Small Area Estimation : Selecting Auxiliary Variables for the Number of Working and School Population
Dhiar Larasati
2025-05-06
Background
This report aims to select auxiliary variables to estimate the number of working and school population at metropolitan area in Central Jawa called Kedungsepur (Kab Kendal, Kab Demak, Kota Semarang, Kab Semarang, Kota Salatiga, Kab Grobogan) using small area estimation. The estimation using SAE estimation is documented on the other file.
- Librrary loading
library(readxl)
library(foreign)
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, unionlibrary(ggplot2)
library(reshape2)
library(sae)## Loading required package: MASS##
## Attaching package: 'MASS'## The following object is masked from 'package:dplyr':
##
## select## Loading required package: lme4## Loading required package: Matrixlibrary(tidyr)##
## Attaching package: 'tidyr'## The following objects are masked from 'package:Matrix':
##
## expand, pack, unpack## The following object is masked from 'package:reshape2':
##
## smithslibrary(haven)
library(survey)## Loading required package: grid## Loading required package: survival##
## Attaching package: 'survey'## The following object is masked from 'package:graphics':
##
## dotchartlibrary(stringr)
2. Prepare Dataset
#READ PODES DATA
list_wm33<- c("3315", "3321", "3322", "3324", "3373", "3374")
podes1 <- read.dbf("podes2024_desa_01.dbf") %>%
mutate (kode_kab=substr(as.character(IDDESA), 1, 4)) %>%
filter(kode_kab %in% list_wm33)
podes2 <- read.dbf("podes2024_desa_02.dbf") %>%
mutate (kode_kab=substr(as.character(IDDESA), 1, 4)) %>%
filter(kode_kab %in% list_wm33)
podes3 <- read.dbf("podes2024_desa_03.dbf") %>%
mutate (kode_kab=substr(as.character(IDDESA), 1, 4)) %>%
filter(kode_kab %in% list_wm33)
podes4 <- read.dbf("podes2024_desa_04.dbf") %>%
mutate (kode_kab=substr(as.character(IDDESA), 1, 4)) %>%
filter(kode_kab %in% list_wm33)
podes <- cbind(
podes1,
podes2[, setdiff(names(podes2), names(podes1))],
podes3[, setdiff(names(podes3), names(podes1))],
podes4[, setdiff(names(podes4), names(podes1))]
)
podes_selected <- podes %>%
dplyr::select(R101, R102, R103, IDDESA,R105,R1005A, R701DK2, R701DK3, R701EK2, R701EK3, R701FK2, R701FK3,
R701GK2, R701GK3, R701HK2, R701HK3, R701IK2, R701IK3, R701JK2, R701JK3, R701KK2, R701KK3, R403A,
R1201A1, R1201A2, R1201A3, R1201A4, R1201A5, R1201A6, R1201A7, R1201A8, R1201A9, R1201A10, R1201A11,
R1201A12, R1201A13, R1201A14, R1201A15, R1201A16, R1205A1, R1205A2, R1205A3, R1206A1, R1206A2, R1206A3,
R1206A4, R1209AK2, R1209BK2, R1209CK2, R1209DK2, R1209EK2, R1209FK2, R1209GK2, R1209HK2, R1209IK2,
R1209JK2, R1207A, R1207B, R1207C, R1207D, R710, R501A1, R501A2, R501B, R704AK2, R704BK2, R704CK2,
R704DK2, R704EK2, R704FK2, R704GK2, R704HK2, R704IK2, R704JK2, R704KK2, R704LK2, R704MK2, R703AK2,
R703AK3, R703BK2, R703BK3, R703CK2, R703CK3, R703DK2, R703DK3, R703EK2, R703EK3, R703FK2, R703FK3,
R703GK2, R703GK3, R1501A_K3, R1501B_K3, R1501C_K3, R513B3, R508A, R508B, R506A, R506B, R1001B2,
R1005D, R706A1, R706A2, R706B, R706C, R706D,R1001A, R1001C1, R1001B2, R1005C)
podes_selected <- podes_selected %>%
mutate(IDKAB = str_replace_all(paste(R101,R102)," ",""))
podes_selected <- podes_selected %>%
mutate(IDAREA = str_replace_all(paste(IDKAB,R103)," ",""))
#READ DE DATA
estimate <- read_xlsx("estimate_1.xlsx") %>%
mutate(IDKAB = as.character(IDKAB),
IDKEC = as.character(IDKEC))
estimate <- estimate %>%
mutate(IDAREA = str_replace_all(paste(IDKAB,IDKEC)," ",""))
3. Prepare variables from PODES data
podes_selected <- podes_selected %>%
mutate(
sum_klg=R501A1+R501A2+R501B,
sum_sd=R701DK2+R701DK3+R701EK2+R701EK3,
sum_smp=R701FK2+R701FK3+R701GK2+R701GK3,
sum_sma=R701HK2+R701HK3+R701IK2+R701IK3+R701JK2+R701JK3,
sum_pt=R701KK2+R701KK3,
sum_desa_agri=case_when(R403A==1 ~1, TRUE ~0),
sum_desa_nonagri=case_when(R403A>1 ~1, TRUE ~0),
sum_imk=R1201A1+R1201A2+R1201A3+R1201A4+R1201A5+R1201A6+R1201A7+R1201A8+R1201A9+R1201A10+R1201A11+R1201A12+R1201A13+R1201A14+R1201A15+R1201A16,
sum_bank=R1205A1+R1205A2+R1205A3,
sum_koperasi=R1206A1+R1206A2+R1206A3+R1206A4,
sum_kredit=case_when(R1207A == 1 |R1207B == 1 | R1207C == 1 |R1207D == 1 ~ 1, TRUE ~0 ),
sum_eko=R1209AK2+R1209BK2+R1209CK2+R1209DK2+R1209EK2+R1209FK2+R1209GK2+R1209HK2+R1209IK2+R1209JK2,
sum_sktm=R710,
sum_health=R704AK2+R704BK2+R704CK2+R704DK2+R704EK2+R704FK2+R704GK2+R704HK2+R704IK2+R704JK2+R704KK2+R704LK2+R704MK2,
sum_skill=R703AK2+R703AK3+R703BK2+R703BK3+R703CK2+R703CK3+R703DK2+R703DK3+R703EK2+R703EK3+R703FK2+R703FK3+R703GK2+R703GK3,
sum_blt= R1501A_K3+R1501B_K3,
sum_padatkarya=R1501C_K3,
sum_kumuh=R513B3,
air=case_when(R508A==3 | R508A==4 | R508A==5 |R508A==9 ~1,
R508A<=2 & R508B==1~1,
R508A<=2 & R508B==2~1,
R508A<=2 & R508B==3~1,
R508A<=2 & R508B==7~1,
TRUE ~ 0),
sanitasi=case_when(R506A<=2 & R506B==1 ~ 1,
TRUE ~ 0),
akses_jalan=case_when((R1001A==1 | R1001A==3) & R1001B2==1 ~1, TRUE ~0),
sinyalinet=case_when(R1005C==1 | R1005C==2 ~1, TRUE ~0),
medis=R706A1+R706A2+R706B+R706C+R706D,
angk_umum=case_when(R1001C1==1 | R1001C1==2 ~1, TRUE ~0)
)
podes_var <- podes_selected %>%
group_by(IDAREA) %>%
summarise(
prop_bts=round(sum(R1005A, na.rm = TRUE)/ sum(sum_klg, na.rm = TRUE)*100,2),
prop_perdesaan = round(sum(case_when(R105 == 2 ~ 1, TRUE ~ 0))/n()*100,2),
prop_sd = round(sum(sum_sd, na.rm = TRUE) / sum(sum_klg, na.rm = TRUE)*100,2),
jml_sd = sum(sum_sd, na.rm = TRUE),
prop_smp =round(sum(sum_smp, na.rm = TRUE) / sum(sum_klg, na.rm = TRUE)*100,2),
jml_smp = sum(sum_smp, na.rm = TRUE),
prop_sma = round(sum(sum_sma, na.rm = TRUE) / sum(sum_klg, na.rm = TRUE)*100,2),
jml_sma = sum(sum_sma, na.rm = TRUE),
prop_pt = round(sum(sum_pt, na.rm = TRUE) / sum(sum_klg, na.rm = TRUE)*100,2),
jml_pt = sum(sum_pt, na.rm = TRUE),
prop_desaagri=round(sum(sum_desa_agri)/n()*100,2),
prop_desanonagri=round(sum(sum_desa_nonagri)/n()*100,2),
prop_imk = round(sum(sum_imk, na.rm = TRUE) / sum(sum_klg, na.rm = TRUE)*100,2),
jml_imk = sum(sum_imk, na.rm = TRUE),
prop_bank= round(sum(sum_bank, na.rm = TRUE)/ sum(sum_klg, na.rm = TRUE)*100,2),
jml_bank = sum(sum_bank, na.rm = TRUE),
prop_koperasi=round(sum(sum_koperasi, na.rm = TRUE)/ sum(sum_klg, na.rm = TRUE)*100,2),
jml_koperasi = sum(sum_koperasi, na.rm = TRUE),
prop_eko=round(sum(sum_eko, na.rm = TRUE)/ sum(sum_klg, na.rm = TRUE)*100,2),
jml_eko = sum(sum_eko, na.rm = TRUE),
prop_kredit=round(sum(sum_kredit, na.rm = TRUE)/sum(sum_klg, na.rm = TRUE)*100,2),
jml_kredit = sum(sum_kredit, na.rm = TRUE),
prop_sktm = round(sum(sum_sktm, na.rm = TRUE) / sum(sum_klg, na.rm = TRUE)*100,2),
prop_health=round(sum(sum_health, na.rm = TRUE)/ sum(sum_klg, na.rm = TRUE)*100,2),
jml_health = sum(sum_health, na.rm = TRUE),
prop_skill=round(sum(sum_skill, na.rm = TRUE)/ sum(sum_klg, na.rm = TRUE)*100,2),
prop_blt = round(sum(sum_blt, na.rm = TRUE) / sum(sum_klg, na.rm = TRUE)*100,2) ,
prop_padatkarya = round(sum(sum_padatkarya, na.rm = TRUE) / sum(sum_klg, na.rm = TRUE)*100,2),
prop_kumuh = round(sum(sum_kumuh, na.rm = TRUE) / sum(sum_klg, na.rm = TRUE)*100,2),
prop_air=round(sum(air)/n()*100,2) ,
prop_sani= round(sum(sanitasi)/n()*100,2),
prop_aksesjalan=round(sum(akses_jalan)/n()*100,2) ,
prop_sinyalinet=round(sum(sinyalinet)/n()*100,2) ,
prop_medis = round(sum(medis, na.rm = TRUE) / sum(sum_klg, na.rm = TRUE)*100,2),
jml_medis = sum(medis, na.rm = TRUE),
prop_angkumum=round(sum(angk_umum)/n()*100,2)
)
4. join Direct Estimate Data with auxiliary data from PODES
#join data set
sae_var <- left_join(podes_var,dplyr::select(estimate,IDAREA,ESTIMATE,RSE),podes_var, by = "IDAREA")
sae_var <- sae_var %>%
na.omit()
sae_eda <-na.omit(sae_var %>%
dplyr::select(!c(IDAREA,RSE)))
5. initial data exploration
#histogram
par(mfrow = c(3,3))
for (var in names(sae_eda[1:9])) {
hist(sae_eda[[var]],
main = paste("Histogram", var),
xlab = var,
col = "skyblue",
border = "black")
}
par(mfrow = c(3,3))
for (var in names(sae_eda[10:18])) {
hist(sae_eda[[var]],
main = paste("Histogram", var),
xlab = var,
col = "skyblue",
border = "black")
}
par(mfrow = c(3,3))
for (var in names(sae_eda[19:27])) {
hist(sae_eda[[var]],
main = paste("Histogram", var),
xlab = var,
col = "skyblue",
border = "black")
}
par(mfrow = c(2,3))
for (var in names(sae_eda[28:32])) {
hist(sae_eda[[var]],
main = paste("Histogram", var),
xlab = var,
col = "skyblue",
border = "black")
}
par(mfrow = c(2,3))
for (var in names(sae_eda[33:37])) {
hist(sae_eda[[var]],
main = paste("Histogram", var),
xlab = var,
col = "skyblue",
border = "black")
}
dev.off() ## null device
## 1par(mfrow = c(1, 1))##correlation checking
summary(sae_eda)## prop_bts prop_perdesaan prop_sd jml_sd
## Min. :0.02000 Min. : 0.00 Min. :0.0800 Min. :19.00
## 1st Qu.:0.07000 1st Qu.: 0.00 1st Qu.:0.1400 1st Qu.:30.00
## Median :0.08000 Median :24.27 Median :0.1700 Median :36.00
## Mean :0.08011 Mean :29.98 Mean :0.1653 Mean :38.96
## 3rd Qu.:0.09000 3rd Qu.:54.07 3rd Qu.:0.1800 3rd Qu.:48.00
## Max. :0.13000 Max. :91.67 Max. :0.2800 Max. :77.00
## prop_smp jml_smp prop_sma jml_sma
## Min. :0.0200 Min. : 3.00 Min. :0.00000 Min. : 1.000
## 1st Qu.:0.0400 1st Qu.: 7.00 1st Qu.:0.02000 1st Qu.: 3.000
## Median :0.0500 Median : 9.50 Median :0.03000 Median : 7.000
## Mean :0.0463 Mean :11.39 Mean :0.03022 Mean : 7.924
## 3rd Qu.:0.0600 3rd Qu.:15.00 3rd Qu.:0.04000 3rd Qu.:11.000
## Max. :0.0800 Max. :42.00 Max. :0.09000 Max. :37.000
## prop_pt jml_pt prop_desaagri prop_desanonagri
## Min. :0.000 Min. : 0.000 Min. : 0.00 Min. : 0.00
## 1st Qu.:0.000 1st Qu.: 0.000 1st Qu.: 8.38 1st Qu.: 14.05
## Median :0.000 Median : 0.000 Median : 50.00 Median : 50.00
## Mean :0.005 Mean : 1.402 Mean : 50.05 Mean : 49.95
## 3rd Qu.:0.010 3rd Qu.: 2.000 3rd Qu.: 85.95 3rd Qu.: 91.62
## Max. :0.070 Max. :16.000 Max. :100.00 Max. :100.00
## prop_imk jml_imk prop_bank jml_bank
## Min. : 0.260 Min. : 115.0 Min. :0.00000 Min. : 0.000
## 1st Qu.: 1.375 1st Qu.: 335.0 1st Qu.:0.01000 1st Qu.: 2.000
## Median : 2.135 Median : 495.5 Median :0.02000 Median : 5.000
## Mean : 3.019 Mean : 664.6 Mean :0.03761 Mean : 9.804
## 3rd Qu.: 3.002 3rd Qu.: 703.5 3rd Qu.:0.05000 3rd Qu.:13.000
## Max. :33.750 Max. :5472.0 Max. :0.38000 Max. :87.000
## prop_koperasi jml_koperasi prop_eko jml_eko
## Min. :0.00000 Min. : 0.00 Min. :2.420 Min. : 345.0
## 1st Qu.:0.02000 1st Qu.: 6.00 1st Qu.:3.655 1st Qu.: 707.2
## Median :0.04000 Median :10.00 Median :4.240 Median :1051.5
## Mean :0.04728 Mean :11.16 Mean :4.424 Mean :1093.6
## 3rd Qu.:0.06000 3rd Qu.:15.00 3rd Qu.:4.968 3rd Qu.:1331.5
## Max. :0.22000 Max. :38.00 Max. :9.290 Max. :3073.0
## prop_kredit jml_kredit prop_sktm prop_health
## Min. :0.01000 Min. : 1.00 Min. : 0.010 Min. :0.1100
## 1st Qu.:0.04000 1st Qu.: 9.00 1st Qu.: 1.657 1st Qu.:0.2400
## Median :0.05500 Median :12.00 Median : 2.975 Median :0.2800
## Mean :0.05707 Mean :12.63 Mean : 3.543 Mean :0.2857
## 3rd Qu.:0.07000 3rd Qu.:16.00 3rd Qu.: 4.713 3rd Qu.:0.3200
## Max. :0.13000 Max. :28.00 Max. :15.400 Max. :0.5300
## jml_health prop_skill prop_blt prop_padatkarya
## Min. : 20.00 Min. :0.00000 Min. : 0.000 Min. : 0.0000
## 1st Qu.: 48.00 1st Qu.:0.01000 1st Qu.: 1.867 1st Qu.: 0.1075
## Median : 63.00 Median :0.02000 Median : 4.450 Median : 1.5700
## Mean : 70.10 Mean :0.03185 Mean : 4.039 Mean : 2.9309
## 3rd Qu.: 80.25 3rd Qu.:0.05250 3rd Qu.: 5.912 3rd Qu.: 4.1075
## Max. :186.00 Max. :0.19000 Max. :16.850 Max. :26.6200
## prop_kumuh prop_air prop_sani prop_aksesjalan
## Min. :0.0000 Min. : 0.00 Min. : 0.00 Min. : 92.31
## 1st Qu.:0.0000 1st Qu.: 62.26 1st Qu.:100.00 1st Qu.:100.00
## Median :0.0000 Median : 93.49 Median :100.00 Median :100.00
## Mean :0.2727 Mean : 76.10 Mean : 94.22 Mean : 99.73
## 3rd Qu.:0.0300 3rd Qu.:100.00 3rd Qu.:100.00 3rd Qu.:100.00
## Max. :5.4000 Max. :100.00 Max. :100.00 Max. :100.00
## prop_sinyalinet prop_medis jml_medis prop_angkumum
## Min. : 53.85 Min. :0.1900 Min. : 30.00 Min. : 15.00
## 1st Qu.: 94.86 1st Qu.:0.3900 1st Qu.: 76.75 1st Qu.: 95.11
## Median :100.00 Median :0.4950 Median :121.00 Median :100.00
## Mean : 96.91 Mean :0.5473 Mean :135.71 Mean : 93.09
## 3rd Qu.:100.00 3rd Qu.:0.6525 3rd Qu.:157.50 3rd Qu.:100.00
## Max. :100.00 Max. :1.5400 Max. :479.00 Max. :100.00
## ESTIMATE
## Min. : 11750
## 1st Qu.: 30451
## Median : 39503
## Mean : 45088
## 3rd Qu.: 53786
## Max. :168045library(corrplot)## corrplot 0.92 loaded?corrplot
cor_matrix <- cor(sae_eda, method = "pearson")
corrplot(cor_matrix, method = "number", type = "upper", tl.cex = 0.7, number.cex = 0.5, number.digits = 2)
#correlation table
cor_df <- data.frame(Variable = rownames(cor_matrix), cor_matrix, row.names = NULL)
cor_value <- cor_df %>%
dplyr::select(Variable,ESTIMATE)
#correlation p-value
cor.mtest <- function(mat) {
mat <- as.matrix(mat)
n <- ncol(mat)
p.mat <- matrix(NA, n, n)
diag(p.mat) <- 0
for (i in 1:(n - 1)) {
for (j in (i + 1):n) {
tmp <- cor.test(mat[, i], mat[, j])
p.mat[i, j] <- p.mat[j, i] <- tmp$p.value
}
}
colnames(p.mat) <- rownames(p.mat) <- colnames(mat)
return(p.mat)
}
p_matrix <- cor.mtest(sae_eda)
cor_pvalue <- as.data.frame(p_matrix) %>%
dplyr::select(ESTIMATE)
cor_pvalue <-cor_pvalue %>%
mutate(p_value = round(ESTIMATE,2))
corr_table <- cbind(cor_value,dplyr::select(cor_pvalue,p_value)) %>%
arrange(p_value)
corr_table## Variable ESTIMATE p_value
## prop_sd prop_sd -0.475319274 0.00
## jml_sd jml_sd 0.522782952 0.00
## jml_smp jml_smp 0.563064097 0.00
## jml_sma jml_sma 0.403730416 0.00
## jml_eko jml_eko 0.616839180 0.00
## prop_kredit prop_kredit -0.437927419 0.00
## prop_health prop_health -0.327415381 0.00
## jml_health jml_health 0.549062363 0.00
## jml_medis jml_medis 0.459198441 0.00
## ESTIMATE ESTIMATE 1.000000000 0.00
## prop_blt prop_blt -0.268346259 0.01
## prop_padatkarya prop_padatkarya -0.273510991 0.01
## jml_pt jml_pt 0.238722953 0.02
## prop_imk prop_imk -0.228774061 0.03
## prop_sktm prop_sktm -0.199842725 0.06
## jml_bank jml_bank 0.179079435 0.09
## jml_koperasi jml_koperasi 0.178415897 0.09
## prop_sani prop_sani 0.176166680 0.09
## prop_desaagri prop_desaagri -0.171948968 0.10
## prop_desanonagri prop_desanonagri 0.171948968 0.10
## prop_medis prop_medis -0.165283189 0.12
## prop_koperasi prop_koperasi -0.156613809 0.14
## prop_eko prop_eko -0.144503566 0.17
## prop_smp prop_smp -0.138659177 0.19
## prop_skill prop_skill -0.130132900 0.22
## prop_sinyalinet prop_sinyalinet 0.125796781 0.23
## prop_kumuh prop_kumuh -0.123563138 0.24
## prop_perdesaan prop_perdesaan -0.106120199 0.31
## prop_bank prop_bank -0.106430887 0.31
## prop_sma prop_sma -0.094411849 0.37
## prop_air prop_air 0.089360189 0.40
## jml_kredit jml_kredit 0.066024108 0.53
## prop_bts prop_bts 0.046835344 0.66
## prop_angkumum prop_angkumum -0.044504444 0.67
## prop_pt prop_pt -0.015271479 0.89
## prop_aksesjalan prop_aksesjalan 0.008481591 0.94
## jml_imk jml_imk -0.006978409 0.95
from the correlation table, we selected some auxiliary variables
that have strong relationship with the number of working and school
population. These selected variables then been used in the estimation
model.
