 1.289932 8.420083
## Cicilan
## 1.077082
# Ringkasan model untuk mendapatkan Adjusted R-squared
summary_model6 <- summary(model6)
# Menampilkan Adjusted R-squared
adjusted_r_squared <- summary_model6$adj.r.squared
cat("Adjusted R-squared: ", adjusted_r_squared, "\n")
## Adjusted R-squared: 0.01504579
# Menghitung Residual Standard Error (RSE)
n <- length(model6$residuals) # Jumlah observasi
p <- length(coef(model6)) # Jumlah parameter (koefisien)
rss <- sum(model6$residuals^2) # Residual sum of squares
rse <- sqrt(rss / (n - p)) # Residual Standard Error
cat("Residual Standard Error (RSE): ", rse, "\n")
## Residual Standard Error (RSE): 38046.61
Penanganan dengan Membuang Outlier
influence <- influence.measures(model)
summary(influence)
## Potentially influential observations of
## lm(formula = Harga ~ `Kamar Tidur` + `Kamar Mandi` + `Luas Tanah` + Garasi + `Luas Bangunan` + Cicilan, data = data) :
##
## dfb.1_ dfb.`KT` dfb.`KM` dfb.`LT` dfb.Gars dfb.`LB` dfb.Ccln dffit
## 101 0.02 -0.03 0.01 0.01 0.01 -0.01 0.00 -0.04
## 141 0.03 -0.04 0.01 0.01 0.02 0.00 0.00 -0.04
## 157 -0.01 0.00 0.01 0.02 0.00 -0.01 0.00 0.02
## 204 0.00 0.08 -0.02 -0.07 -0.38 0.06 0.07 -0.43_*
## 348 -0.48 0.25 0.39 0.91 -0.45 -0.77 -0.02 1.04_*
## 349 -0.03 -0.07 0.20 0.28 -0.12 -0.25 0.03 0.30_*
## 355 -0.01 -0.01 0.04 0.08 -0.01 -0.07 0.00 0.08
## 358 -0.01 -0.01 0.04 0.08 -0.01 -0.07 0.00 0.08
## 446 -0.38 -0.03 1.36_* -0.44 0.17 -1.03_* 0.39 -2.66_*
## 482 0.02 -0.01 -0.02 -0.03 0.00 0.03 0.00 -0.04
## 508 0.01 -0.03 0.05 0.01 0.02 -0.04 0.00 -0.08
## 574 0.01 -0.01 0.01 0.01 0.01 -0.02 -0.01 -0.03
## 583 0.03 0.04 -0.03 -0.12 -0.15 0.09 -0.01 -0.24
## 590 0.00 0.04 0.02 -0.02 -0.25 0.01 0.04 -0.28_*
## 591 0.02 -0.03 0.01 0.02 0.00 -0.02 -0.03 -0.04
## 593 0.01 -0.02 0.00 0.05 0.01 -0.05 0.01 -0.10
## 620 -0.03 0.04 -0.02 0.01 0.04 0.01 -0.24 -0.24
## 632 0.00 0.01 -0.02 -0.03 -0.02 0.03 -0.01 -0.05
## 643 0.09 -0.21 0.20 0.47 -0.15 -0.31 -0.04 0.51_*
## 644 0.22 -0.31 0.18 0.14 0.06 -0.17 0.04 -0.34_*
## 656 0.01 -0.02 0.02 0.02 0.01 -0.02 -0.02 -0.03
## 663 0.03 0.01 -0.03 -0.05 0.03 0.04 -0.01 0.10
## 665 0.00 -0.01 0.02 0.02 -0.01 -0.03 -0.03 -0.05
## 668 -0.05 0.06 -0.03 0.01 0.06 0.02 -0.40 -0.40_*
## 669 -0.08 0.17 -0.13 -0.15 -0.05 0.18 -0.03 0.26_*
## 671 -0.06 0.05 0.08 0.02 -0.01 -0.07 -0.01 0.16
## 674 0.00 0.00 0.00 0.00 0.00 0.00 -0.01 -0.01
## 675 -0.08 0.16 -0.13 -0.15 0.20 0.14 -0.02 0.34_*
## 677 0.42 -0.35 -0.09 0.05 0.12 0.10 -0.05 0.49_*
## 679 0.01 0.00 0.00 0.00 -0.02 0.00 -0.03 -0.04
## 680 -0.10 0.20 -0.10 -0.10 0.01 0.09 0.01 0.29_*
## 682 0.41 -0.35 -0.11 0.01 0.24 0.12 -0.06 0.51_*
## 686 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
## 687 -0.15 0.17 0.01 0.01 -0.04 -0.03 -0.02 0.22
## 688 0.04 -0.02 0.02 0.00 0.02 0.00 -0.01 0.11
## 689 0.04 0.02 -0.06 -0.05 0.04 0.06 -0.01 0.12
## 690 0.03 -0.06 0.13 0.06 0.00 -0.10 0.00 0.16
## 691 -0.05 0.06 0.04 -0.02 0.00 -0.02 -0.01 0.14
## 694 -0.06 0.06 0.03 -0.04 0.12 0.00 -0.02 0.21
## 699 -0.12 0.16 0.02 0.02 -0.03 -0.06 0.01 0.27_*
## 700 -0.03 0.03 -0.01 -0.07 0.19 0.04 -0.04 0.24
## 701 0.00 0.00 0.00 0.00 0.00 0.00 -0.01 -0.01
## 704 -0.23 0.28 0.01 -0.13 -0.03 0.05 0.00 0.39_*
## 705 0.01 -0.02 0.02 0.02 -0.01 -0.02 -0.03 -0.05
## 707 -0.09 0.13 -0.06 -0.08 0.17 0.05 -0.02 0.31_*
## 708 -0.02 0.17 -0.29 0.08 -0.01 -0.10 0.04 -0.64_*
## 713 0.00 0.00 0.00 0.01 0.00 0.00 0.00 0.01
## 714 0.81 -0.72 -0.06 0.08 0.24 0.09 0.06 0.88_*
## 718 -0.12 0.36 -0.40 -0.25 0.05 0.31 0.00 0.50_*
## 720 -0.45 0.38 0.29 0.19 -0.18 -0.31 0.07 0.71_*
## 724 -0.06 0.17 -0.18 -0.25 0.21 0.22 -0.03 0.37_*
## 725 0.02 0.04 -0.08 -0.06 0.04 0.06 -0.03 0.12
## 727 -0.07 0.17 -0.16 -0.23 0.22 0.20 -0.02 0.38_*
## 731 0.04 0.13 -0.24 -0.17 -0.02 0.22 -0.03 0.28_*
## 735 -0.10 0.12 -0.01 -0.03 0.16 -0.01 -0.02 0.30_*
## 736 -0.03 0.03 -0.01 -0.07 0.19 0.04 -0.04 0.24
## 737 0.00 0.00 0.00 0.00 0.00 0.00 -0.01 -0.01
## 740 -0.23 0.28 0.01 -0.13 -0.03 0.05 0.00 0.39_*
## 741 0.01 -0.02 0.02 0.02 -0.01 -0.02 -0.03 -0.05
## 743 -0.09 0.13 -0.06 -0.08 0.17 0.05 -0.02 0.31_*
## 744 0.00 0.05 -0.09 0.02 0.02 -0.03 0.01 -0.20
## 749 0.00 0.00 0.00 0.01 0.00 0.00 0.00 0.01
## 750 0.82 -0.77 -0.14 -0.07 0.72 0.20 -0.02 1.09_*
## 752 0.08 0.24 -0.48 -0.33 -0.04 0.43 -0.05 0.55_*
## 755 0.02 0.00 0.00 -0.01 -0.11 -0.01 -0.02 -0.14
## 756 0.18 -0.07 -0.14 -0.33 0.43 0.29 0.06 0.60_*
## 757 0.03 -0.03 0.01 -0.03 0.10 0.01 -0.02 0.13
## 759 0.03 -0.01 -0.04 -0.02 0.09 0.03 -0.03 0.12
## 760 0.05 0.00 0.00 0.03 0.03 -0.03 0.01 0.18
## 764 0.13 -0.10 0.00 -0.03 0.06 0.03 0.00 0.15
## 766 0.03 0.00 -0.04 -0.06 0.11 0.05 -0.02 0.14
## 767 0.04 0.00 -0.05 -0.07 0.13 0.05 -0.02 0.16
## 930 0.03 -0.01 -0.04 -0.02 -0.01 0.03 0.00 -0.06
## 946 0.09 -0.01 -0.01 -0.11 -0.32 0.10 0.07 -0.41_*
## cov.r cook.d hat
## 101 1.02_* 0.00 0.01
## 141 1.03_* 0.00 0.02_*
## 157 1.03_* 0.00 0.02_*
## 204 1.08_* 0.03 0.08_*
## 348 1.32_* 0.15 0.25_*
## 349 1.09_* 0.01 0.08_*
## 355 1.05_* 0.00 0.04_*
## 358 1.05_* 0.00 0.04_*
## 446 3.56_* 1.01_* 0.72_*
## 482 1.06_* 0.00 0.05_*
## 508 1.04_* 0.00 0.04_*
## 574 1.03_* 0.00 0.02_*
## 583 1.12_* 0.01 0.10_*
## 590 1.05_* 0.01 0.05_*
## 591 1.02_* 0.00 0.02
## 593 1.05_* 0.00 0.04_*
## 620 1.46_* 0.01 0.31_*
## 632 1.05_* 0.00 0.04_*
## 643 1.14_* 0.04 0.13_*
## 644 1.14_* 0.02 0.12_*
## 656 1.03_* 0.00 0.02_*
## 663 0.96_* 0.00 0.00
## 665 1.05_* 0.00 0.04_*
## 668 1.76_* 0.02 0.43_*
## 669 0.99 0.01 0.01
## 671 0.95_* 0.00 0.00
## 674 1.03_* 0.00 0.02
## 675 0.79_* 0.02 0.00
## 677 0.92_* 0.03 0.02
## 679 1.03_* 0.00 0.02_*
## 680 0.78_* 0.01 0.00
## 682 0.93_* 0.04 0.02
## 686 1.02_* 0.00 0.01
## 687 0.95_* 0.01 0.00
## 688 0.94_* 0.00 0.00
## 689 0.94_* 0.00 0.00
## 690 0.95_* 0.00 0.00
## 691 0.96_* 0.00 0.00
## 694 0.91_* 0.01 0.00
## 699 0.79_* 0.01 0.00
## 700 0.95_* 0.01 