Regresi Linear Berganda dan Asumsinya : House Price Prediction
Rafly Raihan Fauzi
4 Juni 2024
Library:
> # install.packages("knitr")
> # install.packages("rmarkdown")
> # install.packages("prettydoc")
> # install.packages("equatiomatic") 1. PENDAHULUAN
1.1 Latar Belakang
Dalam dunia penelitian, statistika memegang peran penting. Hal ini berlaku di semua bidang penelitian. Salah satu teknik statistika yang sering digunakan dalam statistika inferensial untuk menguji hipotesis adalah statistik parametris. Statistik parametris ini lebih sering diterapkan pada analisis data interval dan rasio, namun dengan beberapa persyaratan khusus. Salah satu persyaratannya adalah nilai residual variabel yang dianalisis harus berdistribusi normal (Sugiyono,2004:8).
Statistika mempunyai peranan penting dalam memecahkan masalah yang terjadi pada bidang ilmu lainnya. Dalam penelitian, peneliti selalu berupaya untuk mengidentifikasi hubungan atau pengaruh antara dua atau lebih variabel. Analisis regresi linear dimanfaatkan untuk mengkaji hubungan antar variabel, terutama untuk menemukan pola hubungan yang modelnya belum diketahui secara sempurna, atau untuk memahami bagaimana variasi beberapa variabel bebas (prediktor X atau variabel independen) memengaruhi variabel terikat (respon Y atau variabel dependen) dalam suatu fenomena yang kompleks.
2. TINJAUAN PUSTAKA
2.1 Regresi Linear Sederhana
Regresi linear sederhana adalah metode statistik yang digunakan untuk menganalisis hubungan antara satu variabel independen dan satu variabel dependen dengan tujuan memprediksi nilai variabel dependen berdasarkan nilai variabel independen. Model regresi linear sederhana dinyatakan dengan persamaan: \[ Y_{i} = \beta_{0} + \beta_{1}X_{i} +\varepsilon_{i} \] di mana Y adalah variabel dependen, X adalah variabel independen, \(\beta_{0}\) adalah intercept, \(\beta_{1}\) adalah slope dan \(\varepsilon_{i}\) adalah error atau sisaan.
2.2 Regresi Linear Berganda
Regresi linear berganda adalah teknik statistik yang digunakan untuk menganalisis hubungan antara satu variabel dependen dan dua atau lebih variabel independen. Model ini memperluas regresi linear sederhana dengan memasukkan lebih dari satu prediktor, yang memungkinkan analisis yang lebih komprehensif dan penjelasan yang lebih baik atas variabilitas dalam variabel dependen. Model regresi linear berganda dinyatakan dengan persamaan: \[ Y_{i} = \beta_{0} + \beta_{1}X_{1} + \beta_{2}X_{2} + ... + \beta_{i}X_{i}+\varepsilon_{i} \] di mana \(Y_{i}\) adalah variabel dependen, \(X_{i}\) adalah variabel independen, \(\beta_{i}\) adalah koefisien regresi dan \(\varepsilon_{i}\) adalah error atau sisaan.
2.3 Uji Asumsi Linearitas
Uji asumsi linearitas digunakan dalam analisis regresi linear untuk memastikan bahwa hubungan antara variabel terikat (Y) dan variabel bebas (X) bersifat linier.
\(H_0\): Hubungan antara variabel dependen (Y) dan variabel independen (X) linear
\(H_1\): Hubungan antara variabel dependen (Y) dan variabel independen (X) tidak linear Uji asumsi linearitas memiliki keputusan apabila nilai p-value ≤ \(\alpha\) maka akan menolak \(H_0\) yang dimana model regresi tidak linier, begitupun sebaliknya.
2.4 Uji Asumsi Normalitas
Uji asumsi normalitas digunakan dalam analisis regresi linear untuk memastikan bahwa residual (nilai sisa) dari model regresi berdistribusi normal.
\(H_0\): Residual mengikuti distribusi normal.
\(H_1\): Residual tidak mengikuti distribusi normal.
Uji ini memiliki keputusan apabila nilai p-value ≤ \(\alpha\) maka akan menolak \(H_0\) yang dimana residual tidak mengikuti distribusi normal, begitupun sebaliknya.