Variables that we selected:
a. jml_sd
b. jml_smp
c. jml_sma
d. jml_eko
e. jml_health
f. jml_medis
g. prop_blt
h. prop_sktm
i. jml_bank
j. jml_koperasi
k. prop_sani
#VARIABLE SELECTION
library(MASS)
library(car)## Loading required package: carData##
## Attaching package: 'car'## The following object is masked from 'package:dplyr':
##
## recodepreselected_data <- sae_var %>%
dplyr::select(ESTIMATE,jml_sd,jml_smp,jml_sma,jml_eko,jml_health,
jml_medis,jml_bank,prop_blt,
prop_sktm,jml_koperasi,prop_sani) %>%
na.omit()
preselected_data_SAE <- sae_var %>%
dplyr::select(ESTIMATE, RSE,jml_sd,jml_smp,jml_sma,jml_eko,jml_health,
jml_medis,jml_bank,prop_blt,
prop_sktm,jml_koperasi,prop_sani) %>%
na.omit()
preselected_data_SAE <- preselected_data_SAE %>%
mutate (var_dir = as.numeric(unlist((RSE * ESTIMATE/100)^2)))
write.csv(preselected_data_SAE, "selected variables.csv")
6. linear regression using all selected variables
modelreg = lm(ESTIMATE ~ ., preselected_data)
summary(modelreg)##
## Call:
## lm(formula = ESTIMATE ~ ., data = preselected_data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -24692 -8334 -2054 7515 70267
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 12216.590 10532.850 1.160 0.249557
## jml_sd -273.662 242.169 -1.130 0.261833
## jml_smp 2750.683 773.516 3.556 0.000636 ***
## jml_sma -2302.879 696.628 -3.306 0.001420 **
## jml_eko 27.159 6.604 4.113 9.42e-05 ***
## jml_health 147.599 126.884 1.163 0.248185
## jml_medis 37.850 34.714 1.090 0.278841
## jml_bank -757.127 205.090 -3.692 0.000405 ***
## prop_blt -547.002 656.658 -0.833 0.407320
## prop_sktm -1590.254 646.629 -2.459 0.016078 *
## jml_koperasi -347.565 251.511 -1.382 0.170846
## prop_sani 46.797 91.655 0.511 0.611050
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 14670 on 80 degrees of freedom
## Multiple R-squared: 0.6199, Adjusted R-squared: 0.5676
## F-statistic: 11.86 on 11 and 80 DF, p-value: 8.171e-13- Multicollinearity checking
# Menghitung VIF
vif_values <- vif(modelreg)
# Menampilkan hasil
print(vif_values)## jml_sd jml_smp jml_sma jml_eko jml_health jml_medis
## 4.167203 9.316783 7.021358 4.685233 7.210196 3.489841
## jml_bank prop_blt prop_sktm jml_koperasi prop_sani
## 2.815415 1.614426 1.125657 1.594085 1.151664
VIF values shows that jml_smp and jml_sma may have strong
relationship. We recommended to omit one of them. Since, high schools
are not always available in every sub-district and on the other hand jh
schools mostly available in every subdistrict, we decided to omit
jml_sma on further analysis.
- selecting variables using stepwise, backward, and forward (all variables are included)
# Null model (intercept only)
sae_all_var <-na.omit(sae_var %>%
dplyr::select(!c(IDAREA)))
null_model_all <- lm(ESTIMATE ~ 1, data = sae_eda)
modelreg_all = lm(ESTIMATE ~ ., sae_eda)# Stepwise regression
stepwise_model <- stepAIC(null_model_all, scope = list(lower = null_model_all, upper = modelreg_all), direction = "both")## Start: AIC=1843.36
## ESTIMATE ~ 1
##
## Df Sum of Sq RSS AIC
## + jml_eko 1 1.7237e+10 2.8065e+10 1801.3
## + jml_smp 1 1.4362e+10 3.0939e+10 1810.3
## + jml_health 1 1.3657e+10 3.1644e+10 1812.4
## + jml_sd 1 1.2381e+10 3.2920e+10 1816.0
## + prop_sd 1 1.0235e+10 3.5067e+10 1821.8
## + jml_medis 1 9.5524e+09 3.5749e+10 1823.6
## + prop_kredit 1 8.6879e+09 3.6614e+10 1825.8
## + jml_sma 1 7.3841e+09 3.7917e+10 1829.0
## + prop_health 1 4.8564e+09 4.0445e+10 1834.9
## + prop_padatkarya 1 3.3889e+09 4.1913e+10 1838.2
## + prop_blt 1 3.2621e+09 4.2039e+10 1838.5
## + jml_pt 1 2.5817e+09 4.2720e+10 1840.0
## + prop_imk 1 2.3710e+09 4.2930e+10 1840.4
## + prop_sktm 1 1.8092e+09 4.3492e+10 1841.6
## + jml_bank 1 1.4528e+09 4.3849e+10 1842.4
## + jml_koperasi 1 1.4420e+09 4.3859e+10 1842.4
## + prop_sani 1 1.4059e+09 4.3896e+10 1842.5
## + prop_desaagri 1 1.3394e+09 4.3962e+10 1842.6
## + prop_desanonagri 1 1.3394e+09 4.3962e+10 1842.6
## + prop_medis 1 1.2376e+09 4.4064e+10 1842.8
## + prop_koperasi 1 1.1111e+09 4.4190e+10 1843.1
## <none> 4.5301e+10 1843.4
## + prop_eko 1 9.4595e+08 4.4355e+10 1843.4
## + prop_smp 1 8.7098e+08 4.4430e+10 1843.6
## + prop_skill 1 7.6716e+08 4.4534e+10 1843.8
## + prop_sinyalinet 1 7.1689e+08 4.4585e+10 1843.9
## + prop_kumuh 1 6.9166e+08 4.4610e+10 1844.0
## + prop_bank 1 5.1315e+08 4.4788e+10 1844.3
## + prop_perdesaan 1 5.1016e+08 4.4791e+10 1844.3
## + prop_sma 1 4.0380e+08 4.4898e+10 1844.5
## + prop_air 1 3.6174e+08 4.4940e+10 1844.6
## + jml_kredit 1 1.9748e+08 4.5104e+10 1845.0
## + prop_bts 1 9.9371e+07 4.5202e+10 1845.2
## + prop_angkumum 1 8.9726e+07 4.5212e+10 1845.2
## + prop_pt 1 1.0565e+07 4.5291e+10 1845.3
## + prop_aksesjalan 1 3.2589e+06 4.5298e+10 1845.4
## + jml_imk 1 2.2061e+06 4.5299e+10 1845.4
##
## Step: AIC=1801.31
## ESTIMATE ~ jml_eko
##
## Df Sum of Sq RSS AIC
## + prop_eko 1 1.0102e+10 1.7963e+10 1762.3
## + prop_health 1 6.5430e+09 2.1522e+10 1778.9
## + prop_bank 1 5.9893e+09 2.2075e+10 1781.2
## + prop_sma 1 4.1802e+09 2.3884e+10 1788.5
## + jml_bank 1 3.0669e+09 2.4998e+10 1792.7
## + prop_medis 1 2.3809e+09 2.5684e+10 1795.2
## + prop_koperasi 1 1.7700e+09 2.6295e+10 1797.3
## + jml_smp 1 1.6791e+09 2.6386e+10 1797.6
## + prop_sd 1 1.6432e+09 2.6421e+10 1797.8
## + jml_sd 1 1.3498e+09 2.6715e+10 1798.8
## + prop_pt 1 1.2989e+09 2.6766e+10 1799.0
## + prop_smp 1 1.1367e+09 2.6928e+10 1799.5
## + jml_koperasi 1 1.0745e+09 2.6990e+10 1799.7
## + prop_kredit 1 9.3273e+08 2.7132e+10 1800.2
## + prop_skill 1 8.6577e+08 2.7199e+10 1800.4
## + prop_sktm 1 6.6751e+08 2.7397e+10 1801.1
## + prop_kumuh 1 6.1880e+08 2.7446e+10 1801.3
## <none> 2.8065e+10 1801.3
## + prop_perdesaan 1 5.0687e+08 2.7558e+10 1801.6
## + prop_imk 1 4.2838e+08 2.7636e+10 1801.9
## + jml_health 1 2.2825e+08 2.7836e+10 1802.6
## + jml_medis 1 2.2512e+08 2.7840e+10 1802.6
## + prop_desaagri 1 1.7553e+08 2.7889e+10 1802.7
## + prop_desanonagri 1 1.7553e+08 2.7889e+10 1802.7
## + jml_pt 1 1.5557e+08 2.7909e+10 1802.8
## + prop_sani 1 9.8175e+07 2.7966e+10 1803.0
## + prop_sinyalinet 1 9.1132e+07 2.7974e+10 1803.0
## + jml_kredit 1 7.5865e+07 2.7989e+10 1803.1
## + prop_angkumum 1 4.8239e+07 2.8016e+10 1803.2
## + jml_sma 1 3.7845e+07 2.8027e+10 1803.2
## + jml_imk 1 3.0003e+07 2.8035e+10 1803.2
## + prop_aksesjalan 1 2.8131e+07 2.8037e+10 1803.2
## + prop_padatkarya 1 5.0577e+06 2.8060e+10 1803.3
## + prop_blt 1 4.1066e+06 2.8061e+10 1803.3
## + prop_bts 1 2.2275e+06 2.8062e+10 1803.3
## + prop_air 1 7.3380e+03 2.8065e+10 1803.3
## - jml_eko 1 1.7237e+10 4.5301e+10 1843.4
##
## Step: AIC=1762.26
## ESTIMATE ~ jml_eko + prop_eko
##
## Df Sum of Sq RSS AIC
## + prop_sma 1 2.3051e+09 1.5658e+10 1751.6
## + prop_health 1 1.7104e+09 1.6252e+10 1755.0
## + jml_sma 1 1.5699e+09 1.6393e+10 1755.8
## + prop_bank 1 1.4340e+09 1.6529e+10 1756.6
## + jml_bank 1 1.2012e+09 1.6762e+10 1757.9
## + jml_health 1 1.1498e+09 1.6813e+10 1758.2
## + prop_perdesaan 1 8.2460e+08 1.7138e+10 1759.9
## + prop_bts 1 6.3590e+08 1.7327e+10 1760.9
## + prop_medis 1 6.3240e+08 1.7331e+10 1761.0
## + jml_kredit 1 4.3674e+08 1.7526e+10 1762.0
## + jml_koperasi 1 4.1149e+08 1.7551e+10 1762.1
## <none> 1.7963e+10 1762.3
## + prop_kumuh 1 3.8589e+08 1.7577e+10 1762.3
## + prop_smp 1 3.7987e+08 1.7583e+10 1762.3
## + jml_sd 1 3.7897e+08 1.7584e+10 1762.3
## + prop_air 1 2.6107e+08 1.7702e+10 1762.9
## + prop_skill 1 2.5397e+08 1.7709e+10 1763.0
## + jml_imk 1 2.2753e+08 1.7735e+10 1763.1
## + jml_medis 1 2.1845e+08 1.7744e+10 1763.1
## + prop_imk 1 2.0712e+08 1.7756e+10 1763.2
## + prop_sd 1 1.9114e+08 1.7772e+10 1763.3
## + jml_smp 1 1.0116e+08 1.7862e+10 1763.7
## + prop_padatkarya 1 9.0078e+07 1.7873e+10 1763.8
## + prop_pt 1 7.1957e+07 1.7891e+10 1763.9
## + prop_kredit 1 4.3564e+07 1.7919e+10 1764.0
## + prop_blt 1 3.3555e+07 1.7929e+10 1764.1
## + prop_desaagri 1 2.7956e+07 1.7935e+10 1764.1
## + prop_desanonagri 1 2.7956e+07 1.7935e+10 1764.1
## + prop_sktm 1 1.7852e+07 1.7945e+10 1764.2
## + prop_angkumum 1 1.4419e+07 1.7949e+10 1764.2
## + prop_aksesjalan 1 1.3599e+07 1.7949e+10 1764.2
## + prop_sinyalinet 1 1.1655e+07 1.7951e+10 1764.2
## + prop_koperasi 1 9.6005e+06 1.7953e+10 1764.2
## + prop_sani 1 1.4030e+05 1.7963e+10 1764.3
## + jml_pt 1 8.5666e+04 1.7963e+10 1764.3
## - prop_eko 1 1.0102e+10 2.8065e+10 1801.3
## - jml_eko 1 2.6393e+10 4.4355e+10 1843.4
##
## Step: AIC=1751.62
## ESTIMATE ~ jml_eko + prop_eko + prop_sma
##
## Df Sum of Sq RSS AIC
## + prop_health 1 6.6582e+08 1.4992e+10 1749.6
## + jml_smp 1 4.8135e+08 1.5176e+10 1750.8
## + jml_kredit 1 4.0804e+08 1.5250e+10 1751.2
## + prop_imk 1 3.6736e+08 1.5290e+10 1751.4
## + jml_koperasi 1 3.4225e+08 1.5316e+10 1751.6
## <none> 1.5658e+10 1751.6
## + jml_health 1 3.1732e+08 1.5340e+10 1751.7
## + jml_sd 1 3.0909e+08 1.5349e+10 1751.8
## + prop_kumuh 1 3.0755e+08 1.5350e+10 1751.8
## + jml_imk 1 2.9512e+08 1.5363e+10 1751.9
## + prop_sd 1 2.9113e+08 1.5367e+10 1751.9
## + prop_bank 1 2.7191e+08 1.5386e+10 1752.0
## + prop_smp 1 2.4006e+08 1.5418e+10 1752.2
## + prop_medis 1 2.2716e+08 1.5431e+10 1752.3
## + jml_bank 1 2.1143e+08 1.5446e+10 1752.4
## + prop_perdesaan 1 2.0936e+08 1.5448e+10 1752.4
## + prop_bts 1 1.9342e+08 1.5464e+10 1752.5
## + jml_pt 1 1.7089e+08 1.5487e+10 1752.6
## + prop_sinyalinet 1 1.5095e+08 1.5507e+10 1752.7
## + prop_padatkarya 1 1.3833e+08 1.5519e+10 1752.8
## + prop_kredit 1 1.0639e+08 1.5551e+10 1753.0
## + prop_blt 1 9.0174e+07 1.5568e+10 1753.1
## + prop_pt 1 8.5685e+07 1.5572e+10 1753.1
## + prop_skill 1 6.5384e+07 1.5592e+10 1753.2
## + jml_sma 1 4.2152e+07 1.5616e+10 1753.4
## + prop_air 1 2.3004e+07 1.5635e+10 1753.5
## + jml_medis 1 2.2746e+07 1.5635e+10 1753.5
## + prop_koperasi 1 1.3939e+07 1.5644e+10 1753.5
## + prop_desaagri 1 1.3921e+07 1.5644e+10 1753.5
## + prop_desanonagri 1 1.3921e+07 1.5644e+10 1753.5
## + prop_sktm 1 1.2101e+07 1.5646e+10 1753.5
## + prop_aksesjalan 1 1.1934e+07 1.5646e+10 1753.5
## + prop_angkumum 1 4.3569e+06 1.5653e+10 1753.6
## + prop_sani 1 1.1089e+06 1.5657e+10 1753.6
## - prop_sma 1 2.3051e+09 1.7963e+10 1762.3
## - prop_eko 1 8.2267e+09 2.3884e+10 1788.5
## - jml_eko 1 2.8560e+10 4.4218e+10 1845.1
##
## Step: AIC=1749.63
## ESTIMATE ~ jml_eko + prop_eko + prop_sma + prop_health
##
## Df Sum of Sq RSS AIC
## + jml_smp 1 3.9854e+08 1.4593e+10 1749.2
## + jml_sd 1 3.8915e+08 1.4603e+10 1749.2
## <none> 1.4992e+10 1749.6
## + prop_imk 1 2.9276e+08 1.4699e+10 1749.8
## + jml_imk 1 2.7287e+08 1.4719e+10 1749.9
## + prop_sinyalinet 1 2.4287e+08 1.4749e+10 1750.1
## + prop_sd 1 2.2909e+08 1.4763e+10 1750.2
## + prop_bts 1 2.2504e+08 1.4767e+10 1750.2
## + prop_kumuh 1 2.2217e+08 1.4770e+10 1750.2
## + prop_smp 1 2.0974e+08 1.4782e+10 1750.3
## + prop_perdesaan 1 2.0341e+08 1.4789e+10 1750.4
## + jml_pt 1 1.9928e+08 1.4793e+10 1750.4
## + jml_kredit 1 1.8802e+08 1.4804e+10 1750.5
## + jml_koperasi 1 1.8459e+08 1.4807e+10 1750.5
## + jml_health 1 1.5875e+08 1.4833e+10 1750.7
## + jml_medis 1 8.3207e+07 1.4909e+10 1751.1
## + prop_bank 1 6.2619e+07 1.4929e+10 1751.2
## + prop_padatkarya 1 6.1405e+07 1.4931e+10 1751.2
## + prop_pt 1 5.9560e+07 1.4932e+10 1751.3
## + jml_sma 1 5.4284e+07 1.4938e+10 1751.3