0.01
## 701 1.11_* 0.00 0.09_*
## 704 0.84_* 0.02 0.01
## 705 1.02_* 0.00 0.02
## 707 0.81_* 0.01 0.00
## 708 1.77_* 0.06 0.43_*
## 713 1.05_* 0.00 0.04_*
## 714 0.67_* 0.10 0.01
## 718 0.74_* 0.03 0.01
## 720 0.59_* 0.07 0.01
## 724 0.84_* 0.02 0.00
## 725 0.97_* 0.00 0.00
## 727 0.80_* 0.02 0.00
## 731 0.94_* 0.01 0.01
## 735 0.81_* 0.01 0.00
## 736 0.95_* 0.01 0.01
## 737 1.11_* 0.00 0.09_*
## 740 0.84_* 0.02 0.01
## 741 1.02_* 0.00 0.02
## 743 0.81_* 0.01 0.00
## 744 1.78_* 0.01 0.44_*
## 749 1.05_* 0.00 0.04_*
## 750 0.70_* 0.16 0.02
## 752 0.77_* 0.04 0.01
## 755 1.03_* 0.00 0.02_*
## 756 0.52_* 0.05 0.00
## 757 0.97_* 0.00 0.00
## 759 0.97_* 0.00 0.00
## 760 0.83_* 0.00 0.00
## 764 0.95_* 0.00 0.00
## 766 0.97_* 0.00 0.00
## 767 0.95_* 0.00 0.00
## 930 1.02_* 0.00 0.02
## 946 1.08_* 0.02 0.08_*
outliers <- which(influence$infmat[, "hat"] > (2 * mean(influence$infmat[, "hat"])))
data_clean <- data[-outliers, ]
model7 <- lm(Harga ~ `Kamar Tidur` + `Kamar Mandi` + `Luas Tanah`+`Luas Bangunan` + `Garasi` + `Cicilan`, data = data_clean)
summary(model7)
##
## Call:
## lm(formula = Harga ~ `Kamar Tidur` + `Kamar Mandi` + `Luas Tanah` +
## `Luas Bangunan` + Garasi + Cicilan, data = data_clean)
##
## Residuals:
## Min 1Q Median 3Q Max
## -124.77 -22.46 -8.95 -0.02 691.56
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2.34040 8.70005 0.269 0.788
## `Kamar Tidur` 3.98904 3.88762 1.026 0.305
## `Kamar Mandi` -2.61256 3.35308 -0.779 0.436
## `Luas Tanah` -0.20400 0.04375 -4.663 3.56e-06 ***
## `Luas Bangunan` 0.17681 0.03801 4.652 3.74e-06 ***
## Garasi 13.50445 3.11676 4.333 1.63e-05 ***
## Cicilan 0.48938 0.33893 1.444 0.149
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 72.21 on 964 degrees of freedom
## Multiple R-squared: 0.08739, Adjusted R-squared: 0.08171
## F-statistic: 15.39 on 6 and 964 DF, p-value: < 2.2e-16
t.test(model7$residuals,mu = 0,conf.level=0.95)
##
## One Sample t-test
##
## data: model7$residuals
## t = -6.7414e-16, df = 970, p-value = 1
## alternative hypothesis: true mean is not equal to 0
## 95 percent confidence interval:
## -4.533338 4.533338
## sample estimates:
## mean of x
## -1.557309e-15
dwtest(model7)
##
## Durbin-Watson test
##
## data: model7
## DW = 1.4824, p-value = 2.505e-16
## alternative hypothesis: true autocorrelation is greater than 0
bptest(model7)
##
## studentized Breusch-Pagan test
##
## data: model7
## BP = 42.271, df = 6, p-value = 1.626e-07
ks.test(model7$residuals, "pnorm", mean(model7$residuals), sd(model7$residuals))
## Warning in ks.test.default(model7$residuals, "pnorm", mean(model7$residuals), :
## ties should not be present for the one-sample Kolmogorov-Smirnov test
##
## Asymptotic one-sample Kolmogorov-Smirnov test
##
## data: model7$residuals
## D = 0.34814, p-value < 2.2e-16
## alternative hypothesis: two-sided
shapiro.test(model7$residuals)