2.5 Uji Asumsi Autokorelasi
Uji asumsi autokorelasi digunakan dalam analisis regresi linear untuk memastikan bahwa tidak terdapat korelasi antar residual (nilai sisa) dari model regresi pada periode waktu yang berbeda.
\(H_0\): Tidak terdapat autokorelasi pada residual model regresi
\(H_1\): Terdapat autokorelasi pada residual model regresi
Uji ini memiliki keputusan apabila nilai p-value ≤ \(\alpha\) maka akan menolak \(H_0\) yang dimana terdapat autokorelasi pada residual model regresi, begitupun sebaliknya
2.6 Uji Asumsi Non Multikolinearitas
Uji asumsi non multikolinearitas digunakan dalam analisis regresi linier untuk memastikan bahwa tidak terdapat hubungan linear yang kuat antara variabel independen (penjelasan) dalam model regresi.
\(H_0\): Tidak terdapat multikolinearitas antar variabel independen dalam model regresi
\(H_1\): Terdapat multikolinearitas antar variabel independen dalam model regresi
Uji VIF: \(H_0\): \(VIF_{i}\) < 10 (untuk semua variabel independen i) \(H_1\): \(VIF_{i}\) ≥ 10 (untuk setidaknya satu variabel independen i)
Uji Toleransi: \(H_0\): \(TOL_{i}\) > 0.1 (untuk semua variabel independen i) \(H_1\): \(TOL_{i}\) ≤ 0.1 (untuk setidaknya satu variabel independen i)
Apabila nilai VIF (Variance Inflation Factor) untuk setiap variabel independen dihitung dan dibandingkan dengan nilai kritis (misalnya, 10). Jika nilai VIF lebih besar dari nilai kritis, maka terdapat indikasi multikolinearitas untuk variabel tersebut.
Apabila nilai toleransi (TOL) untuk setiap variabel independen dihitung dan dibandingkan dengan nilai kritis (misalnya, 0.1). Jika nilai toleransi lebih kecil dari nilai kritis, maka terdapat indikasi multikolinearitas untuk variabel tersebut.
2.7 Uji Asumsi Homoskedastisitas
Uji asumsi homoskedastisitas digunakan dalam analisis regresi linier untuk memastikan bahwa variansi residual (nilai sisa) dari model regresi sama untuk semua nilai variabel terikat (Y).
\(H_0\): Terdapat homoskedastisitas, yaitu variansi residual sama untuk semua nilai variabel terikat (Y)
\(H_1\): Tidak terdapat homoskedastisitas, yaitu variansi residual sama untuk semua nilai variabel terikat (Y)
Uji ini memiliki keputusan apabila nilai p-value ≤ \(\alpha\) maka akan menolak \(H_0\) yang dimana tidak terdapat homoskedastisitas, yaitu variansi residual sama untuk semua nilai variabel terikat (Y).
3. SOURCE CODE
3.1 Library
> # Library
> # install.packages("tseries")
> # install.packages("lmtest")
> # install.packages("readr")
> # install.packages("car")3.2 Data
> library(readr)
> library(rmarkdown)
> house_price <- read_csv("E:/output.csv")
> paged_table(house_price)4. HASIL DAN PEMBAHASAN
4.1 Model Regresi Linear
Berdasarkan Data yang digunakan, diperoleh model regresi sebagai berikut :
> library(lmtest)
> regresi= lm(price~bedrooms+sqft_lot+floors+waterfront+condition+yr_built+yr_renovated+as.factor(sqft_living)+as.factor(bathrooms)+as.factor(view)+as.factor(sqft_above)+as.factor(sqft_basement), data = house_price)
> summary(regresi)
Call:
lm(formula = price ~ bedrooms + sqft_lot + floors + waterfront +
condition + yr_built + yr_renovated + as.factor(sqft_living) +