## + prop_skill 1 4.8080e+07 1.4944e+10 1751.3
## + prop_blt 1 3.3914e+07 1.4958e+10 1751.4
## + prop_aksesjalan 1 2.3721e+07 1.4968e+10 1751.5
## + jml_bank 1 2.3050e+07 1.4969e+10 1751.5
## + prop_sktm 1 2.0516e+07 1.4971e+10 1751.5
## + prop_angkumum 1 7.3220e+06 1.4985e+10 1751.6
## + prop_air 1 5.5602e+06 1.4986e+10 1751.6
## + prop_desaagri 1 2.2461e+06 1.4990e+10 1751.6
## + prop_desanonagri 1 2.2461e+06 1.4990e+10 1751.6
## + prop_koperasi 1 1.7526e+06 1.4990e+10 1751.6
## + prop_medis 1 5.4900e+05 1.4991e+10 1751.6
## + prop_sani 1 4.3877e+05 1.4992e+10 1751.6
## - prop_health 1 6.6582e+08 1.5658e+10 1751.6
## + prop_kredit 1 3.2267e+05 1.4992e+10 1751.6
## - prop_sma 1 1.2605e+09 1.6252e+10 1755.0
## - prop_eko 1 5.2595e+09 2.0251e+10 1775.3
## - jml_eko 1 2.5375e+10 4.0367e+10 1838.8
##
## Step: AIC=1749.15
## ESTIMATE ~ jml_eko + prop_eko + prop_sma + prop_health + jml_smp
##
## Df Sum of Sq RSS AIC
## + jml_sd 1 1211439660 1.3382e+10 1743.2
## + prop_sd 1 543666577 1.4050e+10 1747.7
## + jml_imk 1 540905924 1.4053e+10 1747.7
## + jml_pt 1 538773207 1.4055e+10 1747.7
## + jml_kredit 1 485289929 1.4108e+10 1748.0
## + prop_imk 1 395642836 1.4198e+10 1748.6
## <none> 1.4593e+10 1749.2
## + prop_bts 1 275466324 1.4318e+10 1749.4
## + prop_sinyalinet 1 242978773 1.4350e+10 1749.6
## - jml_smp 1 398538515 1.4992e+10 1749.6
## + prop_pt 1 232633164 1.4361e+10 1749.7
## + prop_kumuh 1 177114603 1.4416e+10 1750.0
## + jml_koperasi 1 138900197 1.4455e+10 1750.3
## + prop_blt 1 115759348 1.4478e+10 1750.4
## + prop_sktm 1 92000667 1.4501e+10 1750.6
## + jml_sma 1 83083309 1.4510e+10 1750.6
## + prop_perdesaan 1 81385451 1.4512e+10 1750.6
## + jml_medis 1 76259719 1.4517e+10 1750.7
## + prop_desaagri 1 67645184 1.4526e+10 1750.7
## + prop_desanonagri 1 67645184 1.4526e+10 1750.7
## + prop_skill 1 63504570 1.4530e+10 1750.8
## - prop_health 1 583015576 1.5176e+10 1750.8
## + jml_health 1 61280809 1.4532e+10 1750.8
## + prop_padatkarya 1 39429069 1.4554e+10 1750.9
## + prop_aksesjalan 1 33226974 1.4560e+10 1750.9
## + prop_bank 1 24990257 1.4568e+10 1751.0
## + prop_angkumum 1 20315601 1.4573e+10 1751.0
## + prop_kredit 1 17363335 1.4576e+10 1751.0
## + prop_koperasi 1 6854086 1.4587e+10 1751.1
## + prop_air 1 4353994 1.4589e+10 1751.1
## + jml_bank 1 1458280 1.4592e+10 1751.1
## + prop_medis 1 1052252 1.4592e+10 1751.1
## + prop_smp 1 831561 1.4593e+10 1751.1
## + prop_sani 1 23930 1.4593e+10 1751.2
## - prop_sma 1 1643656244 1.6237e+10 1757.0
## - prop_eko 1 2251215395 1.6845e+10 1760.3
## - jml_eko 1 6874034774 2.1467e+10 1782.7
##
## Step: AIC=1743.18
## ESTIMATE ~ jml_eko + prop_eko + prop_sma + prop_health + jml_smp +
## jml_sd
##
## Df Sum of Sq RSS AIC
## + prop_perdesaan 1 839617119 1.2542e+10 1739.2
## + prop_bts 1 376685098 1.3005e+10 1742.5
## <none> 1.3382e+10 1743.2
## + prop_bank 1 283821678 1.3098e+10 1743.2
## + jml_imk 1 261118562 1.3121e+10 1743.4
## + jml_bank 1 233988146 1.3148e+10 1743.5
## + prop_desaagri 1 210100222 1.3172e+10 1743.7
## + prop_desanonagri 1 210100222 1.3172e+10 1743.7
## + jml_sma 1 207936586 1.3174e+10 1743.7
## + prop_imk 1 199361973 1.3183e+10 1743.8
## + prop_kumuh 1 182413637 1.3200e+10 1743.9
## + prop_aksesjalan 1 117563445 1.3264e+10 1744.4
## + prop_kredit 1 104152415 1.3278e+10 1744.5
## + prop_air 1 83872772 1.3298e+10 1744.6
## + jml_health 1 72817535 1.3309e+10 1744.7
## + prop_koperasi 1 67119676 1.3315e+10 1744.7
## + jml_pt 1 59010742 1.3323e+10 1744.8
## + jml_medis 1 45715525 1.3336e+10 1744.9
## + prop_sani 1 40659362 1.3341e+10 1744.9
## + prop_sinyalinet 1 39792840 1.3342e+10 1744.9
## + prop_angkumum 1 28547347 1.3353e+10 1745.0
## + prop_sd 1 27352278 1.3355e+10 1745.0
## + jml_kredit 1 7734443 1.3374e+10 1745.1
## + prop_blt 1 7005833 1.3375e+10 1745.1
## + prop_padatkarya 1 5373836 1.3377e+10 1745.1
## + prop_smp 1 4842512 1.3377e+10 1745.1
## + jml_koperasi 1 3221449 1.3379e+10 1745.2
## + prop_medis 1 2815553 1.3379e+10 1745.2
## + prop_skill 1 1241172 1.3381e+10 1745.2
## + prop_pt 1 256970 1.3382e+10 1745.2
## + prop_sktm 1 126068 1.3382e+10 1745.2
## - prop_health 1 663062538 1.4045e+10 1745.6
## - jml_sd 1 1211439660 1.4593e+10 1749.2
## - jml_smp 1 1220830890 1.4603e+10 1749.2
## - prop_sma 1 2338049661 1.5720e+10 1756.0
## - prop_eko 1 2754202942 1.6136e+10 1758.4
## - jml_eko 1 7989982849 2.1372e+10 1784.2
##
## Step: AIC=1739.21
## ESTIMATE ~ jml_eko + prop_eko + prop_sma + prop_health + jml_smp +
## jml_sd + prop_perdesaan
##
## Df Sum of Sq RSS AIC
## + prop_bts 1 492392228 1.2050e+10 1737.5
## <none> 1.2542e+10 1739.2
## + jml_medis 1 256461262 1.2286e+10 1739.3
## + jml_health 1 178110242 1.2364e+10 1739.9
## + jml_imk 1 174694412 1.2368e+10 1739.9
## + jml_bank 1 143672995 1.2399e+10 1740.2
## + prop_bank 1 141398098 1.2401e+10 1740.2
## + prop_imk 1 140706593 1.2402e+10 1740.2
## + prop_smp 1 133804831 1.2409e+10 1740.2
## + prop_koperasi 1 121870255 1.2420e+10 1740.3
## + jml_sma 1 118098238 1.2424e+10 1740.3
## + prop_sinyalinet 1 103533257 1.2439e+10 1740.5
## + jml_pt 1 95387900 1.2447e+10 1740.5
## + prop_angkumum 1 84647320 1.2458e+10 1740.6
## + prop_desaagri 1 78442904 1.2464e+10 1740.6
## + prop_desanonagri 1 78442904 1.2464e+10 1740.6
## + prop_medis 1 60549428 1.2482e+10 1740.8
## + prop_aksesjalan 1 42551774 1.2500e+10 1740.9
## + prop_sd 1 34507561 1.2508e+10 1741.0
## + prop_skill 1 33727817 1.2509e+10 1741.0
## + prop_kumuh 1 29123117 1.2513e+10 1741.0
## + prop_blt 1 24886343 1.2517e+10 1741.0
## + prop_pt 1 24043735 1.2518e+10 1741.0
## + jml_kredit 1 22085313 1.2520e+10 1741.0
## + prop_kredit 1 12152532 1.2530e+10 1741.1
## + prop_sani 1 10689643 1.2532e+10 1741.1
## + prop_padatkarya 1 6231703 1.2536e+10 1741.2
## + prop_air 1 6049427 1.2536e+10 1741.2
## + prop_sktm 1 4504525 1.2538e+10 1741.2
## + jml_koperasi 1 744651 1.2542e+10 1741.2
## - prop_health 1 725858759 1.3268e+10 1742.4
## - prop_perdesaan 1 839617119 1.3382e+10 1743.2
## - jml_smp 1 1199225933 1.3742e+10 1745.6
## - prop_sma 1 1376198832 1.3919e+10 1746.8
## - jml_sd 1 1969671328 1.4512e+10 1750.6
## - prop_eko 1 3527240318 1.6070e+10 1760.0
## - jml_eko 1 8387575390 2.0930e+10 1784.3
##
## Step: AIC=1737.53
## ESTIMATE ~ jml_eko + prop_eko + prop_sma + prop_health + jml_smp +
## jml_sd + prop_perdesaan + prop_bts
##
## Df Sum of Sq RSS AIC
## + jml_medis 1 341929546 1.1708e+10 1736.9
## <none> 1.2050e+10 1737.5
## + jml_imk 1 225959153 1.1824e+10 1737.8
## + jml_health 1 216459901 1.1834e+10 1737.9
## + prop_imk 1 171458080 1.1879e+10 1738.2
## + jml_sma 1 160719269 1.1889e+10 1738.3
## + prop_smp 1 152563768 1.1897e+10 1738.4
## + prop_koperasi 1 134517817 1.1915e+10 1738.5
## + prop_medis 1 119866266 1.1930e+10 1738.6
## + prop_bank 1 119781992 1.1930e+10 1738.6
## + jml_bank 1 119429029 1.1931e+10 1738.6
## + prop_sd 1 117462351 1.1933e+10 1738.6
## + jml_pt 1 101494898 1.1948e+10 1738.8
## + prop_sinyalinet 1 77731080 1.1972e+10 1738.9
## + prop_angkumum 1 52296010 1.1998e+10 1739.1
## + prop_air 1 49472239 1.2000e+10 1739.2
## + prop_skill 1 46761315 1.2003e+10 1739.2
## - prop_bts 1 492392228 1.2542e+10 1739.2
## + prop_kumuh 1 31910186 1.2018e+10 1739.3
## + prop_pt 1 30416309 1.2020e+10 1739.3
## + jml_kredit 1 23844856 1.2026e+10 1739.3
## + prop_blt 1 23448639 1.2027e+10 1739.3
## + prop_desaagri 1 22698804 1.2027e+10 1739.4
## + prop_desanonagri 1 22698804 1.2027e+10 1739.4
## + prop_aksesjalan 1 11381104 1.2039e+10 1739.4
## + prop_padatkarya 1 9357355 1.2041e+10 1739.5
## + prop_kredit 1 2727654 1.2047e+10 1739.5
## + prop_sani 1 738720 1.2049e+10 1739.5
## + jml_koperasi 1 548328 1.2049e+10 1739.5
## + prop_sktm 1 230016 1.2050e+10 1739.5
## - prop_health 1 777443104 1.2827e+10 1741.3
## - prop_perdesaan 1 955324250 1.3005e+10 1742.5
## - prop_sma 1 1101353438 1.3151e+10 1743.6
## - jml_smp 1 1353734360 1.3404e+10 1745.3
## - jml_sd 1 2172729222 1.4223e+10 1750.8
## - prop_eko 1 3900970797 1.5951e+10 1761.3
## - jml_eko 1 8420090345 2.0470e+10 1784.3
##
## Step: AIC=1736.88
## ESTIMATE ~ jml_eko + prop_eko + prop_sma + prop_health + jml_smp +
## jml_sd + prop_perdesaan + prop_bts + jml_medis
##
## Df Sum of Sq RSS AIC
## <none> 1.1708e+10 1736.9
## + jml_sma 1 245278470 1.1463e+10 1736.9
## + jml_bank 1 223857199 1.1484e+10 1737.1
## + prop_bank 1 182384214 1.1526e+10 1737.4
## + jml_imk 1 171302743 1.1537e+10 1737.5
## - jml_medis 1 341929546 1.2050e+10 1737.5
## + prop_imk 1 138370871 1.1570e+10 1737.8
## + prop_koperasi 1 135436167 1.1573e+10 1737.8
## + prop_sd 1 83282188 1.1625e+10 1738.2
## + prop_medis 1 81347635 1.1627e+10 1738.2
## + prop_smp 1 80442774 1.1628e+10 1738.2
## + prop_sinyalinet 1 75873321 1.1632e+10 1738.3
## + jml_pt 1 61902809 1.1646e+10 1738.4
## + jml_health 1 61558309 1.1646e+10 1738.4
## + prop_angkumum 1 50061712 1.1658e+10 1738.5
## + prop_skill 1 41476379 1.1667e+10 1738.5
## + prop_air 1 35749054 1.1672e+10 1738.6
## + jml_kredit 1 32298856 1.1676e+10 1738.6
## + prop_desaagri 1 21971861 1.1686e+10 1738.7
## + prop_desanonagri 1 21971861 1.1686e+10 1738.7
## + prop_kumuh 1 17729512 1.1690e+10 1738.7
## + prop_aksesjalan 1 17267392 1.1691e+10 1738.8
## + prop_pt 1 14097347 1.1694e+10 1738.8
## + prop_padatkarya 1 8932783 1.1699e+10 1738.8
## + prop_sani 1 7144883 1.1701e+10 1738.8
## + jml_koperasi 1 4835523 1.1703e+10 1738.8
## + prop_blt 1 1065834 1.1707e+10 1738.9
## + prop_sktm 1 515328 1.1708e+10 1738.9
## + prop_kredit 1 70026 1.1708e+10 1738.9
## - prop_bts 1 577860513 1.2286e+10 1739.3
## - prop_sma 1 951749059 1.2660e+10 1742.1
## - prop_health 1 1117743559 1.2826e+10 1743.3
## - prop_perdesaan 1 1229571510 1.2938e+10 1744.1
## - jml_smp 1 1297788365 1.3006e+10 1744.5
## - jml_sd 1 2332760069 1.4041e+10 1751.6
## - prop_eko 1 2878150472 1.4586e+10 1755.1
## - jml_eko 1 5774440567 1.7482e+10 1771.8# View summary
summary(stepwise_model)##
## Call:
## lm(formula = ESTIMATE ~ jml_eko + prop_eko + prop_sma + prop_health +
## jml_smp + jml_sd + prop_perdesaan + prop_bts + jml_medis,
## data = sae_eda)
##
## Residuals:
## Min 1Q Median 3Q Max
## -20604 -8041 -1200 4452 59782
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 5.916e+04 9.000e+03 6.574 4.24e-09 ***
## jml_eko 4.002e+01 6.293e+00 6.359 1.09e-08 ***
## prop_eko -8.003e+03 1.783e+03 -4.490 2.31e-05 ***
## prop_sma -3.145e+05 1.218e+05 -2.582 0.011607 *
## prop_health -6.748e+04 2.412e+04 -2.798 0.006408 **
## jml_smp 1.420e+03 4.709e+02 3.015 0.003421 **
## jml_sd -7.961e+02 1.970e+02 -4.042 0.000119 ***
## prop_perdesaan 1.846e+02 6.290e+01 2.935 0.004331 **
## prop_bts 1.271e+05 6.320e+04 2.012 0.047529 *
## jml_medis 4.030e+01 2.604e+01 1.548 0.125592
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 11950 on 82 degrees of freedom
## Multiple R-squared: 0.7416, Adjusted R-squared: 0.7132
## F-statistic: 26.14 on 9 and 82 DF, p-value: < 2.2e-16# Forward selection
forward_model <- stepAIC(null_model_all, scope = list(lower = null_model_all, upper = modelreg_all), direction = "forward")## Start: AIC=1843.36
