LBB Regression Model

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0. Read Data

          id            date  price bedrooms bathrooms sqft_living
1 7129300520 20141013T000000 221900        3      1.00        1180
2 6414100192 20141209T000000 538000        3      2.25        2570
3 5631500400 20150225T000000 180000        2      1.00         770
  sqft_lot floors waterfront view condition grade sqft_above sqft_basement
1     5650      1          0    0         3     7       1180             0
2     7242      2          0    0         3     7       2170           400
3    10000      1          0    0         3     6        770             0
  yr_built yr_renovated zipcode     lat     long sqft_living15 sqft_lot15
1     1955            0   98178 47.5112 -122.257          1340       5650
2     1951         1991   98125 47.7210 -122.319          1690       7639
3     1933            0   98028 47.7379 -122.233          2720       8062
 [ reached 'max' / getOption("max.print") -- omitted 3 rows ]

1. Explorasi Data

'data.frame':   21613 obs. of  21 variables:
 $ id           : num  7129300520 6414100192 5631500400 2487200875 1954400510 ...
 $ date         : Factor w/ 372 levels "20140502T000000",..: 165 221 291 221 284 11 57 252 340 306 ...
 $ price        : num  221900 538000 180000 604000 510000 ...
 $ bedrooms     : int  3 3 2 4 3 4 3 3 3 3 ...
 $ bathrooms    : num  1 2.25 1 3 2 4.5 2.25 1.5 1 2.5 ...
 $ 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 6560 ...
 $ floors       : num  1 2 1 1 1 1 2 1 1 2 ...
 $ waterfront   : int  0 0 0 0 0 0 0 0 0 0 ...
 $ view         : int  0 0 0 0 0 0 0 0 0 0 ...
 $ condition    : int  3 3 3 5 3 3 3 3 3 3 ...
 $ grade        : int  7 7 6 7 8 11 7 7 7 7 ...
 $ sqft_above   : int  1180 2170 770 1050 1680 3890 1715 1060 1050 1890 ...
 $ sqft_basement: int  0 400 0 910 0 1530 0 0 730 0 ...
 $ yr_built     : int  1955 1951 1933 1965 1987 2001 1995 1963 1960 2003 ...
 $ yr_renovated : int  0 1991 0 0 0 0 0 0 0 0 ...
 $ zipcode      : int  98178 98125 98028 98136 98074 98053 98003 98198 98146 98038 ...
 $ lat          : num  47.5 47.7 47.7 47.5 47.6 ...
 $ long         : num  -122 -122 -122 -122 -122 ...
 $ sqft_living15: int  1340 1690 2720 1360 1800 4760 2238 1650 1780 2390 ...
 $ sqft_lot15   : int  5650 7639 8062 5000 7503 101930 6819 9711 8113 7570 ...

2. Seleksi Data Berdasarkan Bisnis + Corellation

price: harga

m2_living: luas rumah dalam

m2_lot: luas tanah dalam m2

bedrooms: jumlah kamar tidur

bathrooms: jumlah kamar mandi

floors: jumlah lantai

condition: kondisi rumah 1 buruk - 5 baru

view: jumlah halaman

waterfront: jumlah kolam renang

grade: rating rumah

Korelasi data

Outlier Check

Bedrooms

Bathrooms

m2_living

m2_lot

floors

condition

waterfront

view

3. Modelling

Model Full


Call:
lm(formula = price ~ ., data = data_selected)

Residuals:
     Min       1Q   Median       3Q      Max 
-1231443  -125596   -17532    94899  4558095 

