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: - waterfront -> diubah jadi factor

3. Cleansing Data

library(lubridate)
house <- house %>% 
  mutate(waterfront = factor(waterfront)) %>% 
  glimpse()
#> 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$price)

💡 Insight: - ada banyak outlier pada data tersebut - distribusi persebaran data adalah right skewed - median data kurang lebih adalah 500.000

#korelasi
cor(x = house$price,
    y = house$bedrooms)
#> [1] 0.3083496
cor(x = house$price,
    y = house$bathrooms)
#> [1] 0.5251375
cor(x = house$price,
    y = house$sqft_living)
#> [1] 0.7020351
cor(x = house$price,
    y = house$sqft_lot)
#> [1] 0.08966086
cor(x = house$price,
    y = house$floors)
#> [1] 0.2567939
cor(x = house$price,
    y = house$grade)
#> [1] 0.6674343
cor(x = house$price,
    y = house$yr_built)
#> [1] 0.05401153

💡 Insight: - price dan bedrooms memiliki korelasi positif yang lemah sebesar 0.3083496, artinya semakin tinggi harga, maka jumlah kamar semakin tinggi - price dan bathrooms memiliki korelasi positif yang kuat sebesar 0.5251375, artinya semakin tinggi harga, maka jumlah kamar mandi semakin tinggi - price dan sqft_living memiliki korelasi positif yang kuat sebesar 0.7020351, artinya semakin tinggi harga, maka luas bangunan akan semakin tinggi - price dan sqft_lot memiliki korelasi positif yang sangat lemah sebesar 0.08966086, artinya semakin tinggi harga, maka luas tanah akan semakin tinggi - price dan floors memiliki korelasi positif yang lemah sebesar 0.2567939, artinya semakin tinggi harga, maka jumlah lantai akan semakin tinggi - price dan grade memiliki korelasi positif yang kuat sebesar 0.6674343, artinya semakin tinggi harga, maka nilai grade akan semakin tinggi - price dan yr_buit memiliki korelasi positif yang sangat lemah sebesar 0.05401153, artinya semakin tinggi harga, maka tahun rumah dibuat akan semakin tinggi (rumah semakin baru)

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

#model correlation > 0.5
model_correlation <- lm(formula = price ~ bathrooms + sqft_living + grade,
                        data = house)
#model backward elimination
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 1207325386294410 534854
#> - yr_built     1 183528097123653 1218822838983905 535059
#model forward selection
model_none <- lm(formula = price ~ 1,
                 data = house)

model_forward <- step(object = model_none, #model tanpa prediktor
                      direction = "forward", 
                      scope = list(upper = model_all)) #model dengan semua prediktor
#> Start:  AIC=553875.8
#> price ~ 1
#> 
#>               Df        Sum of Sq              RSS    AIC
#> + sqft_living  1 1435640399598810 1477276362322490 539204
#> + grade        1 1297612620095468 1615304141825832 541134
#> + bathrooms    1  803293306497671 2109623455423628 546904
#> + bedrooms     1  276958595500072 2635958166421226 551718
#> + waterfront   1  206679237434409 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 1367038176921726 537529
#> + yr_built    1  92854405407200 1384421956915290 537802
#> + bedrooms    1  40635382190095 1436640980132394 538603
#> + sqft_lot    1   3011349102420 1474265013220070 539161
#> + floors      1    229913654972 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 108953582123634 1247002236250111 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 1148101634901901 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 1058135652290325 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 13953491780042 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 1037324972515320 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
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 1435640399598810 1477276362322490 539204
#> + grade        1 1297612620095468 1615304141825832 541134
#> + bathrooms    1  803293306497671 2109623455423628 546904
#> + bedrooms     1  276958595500072 2635958166421226 551718
#> + waterfront   1  206679237434409 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 1367038176921726 537529
#> + yr_built     1   92854405407200 1384421956915290 537802
#> + bedrooms     1   40635382190095 1436640980132394 538603
#> + sqft_lot     1    3011349102420 1474265013220070 539161
#> + floors       1     229913654972 1477046448667517 539202
#> + bathrooms    1     147193010785 1477129169311705 539203
#> <none>                            1477276362322490 539204
#> - sqft_living  1 1435640399598810 2912916761921299 553876
#> 
#> Step:  AIC=537353.4
#> price ~ sqft_living + grade
#> 
#>               Df       Sum of Sq              RSS    AIC
#> + yr_built     1 199227645099154 1156728173274590 533921
#> + waterfront   1 108953582123634 1247002236250111 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 259348323452087 1615304141825832 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 1148101634901901 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 241311622806597 1398039796081188 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 1058135652290325 531999
#> + floors       1   4061693690658 1062550673647944 532089
#> + sqft_lot     1   1826102349598 1064786264989004 532135
#> <none>                           1066612367338602 532170
#> - waterfront   1  90115805935988 1156728173274590 533921
#> - yr_built     1 180389868911509 1247002236250111 535545
#> - grade        1 219517939490357 1286130306828959 536213
#> - sqft_living  1 222939932856999 1289552300195601 536270
#> 
#> Step:  AIC=531888.3
#> price ~ sqft_living + grade + yr_built + waterfront + bedrooms
#> 
#>               Df       Sum of Sq              RSS    AIC
#> + bathrooms    1  13953491780042 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 217755228757075 1270465528561039 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 1037324972515320 531574
#> <none>                           1038756808023922 531602
#> - bathrooms    1  13953491780042 1052710299803964 531888
#> - bedrooms     1  19378844266404 1058135652290325 531999
#> - waterfront   1  82547202240690 1121304010264612 533253
#> - sqft_living  1 136922615063114 1175679423087036 534276
#> - grade        1 184390684043560 1223147492067482 535132
#> - yr_built     1 190012863248603 1228769671272524 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 1225152792629687 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 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 1207325386294410 534854
#> - yr_built     1 183528097123653 1218822838983905 535059