as.factor(bathrooms) + as.factor(view) + as.factor(sqft_above) +
as.factor(sqft_basement), data = house_price)
Residuals:
Min 1Q Median 3Q Max
-1579265 -97366 0 88333 24894297
Coefficients: (197 not defined because of singularities)
Estimate Std. Error t value Pr(>|t|)
(Intercept) 4.135e+06 1.237e+06 3.343 0.000838 ***
bedrooms -3.507e+04 1.361e+04 -2.577 0.010014 *
sqft_lot -5.909e-01 2.640e-01 -2.239 0.025251 *
floors 3.126e+04 2.384e+04 1.311 0.189998
waterfront 2.077e+05 1.527e+05 1.360 0.173885
condition 2.274e+04 1.530e+04 1.486 0.137257
yr_built -2.041e+03 4.284e+02 -4.764 1.97e-06 ***
yr_renovated 1.176e+01 1.017e+01 1.156 0.247567
as.factor(sqft_living)380 8.031e+04 7.217e+05 0.111 0.911403
as.factor(sqft_living)420 2.673e+04 7.216e+05 0.037 0.970452
as.factor(sqft_living)430 -1.483e+05 7.226e+05 -0.205 0.837377
as.factor(sqft_living)490 4.641e+04 7.219e+05 0.064 0.948750
as.factor(sqft_living)520 7.146e+04 7.462e+05 0.096 0.923716
as.factor(sqft_living)550 2.053e+06 2.299e+06 0.893 0.371880
as.factor(sqft_living)560 1.407e+05 7.217e+05 0.195 0.845402
as.factor(sqft_living)580 -6.991e+04 7.456e+05 -0.094 0.925302
as.factor(sqft_living)590 2.069e+06 2.242e+06 0.923 0.356182
as.factor(sqft_living)620 3.712e+04 6.523e+05 0.057 0.954624
as.factor(sqft_living)630 1.709e+06 2.248e+06 0.760 0.447168
as.factor(sqft_living)650 1.752e+06 2.196e+06 0.798 0.425183
as.factor(sqft_living)660 -9.100e+04 6.318e+05 -0.144 0.885492
as.factor(sqft_living)670 1.574e+06 2.237e+06 0.703 0.481824
as.factor(sqft_living)680 1.895e+06 2.286e+06 0.829 0.407209
as.factor(sqft_living)690 1.468e+06 2.241e+06 0.655 0.512424
as.factor(sqft_living)700 1.676e+06 2.181e+06 0.769 0.442132
as.factor(sqft_living)710 1.769e+05 5.898e+05 0.300 0.764306
as.factor(sqft_living)720 1.620e+06 2.146e+06 0.755 0.450278
as.factor(sqft_living)730 1.835e+06 2.219e+06 0.827 0.408382
as.factor(sqft_living)740 1.702e+06 2.159e+06 0.788 0.430724
as.factor(sqft_living)750 1.598e+06 2.189e+06 0.730 0.465513
as.factor(sqft_living)760 1.938e+06 2.169e+06 0.893 0.371667
as.factor(sqft_living)770 1.579e+06 2.148e+06 0.735 0.462367
as.factor(sqft_living)780 1.505e+06 2.144e+06 0.702 0.482858
as.factor(sqft_living)790 1.729e+06 2.160e+06 0.800 0.423508
as.factor(sqft_living)800 1.900e+06 2.136e+06 0.890 0.373757
as.factor(sqft_living)810 1.515e+06 2.154e+06 0.703 0.481834
as.factor(sqft_living)820 1.648e+06 2.123e+06 0.776 0.437714
as.factor(sqft_living)830 1.688e+06 2.123e+06 0.795 0.426480
as.factor(sqft_living)840 1.822e+06 2.120e+06 0.859 0.390252
as.factor(sqft_living)850 1.600e+06 2.123e+06 0.754 0.451135
as.factor(sqft_living)860 1.614e+06 2.109e+06 0.765 0.444235
as.factor(sqft_living)870 1.480e+06 2.120e+06 0.698 0.485340
as.factor(sqft_living)880 1.629e+06 2.111e+06 0.772 0.440435
as.factor(sqft_living)890 1.709e+06 2.122e+06 0.805 0.420837
as.factor(sqft_living)900 1.589e+06 2.104e+06 0.755 0.450115
as.factor(sqft_living)910 1.591e+06 2.104e+06 0.756 0.449700
as.factor(sqft_living)920 1.636e+06 2.103e+06 0.778 0.436701
as.factor(sqft_living)930 1.647e+06 2.100e+06 0.784 0.432969
as.factor(sqft_living)940 1.675e+06 2.100e+06 0.797 0.425216