Coefficients:
                Estimate   Std. Error t value            Pr(>|t|)    
(Intercept) -665307.8183   17191.3671 -38.700 <0.0000000000000002 ***
m2_living       594.5217      11.0632  53.739 <0.0000000000000002 ***
m2_lot           -1.1718       0.1267  -9.247 <0.0000000000000002 ***
bedrooms     -38380.0003    2134.0597 -17.985 <0.0000000000000002 ***
bathrooms     29075.7846    3221.7008   9.025 <0.0000000000000002 ***
floors       -47120.4673    3530.2883 -13.347 <0.0000000000000002 ***
condition     51524.9237    2530.6973  20.360 <0.0000000000000002 ***
waterfront   581878.1782   19776.3159  29.423 <0.0000000000000002 ***
view          61576.6924    2341.1371  26.302 <0.0000000000000002 ***
grade        102659.4243    2223.5880  46.168 <0.0000000000000002 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 230000 on 21603 degrees of freedom
Multiple R-squared:  0.6078,    Adjusted R-squared:  0.6077 
F-statistic:  3720 on 9 and 21603 DF,  p-value: < 0.00000000000000022

Interpretasi koefisien:

Setiap kenaikan 1 nilai pada m2_living maka price bertambah sebesar 594.5217

Setiap kenaikan 1 nilai pada m2_lot maka price berkurang sebesar 1.1718

Setiap kenaikan 1 nilai pada bedrooms maka price berkurang sebesar 38380.0003

Setiap kenaikan 1 nilai pada bathrooms maka price bertambah sebesar 29075.7846

Setiap kenaikan 1 nilai pada floors maka price berkurang sebesar 47120.4673

Setiap kenaikan 1 nilai pada condition maka price bertambah sebesar 51524.9237

Setiap kenaikan 1 nilai pada waterfront maka price bertambah sebesar 581878.1782

Setiap kenaikan 1 nilai pada view maka price bertambah sebesar 61576.6924

Setiap kenaikan 1 nilai pada grade maka price bertambah sebesar 102659.4243

##Adj R-Square:

0.60, berarti predictor yang dipilih menjelaskan 60% informasi, sisanya yaitu 40% dijelaskan oleh variable lainnya.

4. Feature Selection

Stepwise (Backward)

Start:  AIC=533662.3
price ~ m2_living + m2_lot + bedrooms + bathrooms + floors + 
    condition + waterfront + view + grade

             Df       Sum of Sq              RSS    AIC
<none>                          1142336728298222 533662
- bathrooms   1   4306977080413 1146643705378635 533742
- m2_lot      1   4521106021818 1146857834320040 533746
- floors      1   9420607646769 1151757335944991 533838
- bedrooms    1  17103181270161 1159439909568383 533981
- condition   1  21919689506038 1164256417804259 534071
- view        1  36581294998829 1178918023297051 534342
- waterfront  1  45777643537833 1188114371836054 534510
- grade       1 112711720747852 1255048449046074 535694
- m2_living   1 152705668498510 1295042396796732 536372

Call:
lm(formula = price ~ m2_living + m2_lot + bedrooms + bathrooms + 
    floors + condition + waterfront + view + grade, data = data_selected)

Residuals:
     Min       1Q   Median       3Q      Max 
-1231443  -125596   -17532    94899  4558095 

Coefficients:
                Estimate   Std. Error t value            Pr(>|t|)    
(Intercept) -665307.8183   17191.3671 -38.700 <0.0000000000000002 ***
m2_living       594.5217      11.0632  53.739 <0.0000000000000002 ***
m2_lot           -1.1718       0.1267  -9.247 <0.0000000000000002 ***
bedrooms     -38380.0003    2134.0597 -17.985 <0.0000000000000002 ***
bathrooms     29075.7846    3221.7008   9.025 <0.0000000000000002 ***
floors       -47120.4673    3530.2883 -13.347 <0.0000000000000002 ***
condition     51524.9237    2530.6973  20.360 <0.0000000000000002 ***
waterfront   581878.1782   19776.3159  29.423 <0.0000000000000002 ***
view          61576.6924    2341.1371  26.302 <0.0000000000000002 ***
grade        102659.4243    2223.5880  46.168 <0.0000000000000002 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 230000 on 21603 degrees of freedom
Multiple R-squared:  0.6078,    Adjusted R-squared:  0.6077 
F-statistic:  3720 on 9 and 21603 DF,  p-value: < 0.00000000000000022