## ESTIMATE ~ 1
##
## Df Sum of Sq RSS AIC
## + jml_eko 1 1.7237e+10 2.8065e+10 1801.3
## + jml_smp 1 1.4362e+10 3.0939e+10 1810.3
## + jml_health 1 1.3657e+10 3.1644e+10 1812.4
## + jml_sd 1 1.2381e+10 3.2920e+10 1816.0
## + prop_sd 1 1.0235e+10 3.5067e+10 1821.8
## + jml_medis 1 9.5524e+09 3.5749e+10 1823.6
## + prop_kredit 1 8.6879e+09 3.6614e+10 1825.8
## + jml_sma 1 7.3841e+09 3.7917e+10 1829.0
## + prop_health 1 4.8564e+09 4.0445e+10 1834.9
## + prop_padatkarya 1 3.3889e+09 4.1913e+10 1838.2
## + prop_blt 1 3.2621e+09 4.2039e+10 1838.5
## + jml_pt 1 2.5817e+09 4.2720e+10 1840.0
## + prop_imk 1 2.3710e+09 4.2930e+10 1840.4
## + prop_sktm 1 1.8092e+09 4.3492e+10 1841.6
## + jml_bank 1 1.4528e+09 4.3849e+10 1842.4
## + jml_koperasi 1 1.4420e+09 4.3859e+10 1842.4
## + prop_sani 1 1.4059e+09 4.3896e+10 1842.5
## + prop_desaagri 1 1.3394e+09 4.3962e+10 1842.6
## + prop_desanonagri 1 1.3394e+09 4.3962e+10 1842.6
## + prop_medis 1 1.2376e+09 4.4064e+10 1842.8
## + prop_koperasi 1 1.1111e+09 4.4190e+10 1843.1
## <none> 4.5301e+10 1843.4
## + prop_eko 1 9.4595e+08 4.4355e+10 1843.4
## + prop_smp 1 8.7098e+08 4.4430e+10 1843.6
## + prop_skill 1 7.6716e+08 4.4534e+10 1843.8
## + prop_sinyalinet 1 7.1689e+08 4.4585e+10 1843.9
## + prop_kumuh 1 6.9166e+08 4.4610e+10 1844.0
## + prop_bank 1 5.1315e+08 4.4788e+10 1844.3
## + prop_perdesaan 1 5.1016e+08 4.4791e+10 1844.3
## + prop_sma 1 4.0380e+08 4.4898e+10 1844.5
## + prop_air 1 3.6174e+08 4.4940e+10 1844.6
## + jml_kredit 1 1.9748e+08 4.5104e+10 1845.0
## + prop_bts 1 9.9371e+07 4.5202e+10 1845.2
## + prop_angkumum 1 8.9726e+07 4.5212e+10 1845.2
## + prop_pt 1 1.0565e+07 4.5291e+10 1845.3
## + prop_aksesjalan 1 3.2589e+06 4.5298e+10 1845.4
## + jml_imk 1 2.2061e+06 4.5299e+10 1845.4
##
## Step: AIC=1801.31
## ESTIMATE ~ jml_eko
##
## Df Sum of Sq RSS AIC
## + prop_eko 1 1.0102e+10 1.7963e+10 1762.3
## + prop_health 1 6.5430e+09 2.1522e+10 1778.9
## + prop_bank 1 5.9893e+09 2.2075e+10 1781.2
## + prop_sma 1 4.1802e+09 2.3884e+10 1788.5
## + jml_bank 1 3.0669e+09 2.4998e+10 1792.7
## + prop_medis 1 2.3809e+09 2.5684e+10 1795.2
## + prop_koperasi 1 1.7700e+09 2.6295e+10 1797.3
## + jml_smp 1 1.6791e+09 2.6386e+10 1797.6
## + prop_sd 1 1.6432e+09 2.6421e+10 1797.8
## + jml_sd 1 1.3498e+09 2.6715e+10 1798.8
## + prop_pt 1 1.2989e+09 2.6766e+10 1799.0
## + prop_smp 1 1.1367e+09 2.6928e+10 1799.5
## + jml_koperasi 1 1.0745e+09 2.6990e+10 1799.7
## + prop_kredit 1 9.3273e+08 2.7132e+10 1800.2
## + prop_skill 1 8.6577e+08 2.7199e+10 1800.4
## + prop_sktm 1 6.6751e+08 2.7397e+10 1801.1
## + prop_kumuh 1 6.1880e+08 2.7446e+10 1801.3
## <none> 2.8065e+10 1801.3
## + prop_perdesaan 1 5.0687e+08 2.7558e+10 1801.6
## + prop_imk 1 4.2838e+08 2.7636e+10 1801.9
## + jml_health 1 2.2825e+08 2.7836e+10 1802.6
## + jml_medis 1 2.2512e+08 2.7840e+10 1802.6
## + prop_desaagri 1 1.7553e+08 2.7889e+10 1802.7
## + prop_desanonagri 1 1.7553e+08 2.7889e+10 1802.7
## + jml_pt 1 1.5557e+08 2.7909e+10 1802.8
## + prop_sani 1 9.8175e+07 2.7966e+10 1803.0
## + prop_sinyalinet 1 9.1132e+07 2.7974e+10 1803.0
## + jml_kredit 1 7.5865e+07 2.7989e+10 1803.1
## + prop_angkumum 1 4.8239e+07 2.8016e+10 1803.2
## + jml_sma 1 3.7845e+07 2.8027e+10 1803.2
## + jml_imk 1 3.0003e+07 2.8035e+10 1803.2
## + prop_aksesjalan 1 2.8131e+07 2.8037e+10 1803.2
## + prop_padatkarya 1 5.0577e+06 2.8060e+10 1803.3
## + prop_blt 1 4.1066e+06 2.8061e+10 1803.3
## + prop_bts 1 2.2275e+06 2.8062e+10 1803.3
## + prop_air 1 7.3380e+03 2.8065e+10 1803.3
##
## Step: AIC=1762.26
## ESTIMATE ~ jml_eko + prop_eko
##
## Df Sum of Sq RSS AIC
## + prop_sma 1 2305148859 1.5658e+10 1751.6
## + prop_health 1 1710427949 1.6252e+10 1755.0
## + jml_sma 1 1569929414 1.6393e+10 1755.8
## + prop_bank 1 1434043626 1.6529e+10 1756.6
## + jml_bank 1 1201177908 1.6762e+10 1757.9
## + jml_health 1 1149806135 1.6813e+10 1758.2
## + prop_perdesaan 1 824595597 1.7138e+10 1759.9
## + prop_bts 1 635902746 1.7327e+10 1760.9
## + prop_medis 1 632404825 1.7331e+10 1761.0
## + jml_kredit 1 436740601 1.7526e+10 1762.0
## + jml_koperasi 1 411491190 1.7551e+10 1762.1
## <none> 1.7963e+10 1762.3
## + prop_kumuh 1 385893422 1.7577e+10 1762.3
## + prop_smp 1 379871263 1.7583e+10 1762.3
## + jml_sd 1 378971171 1.7584e+10 1762.3
## + prop_air 1 261073774 1.7702e+10 1762.9
## + prop_skill 1 253972604 1.7709e+10 1763.0
## + jml_imk 1 227531484 1.7735e+10 1763.1
## + jml_medis 1 218445535 1.7744e+10 1763.1
## + prop_imk 1 207116648 1.7756e+10 1763.2
## + prop_sd 1 191137926 1.7772e+10 1763.3
## + jml_smp 1 101160564 1.7862e+10 1763.7
## + prop_padatkarya 1 90077871 1.7873e+10 1763.8
## + prop_pt 1 71956694 1.7891e+10 1763.9
## + prop_kredit 1 43563729 1.7919e+10 1764.0
## + prop_blt 1 33555139 1.7929e+10 1764.1
## + prop_desaagri 1 27955998 1.7935e+10 1764.1
## + prop_desanonagri 1 27955998 1.7935e+10 1764.1
## + prop_sktm 1 17852391 1.7945e+10 1764.2
## + prop_angkumum 1 14419091 1.7949e+10 1764.2
## + prop_aksesjalan 1 13598632 1.7949e+10 1764.2
## + prop_sinyalinet 1 11654638 1.7951e+10 1764.2
## + prop_koperasi 1 9600474 1.7953e+10 1764.2
## + prop_sani 1 140303 1.7963e+10 1764.3
## + jml_pt 1 85666 1.7963e+10 1764.3
##
## Step: AIC=1751.62
## ESTIMATE ~ jml_eko + prop_eko + prop_sma
##
## Df Sum of Sq RSS AIC
## + prop_health 1 665823309 1.4992e+10 1749.6
## + jml_smp 1 481346248 1.5176e+10 1750.8
## + jml_kredit 1 408039008 1.5250e+10 1751.2
## + prop_imk 1 367360335 1.5290e+10 1751.4
## + jml_koperasi 1 342248793 1.5316e+10 1751.6
## <none> 1.5658e+10 1751.6
## + jml_health 1 317318124 1.5340e+10 1751.7
## + jml_sd 1 309092528 1.5349e+10 1751.8
## + prop_kumuh 1 307550266 1.5350e+10 1751.8
## + jml_imk 1 295118623 1.5363e+10 1751.9
## + prop_sd 1 291129076 1.5367e+10 1751.9
## + prop_bank 1 271906046 1.5386e+10 1752.0
## + prop_smp 1 240055001 1.5418e+10 1752.2
## + prop_medis 1 227163400 1.5431e+10 1752.3
## + jml_bank 1 211425746 1.5446e+10 1752.4
## + prop_perdesaan 1 209363654 1.5448e+10 1752.4
## + prop_bts 1 193422266 1.5464e+10 1752.5
## + jml_pt 1 170886557 1.5487e+10 1752.6
## + prop_sinyalinet 1 150945806 1.5507e+10 1752.7
## + prop_padatkarya 1 138326882 1.5519e+10 1752.8
## + prop_kredit 1 106386245 1.5551e+10 1753.0
## + prop_blt 1 90173516 1.5568e+10 1753.1
## + prop_pt 1 85684844 1.5572e+10 1753.1
## + prop_skill 1 65384134 1.5592e+10 1753.2
## + jml_sma 1 42151674 1.5616e+10 1753.4
## + prop_air 1 23004038 1.5635e+10 1753.5
## + jml_medis 1 22746435 1.5635e+10 1753.5
## + prop_koperasi 1 13939480 1.5644e+10 1753.5
## + prop_desaagri 1 13920541 1.5644e+10 1753.5
## + prop_desanonagri 1 13920541 1.5644e+10 1753.5
## + prop_sktm 1 12101477 1.5646e+10 1753.5
## + prop_aksesjalan 1 11934236 1.5646e+10 1753.5
## + prop_angkumum 1 4356921 1.5653e+10 1753.6
## + prop_sani 1 1108949 1.5657e+10 1753.6
##
## Step: AIC=1749.63
## ESTIMATE ~ jml_eko + prop_eko + prop_sma + prop_health
##
## Df Sum of Sq RSS AIC
## + jml_smp 1 398538515 1.4593e+10 1749.2
## + jml_sd 1 389147286 1.4603e+10 1749.2
## <none> 1.4992e+10 1749.6
## + prop_imk 1 292760755 1.4699e+10 1749.8
## + jml_imk 1 272872517 1.4719e+10 1749.9
## + prop_sinyalinet 1 242870452 1.4749e+10 1750.1
## + prop_sd 1 229090762 1.4763e+10 1750.2
## + prop_bts 1 225040057 1.4767e+10 1750.2
## + prop_kumuh 1 222170266 1.4770e+10 1750.2
## + prop_smp 1 209744235 1.4782e+10 1750.3
## + prop_perdesaan 1 203413131 1.4789e+10 1750.4
## + jml_pt 1 199281620 1.4793e+10 1750.4
## + jml_kredit 1 188022652 1.4804e+10 1750.5
## + jml_koperasi 1 184587115 1.4807e+10 1750.5
## + jml_health 1 158750737 1.4833e+10 1750.7
## + jml_medis 1 83206692 1.4909e+10 1751.1
## + prop_bank 1 62618872 1.4929e+10 1751.2
## + prop_padatkarya 1 61404667 1.4931e+10 1751.2
## + prop_pt 1 59560330 1.4932e+10 1751.3
## + jml_sma 1 54283899 1.4938e+10 1751.3
## + prop_skill 1 48080450 1.4944e+10 1751.3
## + prop_blt 1 33913946 1.4958e+10 1751.4
## + prop_aksesjalan 1 23720556 1.4968e+10 1751.5
## + jml_bank 1 23049945 1.4969e+10 1751.5
## + prop_sktm 1 20515568 1.4971e+10 1751.5
## + prop_angkumum 1 7321995 1.4985e+10 1751.6
## + prop_air 1 5560203 1.4986e+10 1751.6
## + prop_desaagri 1 2246122 1.4990e+10 1751.6
## + prop_desanonagri 1 2246122 1.4990e+10 1751.6
## + prop_koperasi 1 1752557 1.4990e+10 1751.6
## + prop_medis 1 548998 1.4991e+10 1751.6
## + prop_sani 1 438770 1.4992e+10 1751.6
## + prop_kredit 1 322667 1.4992e+10 1751.6
##
## Step: AIC=1749.15
## ESTIMATE ~ jml_eko + prop_eko + prop_sma + prop_health + jml_smp
##
## Df Sum of Sq RSS AIC
## + jml_sd 1 1211439660 1.3382e+10 1743.2
## + prop_sd 1 543666577 1.4050e+10 1747.7
## + jml_imk 1 540905924 1.4053e+10 1747.7
## + jml_pt 1 538773207 1.4055e+10 1747.7
## + jml_kredit 1 485289929 1.4108e+10 1748.0
## + prop_imk 1 395642836 1.4198e+10 1748.6
## <none> 1.4593e+10 1749.2
## + prop_bts 1 275466324 1.4318e+10 1749.4
## + prop_sinyalinet 1 242978773 1.4350e+10 1749.6
## + prop_pt 1 232633164 1.4361e+10 1749.7
## + prop_kumuh 1 177114603 1.4416e+10 1750.0
## + jml_koperasi 1 138900197 1.4455e+10 1750.3
## + prop_blt 1 115759348 1.4478e+10 1750.4
## + prop_sktm 1 92000667 1.4501e+10 1750.6
## + jml_sma 1 83083309 1.4510e+10 1750.6
## + prop_perdesaan 1 81385451 1.4512e+10 1750.6
## + jml_medis 1 76259719 1.4517e+10 1750.7
## + prop_desaagri 1 67645184 1.4526e+10 1750.7
## + prop_desanonagri 1 67645184 1.4526e+10 1750.7
## + prop_skill 1 63504570 1.4530e+10 1750.8
## + jml_health 1 61280809 1.4532e+10 1750.8
## + prop_padatkarya 1 39429069 1.4554e+10 1750.9
## + prop_aksesjalan 1 33226974 1.4560e+10 1750.9
## + prop_bank 1 24990257 1.4568e+10 1751.0
## + prop_angkumum 1 20315601 1.4573e+10 1751.0
## + prop_kredit 1 17363335 1.4576e+10 1751.0
## + prop_koperasi 1 6854086 1.4587e+10 1751.1
## + prop_air 1 4353994 1.4589e+10 1751.1
## + jml_bank 1 1458280 1.4592e+10 1751.1
## + prop_medis 1 1052252 1.4592e+10 1751.1
## + prop_smp 1 831561 1.4593e+10 1751.1
## + prop_sani 1 23930 1.4593e+10 1751.2
##
## Step: AIC=1743.18
## ESTIMATE ~ jml_eko + prop_eko + prop_sma + prop_health + jml_smp +
## jml_sd
##
## Df Sum of Sq RSS AIC
## + prop_perdesaan 1 839617119 1.2542e+10 1739.2
## + prop_bts 1 376685098 1.3005e+10 1742.5
## <none> 1.3382e+10 1743.2
## + prop_bank 1 283821678 1.3098e+10 1743.2
## + jml_imk 1 261118562 1.3121e+10 1743.4
## + jml_bank 1 233988146 1.3148e+10 1743.5
## + prop_desaagri 1 210100222 1.3172e+10 1743.7
## + prop_desanonagri 1 210100222 1.3172e+10 1743.7
## + jml_sma 1 207936586 1.3174e+10 1743.7
## + prop_imk 1 199361973 1.3183e+10 1743.8
## + prop_kumuh 1 182413637 1.3200e+10 1743.9
## + prop_aksesjalan 1 117563445 1.3264e+10 1744.4
## + prop_kredit 1 104152415 1.3278e+10 1744.5
## + prop_air 1 83872772 1.3298e+10 1744.6
## + jml_health 1 72817535 1.3309e+10 1744.7
## + prop_koperasi 1 67119676 1.3315e+10 1744.7
## + jml_pt 1 59010742 1.3323e+10 1744.8
## + jml_medis 1 45715525 1.3336e+10 1744.9
## + prop_sani 1 40659362 1.3341e+10 1744.9
## + prop_sinyalinet 1 39792840 1.3342e+10 1744.9
## + prop_angkumum 1 28547347 1.3353e+10 1745.0
## + prop_sd 1 27352278 1.3355e+10 1745.0
## + jml_kredit 1 7734443 1.3374e+10 1745.1
## + prop_blt 1 7005833 1.3375e+10 1745.1
## + prop_padatkarya 1 5373836 1.3377e+10 1745.1
## + prop_smp 1 4842512 1.3377e+10 1745.1
## + jml_koperasi 1 3221449 1.3379e+10 1745.2
## + prop_medis 1 2815553 