1 Business Problem

Sebagai seorang penjual properti, kita ingin membuat model yang mana dapat memprediksi harga properti berdasarkan beberapa informasi yang ada pada data.

Tentukan variabel:

  • target: price
  • prediktor: seluruh variabel terkecuali price

2 Data Wrangling & EDA

1. Read data house_data.csv

house <- read.csv("data_input/house_data.csv")
head(house)

2. Cek struktur data

glimpse(house)
#> Rows: 21,613
#> Columns: 9
#> $ price       <int> 221900, 538000, 180000, 604000, 510000, 1225000, 257500, 2…
#> $ bedrooms    <int> 3, 3, 2, 4, 3, 4, 3, 3, 3, 3, 3, 2, 3, 3, 5, 4, 3, 4, 2, 3…
#> $ bathrooms   <dbl> 1.00, 2.25, 1.00, 3.00, 2.00, 4.50, 2.25, 1.50, 1.00, 2.50…
#> $ sqft_living <int> 1180, 2570, 770, 1960, 1680, 5420, 1715, 1060, 1780, 1890,…
#> $ sqft_lot    <int> 5650, 7242, 10000, 5000, 8080, 101930, 6819, 9711, 7470, 6…
#> $ floors      <dbl> 1.0, 2.0, 1.0, 1.0, 1.0, 1.0, 2.0, 1.0, 1.0, 2.0, 1.0, 1.0…
#> $ waterfront  <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…
#> $ grade       <int> 7, 7, 6, 7, 8, 11, 7, 7, 7, 7, 8, 7, 7, 7, 7, 9, 7, 7, 7, …
#> $ yr_built    <int> 1955, 1951, 1933, 1965, 1987, 2001, 1995, 1963, 1960, 2003…

💡 Hasil pemeriksaan struktur data: - Data memiliki 21,613 baris dan 9 kolom (variabel) - Variabel yang bersifat numerik adalah bathrooms dan floors - Variabel yang bersifat integer adalah price, bedrooms, sqft_living, sqft_lot, grade, dan yr_built - Variabel yang perlu diubah tipe datanya adalah waterfront menjadi tipe factor.

3. Cleansing Data

house_clean <- house %>% 
  mutate(waterfront = as.factor(waterfront))

glimpse(house_clean)
#> Rows: 21,613
#> Columns: 9
#> $ price       <int> 221900, 538000, 180000, 604000, 510000, 1225000, 257500, 2…
#> $ bedrooms    <int> 3, 3, 2, 4, 3, 4, 3, 3, 3, 3, 3, 2, 3, 3, 5, 4, 3, 4, 2, 3…
#> $ bathrooms   <dbl> 1.00, 2.25, 1.00, 3.00, 2.00, 4.50, 2.25, 1.50, 1.00, 2.50…
#> $ sqft_living <int> 1180, 2570, 770, 1960, 1680, 5420, 1715, 1060, 1780, 1890,…
#> $ sqft_lot    <int> 5650, 7242, 10000, 5000, 8080, 101930, 6819, 9711, 7470, 6…
#> $ floors      <dbl> 1.0, 2.0, 1.0, 1.0, 1.0, 1.0, 2.0, 1.0, 1.0, 2.0, 1.0, 1.0…
#> $ waterfront  <fct> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…
#> $ grade       <int> 7, 7, 6, 7, 8, 11, 7, 7, 7, 7, 8, 7, 7, 7, 7, 9, 7, 7, 7, …
#> $ yr_built    <int> 1955, 1951, 1933, 1965, 1987, 2001, 1995, 1963, 1960, 2003…

3. EDA

#persebaran data
boxplot(house_clean$price)

#korelasi
library(GGally)
ggcorr(house_clean,label = TRUE )

💡 Insight: - Yang memiliki korelasi kuat terhadap variabel price adalah variabel sqft_living dan grade.