##
## Shapiro-Wilk normality test
##
## data: model7$residuals
## W = 0.4374, p-value < 2.2e-16
Kuadrat Non Outlier
model8 <- lm(1/Harga ~ `Kamar Tidur` + `Kamar Mandi` + `Luas Tanah` + `Garasi` + `Luas Bangunan` + `Cicilan`, data = data_clean)
summary(model8)
##
## Call:
## lm(formula = 1/Harga ~ `Kamar Tidur` + `Kamar Mandi` + `Luas Tanah` +
## Garasi + `Luas Bangunan` + Cicilan, data = data_clean)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.6931 -0.3056 -0.0660 0.1994 9.0184
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.9871235 0.0753193 26.383 < 2e-16 ***
## `Kamar Tidur` -0.1652884 0.0336564 -4.911 1.06e-06 ***
## `Kamar Mandi` -0.2297790 0.0290287 -7.916 6.74e-15 ***
## `Luas Tanah` -0.0004239 0.0003787 -1.119 0.26335
## Garasi -0.0075801 0.0269828 -0.281 0.77883
## `Luas Bangunan` 0.0001028 0.0003290 0.313 0.75471
## Cicilan -0.0081541 0.0029342 -2.779 0.00556 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.6251 on 964 degrees of freedom
## Multiple R-squared: 0.3245, Adjusted R-squared: 0.3202
## F-statistic: 77.16 on 6 and 964 DF, p-value: < 2.2e-16
t.test(model8$residuals,mu = 0,conf.level=0.95)
##
## One Sample t-test
##
## data: model8$residuals
## t = -1.8484e-15, df = 970, p-value = 1
## alternative hypothesis: true mean is not equal to 0
## 95 percent confidence interval:
## -0.03924663 0.03924663
## sample estimates:
## mean of x
## -3.696674e-17
dwtest(model8)
##
## Durbin-Watson test
##
## data: model8
## DW = 1.4579, p-value < 2.2e-16
## alternative hypothesis: true autocorrelation is greater than 0
bptest(model8)
##
## studentized Breusch-Pagan test
##
## data: model8
## BP = 10.205, df = 6, p-value = 0.1163
ks.test(model8$residuals, "pnorm", mean(model8$residuals), sd(model8$residuals))
## Warning in ks.test.default(model8$residuals, "pnorm", mean(model8$residuals), :
## ties should not be present for the one-sample Kolmogorov-Smirnov test
##
## Asymptotic one-sample Kolmogorov-Smirnov test
##
## data: model8$residuals
## D = 0.12987, p-value = 1.191e-14
## alternative hypothesis: two-sided
shapiro.test(model8$residuals)
##
## Shapiro-Wilk normality test
##
## data: model8$residuals
## W = 0.72478, p-value < 2.2e-16
vif(model8)
## `Kamar Tidur` `Kamar Mandi` `Luas Tanah` Garasi `Luas Bangunan`
## 2.243711 2.267869 2.591888 1.295912 3.374868
## Cicilan
## 2.758751
Regresi Lasso
# Install glmnet if necessary
library(glmnet)
## Warning: package 'glmnet' was built under R version 4.5.3
## Loading required package: Matrix
## Loaded glmnet 5.1
# Misalkan data sudah ada dalam variabel x (prediktor) dan y (respons)
x <- model.matrix(I(Harga^2) ~ `Kamar Tidur` + `Kamar Mandi` + `Luas Tanah`+`Luas Bangunan` + Garasi + Cicilan, data=data)[,-1]
y <- data$Harga
# Lakukan regresi Lasso
lasso_model <- glmnet(x, y, alpha = 1)
# Untuk cross-validation dan memilih nilai lambda yang optimal
cv_lasso <- cv.glmnet(x, y, alpha = 1)
best_lambda <- cv_lasso$lambda.min