as.factor(sqft_living)950 1.565e+06 2.088e+06 0.749 0.453756
as.factor(sqft_living)960 1.604e+06 2.086e+06 0.769 0.442174
as.factor(sqft_living)970 1.601e+06 2.090e+06 0.766 0.443857
as.factor(sqft_living)980 1.623e+06 2.085e+06 0.778 0.436434
as.factor(sqft_living)982 1.416e+05 7.468e+05 0.190 0.849683
as.factor(sqft_living)990 1.677e+06 2.094e+06 0.801 0.423059
as.factor(sqft_living)998 -2.408e+04 6.746e+05 -0.036 0.971528
as.factor(sqft_living)1000 1.511e+06 2.083e+06 0.725 0.468311
as.factor(sqft_living)1010 1.519e+06 2.075e+06 0.732 0.464048
as.factor(sqft_living)1020 1.637e+06 2.075e+06 0.789 0.430063
as.factor(sqft_living)1030 1.677e+06 2.074e+06 0.808 0.418865
as.factor(sqft_living)1040 1.637e+06 2.071e+06 0.791 0.429273
as.factor(sqft_living)1050 1.536e+06 2.066e+06 0.743 0.457272
as.factor(sqft_living)1060 1.607e+06 2.063e+06 0.779 0.436219
as.factor(sqft_living)1068 7.881e+04 7.469e+05 0.106 0.915972
as.factor(sqft_living)1070 1.635e+06 2.066e+06 0.791 0.428887
as.factor(sqft_living)1080 1.394e+06 2.061e+06 0.676 0.498807
as.factor(sqft_living)1088 7.129e+04 7.469e+05 0.095 0.923958
as.factor(sqft_living)1090 1.509e+06 2.058e+06 0.733 0.463472
as.factor(sqft_living)1092 1.410e+05 7.460e+05 0.189 0.850058
as.factor(sqft_living)1100 1.514e+06 2.054e+06 0.737 0.460898
as.factor(sqft_living)1110 1.679e+06 2.055e+06 0.817 0.413859
as.factor(sqft_living)1120 1.766e+06 2.054e+06 0.859 0.390175
as.factor(sqft_living)1130 1.647e+06 2.060e+06 0.799 0.424118
as.factor(sqft_living)1140 1.539e+06 2.048e+06 0.752 0.452272
as.factor(sqft_living)1150 1.504e+06 2.043e+06 0.736 0.461884
as.factor(sqft_living)1159 3.658e+05 7.464e+05 0.490 0.624073
as.factor(sqft_living)1160 1.557e+06 2.045e+06 0.762 0.446388
as.factor(sqft_living)1170 1.565e+06 2.041e+06 0.767 0.443291
as.factor(sqft_living)1175 1.742e+06 2.208e+06 0.789 0.430142
as.factor(sqft_living)1180 2.806e+06 2.040e+06 1.376 0.169040
as.factor(sqft_living)1190 1.451e+06 2.042e+06 0.710 0.477523
as.factor(sqft_living)1200 1.487e+06 2.035e+06 0.731 0.464925
as.factor(sqft_living)1210 1.547e+06 2.039e+06 0.759 0.447925
as.factor(sqft_living)1212 1.366e+05 7.476e+05 0.183 0.855058
as.factor(sqft_living)1220 1.526e+06 2.033e+06 0.751 0.452778
as.factor(sqft_living)1230 1.547e+06 2.030e+06 0.762 0.446104
as.factor(sqft_living)1232 1.702e+05 7.472e+05 0.228 0.819800
as.factor(sqft_living)1240 1.629e+06 2.028e+06 0.803 0.421885
as.factor(sqft_living)1250 1.599e+06 2.028e+06 0.789 0.430298
as.factor(sqft_living)1255 1.800e+05 7.485e+05 0.241 0.809932
as.factor(sqft_living)1260 1.571e+06 2.027e+06 0.775 0.438249
as.factor(sqft_living)1270 1.574e+06 2.019e+06 0.779 0.435742
as.factor(sqft_living)1280 1.539e+06 2.002e+06 0.769 0.442115
as.factor(sqft_living)1290 1.582e+06 2.021e+06 0.783 0.433778
as.factor(sqft_living)1295 9.289e+05 8.479e+05 1.096 0.273326
as.factor(sqft_living)1296 2.796e+05 7.488e+05 0.373 0.708859
as.factor(sqft_living)1300 1.537e+06 2.016e+06 0.763 0.445788
as.factor(sqft_living)1310 1.564e+06 2.017e+06 0.775 0.438194
as.factor(sqft_living)1320 1.524e+06 2.013e+06 0.757 0.449159