3 Modeling

Buatlah 3 model berdasarkan feature selection yg telah dipelajari 1. model all predictor 2. model selection based on correlation (korelasi > 0.5) 3. model selection hasil stepwise (backward/forward/both)

model_all <- lm(formula = price ~ .,
                data = house_clean)

model_none <- lm(formula = price ~ 1,
                data = house_clean)

model_selection <- lm(formula = price ~ sqft_living + grade,
                data = house_clean)

model_backward <- step(object = model_all,
                       direction = "backward")
#> Start:  AIC=531533.8
#> price ~ bedrooms + bathrooms + sqft_living + sqft_lot + floors + 
#>     waterfront + grade + yr_built
#> 
#>               Df       Sum of Sq              RSS    AIC
#> <none>                           1035294741860252 531534
#> - floors       1   1218939726736 1036513681586988 531557
#> - sqft_lot     1   2030230655068 1037324972515320 531574
#> - bathrooms    1  10844095263314 1046138837123566 531757
#> - bedrooms     1  19802603600782 1055097345461034 531941
#> - waterfront   1  82402185733932 1117696927594184 533187
#> - sqft_living  1 140116227741713 1175410969601965 534275
#> - grade        1 172030644434158 1207325386294409 534854
#> - yr_built     1 183528097123653 1218822838983905 535059
model_forward <- step(object = model_none,
                      direction = "forward", 
                      scope = list(upper = model_all))
#> Start:  AIC=553875.8
#> price ~ 1
#> 
#>               Df        Sum of Sq              RSS    AIC
#> + sqft_living  1 1435640399598809 1477276362322490 539204
#> + grade        1 1297612620095470 1615304141825828 541134
#> + bathrooms    1  803293306497671 2109623455423628 546904
#> + bedrooms     1  276958595500073 2635958166421226 551718
#> + waterfront   1  206679237434408 2706237524486890 552287
#> + floors       1  192086763313773 2720829998607526 552403
#> + sqft_lot     1   23417141523777 2889499620397522 553703
#> + yr_built     1    8497693415832 2904419068505468 553815
#> <none>                            2912916761921299 553876
#> 
#> Step:  AIC=539203.5
#> price ~ sqft_living
#> 
#>              Df       Sum of Sq              RSS    AIC
#> + grade       1 121320543948745 1355955818373745 537353
#> + waterfront  1 110238185400763 1367038176921727 537529
#> + yr_built    1  92854405407200 1384421956915290 537802
#> + bedrooms    1  40635382190095 1436640980132395 538603
#> + sqft_lot    1   3011349102420 1474265013220070 539161
#> + floors      1    229913654973 1477046448667517 539202
#> + bathrooms   1    147193010785 1477129169311705 539203
#> <none>                          1477276362322490 539204
#> 
#> Step:  AIC=537353.4
#> price ~ sqft_living + grade
#> 
#>              Df       Sum of Sq              RSS    AIC
#> + yr_built    1 199227645099154 1156728173274590 533921
#> + waterfront  1 108953582123633 1247002236250112 535545
#> + bedrooms    1  22141328690666 1333814489683078 537000
#> + floors      1   9622247208765 1346333571164980 537202
#> + bathrooms   1   7651853153980 1348303965219765 537233
#> + sqft_lot    1   2020142096807 1353935676276938 537323
#> <none>                          1355955818373745 537353
#> 
#> Step:  AIC=533920.9
#> price ~ sqft_living + grade + yr_built
#> 
#>              Df      Sum of Sq              RSS    AIC
#> + waterfront  1 90115805935988 1066612367338602 532170
#> + bedrooms    1 20121301261862 1136606872012728 533544
#> + bathrooms   1  8626538372689 1148101634901902 533761
#> + floors      1  4395842729126 1152332330545465 533841
#> + sqft_lot    1  1713565021968 1155014608252622 533891
#> <none>                         1156728173274590 533921
#> 
#> Step:  AIC=532169.9
#> price ~ sqft_living + grade + yr_built + waterfront
#> 
#>             Df      Sum of Sq              RSS    AIC
#> + bedrooms   1 13902067534638 1052710299803964 531888