# Lihat koefisien model pada lambda terbaik
coef(lasso_model, s = best_lambda)
## 7 x 1 sparse Matrix of class "dgCMatrix"
## s=1.045058
## (Intercept) 9.054449199
## `Kamar Tidur` 0.747238204
## `Kamar Mandi` .
## `Luas Tanah` -0.027414594
## `Luas Bangunan` 0.024309742
## Garasi 11.813302110
## Cicilan 0.004905426
# Variabel yang dipilih oleh Lasso (koefisien tidak nol)
selected_vars <- rownames(coef(lasso_model, s = best_lambda))[which(coef(lasso_model, s = best_lambda) != 0)]
# Membuat model linier berdasarkan variabel yang dipilih oleh Lasso
formula_lasso <- as.formula(paste("Harga ~", paste(selected_vars[-1], collapse = " + "))) # -1 untuk menghapus intercept
ols_model <- lm(formula_lasso, data = data_clean)
# Lihat ringkasan model OLS
summary(ols_model)
##
## Call:
## lm(formula = formula_lasso, data = data_clean)
##
## Residuals:
## Min 1Q Median 3Q Max
## -120.54 -22.83 -9.16 -0.09 691.43
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2.0729 8.6915 0.239 0.812
## `Kamar Tidur` 2.3969 3.3066 0.725 0.469
## `Luas Tanah` -0.2025 0.0437 -4.634 4.08e-06 ***
## `Luas Bangunan` 0.1720 0.0375 4.587 5.08e-06 ***
## Garasi 13.1424 3.0813 4.265 2.19e-05 ***
## Cicilan 0.4661 0.3375 1.381 0.168
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 72.19 on 965 degrees of freedom
## Multiple R-squared: 0.08682, Adjusted R-squared: 0.08208
## F-statistic: 18.35 on 5 and 965 DF, p-value: < 2.2e-16
t.test(ols_model$residuals,mu = 0,conf.level=0.95)
##
## One Sample t-test
##
## data: ols_model$residuals
## t = -3.8831e-15, df = 970, p-value = 1
## alternative hypothesis: true mean is not equal to 0
## 95 percent confidence interval:
## -4.534765 4.534765
## sample estimates:
## mean of x
## -8.973089e-15
dwtest(ols_model)
##
## Durbin-Watson test
##
## data: ols_model
## DW = 1.4801, p-value < 2.2e-16
## alternative hypothesis: true autocorrelation is greater than 0
bptest(ols_model)
##
## studentized Breusch-Pagan test
##
## data: ols_model
## BP = 40.592, df = 5, p-value = 1.134e-07
ks.test(ols_model$residuals, "pnorm", mean(ols_model$residuals), sd(ols_model$residuals))
## Warning in ks.test.default(ols_model$residuals, "pnorm",
## mean(ols_model$residuals), : ties should not be present for the one-sample
## Kolmogorov-Smirnov test
##
## Asymptotic one-sample Kolmogorov-Smirnov test
##
## data: ols_model$residuals
## D = 0.34993, p-value < 2.2e-16
## alternative hypothesis: two-sided
shapiro.test(ols_model$residuals)
##
## Shapiro-Wilk normality test
##
## data: ols_model$residuals
## W = 0.43667, p-value < 2.2e-16
Regresi robust
library(robustbase)
## Warning: package 'robustbase' was built under R version 4.5.3
# Misalkan data sudah ada dalam variabel x (prediktor) dan y (respons)
x <- model.matrix(I(Harga^2) ~ `Kamar Tidur` + `Kamar Mandi` + `Luas Tanah` +`Luas Bangunan`+ Garasi + Cicilan, data=data)[,-1]
y <- data$Harga