as.factor(sqft_living)1330 1.559e+06 2.015e+06 0.774 0.439156
as.factor(sqft_living)1340 1.395e+06 2.010e+06 0.694 0.487709
as.factor(sqft_living)1347 1.555e+05 7.476e+05 0.208 0.835214
as.factor(sqft_living)1350 1.475e+06 2.010e+06 0.734 0.463071
as.factor(sqft_living)1352 1.536e+05 7.476e+05 0.206 0.837178
as.factor(sqft_living)1360 1.531e+06 2.006e+06 0.763 0.445438
as.factor(sqft_living)1370 1.506e+06 2.005e+06 0.752 0.452377
as.factor(sqft_living)1380 1.611e+06 2.006e+06 0.803 0.422009
as.factor(sqft_living)1384 4.805e+05 7.743e+05 0.621 0.534865
as.factor(sqft_living)1390 1.391e+06 2.000e+06 0.696 0.486665
as.factor(sqft_living)1392 2.297e+05 7.220e+05 0.318 0.750421
as.factor(sqft_living)1396 1.207e+05 7.463e+05 0.162 0.871479
as.factor(sqft_living)1400 1.415e+06 1.998e+06 0.708 0.478924
as.factor(sqft_living)1405 1.581e+06 2.108e+06 0.750 0.453241
as.factor(sqft_living)1408 2.383e+05 7.471e+05 0.319 0.749747
as.factor(sqft_living)1410 1.570e+06 1.995e+06 0.787 0.431478
as.factor(sqft_living)1413 1.539e+05 7.465e+05 0.206 0.836688
as.factor(sqft_living)1420 1.487e+06 1.996e+06 0.745 0.456430
as.factor(sqft_living)1430 1.513e+06 1.994e+06 0.759 0.447913
as.factor(sqft_living)1440 1.474e+06 1.987e+06 0.741 0.458477
as.factor(sqft_living)1444 4.872e+05 7.500e+05 0.650 0.515953
as.factor(sqft_living)1445 1.573e+06 2.047e+06 0.769 0.442079
as.factor(sqft_living)1450 1.461e+06 1.991e+06 0.734 0.462942
as.factor(sqft_living)1460 1.476e+06 1.989e+06 0.742 0.458090
as.factor(sqft_living)1463 1.750e+05 7.480e+05 0.234 0.815055
as.factor(sqft_living)1470 1.476e+06 1.986e+06 0.743 0.457465
as.factor(sqft_living)1480 1.464e+06 1.985e+06 0.738 0.460841
as.factor(sqft_living)1481 8.829e+04 7.473e+05 0.118 0.905953
as.factor(sqft_living)1490 1.592e+06 1.982e+06 0.803 0.421948
as.factor(sqft_living)1494 -3.720e+05 7.638e+05 -0.487 0.626265
as.factor(sqft_living)1495 1.629e+04 1.009e+06 0.016 0.987119
as.factor(sqft_living)1500 1.460e+06 1.980e+06 0.738 0.460821
as.factor(sqft_living)1510 1.548e+06 1.980e+06 0.782 0.434439
as.factor(sqft_living)1520 1.575e+06 1.980e+06 0.795 0.426446
as.factor(sqft_living)1530 1.436e+06 1.977e+06 0.726 0.467710
as.factor(sqft_living)1540 1.535e+06 1.975e+06 0.778 0.436906
as.factor(sqft_living)1550 1.058e+06 1.972e+06 0.536 0.591812
as.factor(sqft_living)1560 1.477e+06 1.974e+06 0.748 0.454305
as.factor(sqft_living)1570 1.420e+06 1.969e+06 0.721 0.470686
as.factor(sqft_living)1571 2.450e+05 7.488e+05 0.327 0.743594
as.factor(sqft_living)1580 1.466e+06 1.968e+06 0.745 0.456370
as.factor(sqft_living)1584 1.153e+05 7.473e+05 0.154 0.877406
as.factor(sqft_living)1590 1.381e+06 1.968e+06 0.702 0.482684
as.factor(sqft_living)1600 1.513e+06 1.963e+06 0.771 0.440922
as.factor(sqft_living)1601 2.050e+05 7.472e+05 0.274 0.783794
as.factor(sqft_living)1606 2.498e+05 7.476e+05 0.334 0.738267
as.factor(sqft_living)1610 1.421e+06 1.964e+06 0.723 0.469488
as.factor(sqft_living)1620 1.497e+06 1.962e+06 0.763 0.445441
as.factor(sqft_living)1630 1.483e+06 1.960e+06 0.757 0.449369
as.factor(sqft_living)1640 1.560e+06 1.956e+06 0.797 0.425411
as.factor(sqft_living)1650 1.446e+06 1.957e+06 0.739 0.460011