Interpretasi koefisien:

Setiap kenaikan 1 nilai pada m2_living maka price bertambah sebesar 594.5217

Setiap kenaikan 1 nilai pada m2_lot maka price berkurang sebesar 1.1718

Setiap kenaikan 1 nilai pada bedrooms maka price berkurang sebesar 38380.0003

Setiap kenaikan 1 nilai pada bathrooms maka price bertambah sebesar 29075.7846

Setiap kenaikan 1 nilai pada floors maka price berkurang sebesar 47120.4673

Setiap kenaikan 1 nilai pada condition maka price bertambah sebesar 51524.9237

Setiap kenaikan 1 nilai pada waterfront maka price bertambah sebesar 581878.1782

Setiap kenaikan 1 nilai pada view maka price bertambah sebesar 61576.6924

Setiap kenaikan 1 nilai pada grade maka price bertambah sebesar 102659.4243

Adj R-Square

memiliki adj r-sq 0.60, berarti predictor yang dipilih menjelaskan 60% informasi, sisanya yaitu 40% dijelaskan oleh variable lainnya.

Regsubset

5. Error

RMSE (Root Mean Square Error)

[1] 229900.3
[1]   75000 7700000

MAE (Mean Absolute Error)

[1] 152322.6
[1]   75000 7700000

MAPE (Mean Absolute Percentage Error)

[1] 0.3192653

6. Asumsi

1. Residual Menyebar Normal (Normality)

H0: Residual menyebar normal H1: Residual tidak menyebar normal

jika p-value < alpha (0.05) maka tolak h0

residual dinyatakan normal ketika p-value > 0.05 (asumsi terpenuhi)

Histogram

Shapiro Test

Tidak bisa karena sample size lebih dari 5000

Lillie Test


    Lilliefors (Kolmogorov-Smirnov) normality test

data:  model_backward$residuals
D = 0.093559, p-value < 0.00000000000000022

QQ Plot

Residual Tidak Berpola

h0: Model Homoscedasticity h1: Model Heteroscedasticity

model dinyatakan Homoscedasticity bila p-value > alpha semakin mendekati 1 semakin bagus

hasil: p-value = 0.00000000000000022


    studentized Breusch-Pagan test

data:  model_backward
BP = 2560.5, df = 9, p-value < 0.00000000000000022

3. Tiap X tidak memiliki hubungan (Multicolinearity)

nilai vif yang bagus di bawah 10

hasil: semua predictor yang dipilih multicolinearitynya < 10

 m2_living     m2_lot   bedrooms  bathrooms     floors  condition 
  3.920194   1.046210   1.610096   2.290920   1.551479   1.108446 
waterfront       view      grade 
  1.196494   1.315486   2.792147

4. Linearity

h0: korelasi = 0 h1: korelasi != 0

membandingkan 2 variabel untuk menguji apakah kedua variable tersebut memiliki korelasi linear

hasil: p-value < alpha (0.05)

            x     y
1       price price
2   m2_living price
3      m2_lot price
4    bedrooms price
5   bathrooms price
6      floors price
7   condition price
8  waterfront price
9        view price
10      grade price
                                                                                                                                                                                                                                                                                      p_value
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4  0.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
5  0.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
6  0.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000003812102
7  0.0000000893565406245876391372784559863351461217462201602756977081298828125000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
8  0.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
9  0.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
10 0.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

7. Kesimpulan

4 dari 4 Asumsi terpenuhi sehingga model bisa dikatakan fit. model_backward memiliki adjusted R-sq sebesar 0.60 artinya predictor yang dipilih mampu menjelaskan 60% informasi, sisanya 40% dijelaskan oleh variable lainnya.

Risal Andika (Hydra Night B)

2019-08-08