# Membuat model regresi robust
robust_model <- lmrob(Harga ~ `Kamar Tidur` + `Kamar Mandi` + `Luas Tanah` +`Luas Bangunan`+ Garasi + Cicilan, data=data_clean)
# Ringkasan hasil model robust
summary(robust_model)
##
## Call:
## lmrob(formula = Harga ~ `Kamar Tidur` + `Kamar Mandi` + `Luas Tanah` + `Luas Bangunan` +
## Garasi + Cicilan, data = data_clean)
## \--> method = "MM"
## Residuals:
## Min 1Q Median 3Q Max
## -19.802649 -0.061399 0.009579 0.084637 758.817336
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.287e-01 1.159e-02 11.103 <2e-16 ***
## `Kamar Tidur` -1.882e-03 5.491e-03 -0.343 0.7319
## `Kamar Mandi` 2.016e-03 4.609e-03 0.437 0.6619
## `Luas Tanah` -6.476e-05 6.782e-05 -0.955 0.3399
## `Luas Bangunan` 2.673e-04 1.151e-04 2.322 0.0204 *
## Garasi 3.691e-03 3.974e-03 0.929 0.3533
## Cicilan 2.658e-01 9.319e-04 285.206 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Robust residual standard error: 0.1033
## Multiple R-squared: 0.9983, Adjusted R-squared: 0.9983
## Convergence in 13 IRWLS iterations
##
## Robustness weights:
## 101 observations c(173,174,175,185,213,216,217,231,232,427,526,548,549,599,618,637,638,640,641,642,643,644,645,646,647,648,649,650,651,652,653,654,655,656,657,658,659,660,661,662,663,664,665,666,667,668,669,670,671,672,673,674,675,676,677,678,680,682,683,684,685,686,687,688,689,690,691,692,693,694,695,696,697,698,699,700,701,702,703,704,705,706,707,708,709,710,713,714,715,716,717,718,719,720,721,722,723,724,725,726,727)
## are outliers with |weight| = 0 ( < 0.0001);
## 67 weights are ~= 1. The remaining 803 ones are summarized as
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.08723 0.91960 0.95710 0.94100 0.98820 0.99890
## Algorithmic parameters:
## tuning.chi bb tuning.psi refine.tol
## 1.548e+00 5.000e-01 4.685e+00 1.000e-07
## rel.tol scale.tol solve.tol zero.tol
## 1.000e-07 1.000e-10 1.000e-07 1.000e-10
## eps.outlier eps.x warn.limit.reject warn.limit.meanrw
## 1.030e-04 1.637e-09 5.000e-01 5.000e-01
## nResample max.it best.r.s k.fast.s k.max
## 500 50 2 1 200
## maxit.scale trace.lev mts compute.rd fast.s.large.n
## 200 0 1000 0 2000
## psi subsampling cov
## "bisquare" "nonsingular" ".vcov.avar1"
## compute.outlier.stats
## "SM"
## seed : int(0)
dwtest(robust_model)
##
## Durbin-Watson test
##
## data: robust_model
## DW = 1.4824, p-value = 2.505e-16
## alternative hypothesis: true autocorrelation is greater than 0
bptest(robust_model)
##
## studentized Breusch-Pagan test
##
## data: robust_model
## BP = 42.271, df = 6, p-value = 1.626e-07
ks.test(robust_model$residuals, "pnorm", mean(robust_model$residuals), sd(robust_model$residuals))
## Warning in ks.test.default(robust_model$residuals, "pnorm",
## mean(robust_model$residuals), : ties should not be present for the one-sample
## Kolmogorov-Smirnov test
##
## Asymptotic one-sample Kolmogorov-Smirnov test
##
## data: robust_model$residuals
## D = 0.49597, p-value < 2.2e-16
## alternative hypothesis: two-sided
shapiro.test(robust_model$residuals)