1.3379e+10 1745.2
## + prop_skill 1 1241172 1.3381e+10 1745.2
## + prop_pt 1 256970 1.3382e+10 1745.2
## + prop_sktm 1 126068 1.3382e+10 1745.2
##
## Step: AIC=1739.21
## ESTIMATE ~ jml_eko + prop_eko + prop_sma + prop_health + jml_smp +
## jml_sd + prop_perdesaan
##
## Df Sum of Sq RSS AIC
## + prop_bts 1 492392228 1.2050e+10 1737.5
## <none> 1.2542e+10 1739.2
## + jml_medis 1 256461262 1.2286e+10 1739.3
## + jml_health 1 178110242 1.2364e+10 1739.9
## + jml_imk 1 174694412 1.2368e+10 1739.9
## + jml_bank 1 143672995 1.2399e+10 1740.2
## + prop_bank 1 141398098 1.2401e+10 1740.2
## + prop_imk 1 140706593 1.2402e+10 1740.2
## + prop_smp 1 133804831 1.2409e+10 1740.2
## + prop_koperasi 1 121870255 1.2420e+10 1740.3
## + jml_sma 1 118098238 1.2424e+10 1740.3
## + prop_sinyalinet 1 103533257 1.2439e+10 1740.5
## + jml_pt 1 95387900 1.2447e+10 1740.5
## + prop_angkumum 1 84647320 1.2458e+10 1740.6
## + prop_desaagri 1 78442904 1.2464e+10 1740.6
## + prop_desanonagri 1 78442904 1.2464e+10 1740.6
## + prop_medis 1 60549428 1.2482e+10 1740.8
## + prop_aksesjalan 1 42551774 1.2500e+10 1740.9
## + prop_sd 1 34507561 1.2508e+10 1741.0
## + prop_skill 1 33727817 1.2509e+10 1741.0
## + prop_kumuh 1 29123117 1.2513e+10 1741.0
## + prop_blt 1 24886343 1.2517e+10 1741.0
## + prop_pt 1 24043735 1.2518e+10 1741.0
## + jml_kredit 1 22085313 1.2520e+10 1741.0
## + prop_kredit 1 12152532 1.2530e+10 1741.1
## + prop_sani 1 10689643 1.2532e+10 1741.1
## + prop_padatkarya 1 6231703 1.2536e+10 1741.2
## + prop_air 1 6049427 1.2536e+10 1741.2
## + prop_sktm 1 4504525 1.2538e+10 1741.2
## + jml_koperasi 1 744651 1.2542e+10 1741.2
##
## Step: AIC=1737.53
## ESTIMATE ~ jml_eko + prop_eko + prop_sma + prop_health + jml_smp +
## jml_sd + prop_perdesaan + prop_bts
##
## Df Sum of Sq RSS AIC
## + jml_medis 1 341929546 1.1708e+10 1736.9
## <none> 1.2050e+10 1737.5
## + jml_imk 1 225959153 1.1824e+10 1737.8
## + jml_health 1 216459901 1.1834e+10 1737.9
## + prop_imk 1 171458080 1.1879e+10 1738.2
## + jml_sma 1 160719269 1.1889e+10 1738.3
## + prop_smp 1 152563768 1.1897e+10 1738.4
## + prop_koperasi 1 134517817 1.1915e+10 1738.5
## + prop_medis 1 119866266 1.1930e+10 1738.6
## + prop_bank 1 119781992 1.1930e+10 1738.6
## + jml_bank 1 119429029 1.1931e+10 1738.6
## + prop_sd 1 117462351 1.1933e+10 1738.6
## + jml_pt 1 101494898 1.1948e+10 1738.8
## + prop_sinyalinet 1 77731080 1.1972e+10 1738.9
## + prop_angkumum 1 52296010 1.1998e+10 1739.1
## + prop_air 1 49472239 1.2000e+10 1739.2
## + prop_skill 1 46761315 1.2003e+10 1739.2
## + prop_kumuh 1 31910186 1.2018e+10 1739.3
## + prop_pt 1 30416309 1.2020e+10 1739.3
## + jml_kredit 1 23844856 1.2026e+10 1739.3
## + prop_blt 1 23448639 1.2027e+10 1739.3
## + prop_desaagri 1 22698804 1.2027e+10 1739.4
## + prop_desanonagri 1 22698804 1.2027e+10 1739.4
## + prop_aksesjalan 1 11381104 1.2039e+10 1739.4
## + prop_padatkarya 1 9357355 1.2041e+10 1739.5
## + prop_kredit 1 2727654 1.2047e+10 1739.5
## + prop_sani 1 738720 1.2049e+10 1739.5
## + jml_koperasi 1 548328 1.2049e+10 1739.5
## + prop_sktm 1 230016 1.2050e+10 1739.5
##
## Step: AIC=1736.88
## ESTIMATE ~ jml_eko + prop_eko + prop_sma + prop_health + jml_smp +
## jml_sd + prop_perdesaan + prop_bts + jml_medis
##
## Df Sum of Sq RSS AIC
## <none> 1.1708e+10 1736.9
## + jml_sma 1 245278470 1.1463e+10 1736.9
## + jml_bank 1 223857199 1.1484e+10 1737.1
## + prop_bank 1 182384214 1.1526e+10 1737.4
## + jml_imk 1 171302743 1.1537e+10 1737.5
## + prop_imk 1 138370871 1.1570e+10 1737.8
## + prop_koperasi 1 135436167 1.1573e+10 1737.8
## + prop_sd 1 83282188 1.1625e+10 1738.2
## + prop_medis 1 81347635 1.1627e+10 1738.2
## + prop_smp 1 80442774 1.1628e+10 1738.2
## + prop_sinyalinet 1 75873321 1.1632e+10 1738.3
## + jml_pt 1 61902809 1.1646e+10 1738.4
## + jml_health 1 61558309 1.1646e+10 1738.4
## + prop_angkumum 1 50061712 1.1658e+10 1738.5
## + prop_skill 1 41476379 1.1667e+10 1738.5
## + prop_air 1 35749054 1.1672e+10 1738.6
## + jml_kredit 1 32298856 1.1676e+10 1738.6
## + prop_desaagri 1 21971861 1.1686e+10 1738.7
## + prop_desanonagri 1 21971861 1.1686e+10 1738.7
## + prop_kumuh 1 17729512 1.1690e+10 1738.7
## + prop_aksesjalan 1 17267392 1.1691e+10 1738.8
## + prop_pt 1 14097347 1.1694e+10 1738.8
## + prop_padatkarya 1 8932783 1.1699e+10 1738.8
## + prop_sani 1 7144883 1.1701e+10 1738.8
## + jml_koperasi 1 4835523 1.1703e+10 1738.8
## + prop_blt 1 1065834 1.1707e+10 1738.9
## + prop_sktm 1 515328 1.1708e+10 1738.9
## + prop_kredit 1 70026 1.1708e+10 1738.9# View summary
summary(forward_model)##
## Call:
## lm(formula = ESTIMATE ~ jml_eko + prop_eko + prop_sma + prop_health +
## jml_smp + jml_sd + prop_perdesaan + prop_bts + jml_medis,
## data = sae_eda)
##
## Residuals:
## Min 1Q Median 3Q Max
## -20604 -8041 -1200 4452 59782
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 5.916e+04 9.000e+03 6.574 4.24e-09 ***
## jml_eko 4.002e+01 6.293e+00 6.359 1.09e-08 ***
## prop_eko -8.003e+03 1.783e+03 -4.490 2.31e-05 ***
## prop_sma -3.145e+05 1.218e+05 -2.582 0.011607 *
## prop_health -6.748e+04 2.412e+04 -2.798 0.006408 **
## jml_smp 1.420e+03 4.709e+02 3.015 0.003421 **
## jml_sd -7.961e+02 1.970e+02 -4.042 0.000119 ***
## prop_perdesaan 1.846e+02 6.290e+01 2.935 0.004331 **
## prop_bts 1.271e+05 6.320e+04 2.012 0.047529 *
## jml_medis 4.030e+01 2.604e+01 1.548 0.125592
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 11950 on 82 degrees of freedom
## Multiple R-squared: 0.7416, Adjusted R-squared: 0.7132
## F-statistic: 26.14 on 9 and 82 DF, p-value: < 2.2e-16# Backward elimination
backward_model <- stepAIC(modelreg_all, direction = "backward")## Start: AIC=1748.38
## ESTIMATE ~ prop_bts + prop_perdesaan + prop_sd + jml_sd + prop_smp +
## jml_smp + prop_sma + jml_sma + prop_pt + jml_pt + prop_desaagri +
## prop_desanonagri + prop_imk + jml_imk + prop_bank + jml_bank +
## prop_koperasi + jml_koperasi + prop_eko + jml_eko + prop_kredit +
## jml_kredit + prop_sktm + prop_health + jml_health + prop_skill +
## prop_blt + prop_padatkarya + prop_kumuh + prop_air + prop_sani +
## prop_aksesjalan + prop_sinyalinet + prop_medis + jml_medis +
## prop_angkumum
##
##
## Step: AIC=1748.38
## ESTIMATE ~ prop_bts + prop_perdesaan + prop_sd + jml_sd + prop_smp +
## jml_smp + prop_sma + jml_sma + prop_pt + jml_pt + prop_desaagri +
## prop_imk + jml_imk + prop_bank + jml_bank + prop_koperasi +
## jml_koperasi + prop_eko + jml_eko + prop_kredit + jml_kredit +
## prop_sktm + prop_health + jml_health + prop_skill + prop_blt +
## prop_padatkarya + prop_kumuh + prop_air + prop_sani + prop_aksesjalan +
## prop_sinyalinet + prop_medis + jml_medis + prop_angkumum
##
## Df Sum of Sq RSS AIC
## - prop_padatkarya 1 64237 7538561537 1746.4
## - prop_imk 1 1848455 7540345755 1746.4
## - prop_sani 1 5193054 7543690354 1746.4
## - prop_angkumum 1 5471793 7543969093 1746.4
## - prop_sinyalinet 1 10455915 7548953214 1746.5
## - prop_desaagri 1 11516610 7550013910 1746.5
## - prop_sktm 1 15081154 7553578453 1746.6
## - jml_imk 1 15302453 7553799753 1746.6
## - prop_medis 1 17481401 7555978701 1746.6
## - prop_aksesjalan 1 20381102 7558878402 1746.6
## - prop_skill 1 26527829 7565025129 1746.7
## - prop_kumuh 1 33557374 7572054674 1746.8
## - jml_sd 1 63046515 7601543815 1747.1
## - jml_medis 1 67590299 7606087599 1747.2
## - prop_blt 1 69867278 7608364578 1747.2
## - prop_sd 1 84597193 7623094493 1747.4
## - prop_air 1 122963669 7661460969 1747.9
## - prop_pt 1 157818031 7696315331 1748.3
## - prop_smp 1 157993361 7696490660 1748.3
## <none> 7538497300 1748.4
## - jml_pt 1 165803226 7704300525 1748.4
## - prop_bank 1 189462167 7727959467 1748.7
## - prop_eko 1 213709815 7752207115 1749.0
## - jml_health 1 255321782 7793819082 1749.4
## - jml_bank 1 312459871 7850957171 1750.1
## - jml_kredit 1 330213919 7868711218 1750.3
## - prop_sma 1 343210829 7881708129 1750.5
## - jml_eko 1 464565685 8003062984 1751.9
## - prop_kredit 1 486248786 8024746086 1752.1
## - prop_health 1 514102893 8052600193 1752.5
## - prop_perdesaan 1 579897669 8118394968 1753.2
## - jml_smp 1 589974418 8128471718 1753.3
## - jml_sma 1 618344625 8156841925 1753.6
## - prop_bts 1 647048234 8185545533 1754.0
## - jml_koperasi 1 748843290 8287340589 1755.1
## - prop_koperasi 1 928951710 8467449010 1757.1
##
## Step: AIC=1746.38
## ESTIMATE ~ prop_bts + prop_perdesaan + prop_sd + jml_sd + prop_smp +
## jml_smp + prop_sma + jml_sma + prop_pt + jml_pt + prop_desaagri +
## prop_imk + jml_imk + prop_bank + jml_bank + prop_koperasi +
## jml_koperasi + prop_eko + jml_eko + prop_kredit + jml_kredit +
## prop_sktm + prop_health + jml_health + prop_skill + prop_blt +
## prop_kumuh + prop_air + prop_sani + prop_aksesjalan + prop_sinyalinet +
## prop_medis + jml_medis + prop_angkumum
##
## Df Sum of Sq RSS AIC
## - prop_imk 1 1907706 7540469243 1744.4
## - prop_angkumum 1 5414115 7543975652 1744.4
## - prop_sani 1 6000720 7544562257 1744.5
## - prop_sinyalinet 1 10637837 7549199374 1744.5
## - prop_desaagri 1 12468095 7551029632 1744.5
## - prop_sktm 1 15023117 7553584654 1744.6
## - jml_imk 1 15511950 7554073487 1744.6
## - prop_medis 1 17527564 7556089100 1744.6
## - prop_aksesjalan 1 20969050 7559530587 1744.6
## - prop_skill 1 26605040 7565166577 1744.7
## - prop_kumuh 1 34430827 7572992364 1744.8
## - jml_sd 1 62983891 7601545427 1745.1
## - jml_medis 1 67746872 7606308409 1745.2
## - prop_blt 1 72204745 7610766282 1745.3
## - prop_sd 1 84624873 7623186409 1745.4
## - prop_air 1 126165740 7664727277 1745.9
## - prop_smp 1 158822266 7697383803 1746.3
## - prop_pt 1 161102555 7699664091 1746.3
## <none> 7538561537 1746.4
## - jml_pt 1 169233539 7707795076 1746.4
## - prop_bank 1 193779085 7732340621 1746.7
## - prop_eko 1 214055753 7752617289 1747.0
## - jml_health 1 255315049 7793876586 1747.4
## - jml_bank 1 319260455 7857821992 1748.2
## - jml_kredit 1 330731727 7869293264 1748.3
## - prop_sma 1 351020074 7889581611 1748.6
## - jml_eko 1 464703952 8003265488 1749.9
## - prop_kredit 1 498253151 8036814688 1750.3
## - prop_health 1 514039400 8052600936 1750.5
## - jml_smp 1 590140491 8128702028 1751.3
## - prop_perdesaan 1 602227796 8140789332 1751.5
## - jml_sma 1 625502385 8164063921 1751.7
## - prop_bts 1 648031633 8186593169 1752.0
## - jml_koperasi 1 748779699 8287341236 1753.1
## - prop_koperasi 1 929852661 8468414198 1755.1
##
## Step: AIC=1744.4
## ESTIMATE ~ prop_bts + prop_perdesaan + prop_sd + jml_sd + prop_smp +
## jml_smp + prop_sma + jml_sma + prop_pt + jml_pt + prop_desaagri +
## jml_imk + prop_bank + jml_bank + prop_koperasi + jml_koperasi +
## prop_eko + jml_eko + prop_kredit + jml_kredit + prop_sktm +
## prop_health + jml_health + prop_skill + prop_blt + prop_kumuh +
## prop_air + prop_sani + prop_aksesjalan + prop_sinyalinet +
## prop_medis + jml_medis + prop_angkumum
##
## Df Sum of Sq RSS AIC
## - prop_sani 1 5069315 7545538558 1742.5
## - prop_angkumum 1 5078623 7545547865 1742.5
## - prop_sinyalinet 1 10072108 7550541351 1742.5
## - prop_desaagri 1 12113414 7552582657 1742.5
## - prop_sktm 1 14192579 7554661822 1742.6
## - prop_aksesjalan 1 20002138 7560471381 1742.7
## - prop_medis 1 24579891 7565049133 1742.7