#> + bathrooms  1  8476715048277 1058135652290326 531999
#> + floors     1  4061693690658 1062550673647944 532089
#> + sqft_lot   1  1826102349598 1064786264989004 532135
#> <none>                        1066612367338602 532170
#> 
#> Step:  AIC=531888.3
#> price ~ sqft_living + grade + yr_built + waterfront + bedrooms
#> 
#>             Df      Sum of Sq              RSS    AIC
#> + bathrooms  1 13953491780043 1038756808023922 531602
#> + floors     1  4176630866150 1048533668937814 531804
#> + sqft_lot   1  2870998480425 1049839301323540 531831
#> <none>                        1052710299803964 531888
#> 
#> Step:  AIC=531602
#> price ~ sqft_living + grade + yr_built + waterfront + bedrooms + 
#>     bathrooms
#> 
#>            Df     Sum of Sq              RSS    AIC
#> + sqft_lot  1 2243126436934 1036513681586988 531557
#> + floors    1 1431835508601 1037324972515321 531574
#> <none>                      1038756808023922 531602
#> 
#> Step:  AIC=531557.2
#> price ~ sqft_living + grade + yr_built + waterfront + bedrooms + 
#>     bathrooms + sqft_lot
#> 
#>          Df     Sum of Sq              RSS    AIC
#> + floors  1 1218939726736 1035294741860252 531534
#> <none>                    1036513681586988 531557
#> 
#> Step:  AIC=531533.8
#> price ~ sqft_living + grade + yr_built + waterfront + bedrooms + 
#>     bathrooms + sqft_lot + floors
model_both <- step(object = model_none,
                   direction = "both",
                   scope = list(upper = model_all))
#> Start:  AIC=553875.8
#> price ~ 1
#> 
#>               Df        Sum of Sq              RSS    AIC
#> + sqft_living  1 1435640399598809 1477276362322490 539204
#> + grade        1 1297612620095470 1615304141825828 541134
#> + bathrooms    1  803293306497671 2109623455423628 546904
#> + bedrooms     1  276958595500073 2635958166421226 551718
#> + waterfront   1  206679237434408 2706237524486890 552287
#> + floors       1  192086763313773 2720829998607526 552403
#> + sqft_lot     1   23417141523777 2889499620397522 553703
#> + yr_built     1    8497693415832 2904419068505468 553815
#> <none>                            2912916761921299 553876
#> 
#> Step:  AIC=539203.5
#> price ~ sqft_living
#> 
#>               Df        Sum of Sq              RSS    AIC
#> + grade        1  121320543948745 1355955818373745 537353
#> + waterfront   1  110238185400763 1367038176921727 537529
#> + yr_built     1   92854405407200 1384421956915290 537802
#> + bedrooms     1   40635382190095 1436640980132395 538603
#> + sqft_lot     1    3011349102420 1474265013220070 539161
#> + floors       1     229913654973 1477046448667517 539202
#> + bathrooms    1     147193010785 1477129169311705 539203
#> <none>                            1477276362322490 539204
#> - sqft_living  1 1435640399598809 2912916761921299 553876
#> 
#> Step:  AIC=537353.4
#> price ~ sqft_living + grade
#> 
#>               Df       Sum of Sq              RSS    AIC
#> + yr_built     1 199227645099154 1156728173274590 533921
#> + waterfront   1 108953582123633 1247002236250112 535545
#> + bedrooms     1  22141328690666 1333814489683078 537000
#> + floors       1   9622247208765 1346333571164980 537202
#> + bathrooms    1   7651853153980 1348303965219765 537233
#> + sqft_lot     1   2020142096807 1353935676276938 537323
#> <none>                           1355955818373745 537353
#> - grade        1 121320543948745 1477276362322490 539204
#> - sqft_living  1 259348323452084 1615304141825828 541134
#> 
#> Step:  AIC=533920.9
#> price ~ sqft_living + grade + yr_built
#> 
#>               Df       Sum of Sq              RSS    AIC
#> + waterfront   1  90115805935988 1066612367338602 532170
#> + bedrooms     1  20121301261862 1136606872012728 533544
#> + bathrooms    1   8626538372689 1148101634901902 533761
#> + floors       1   4395842729126 1152332330545465 533841