##
## Shapiro-Wilk normality test
##
## data: robust_model$residuals
## W = 0.24031, p-value < 2.2e-16
Regresi Quantile
library(quantreg)
## Warning: package 'quantreg' was built under R version 4.5.3
## Loading required package: SparseM
## Warning: package 'SparseM' was built under R version 4.5.3
##
## Attaching package: 'SparseM'
## The following object is masked from 'package:Matrix':
##
## det
quantile_model <- rq(I(Harga^2) ~ `Kamar Tidur` + `Kamar Mandi` + `Luas Tanah`+`Luas Bangunan` + Garasi + Cicilan, data = data, tau = 0.5) # Median regression
summary(quantile_model)
## Warning in summary.rq(quantile_model): 266 non-positive fis
##
## Call: rq(formula = I(Harga^2) ~ `Kamar Tidur` + `Kamar Mandi` + `Luas Tanah` +
## `Luas Bangunan` + Garasi + Cicilan, tau = 0.5, data = data)
##
## tau: [1] 0.5
##
## Coefficients:
## Value Std. Error t value Pr(>|t|)
## (Intercept) 8.07042 14.39373 0.56069 0.57513
## `Kamar Tidur` -8.47098 9.92308 -0.85366 0.39349
## `Kamar Mandi` -3.82215 1.94283 -1.96731 0.04942
## `Luas Tanah` -0.04061 0.08515 -0.47691 0.63353
## `Luas Bangunan` 0.21066 0.26389 0.79827 0.42490
## Garasi 1.33353 1.44286 0.92423 0.35559
## Cicilan 2.63520 2.62065 1.00555 0.31487
dwtest(quantile_model)
##
## Durbin-Watson test
##
## data: quantile_model
## DW = 1.9168, p-value = 0.08873
## alternative hypothesis: true autocorrelation is greater than 0
bptest(quantile_model)
##
## studentized Breusch-Pagan test
##
## data: quantile_model
## BP = 8.0494, df = 6, p-value = 0.2345
ks.test(quantile_model$residuals, "pnorm", mean(quantile_model$residuals), sd(quantile_model$residuals))
## Warning in ks.test.default(quantile_model$residuals, "pnorm",
## mean(quantile_model$residuals), : ties should not be present for the one-sample
## Kolmogorov-Smirnov test
##
## Asymptotic one-sample Kolmogorov-Smirnov test
##
## data: quantile_model$residuals
## D = 0.47739, p-value < 2.2e-16
## alternative hypothesis: two-sided
shapiro.test(quantile_model$residuals)
##
## Shapiro-Wilk normality test
##
## data: quantile_model$residuals
## W = 0.15938, p-value < 2.2e-16
# Pseudo R-squared calculation (as no adjusted R-squared is provided by rq)
pseudo_r_squared <- 1 - (quantile_model$rho / sum((data$Harga^2 - mean(data$Harga^2))^2))
# Residual Standard Error (RSE) approximation
n <- length(quantile_model$residuals)
p <- length(quantile_model$coefficients)
residuals <- quantile_model$residuals
rse <- sqrt(sum(residuals^2) / (n - p))
# Display results
cat("Pseudo R-squared: ", pseudo_r_squared, "\n")
## Pseudo R-squared: 0.9999978
cat("Residual Standard Error (RSE): ", rse, "\n")
## Residual Standard Error (RSE): 38968.26
Regresi
library(nlme)
##
## Attaching package: 'nlme'
## The following object is masked from 'package:dplyr':
##
## collapse
library(lmtest)
library(lme4)