## - prop_skill 1 25032699 7565501942 1742.7
## - prop_kumuh 1 37976478 7578445721 1742.9
## - jml_sd 1 67768731 7608237974 1743.2
## - prop_blt 1 70312043 7610781286 1743.3
## - prop_sd 1 82749905 7623219148 1743.4
## - jml_medis 1 86952336 7627421579 1743.5
## - prop_air 1 126616867 7667086110 1743.9
## - prop_smp 1 157043214 7697512457 1744.3
## - prop_pt 1 165461350 7705930593 1744.4
## <none> 7540469243 1744.4
## - jml_pt 1 175576192 7716045435 1744.5
## - prop_bank 1 193931614 7734400856 1744.7
## - jml_imk 1 197328989 7737798232 1744.8
## - prop_eko 1 220326872 7760796115 1745.0
## - jml_health 1 253415972 7793885214 1745.4
## - jml_bank 1 319733972 7860203215 1746.2
## - jml_kredit 1 330490434 7870959676 1746.3
## - prop_sma 1 370702312 7911171555 1746.8
## - jml_eko 1 479003885 8019473127 1748.1
## - prop_kredit 1 510783362 8051252604 1748.4
## - prop_health 1 513017374 8053486617 1748.5
## - prop_perdesaan 1 607266698 8147735941 1749.5
## - jml_smp 1 613446206 8153915449 1749.6
## - jml_sma 1 652575063 8193044306 1750.0
## - prop_bts 1 654796799 8195266042 1750.1
## - jml_koperasi 1 757013407 8297482650 1751.2
## - prop_koperasi 1 935543982 8476013224 1753.2
##
## Step: AIC=1742.46
## ESTIMATE ~ prop_bts + prop_perdesaan + prop_sd + jml_sd + prop_smp +
## jml_smp + prop_sma + jml_sma + prop_pt + jml_pt + prop_desaagri +
## jml_imk + prop_bank + jml_bank + prop_koperasi + jml_koperasi +
## prop_eko + jml_eko + prop_kredit + jml_kredit + prop_sktm +
## prop_health + jml_health + prop_skill + prop_blt + prop_kumuh +
## prop_air + prop_aksesjalan + prop_sinyalinet + prop_medis +
## jml_medis + prop_angkumum
##
## Df Sum of Sq RSS AIC
## - prop_angkumum 1 5931954 7551470512 1740.5
## - prop_desaagri 1 10974130 7556512688 1740.6
## - prop_sinyalinet 1 13914001 7559452559 1740.6
## - prop_sktm 1 17612568 7563151126 1740.7
## - prop_aksesjalan 1 17872482 7563411040 1740.7
## - prop_skill 1 21845881 7567384439 1740.7
## - prop_medis 1 29745231 7575283789 1740.8
## - prop_kumuh 1 43469105 7589007663 1741.0
## - prop_blt 1 71711016 7617249574 1741.3
## - prop_sd 1 79970501 7625509059 1741.4
## - jml_sd 1 82548833 7628087391 1741.5
## - jml_medis 1 91923258 7637461816 1741.6
## - prop_air 1 124204311 7669742869 1742.0
## - prop_pt 1 164821207 7710359765 1742.5
## <none> 7545538558 1742.5
## - jml_pt 1 175965148 7721503706 1742.6
## - prop_smp 1 188644357 7734182915 1742.7
## - jml_imk 1 195274573 7740813131 1742.8
## - prop_bank 1 210261130 7755799688 1743.0
## - prop_eko 1 219628705 7765167263 1743.1
## - jml_health 1 265304951 7810843509 1743.6
## - jml_kredit 1 331110573 7876649131 1744.4
## - jml_bank 1 343467281 7889005839 1744.6
## - prop_sma 1 407340975 7952879533 1745.3
## - jml_eko 1 484074064 8029612622 1746.2
## - prop_kredit 1 511247582 8056786140 1746.5
## - prop_health 1 521330612 8066869170 1746.6
## - prop_perdesaan 1 602644032 8148182590 1747.5
## - prop_bts 1 649730706 8195269264 1748.1
## - jml_smp 1 661283377 8206821935 1748.2
## - jml_sma 1 694858609 8240397167 1748.6
## - jml_koperasi 1 752905007 8298443565 1749.2
## - prop_koperasi 1 932996439 8478534997 1751.2
##
## Step: AIC=1740.54
## ESTIMATE ~ prop_bts + prop_perdesaan + prop_sd + jml_sd + prop_smp +
## jml_smp + prop_sma + jml_sma + prop_pt + jml_pt + prop_desaagri +
## jml_imk + prop_bank + jml_bank + prop_koperasi + jml_koperasi +
## prop_eko + jml_eko + prop_kredit + jml_kredit + prop_sktm +
## prop_health + jml_health + prop_skill + prop_blt + prop_kumuh +
## prop_air + prop_aksesjalan + prop_sinyalinet + prop_medis +
## jml_medis
##
## Df Sum of Sq RSS AIC
## - prop_sinyalinet 1 11734702 7563205214 1738.7
## - prop_desaagri 1 12306015 7563776527 1738.7
## - prop_aksesjalan 1 14925527 7566396039 1738.7
## - prop_skill 1 17904339 7569374851 1738.8
## - prop_sktm 1 19653349 7571123861 1738.8
## - prop_medis 1 27719731 7579190243 1738.9
## - prop_kumuh 1 46590175 7598060687 1739.1
## - prop_sd 1 77016269 7628486781 1739.5
## - jml_sd 1 82051440 7633521952 1739.5
## - prop_blt 1 84997240 7636467752 1739.6
## - jml_medis 1 89343525 7640814037 1739.6
## - prop_air 1 144663055 7696133567 1740.3
## - prop_pt 1 161170593 7712641105 1740.5
## <none> 7551470512 1740.5
## - jml_pt 1 172218464 7723688976 1740.6
## - prop_smp 1 190487057 7741957569 1740.8
## - jml_imk 1 197692613 7749163125 1740.9
## - prop_bank 1 214114735 7765585247 1741.1
## - prop_eko 1 217541520 7769012032 1741.2
## - jml_health 1 277069036 7828539548 1741.8
## - jml_bank 1 348146300 7899616812 1742.7
## - jml_kredit 1 350103214 7901573726 1742.7
## - prop_sma 1 407414165 7958884677 1743.4
## - jml_eko 1 482504782 8033975294 1744.2
## - prop_kredit 1 526114748 8077585260 1744.7
## - prop_health 1 538767596 8090238108 1744.9
## - prop_perdesaan 1 609846770 8161317282 1745.7
## - jml_smp 1 665310904 8216781416 1746.3
## - prop_bts 1 676008496 8227479008 1746.4
## - jml_sma 1 695213642 8246684154 1746.6
## - jml_koperasi 1 787775080 8339245592 1747.7
## - prop_koperasi 1 970173696 8521644208 1749.7
##
## Step: AIC=1738.68
## ESTIMATE ~ prop_bts + prop_perdesaan + prop_sd + jml_sd + prop_smp +
## jml_smp + prop_sma + jml_sma + prop_pt + jml_pt + prop_desaagri +
## jml_imk + prop_bank + jml_bank + prop_koperasi + jml_koperasi +
## prop_eko + jml_eko + prop_kredit + jml_kredit + prop_sktm +
## prop_health + jml_health + prop_skill + prop_blt + prop_kumuh +
## prop_air + prop_aksesjalan + prop_medis + jml_medis
##
## Df Sum of Sq RSS AIC
## - prop_desaagri 1 7621669 7570826882 1736.8
## - prop_aksesjalan 1 10414431 7573619644 1736.8
## - prop_skill 1 12639061 7575844274 1736.8
## - prop_sktm 1 13018652 7576223866 1736.8
## - prop_medis 1 30759984 7593965197 1737.0
## - prop_kumuh 1 43969921 7607175134 1737.2
## - jml_sd 1 78475499 7641680713 1737.6
## - prop_blt 1 81918805 7645124019 1737.7
## - jml_medis 1 90546650 7653751864 1737.8
## - prop_sd 1 97241968 7660447182 1737.8
## - prop_air 1 142539964 7705745177 1738.4
## - prop_pt 1 161333092 7724538306 1738.6
## <none> 7563205214 1738.7
## - jml_pt 1 172496298 7735701512 1738.8
## - prop_smp 1 193575357 7756780570 1739.0
## - prop_eko 1 217374694 7780579908 1739.3
## - jml_imk 1 221804443 7785009657 1739.3
## - prop_bank 1 226238326 7789443539 1739.4
## - jml_health 1 279682745 7842887958 1740.0
## - jml_bank 1 365004837 7928210050 1741.0
## - jml_kredit 1 409168523 7972373737 1741.5
## - prop_sma 1 413825461 7977030675 1741.6
## - jml_eko 1 478698454 8041903667 1742.3
## - prop_health 1 538852052 8102057265 1743.0
## - prop_perdesaan 1 607759542 8170964756 1743.8
## - prop_kredit 1 629816422 8193021635 1744.0
## - jml_smp 1 682863983 8246069197 1744.6
## - jml_sma 1 697638689 8260843903 1744.8
## - prop_bts 1 734575943 8297781156 1745.2
## - jml_koperasi 1 776223615 8339428828 1745.7
## - prop_koperasi 1 960145119 8523350333 1747.7
##
## Step: AIC=1736.77
## ESTIMATE ~ prop_bts + prop_perdesaan + prop_sd + jml_sd + prop_smp +
## jml_smp + prop_sma + jml_sma + prop_pt + jml_pt + jml_imk +
## prop_bank + jml_bank + prop_koperasi + jml_koperasi + prop_eko +
## jml_eko + prop_kredit + jml_kredit + prop_sktm + prop_health +
## jml_health + prop_skill + prop_blt + prop_kumuh + prop_air +
## prop_aksesjalan + prop_medis + jml_medis
##
## Df Sum of Sq RSS AIC
## - prop_skill 1 8387030 7579213912 1734.9
## - prop_sktm 1 9629629 7580456511 1734.9
## - prop_aksesjalan 1 10294049 7581120931 1734.9
## - prop_kumuh 1 38890633 7609717515 1735.2
## - prop_medis 1 45106727 7615933609 1735.3
## - prop_blt 1 75277236 7646104118 1735.7
## - jml_sd 1 91675999 7662502881 1735.9
## - prop_sd 1 96092679 7666919562 1735.9
## - jml_medis 1 109894476 7680721358 1736.1
## - prop_air 1 138706513 7709533396 1736.4
## - prop_pt 1 162586490 7733413372 1736.7
## <none> 7570826882 1736.8
## - jml_pt 1 173405447 7744232329 1736.9
## - prop_smp 1 194120032 7764946915 1737.1
## - prop_eko 1 217688611 7788515493 1737.4
## - jml_imk 1 219426833 7790253715 1737.4
## - prop_bank 1 244967296 7815794179 1737.7
## - jml_health 1 283099496 7853926378 1738.2
## - jml_bank 1 382394911 7953221793 1739.3
## - jml_kredit 1 402594364 7973421247 1739.5
## - prop_sma 1 413793724 7984620606 1739.7
## - jml_eko 1 493824260 8064651142 1740.6
## - prop_health 1 549911814 8120738696 1741.2
## - prop_kredit 1 629810934 8200637816 1742.1
## - jml_smp 1 675479006 8246305888 1742.6
## - jml_sma 1 690310565 8261137447 1742.8
## - prop_bts 1 781759065 8352585947 1743.8
## - jml_koperasi 1 841821286 8412648168 1744.5
## - prop_perdesaan 1 916022477 8486849359 1745.3
## - prop_koperasi 1 1012280169 8583107051 1746.3
##
## Step: AIC=1734.87
## ESTIMATE ~ prop_bts + prop_perdesaan + prop_sd + jml_sd + prop_smp +
## jml_smp + prop_sma + jml_sma + prop_pt + jml_pt + jml_imk +
## prop_bank + jml_bank + prop_koperasi + jml_koperasi + prop_eko +
## jml_eko + prop_kredit + jml_kredit + prop_sktm + prop_health +
## jml_health + prop_blt + prop_kumuh + prop_air + prop_aksesjalan +
## prop_medis + jml_medis
##
## Df Sum of Sq RSS AIC
## - prop_sktm 1 6966498 7586180410 1733.0
## - prop_aksesjalan 1 9874653 7589088565 1733.0
## - prop_medis 1 42038612 7621252523 1733.4
## - prop_kumuh 1 42151945 7621365857 1733.4
## - prop_blt 1 88426524 7667640436 1733.9
## - prop_sd 1 89416625 7668630537 1734.0
## - jml_sd 1 92880624 7672094536 1734.0
## - jml_medis 1 105633503 7684847415 1734.2
## - prop_air 1 150001571 7729215482 1734.7
## - prop_pt 1 155120423 7734334335 1734.7
## - jml_pt 1 165963313 7745177225 1734.9
## <none> 7579213912 1734.9
## - prop_eko 1 213594250 7792808161 1735.4
## - prop_smp 1 214552899 7793766811 1735.4
## - jml_imk 1 234759510 7813973422 1735.7
## - prop_bank 1 256734087 7835947999 1735.9
## - jml_health 1 302906373 7882120285 1736.5
## - jml_bank 1 397755932 7976969844 1737.6
## - jml_kredit 1 424652391 8003866303 1737.9
## - prop_sma 1 430185859 8009399771 1738.0
## - jml_eko 1 489654583 8068868495 1738.6
## - prop_health 1 572468313 8151682225 1739.6
## - prop_kredit 1 638905912 8218119823 1740.3
## - jml_smp 1 701232647 8280446559 1741.0
## - jml_sma 1 705062845 8284276757 1741.1
## - prop_bts 1 779832333 8359046245 1741.9
## - jml_koperasi 1 834788319 8414002231 1742.5
## - prop_perdesaan 1 908276753 8487490665 1743.3
## - prop_koperasi 1 1007756025 8586969937 1744.4
##
## Step: AIC=1732.96
## ESTIMATE ~ prop_bts + prop_perdesaan + prop_sd + jml_sd + prop_smp +
## jml_smp + prop_sma + jml_sma + prop_pt + jml_pt + jml_imk +
## prop_bank + jml_bank + prop_koperasi + jml_koperasi + prop_eko +
## jml_eko + prop_kredit + jml_kredit + prop_health + jml_health +
## prop_blt + prop_kumuh + prop_air + prop_aksesjalan + prop_medis +
## jml_medis
##
## Df Sum of Sq RSS AIC
## - prop_aksesjalan 1 11432019 7597612429 1731.1
## - prop_kumuh 1 37565643 7623746052 1731.4
## - prop_medis 1 43018215 7629198624 1731.5
## - prop_blt 1 89132751 7675313160 1732.0
## - jml_sd 1 92020938 7678201348 1732.1
## - prop_sd 1 96587868 7682768277 1732.1
## - jml_medis 1 105065044 7691245454 1732.2
## - prop_air 1 145266501 7731446911 1732.7
## - prop_pt 1 152124910 7738305319 1732.8
## - jml_pt 1 162608899 7748789309 1732.9