#> + sqft_lot     1   1713565021968 1155014608252622 533891
#> <none>                           1156728173274590 533921
#> - yr_built     1 199227645099154 1355955818373745 537353
#> - grade        1 227693783640699 1384421956915290 537802
#> - sqft_living  1 241311622806594 1398039796081185 538014
#> 
#> Step:  AIC=532169.9
#> price ~ sqft_living + grade + yr_built + waterfront
#> 
#>               Df       Sum of Sq              RSS    AIC
#> + bedrooms     1  13902067534638 1052710299803964 531888
#> + bathrooms    1   8476715048277 1058135652290326 531999
#> + floors       1   4061693690658 1062550673647944 532089
#> + sqft_lot     1   1826102349598 1064786264989004 532135
#> <none>                           1066612367338602 532170
#> - waterfront   1  90115805935988 1156728173274590 533921
#> - yr_built     1 180389868911509 1247002236250112 535545
#> - grade        1 219517939490357 1286130306828959 536213
#> - sqft_living  1 222939932856996 1289552300195599 536270
#> 
#> Step:  AIC=531888.3
#> price ~ sqft_living + grade + yr_built + waterfront + bedrooms
#> 
#>               Df       Sum of Sq              RSS    AIC
#> + bathrooms    1  13953491780043 1038756808023922 531602
#> + floors       1   4176630866150 1048533668937814 531804
#> + sqft_lot     1   2870998480425 1049839301323540 531831
#> <none>                           1052710299803964 531888
#> - bedrooms     1  13902067534638 1066612367338602 532170
#> - waterfront   1  83896572208764 1136606872012728 533544
#> - yr_built     1 179366335438934 1232076635242899 535287
#> - grade        1 198282580205801 1250992880009766 535616
#> - sqft_living  1 217755228757072 1270465528561036 535950
#> 
#> Step:  AIC=531602
#> price ~ sqft_living + grade + yr_built + waterfront + bedrooms + 
#>     bathrooms
#> 
#>               Df       Sum of Sq              RSS    AIC
#> + sqft_lot     1   2243126436934 1036513681586988 531557
#> + floors       1   1431835508601 1037324972515321 531574
#> <none>                           1038756808023922 531602
#> - bathrooms    1  13953491780043 1052710299803964 531888
#> - bedrooms     1  19378844266404 1058135652290326 531999
#> - waterfront   1  82547202240690 1121304010264612 533253
#> - sqft_living  1 136922615063114 1175679423087036 534276
#> - grade        1 184390684043560 1223147492067482 535132
#> - yr_built     1 190012863248603 1228769671272525 535231
#> 
#> Step:  AIC=531557.2
#> price ~ sqft_living + grade + yr_built + waterfront + bedrooms + 
#>     bathrooms + sqft_lot
#> 
#>               Df       Sum of Sq              RSS    AIC
#> + floors       1   1218939726736 1035294741860252 531534
#> <none>                           1036513681586988 531557
#> - sqft_lot     1   2243126436934 1038756808023922 531602
#> - bathrooms    1  13325619736552 1049839301323540 531831
#> - bedrooms     1  20298780261196 1056812461848184 531974
#> - waterfront   1  82496530390614 1119010211977602 533210
#> - sqft_living  1 138930506698738 1175444188285726 534274
#> - grade        1 182635783415639 1219149465002627 535063
#> - yr_built     1 188639111042699 1225152792629688 535169
#> 
#> Step:  AIC=531533.8
#> price ~ sqft_living + grade + yr_built + waterfront + bedrooms + 
#>     bathrooms + sqft_lot + floors
#> 
#>               Df       Sum of Sq              RSS    AIC
#> <none>                           1035294741860252 531534
#> - floors       1   1218939726736 1036513681586988 531557
#> - sqft_lot     1   2030230655068 1037324972515321 531574
#> - bathrooms    1  10844095263314 1046138837123566 531757
#> - bedrooms     1  19802603600782 1055097345461034 531941
#> - waterfront   1  82402185733932 1117696927594184 533187
#> - sqft_living  1 140116227741712 1175410969601964 534275
#> - grade        1 172030644434158 1207325386294410 534854
#> - yr_built     1 183528097123652 1218822838983905 535059