## Warning: package 'lme4' was built under R version 4.5.3
## Registered S3 method overwritten by 'lme4':
## method from
## na.action.merMod car
##
## Attaching package: 'lme4'
## The following object is masked from 'package:nlme':
##
## lmList
# Misalkan data sudah ada dalam data_clean
# Membuat model GLS dengan heteroskedastisitas dan autokorelasi
gls_model_ar1 <- glm(I(Harga^2) ~ `Kamar Tidur` + `Kamar Mandi` + `Luas Tanah`+`Luas Bangunan` + Garasi + Cicilan, data = data)
# Ringkasan model GLS
summary(gls_model_ar1)
##
## Call:
## glm(formula = I(Harga^2) ~ `Kamar Tidur` + `Kamar Mandi` + `Luas Tanah` +
## `Luas Bangunan` + Garasi + Cicilan, data = data)
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 4301.444 3672.522 1.171 0.24177
## `Kamar Tidur` 985.926 1404.692 0.702 0.48292
## `Kamar Mandi` -1774.895 964.316 -1.841 0.06598 .
## `Luas Tanah` -25.248 9.205 -2.743 0.00620 **
## `Luas Bangunan` 20.547 7.553 2.720 0.00663 **
## Garasi 4912.488 1229.822 3.994 6.96e-05 ***
## Cicilan -3.298 26.912 -0.123 0.90249
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for gaussian family taken to be 1447544861)
##
## Null deviance: 1.4902e+12 on 1014 degrees of freedom
## Residual deviance: 1.4591e+12 on 1008 degrees of freedom
## AIC: 24299
##
## Number of Fisher Scoring iterations: 2
# Uji Durbin-Watson
dwtest(gls_model_ar1)
##
## Durbin-Watson test
##
## data: gls_model_ar1
## DW = 1.9168, p-value = 0.08873
## alternative hypothesis: true autocorrelation is greater than 0
# Uji Kolmogorov-Smirnov untuk normalitas residual
residuals_gls <- residuals(gls_model_ar1)
ks.test(residuals_gls, "pnorm", mean=mean(residuals_gls), sd=sd(residuals_gls))
## Warning in ks.test.default(residuals_gls, "pnorm", mean = mean(residuals_gls),
## : ties should not be present for the one-sample Kolmogorov-Smirnov test
##
## Asymptotic one-sample Kolmogorov-Smirnov test
##
## data: residuals_gls
## D = 0.42272, p-value < 2.2e-16
## alternative hypothesis: two-sided
shapiro.test(residuals_gls)
##
## Shapiro-Wilk normality test
##
## data: residuals_gls
## W = 0.24236, p-value < 2.2e-16
# Uji Breusch-Pagan untuk heteroskedastisitas
bptest(gls_model_ar1)
##
## studentized Breusch-Pagan test
##
## data: gls_model_ar1
## BP = 8.0494, df = 6, p-value = 0.2345
# Menghitung Pseudo R-squared (McFadden's R-squared)
null_model <- glm(I(Harga^2) ~ 1, data = data) # Model null tanpa prediktor
ll_full <- logLik(gls_model_ar1) # Log likelihood dari model penuh
ll_null <- logLik(null_model) # Log likelihood dari model null
pseudo_r_squared <- 1 - (as.numeric(ll_full) / as.numeric(ll_null))
# Menghitung Residual Standard Error (RSE)
n <- length(residuals_gls)
p <- length(coef(gls_model_ar1))
rss <- sum(residuals_gls^2) # Residual sum of squares
rse <- sqrt(rss / (n - p))
# Menampilkan hasil
cat("Pseudo R-squared (McFadden): ", pseudo_r_squared, "\n")
## Pseudo R-squared (McFadden): 0.0008809646
cat("Residual Standard Error (RSE): ", rse, "\n")
## Residual Standard Error (RSE): 38046.61