## <none> 7586180410 1733.0
## - prop_smp 1 224184035 7810364444 1733.6
## - prop_eko 1 227396345 7813576754 1733.7
## - jml_imk 1 238084704 7824265113 1733.8
## - prop_bank 1 262592756 7848773165 1734.1
## - jml_health 1 302883923 7889064333 1734.6
## - jml_bank 1 399421404 7985601813 1735.7
## - prop_sma 1 428892311 8015072721 1736.0
## - jml_eko 1 497005963 8083186373 1736.8
## - jml_kredit 1 497261513 8083441922 1736.8
## - prop_health 1 575221263 8161401673 1737.7
## - jml_sma 1 701807844 8287988253 1739.1
## - jml_smp 1 707740538 8293920948 1739.2
## - prop_kredit 1 725945520 8312125930 1739.4
## - prop_bts 1 783995497 8370175907 1740.0
## - jml_koperasi 1 831009948 8417190358 1740.5
## - prop_perdesaan 1 907819627 8494000037 1741.4
## - prop_koperasi 1 1001521137 8587701546 1742.4
##
## Step: AIC=1731.1
## ESTIMATE ~ prop_bts + prop_perdesaan + prop_sd + jml_sd + prop_smp +
## jml_smp + prop_sma + jml_sma + prop_pt + jml_pt + jml_imk +
## prop_bank + jml_bank + prop_koperasi + jml_koperasi + prop_eko +
## jml_eko + prop_kredit + jml_kredit + prop_health + jml_health +
## prop_blt + prop_kumuh + prop_air + prop_medis + jml_medis
##
## Df Sum of Sq RSS AIC
## - prop_kumuh 1 31865545 7629477974 1729.5
## - prop_medis 1 49797125 7647409554 1729.7
## - prop_blt 1 79744374 7677356802 1730.1
## - jml_sd 1 90963028 7688575457 1730.2
## - prop_sd 1 98398345 7696010774 1730.3
## - jml_medis 1 114440179 7712052608 1730.5
## - prop_air 1 136483880 7734096309 1730.7
## - prop_pt 1 145174564 7742786993 1730.8
## - jml_pt 1 155016584 7752629013 1731.0
## <none> 7597612429 1731.1
## - prop_smp 1 215868791 7813481219 1731.7
## - jml_imk 1 246242249 7843854678 1732.0
## - prop_bank 1 260517733 7858130162 1732.2
## - prop_eko 1 263493684 7861106113 1732.2
## - jml_health 1 294483976 7892096405 1732.6
## - jml_bank 1 395939174 7993551603 1733.8
## - prop_sma 1 428095281 8025707709 1734.1
## - jml_kredit 1 486632244 8084244673 1734.8
## - jml_eko 1 544913810 8142526238 1735.5
## - prop_health 1 565128672 8162741101 1735.7
## - jml_sma 1 693676804 8291289232 1737.1
## - jml_smp 1 696463404 8294075832 1737.2
## - prop_kredit 1 728284655 8325897084 1737.5
## - prop_bts 1 813187319 8410799748 1738.5
## - jml_koperasi 1 896801952 8494414381 1739.4
## - prop_perdesaan 1 954000782 8551613211 1740.0
## - prop_koperasi 1 1077767617 8675380046 1741.3
##
## Step: AIC=1729.48
## ESTIMATE ~ prop_bts + prop_perdesaan + prop_sd + jml_sd + prop_smp +
## jml_smp + prop_sma + jml_sma + prop_pt + jml_pt + jml_imk +
## prop_bank + jml_bank + prop_koperasi + jml_koperasi + prop_eko +
## jml_eko + prop_kredit + jml_kredit + prop_health + jml_health +
## prop_blt + prop_air + prop_medis + jml_medis
##
## Df Sum of Sq RSS AIC
## - prop_medis 1 45987314 7675465288 1728.0
## - prop_blt 1 85401096 7714879071 1728.5
## - jml_sd 1 86587661 7716065635 1728.5
## - prop_sd 1 105177117 7734655091 1728.7
## - jml_medis 1 114138588 7743616562 1728.8
## - prop_air 1 131847811 7761325786 1729.1
## - prop_pt 1 136719895 7766197869 1729.1
## - jml_pt 1 149643591 7779121565 1729.3
## <none> 7629477974 1729.5
## - prop_smp 1 199090797 7828568771 1729.8
## - jml_imk 1 247344563 7876822537 1730.4
## - prop_bank 1 253677396 7883155370 1730.5
## - prop_eko 1 266940998 7896418972 1730.7
## - jml_health 1 294002534 7923480508 1731.0
## - jml_bank 1 387996647 8017474621 1732.0
## - prop_sma 1 408036646 8037514620 1732.3
## - jml_kredit 1 493732188 8123210162 1733.2
## - jml_eko 1 549812043 8179290017 1733.9
## - prop_health 1 571536180 8201014154 1734.1
## - jml_sma 1 668040471 8297518446 1735.2
## - jml_smp 1 672452823 8301930797 1735.2
## - prop_kredit 1 722444065 8351922039 1735.8
## - prop_bts 1 818585290 8448063264 1736.9
## - jml_koperasi 1 928614005 8558091979 1738.0
## - prop_koperasi 1 1108385391 8737863365 1740.0
## - prop_perdesaan 1 1132865691 8762343665 1740.2
##
## Step: AIC=1728.03
## ESTIMATE ~ prop_bts + prop_perdesaan + prop_sd + jml_sd + prop_smp +
## jml_smp + prop_sma + jml_sma + prop_pt + jml_pt + jml_imk +
## prop_bank + jml_bank + prop_koperasi + jml_koperasi + prop_eko +
## jml_eko + prop_kredit + jml_kredit + prop_health + jml_health +
## prop_blt + prop_air + jml_medis
##
## Df Sum of Sq RSS AIC
## - prop_blt 1 86391732 7761857019 1727.1
## - jml_sd 1 88072777 7763538064 1727.1
## - prop_sd 1 98928142 7774393430 1727.2
## - jml_medis 1 114528652 7789993939 1727.4
## - prop_air 1 131814869 7807280156 1727.6
## - prop_pt 1 154063736 7829529024 1727.9
## - jml_pt 1 162409418 7837874706 1728.0
## <none> 7675465288 1728.0
## - prop_smp 1 204395352 7879860640 1728.5
## - prop_eko 1 234210235 7909675523 1728.8
## - jml_imk 1 259873831 7935339119 1729.1
## - prop_bank 1 282840209 7958305496 1729.4
## - prop_sma 1 386235509 8061700797 1730.5
## - jml_bank 1 422998550 8098463838 1731.0
## - jml_eko 1 505313276 8180778563 1731.9
## - jml_kredit 1 564929597 8240394884 1732.6
## - jml_health 1 592274143 8267739431 1732.9
## - jml_sma 1 630829136 8306294424 1733.3
## - jml_smp 1 665639733 8341105020 1733.7
## - prop_kredit 1 742898376 8418363663 1734.5
## - prop_bts 1 860138166 8535603454 1735.8
## - jml_koperasi 1 902162731 8577628019 1736.3
## - prop_health 1 1085383504 8760848792 1738.2
## - prop_koperasi 1 1091518896 8766984184 1738.3
## - prop_perdesaan 1 1251330794 8926796081 1739.9
##
## Step: AIC=1727.06
## ESTIMATE ~ prop_bts + prop_perdesaan + prop_sd + jml_sd + prop_smp +
## jml_smp + prop_sma + jml_sma + prop_pt + jml_pt + jml_imk +
## prop_bank + jml_bank + prop_koperasi + jml_koperasi + prop_eko +
## jml_eko + prop_kredit + jml_kredit + prop_health + jml_health +
## prop_air + jml_medis
##
## Df Sum of Sq RSS AIC
## - jml_sd 1 79770922 7841627942 1726.0
## - jml_medis 1 87357767 7849214787 1726.1
## - prop_sd 1 111213827 7873070846 1726.4
## - prop_air 1 119799976 7881656995 1726.5
## - prop_smp 1 165396561 7927253580 1727.0
## <none> 7761857019 1727.1
## - jml_pt 1 177927543 7939784563 1727.2
## - prop_pt 1 183175257 7945032277 1727.2
## - jml_imk 1 228326776 7990183795 1727.7
## - prop_eko 1 236611336 7998468355 1727.8
## - prop_bank 1 269404109 8031261128 1728.2
## - prop_sma 1 346076757 8107933776 1729.1
## - jml_bank 1 417013138 8178870157 1729.9
## - jml_eko 1 488180308 8250037327 1730.7
## - jml_kredit 1 512484574 8274341593 1731.0
## - jml_sma 1 572579039 8334436058 1731.6
## - jml_health 1 575584984 8337442004 1731.7
## - jml_smp 1 604275906 8366132925 1732.0
## - prop_kredit 1 749736452 8511593471 1733.5
## - prop_bts 1 822592918 8584449937 1734.3
## - jml_koperasi 1 866917101 8628774120 1734.8
## - prop_health 1 1045002815 8806859835 1736.7
## - prop_koperasi 1 1058351053 8820208072 1736.8
## - prop_perdesaan 1 1295522224 9057379243 1739.3
##
## Step: AIC=1726
## ESTIMATE ~ prop_bts + prop_perdesaan + prop_sd + prop_smp + jml_smp +
## prop_sma + jml_sma + prop_pt + jml_pt + jml_imk + prop_bank +
## jml_bank + prop_koperasi + jml_koperasi + prop_eko + jml_eko +
## prop_kredit + jml_kredit + prop_health + jml_health + prop_air +
## jml_medis
##
## Df Sum of Sq RSS AIC
## - jml_medis 1 65614032 7907241974 1724.8
## - prop_smp 1 95698111 7937326053 1725.1
## - prop_eko 1 167377579 8009005521 1726.0
## <none> 7841627942 1726.0
## - prop_air 1 202403631 8044031573 1726.3
## - prop_bank 1 217051677 8058679618 1726.5
## - prop_pt 1 240794656 8082422598 1726.8
## - jml_imk 1 243981330 8085609272 1726.8
## - jml_pt 1 249016423 8090644365 1726.9
## - prop_sma 1 274669347 8116297289 1727.2
## - jml_bank 1 352074849 8193702791 1728.0
## - jml_eko 1 408459992 8250087934 1728.7
## - jml_sma 1 494576991 8336204933 1729.6
## - jml_health 1 507348563 8348976505 1729.8
## - jml_smp 1 532194276 8373822218 1730.0
## - jml_koperasi 1 851821904 8693449845 1733.5
## - jml_kredit 1 886649054 8728276996 1733.9
## - prop_bts 1 948568284 8790196226 1734.5
## - prop_health 1 971034019 8812661961 1734.8
## - prop_koperasi 1 1050664593 8892292535 1735.6
## - prop_kredit 1 1239573107 9081201049 1737.5
## - prop_perdesaan 1 1288056494 9129684436 1738.0
## - prop_sd 1 1291022194 9132650136 1738.0
##
## Step: AIC=1724.77
## ESTIMATE ~ prop_bts + prop_perdesaan + prop_sd + prop_smp + jml_smp +
## prop_sma + jml_sma + prop_pt + jml_pt + jml_imk + prop_bank +
## jml_bank + prop_koperasi + jml_koperasi + prop_eko + jml_eko +
## prop_kredit + jml_kredit + prop_health + jml_health + prop_air
##
## Df Sum of Sq RSS AIC
## - prop_eko 1 116051159 8023293132 1724.1
## - prop_smp 1 158030314 8065272288 1724.6
## <none> 7907241974 1724.8
## - prop_air 1 203351090 8110593063 1725.1
## - jml_imk 1 279916277 8187158250 1726.0
## - prop_pt 1 283202122 8190444096 1726.0
## - jml_pt 1 285498634 8192740607 1726.0
## - prop_sma 1 287742292 8194984265 1726.1
## - prop_bank 1 287940273 8195182246 1726.1
## - jml_eko 1 343488605 8250730578 1726.7
## - jml_bank 1 425095972 8332337946 1727.6
## - jml_sma 1 505730883 8412972856 1728.5
## - jml_smp 1 621913008 8529154982 1729.7
## - jml_koperasi 1 786303533 8693545506 1731.5
## - jml_health 1 846521018 8753762992 1732.1
## - prop_bts 1 900168286 8807410260 1732.7
## - prop_koperasi 1 985261114 8892503088 1733.6
## - jml_kredit 1 1086836837 8994078811 1734.6
## - prop_perdesaan 1 1222791427 9130033400 1736.0
## - prop_health 1 1259697954 9166939928 1736.4
## - prop_sd 1 1344495861 9251737835 1737.2
## - prop_kredit 1 1658346234 9565588208 1740.3
##
## Step: AIC=1724.11
## ESTIMATE ~ prop_bts + prop_perdesaan + prop_sd + prop_smp + jml_smp +
## prop_sma + jml_sma + prop_pt + jml_pt + jml_imk + prop_bank +
## jml_bank + prop_koperasi + jml_koperasi + jml_eko + prop_kredit +
## jml_kredit + prop_health + jml_health + prop_air
##
## Df Sum of Sq RSS AIC
## <none> 8.0233e+09 1724.1
## - prop_air 1 203847406 8.2271e+09 1724.4
## - prop_smp 1 236474847 8.2598e+09 1724.8
## - jml_imk 1 289356364 8.3126e+09 1725.4
## - prop_sma 1 293430609 8.3167e+09 1725.4
## - prop_bank 1 361644236 8.3849e+09 1726.2
## - jml_eko 1 457944121 8.4812e+09 1727.2
## - jml_pt 1 475781167 8.4991e+09 1727.4
## - jml_sma 1 483167185 8.5065e+09 1727.5
## - prop_pt 1 501009354 8.5243e+09 1727.7
## - jml_bank 1 515932679 8.5392e+09 1727.8
## - jml_koperasi 1 683657126 8.7070e+09 1729.6
## - jml_smp 1 718539441 8.7418e+09 1730.0
## - prop_bts 1 867779330 8.8911e+09 1731.6
## - prop_koperasi 1 872172213 8.8955e+09 1731.6
## - jml_kredit 1 1169748793 9.1930e+09 1734.6
## - prop_perdesaan 1 1207283228 9.2306e+09 1735.0
## - prop_sd 1 1584979002 9.6083e+09 1738.7
## - jml_health 1 1638675495 9.6620e+09 1739.2
## - prop_kredit 1 1930852887 9.9541e+09 1742.0
## - prop_health 1 2495729002 1.0519e+10 1747.0# View summary
summary(backward_model)##
## Call:
## lm(formula = ESTIMATE ~ prop_bts + prop_perdesaan + prop_sd +
## prop_smp + jml_smp + prop_sma + jml_sma + prop_pt + jml_pt +
## jml_imk + prop_bank + jml_bank + prop_koperasi + jml_koperasi +
## jml_eko + prop_kredit + jml_kredit + prop_health + jml_health +
## prop_air, data = sae_eda)
##
## Residuals:
## Min 1Q Median 3Q Max
## -16318 -7088 -972 4873 36596
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 4.954e+04 1.253e+04 3.954 0.000179 ***