model_backward, model_forward, dan model_both menghasilkan AIC yang sama yaitu 531533.8 dan menggunakan semua prediktor kecuali price.

#menambahkan hasil prediksi dari ke ketiga model ke kolom baru
house$pred_all <- predict(object = model_all, newdata = house)
house$pred_correlation <- predict(object = model_correlation, newdata = house)
house$pred_backward<- predict(object = model_backward, newdata = house)
head(house)

4 Evaluasi model

Berdasarkan RMSE model regresi manakah yang terbaik?

#RMSE model_all
RMSE(y_pred = house$pred_all, 
     y_true = house$price)
#> [1] 218864.1
#RMSE model_correlation
RMSE(y_pred = house$pred_correlation, 
     y_true = house$price)
#> [1] 249767.8
#RMSE model_backward
RMSE(y_pred = house$pred_backward, 
     y_true = house$price)
#> [1] 218864.1

💡 Kesimpulan : model yang memberikan error paling kecil dalam memprediksi nilai price adalah model_all dan model_correlation dengan nilai RMSE sebesar 218864.1

5 Interpretasi Model Terbaik:

summary(model_all)
#> 
#> Call:
#> lm(formula = price ~ ., data = house)
#> 
#> 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: - prediktor kategorik: waterfront - waterfront = 0 menjadi basis - waterfront = 1, yaitu 721804.73094, artinya nilai price akan meningkat sebesar 721804.73094 apabila rumah tersebut memiliki waterfront dan variabel prediktor lainnya bernilai tetap

2. Interpretasi coefficient untuk prediktor numerik:

  • bedrooms: -41484.20936, artinya price akan berkurang sebesar 41484.20936 dengan catatan variabel prediktor lainnya bernilai tetap
  • bathrooms: 51710.08964, artinya price akan meningkat sebesar 51710.08964 dengan catatan variabel prediktor lainnya bernilai tetap
  • sqft_living: 177.91392, artinya price akan meningkat sebesar 177.91392 dengan catatan variabel prediktor lainnya bernilai tetap
  • sqft_lot: -0.23947, artinya price akan berkurang sebesar 0.23947 dengan catatan variabel prediktor lainnya bernilai tetap
  • floors: 17283.13337, artinya price akan meningkat sebesar 17283.13337 dengan catatan variabel prediktor lainnya bernilai tetap
  • grade: 128813.92794, artinya price akan meningkat sebesar 128813.92794 dengan catatan variabel prediktor lainnya bernilai tetap
  • yr_built: -3963.73577, artinya price akan berkurang sebesar 3963.73577 dengan catatan variabel prediktor lainnya bernilai tetap

3. Signifikansi prediktor:

  • hasil p-value dari seluruh prediktor < 0.05 maka seluruh prediktor (bedrooms, bathrooms, sqft_living, sqft_lot, floors, waterfront, grade, yr_built) memiliki pengaruh yang signifikan terhadap target (price).

4. Adjusted R Squared:

  • Adjusted R Squared: 0.6445, artinya model dapat menjelaskan price dengan baik, yakni sebesar 64.45%