4 Evaluasi model

Berdasarkan RMSE model regresi manakah yang terbaik?

# Hasil Prediksi untuk setiap model
house_clean$pred_all <- predict(object = model_all, newdata = house_clean)
house_clean$pred_selection <- predict(object = model_selection, newdata = house_clean)
house_clean$pred_backward <- predict(object = model_backward, newdata = house_clean)
house_clean$pred_forward <- predict(object = model_forward, newdata = house_clean)
house_clean$pred_both<- predict(object = model_both, newdata = house_clean)

# RMSE model_all
RMSE(y_pred = house_clean$pred_all,
     y_true = house_clean$price)
#> [1] 218864.1
# RMSE model_selection
RMSE(y_pred = house_clean$pred_selection,
     y_true = house_clean$price)
#> [1] 250475.5
# RMSE model_forward
RMSE(y_pred = house_clean$pred_forward,
     y_true = house_clean$price)
#> [1] 218864.1
# RMSE model_backward
RMSE(y_pred = house_clean$pred_backward,
     y_true = house_clean$price)
#> [1] 218864.1
# RMSE model_both
RMSE(y_pred = house_clean$pred_both,
     y_true = house_clean$price)
#> [1] 218864.1

💡 Kesimpulan : Berdasarkan RMSE, model terbaik yang dapat digunakan adalah semua model kecuali model selection.

5 Interpretasi Model Terbaik:

summary(model_all)
#> 
#> Call:
#> lm(formula = price ~ ., data = house_clean)
#> 
#> Residuals:
#>      Min       1Q   Median       3Q      Max 
#> -1384206  -112972   -10077    91060  4251811 
#> 
#> Coefficients:
#>                  Estimate    Std. Error t value             Pr(>|t|)    
#> (Intercept) 6999106.70657  121576.94670  57.569 < 0.0000000000000002 ***
#> bedrooms     -41484.20936    2040.73489 -20.328 < 0.0000000000000002 ***
#> bathrooms     51710.08964    3437.50666  15.043 < 0.0000000000000002 ***
#> sqft_living     177.91392       3.29026  54.073 < 0.0000000000000002 ***
#> sqft_lot         -0.23947       0.03679  -6.509      0.0000000000774 ***
#> floors        17283.13337    3426.85939   5.043      0.0000004609553 ***
#> waterfront1  721804.73094   17406.65326  41.467 < 0.0000000000000002 ***
#> grade        128813.92794    2149.93255  59.915 < 0.0000000000000002 ***
#> yr_built      -3963.73577      64.04988 -61.885 < 0.0000000000000002 ***
#> ---
#> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#> 
#> Residual standard error: 218900 on 21604 degrees of freedom
#> Multiple R-squared:  0.6446, Adjusted R-squared:  0.6445 
#> F-statistic:  4898 on 8 and 21604 DF,  p-value: < 0.00000000000000022

1. Interpretasi coefficient untuk prediktor kategorik:

  • waterfront = 0 menjadi basis
  • waterfront = 1 bernilai 721804.73094. Hal ini berarti nilai price akan meningkat sebesar 721804.73094 jika memiliki waterfront dan variabel prediktor lainnya tetap.

2. Interpretasi coefficient untuk prediktor numerik:

  • bedrooms = -41484.20936, artinya nilai price akan menurun sebesar 41484.20936 dengan catatan nilai prediktor lain bernilai tetap.
  • bathrooms = 51710.08964, artinya nilai price akan meningkat sebesar 51710.08964 dengan catatan nilai prediktor lain bernilai tetap.
  • sqft_living = 177.91392, artinya nilai price akan meningkat sebesar 177.91392 dengan catatan nilai prediktor lain bernilai tetap.
  • sqft_lot = -0.23947, artinya nilai price akan menurun sebesar 0.23947 dengan catatan nilai prediktor lain bernilai tetap.
  • floors = 17283.13337, artinya nilai price akan meningkat sebesar 17283.13337 dengan catatan nilai prediktor lain bernilai tetap.
  • grade = 128813.92794, artinya nilai price akan meningkat sebesar 128813.92794 dengan catatan nilai prediktor lain bernilai tetap.
  • yr_built = -3963.73577, artinya nilai price akan menurun sebesar 3963.73577 dengan catatan nilai prediktor lain bernilai tetap.

3. Signifikansi prediktor:

  • Semua variabel prediktor berpengaruh signifikan terhadap variabel price.

4. Adjusted R Squared:

  • Bernilai 0.6445 . Hal ini menunjukkan model_all dapat menjelaskan price sebesar 64.45%.