## prop_bts 1.630e+05 5.882e+04 2.771 0.007126 **
## prop_perdesaan 2.159e+02 6.606e+01 3.269 0.001668 **
## prop_sd -2.274e+05 6.073e+04 -3.745 0.000363 ***
## prop_smp -3.499e+05 2.419e+05 -1.447 0.152412
## jml_smp 2.880e+03 1.142e+03 2.522 0.013928 *
## prop_sma 4.392e+05 2.726e+05 1.611 0.111528
## jml_sma -2.430e+03 1.175e+03 -2.068 0.042307 *
## prop_pt -1.034e+06 4.909e+05 -2.106 0.038777 *
## jml_pt 4.202e+03 2.048e+03 2.052 0.043868 *
## jml_imk -2.955e+00 1.847e+00 -1.600 0.113999
## prop_bank 3.471e+05 1.940e+05 1.789 0.077891 .
## jml_bank -1.793e+03 8.391e+02 -2.137 0.036067 *
## prop_koperasi 3.100e+05 1.116e+05 2.778 0.006989 **
## jml_koperasi -1.371e+03 5.574e+02 -2.460 0.016345 *
## jml_eko 1.121e+01 5.567e+00 2.013 0.047900 *
## prop_kredit 6.861e+05 1.660e+05 4.134 9.65e-05 ***
## jml_kredit -2.446e+03 7.604e+02 -3.217 0.001950 **
## prop_health -2.697e+05 5.740e+04 -4.699 1.24e-05 ***
## jml_health 8.733e+02 2.293e+02 3.808 0.000295 ***
## prop_air 6.220e+01 4.631e+01 1.343 0.183520
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 10630 on 71 degrees of freedom
## Multiple R-squared: 0.8229, Adjusted R-squared: 0.773
## F-statistic: 16.49 on 20 and 71 DF, p-value: < 2.2e-16- selecting variables using stepwise, backward, and forward (only variables that significantly correlated with ESTIMATE)
# Null model (intercept only)
preselected_data <- sae_var %>%
dplyr::select(ESTIMATE,jml_sd,jml_smp,jml_eko,jml_health,
jml_medis,jml_bank,prop_blt,
prop_sktm,jml_koperasi, prop_sani) %>%
na.omit()
null_model <- lm(ESTIMATE ~ 1, data = preselected_data)
modelreg = lm(ESTIMATE ~ ., preselected_data)# Stepwise regression
stepwise_model <- stepAIC(null_model, scope = list(lower = null_model, upper = modelreg), direction = "both")## Start: AIC=1843.36
## ESTIMATE ~ 1
##
## Df Sum of Sq RSS AIC
## + jml_eko 1 1.7237e+10 2.8065e+10 1801.3
## + jml_smp 1 1.4362e+10 3.0939e+10 1810.3
## + jml_health 1 1.3657e+10 3.1644e+10 1812.4
## + jml_sd 1 1.2381e+10 3.2920e+10 1816.0
## + jml_medis 1 9.5524e+09 3.5749e+10 1823.6
## + prop_blt 1 3.2621e+09 4.2039e+10 1838.5
## + prop_sktm 1 1.8092e+09 4.3492e+10 1841.6
## + jml_bank 1 1.4528e+09 4.3849e+10 1842.4
## + jml_koperasi 1 1.4420e+09 4.3859e+10 1842.4
## + prop_sani 1 1.4059e+09 4.3896e+10 1842.5
## <none> 4.5301e+10 1843.4
##
## Step: AIC=1801.31
## ESTIMATE ~ jml_eko
##
## Df Sum of Sq RSS AIC
## + jml_bank 1 3.0669e+09 2.4998e+10 1792.7
## + jml_smp 1 1.6791e+09 2.6386e+10 1797.6
## + jml_sd 1 1.3498e+09 2.6715e+10 1798.8
## + jml_koperasi 1 1.0745e+09 2.6990e+10 1799.7
## + prop_sktm 1 6.6751e+08 2.7397e+10 1801.1
## <none> 2.8065e+10 1801.3
## + jml_health 1 2.2825e+08 2.7836e+10 1802.6
## + jml_medis 1 2.2512e+08 2.7840e+10 1802.6
## + prop_sani 1 9.8175e+07 2.7966e+10 1803.0
## + prop_blt 1 4.1066e+06 2.8061e+10 1803.3
## - jml_eko 1 1.7237e+10 4.5301e+10 1843.4
##
## Step: AIC=1792.66
## ESTIMATE ~ jml_eko + jml_bank
##
## Df Sum of Sq RSS AIC
## + jml_smp 1 1.6590e+09 2.3339e+10 1788.3
## + prop_sktm 1 1.5112e+09 2.3487e+10 1788.9
## + jml_medis 1 1.2534e+09 2.3744e+10 1789.9
## + jml_koperasi 1 1.2021e+09 2.3796e+10 1790.1
## + jml_health 1 1.1695e+09 2.3828e+10 1790.3
## <none> 2.4998e+10 1792.7
## + prop_blt 1 3.8617e+08 2.4612e+10 1793.2
## + jml_sd 1 2.5636e+08 2.4741e+10 1793.7
## + prop_sani 1 1.1310e+08 2.4885e+10 1794.2
## - jml_bank 1 3.0669e+09 2.8065e+10 1801.3
## - jml_eko 1 1.8851e+10 4.3849e+10 1842.4
##
## Step: AIC=1788.35
## ESTIMATE ~ jml_eko + jml_bank + jml_smp
##
## Df Sum of Sq RSS AIC
## + prop_sktm 1 1744026011 2.1595e+10 1783.2
## + jml_koperasi 1 903677972 2.2435e+10 1786.7
## + jml_medis 1 685249061 2.2653e+10 1787.6
## + prop_blt 1 652207422 2.2686e+10 1787.7
## <none> 2.3339e+10 1788.3
## + jml_health 1 340542854 2.2998e+10 1789.0
## + jml_sd 1 167822042 2.3171e+10 1789.7
## + prop_sani 1 80744600 2.3258e+10 1790.0
## - jml_smp 1 1659049169 2.4998e+10 1792.7
## - jml_bank 1 3046839845 2.6386e+10 1797.6
## - jml_eko 1 7406845179 3.0746e+10 1811.7
##
## Step: AIC=1783.2
## ESTIMATE ~ jml_eko + jml_bank + jml_smp + prop_sktm
##
## Df Sum of Sq RSS AIC
## + jml_koperasi 1 780059216 2.0815e+10 1781.8
## + jml_medis 1 573441907 2.1021e+10 1782.7
## <none> 2.1595e+10 1783.2
## + prop_blt 1 370649216 2.1224e+10 1783.6
## + jml_health 1 277859856 2.1317e+10 1784.0
## + prop_sani 1 154071499 2.1441e+10 1784.5
## + jml_sd 1 87637173 2.1507e+10 1784.8
## - prop_sktm 1 1744026011 2.3339e+10 1788.3
## - jml_smp 1 1891825841 2.3487e+10 1788.9
## - jml_bank 1 3968337327 2.5563e+10 1796.7
## - jml_eko 1 7312937251 2.8908e+10 1808.0
##
## Step: AIC=1781.82
## ESTIMATE ~ jml_eko + jml_bank + jml_smp + prop_sktm + jml_koperasi
##
## Df Sum of Sq RSS AIC
## + jml_medis 1 846963714 1.9968e+10 1780.0
## + jml_health 1 567831131 2.0247e+10 1781.3
## <none> 2.0815e+10 1781.8
## + prop_blt 1 228683070 2.0586e+10 1782.8
## + prop_sani 1 221338530 2.0593e+10 1782.8
## - jml_koperasi 1 780059216 2.1595e+10 1783.2
## + jml_sd 1 15382496 2.0799e+10 1783.8
## - jml_smp 1 1581776468 2.2396e+10 1786.5
## - prop_sktm 1 1620407255 2.2435e+10 1786.7
## - jml_bank 1 4045570903 2.4860e+10 1796.2
## - jml_eko 1 7985137165 2.8800e+10 1809.7
##
## Step: AIC=1779.99
## ESTIMATE ~ jml_eko + jml_bank + jml_smp + prop_sktm + jml_koperasi +
## jml_medis
##
## Df Sum of Sq RSS AIC
## <none> 1.9968e+10 1780.0
## + prop_blt 1 146203505 1.9821e+10 1781.3
## + prop_sani 1 139397019 1.9828e+10 1781.3
## + jml_health 1 72979030 1.9895e+10 1781.7
## + jml_sd 1 59837492 1.9908e+10 1781.7
## - jml_medis 1 846963714 2.0815e+10 1781.8
## - jml_smp 1 926416694 2.0894e+10 1782.2
## - jml_koperasi 1 1053581023 2.1021e+10 1782.7
## - prop_sktm 1 1467917868 2.1436e+10 1784.5
## - jml_bank 1 4853214686 2.4821e+10 1798.0
## - jml_eko 1 6877353608 2.6845e+10 1805.2# View summary
summary(stepwise_model)##
## Call:
## lm(formula = ESTIMATE ~ jml_eko + jml_bank + jml_smp + prop_sktm +
## jml_koperasi + jml_medis, data = preselected_data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -24564 -9629 -2595 9519 83481
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 15181.575 4884.030 3.108 0.00256 **
## jml_eko 30.612 5.658 5.411 5.69e-07 ***
## jml_bank -804.880 177.080 -4.545 1.80e-05 ***
## jml_smp 757.440 381.416 1.986 0.05027 .
## prop_sktm -1654.131 661.718 -2.500 0.01435 *
## jml_koperasi -522.692 246.812 -2.118 0.03711 *
## jml_medis 54.437 28.669 1.899 0.06098 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 15330 on 85 degrees of freedom
## Multiple R-squared: 0.5592, Adjusted R-squared: 0.5281
## F-statistic: 17.97 on 6 and 85 DF, p-value: 2.376e-13# Forward selection
forward_model <- stepAIC(null_model, scope = list(lower = null_model, upper = modelreg), direction = "forward")## Start: AIC=1843.36
## ESTIMATE ~ 1
##
## Df Sum of Sq RSS AIC
## + jml_eko 1 1.7237e+10 2.8065e+10 1801.3
## + jml_smp 1 1.4362e+10 3.0939e+10 1810.3
## + jml_health 1 1.3657e+10 3.1644e+10 1812.4
## + jml_sd 1 1.2381e+10 3.2920e+10 1816.0
## + jml_medis 1 9.5524e+09 3.5749e+10 1823.6
## + prop_blt 1 3.2621e+09 4.2039e+10 1838.5
## + prop_sktm 1 1.8092e+09 4.3492e+10 1841.6
## + jml_bank 1 1.4528e+09 4.3849e+10 1842.4
## + jml_koperasi 1 1.4420e+09 4.3859e+10 1842.4
## + prop_sani 1 1.4059e+09 4.3896e+10 1842.5
## <none> 4.5301e+10 1843.4
##
## Step: AIC=1801.31
## ESTIMATE ~ jml_eko
##
## Df Sum of Sq RSS AIC
## + jml_bank 1 3066912684 2.4998e+10 1792.7
## + jml_smp 1 1679122008 2.6386e+10 1797.6
## + jml_sd 1 1349834061 2.6715e+10 1798.8
## + jml_koperasi 1 1074524765 2.6990e+10 1799.7
## + prop_sktm 1 667512088 2.7397e+10 1801.1
## <none> 2.8065e+10 1801.3
## + jml_health 1 228245515 2.7836e+10 1802.6
## + jml_medis 1 225123005 2.7840e+10 1802.6
## + prop_sani 1 98174662 2.7966e+10 1803.0
## + prop_blt 1 4106565 2.8061e+10 1803.3
##
## Step: AIC=1792.66
## ESTIMATE ~ jml_eko + jml_bank
##
## Df Sum of Sq RSS AIC
## + jml_smp 1 1659049169 2.3339e+10 1788.3
## + prop_sktm 1 1511249340 2.3487e+10 1788.9
## + jml_medis 1 1253366537 2.3744e+10 1789.9
## + jml_koperasi 1 1202094546 2.3796e+10 1790.1
## + jml_health 1 1169465061 2.3828e+10 1790.3
## <none> 2.4998e+10 1792.7
## + prop_blt 1 386173140 2.4612e+10 1793.2
## + jml_sd 1 256356602 2.4741e+10 1793.7
## + prop_sani 1 113101014 2.4885e+10 1794.2
##
## Step: AIC=1788.35
## ESTIMATE ~ jml_eko + jml_bank + jml_smp
##
## Df Sum of Sq RSS AIC
## + prop_sktm 1 1744026011 2.1595e+10 1783.2
## + jml_koperasi 1 903677972 2.2435e+10 1786.7
## + jml_medis 1 685249061 2.2653e+10 1787.6
## + prop_blt 1 652207422 2.2686e+10 1787.7
## <none> 2.3339e+10 1788.3
## + jml_health 1 340542854 2.2998e+10 1789.0
## + jml_sd 1 167822042 2.3171e+10 1789.7
## + prop_sani 1 80744600 2.3258e+10 1790.0
##
## Step: AIC=1783.2
## ESTIMATE ~ jml_eko + jml_bank + jml_smp + prop_sktm
##
## Df Sum of Sq RSS AIC
## + jml_koperasi 1 780059216 2.0815e+10 1781.8
## + jml_medis 1 573441907 2.1021e+10 1782.7
## <none> 2.1595e+10 1783.2
## + prop_blt 1 370649216 2.1224e+10 1783.6
## + jml_health 1 277859856 2.1317e+10 1784.0
## + prop_sani 1 154071499 2.1441e+10 1784.5
## + jml_sd 1 87637173 2.1507e+10 1784.8
##
## Step: AIC=1781.82
## ESTIMATE ~ jml_eko + jml_bank + jml_smp + prop_sktm + jml_koperasi
##
## Df Sum of Sq RSS AIC
## + jml_medis 1 846963714 1.9968e+10 1780.0
## + jml_health 1 567831131 2.0247e+10 1781.3
## <none> 2.0815e+10 1781.8
## + prop_blt 1 228683070 2.0586e+10 1782.8
## + prop_sani 1 221338530 2.0593e+10 1782.8
## + jml_sd 1 15382496 2.0799e+10 1783.8
##
## Step: AIC=1779.99
## ESTIMATE ~ jml_eko + jml_bank + jml_smp + prop_sktm + jml_koperasi +
## jml_medis
##
## Df Sum of Sq RSS AIC
## <none> 1.9968e+10 1780.0
## + prop_blt 1 146203505 1.9821e+10 1781.3
## + prop_sani 1 139397019 1.9828e+10 1781.3
## + jml_health 1 72979030 1.9895e+10 1781.7
## + jml_sd 1 59837492 1.9908e+10 1781.7# View summary
summary(forward_model)##
## Call:
## lm(formula = ESTIMATE ~ jml_eko + jml_bank + jml_smp + prop_sktm +
## jml_koperasi + jml_medis, data = preselected_data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -24564 -9629 -2595 9519 83481
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 15181.575 4884.030 3.108 0.00256 **
## jml_eko 30.612 5.658 5.411 5.69e-07 ***
## jml_bank -804.880 177.080 -4.545 1.80e-05 ***
## jml_smp 757.440 381.416 1.986 0.05027 .
## prop_sktm -1654.131 661.718 -2.500 0.01435 *
## jml_koperasi -522.692 246.812 -2.118 0.03711 *
## jml_medis 54.437 28.669 1.899 0.06098 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 15330 on 85 degrees of freedom
## Multiple R-squared: 0.5592, Adjusted R-squared: 0.5281
## F-statistic: 17.97 on 6 and 85 DF, p-value: 2.376e-13# Backward elimination
backward_model <- stepAIC(modelreg, direction = "backward")## Start: AIC=1786.16
## ESTIMATE ~ jml_sd + jml_smp + jml_eko + jml_health + jml_medis +
## jml_bank + prop_blt + prop_sktm + jml_koperasi + prop_sani
##
## Df Sum of Sq RSS AIC
## - jml_sd 1 18814185 1.9592e+10 1784.2
## - prop_sani 1 91526880 1.9665e+10 1784.6
## - prop_blt 1 116979598 1.9690e+10 1784.7
## - jml_health 1 142802255 1.9716e+10 1784.8
## - jml_medis 1 218664752 1.9792e+10 1785.2
## <none> 1.9573e+10 1786.2
## - jml_smp 1 530735198 2.0104e+10 1786.6
## - jml_koperasi 1 969395707 2.0543e+10 1788.6
## - prop_sktm 1 1299236945 2.0872e+10 1790.1
## - jml_eko 1 3874885961 2.3448e+10 1800.8
## - jml_bank 1 4215071803 2.3788e+10 1802.1
##
## Step: AIC=1784.25
## ESTIMATE ~ jml_smp + jml_eko + jml_health + jml_medis + jml_bank +
## prop_blt + prop_sktm + jml_koperasi + prop_sani
##
## Df Sum of Sq RSS AIC
## - prop_sani 1 107800328 1.9700e+10 1782.8
## - jml_health 1 135608884 1.9728e+10 1782.9
## - prop_blt 1 141898876 1.9734e+10 1782.9
## - jml_medis 1 208600393 1.9801e+10 1783.2
## <none> 1.9592e+10 1784.2
## - jml_smp 1 631331410 2.0223e+10 1785.2
## - jml_koperasi 1 1028999269 2.0621e+10 1787.0
## - prop_sktm 1 1330319568 2.0922e+10 1788.3
## - jml_eko 1 4169132661 2.3761e+10 1800.0
## - jml_bank 1 5026856718 2.4619e+10 1803.3
##
## Step: AIC=1782.75
## ESTIMATE ~ jml_smp + jml_eko + jml_health + jml_medis + jml_bank +
## prop_blt + prop_sktm + jml_koperasi
##
## Df Sum of Sq RSS AIC
## - jml_health 1 121602297 1.9821e+10 1781.3
## - prop_blt 1 194826772 1.9895e+10 1781.7
## - jml_medis 1 245080270 1.9945e+10 1781.9
## <none> 1.9700e+10 1782.8
## - jml_smp 1 669863723 2.0370e+10 1783.8
## - jml_koperasi 1 969765487 2.0670e+10 1785.2
## - prop_sktm 1 1264058059 2.0964e+10 1786.5
## - jml_eko 1 4198198609 2.3898e+10 1798.5
## - jml_bank 1 5082088403 2.4782e+10 1801.9
##
## Step: AIC=1781.32
## ESTIMATE ~ jml_smp + jml_eko + jml_medis + jml_bank + prop_blt +
## prop_sktm + jml_koperasi
##
## Df Sum of Sq RSS AIC
## - prop_blt 1 146203505 1.9968e+10 1780.0
## <none> 1.9821e+10 1781.3
## - jml_medis 1 764484149 2.0586e+10 1782.8
## - jml_koperasi 1 895351203 2.0717e+10 1783.4
## - jml_smp 1 1027888071 2.0849e+10 1784.0
## - prop_sktm 1 1308597227 2.1130e+10 1785.2
## - jml_bank 1 4984640788 2.4806e+10 1800.0
## - jml_eko 1 5965694241 2.5787e+10 1803.5
##
## Step: AIC=1779.99
## ESTIMATE ~ jml_smp + jml_eko + jml_medis + jml_bank + prop_sktm +
## jml_koperasi
##
## Df Sum of Sq RSS AIC
## <none> 1.9968e+10 1780.0
## - jml_medis 1 846963714 2.0815e+10 1781.8
## - jml_smp 1 926416694 2.0894e+10 1782.2
## - jml_koperasi 1 1053581023 2.1021e+10 1782.7
## - prop_sktm 1 1467917868 2.1436e+10 1784.5
## - jml_bank 1 4853214686 2.4821e+10 1798.0
## - jml_eko 1 6877353608 2.6845e+10 1805.2# View summary
summary(backward_model)##
## Call:
## lm(formula = ESTIMATE ~ jml_smp + jml_eko + jml_medis + jml_bank +
## prop_sktm + jml_koperasi, data = preselected_data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -24564 -9629 -2595 9519 83481
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 15181.575 4884.030 3.108 0.00256 **
## jml_smp 757.440 381.416 1.986 0.05027 .
## jml_eko 30.612 5.658 5.411 5.69e-07 ***
## jml_medis 54.437 28.669 1.899 0.06098 .
## jml_bank -804.880 177.080 -4.545 1.80e-05 ***
## prop_sktm -1654.131 661.718 -2.500 0.01435 *
## jml_koperasi -522.692 246.812 -2.118 0.03711 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 15330 on 85 degrees of freedom
## Multiple R-squared: 0.5592, Adjusted R-squared: 0.5281
## F-statistic: 17.97 on 6 and 85 DF, p-value: 2.376e-13
variables selected for the model are:
a. jml_smp
b. jml_eko
c. jml_medis
d. jml_bank
e. prop_sktm
f. jml_koperasi