as.factor(sqft_living)1651 -8.677e+03 7.462e+05 -0.012 0.990723
as.factor(sqft_living)1658 1.366e+05 7.466e+05 0.183 0.854843
as.factor(sqft_living)1660 1.538e+06 1.953e+06 0.788 0.430857
as.factor(sqft_living)1670 1.553e+06 1.952e+06 0.795 0.426416
as.factor(sqft_living)1680 1.481e+06 1.950e+06 0.759 0.447726
as.factor(sqft_living)1689 6.923e+04 7.494e+05 0.092 0.926406
as.factor(sqft_living)1690 1.393e+06 1.951e+06 0.714 0.475254
as.factor(sqft_living)1700 1.407e+06 1.949e+06 0.722 0.470371
as.factor(sqft_living)1710 1.718e+06 1.951e+06 0.881 0.378457
as.factor(sqft_living)1715 9.594e+04 7.468e+05 0.128 0.897783
as.factor(sqft_living)1720 1.465e+06 1.944e+06 0.754 0.451168
as.factor(sqft_living)1726 2.853e+05 7.491e+05 0.381 0.703341
as.factor(sqft_living)1730 1.352e+06 1.946e+06 0.695 0.487283
as.factor(sqft_living)1740 1.493e+06 1.947e+06 0.767 0.443235
as.factor(sqft_living)1750 1.440e+06 1.943e+06 0.741 0.458529
as.factor(sqft_living)1760 1.471e+06 1.939e+06 0.758 0.448218
as.factor(sqft_living)1765 9.097e+04 7.468e+05 0.122 0.903049
as.factor(sqft_living)1769 1.934e+05 6.536e+05 0.296 0.767273
as.factor(sqft_living)1770 1.494e+06 1.940e+06 0.770 0.441405
as.factor(sqft_living)1780 1.411e+06 1.937e+06 0.729 0.466352
as.factor(sqft_living)1785 8.351e+05 8.485e+05 0.984 0.325106
as.factor(sqft_living)1790 1.483e+06 1.938e+06 0.765 0.444112
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as.factor(sqft_living)4430 1.215e+06 6.607e+05 1.839 0.066018 .
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as.factor(sqft_living)4510 1.838e+06 7.657e+05 2.400 0.016438 *
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as.factor(sqft_living)4580 1.519e+06 7.833e+05 1.939 0.052612 .
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as.factor(sqft_living)4670 1.571e+06 9.354e+05 1.680 0.093066 .
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as.factor(sqft_living)4730 2.055e+06 8.142e+05 2.525 0.011629 *
as.factor(sqft_living)4740 1.099e+06 6.602e+05 1.665 0.096051 .
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as.factor(sqft_living)5300 1.769e+06 8.445e+05 2.095 0.036228 *
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as.factor(sqft_living)5420 1.401e+06 7.949e+05 1.762 0.078094 .
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as.factor(sqft_living)5480 1.950e+06 9.471e+05 2.059 0.039560 *
as.factor(sqft_living)5520 1.052e+06 7.522e+05 1.399 0.161953
as.factor(sqft_living)5550 4.344e+06 1.964e+06 2.212 0.027056 *
as.factor(sqft_living)5584 1.525e+06 7.856e+05 1.941 0.052373 .
as.factor(sqft_living)5660 -4.006e+05 1.372e+06 -0.292 0.770279
as.factor(sqft_living)5700 2.260e+06 1.955e+06 1.156 0.247759
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as.factor(sqft_living)5780 2.839e+06 1.218e+06 2.331 0.019804 *
as.factor(sqft_living)5850 1.187e+06 9.412e+05 1.261 0.207418
as.factor(sqft_living)5860 8.911e+05 9.020e+05 0.988 0.323236
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as.factor(sqft_living)5990 2.223e+06 1.232e+06 1.805 0.071149 .
as.factor(sqft_living)6040 1.424e+06 7.981e+05 1.784 0.074463 .
as.factor(sqft_living)6050 1.826e+06 1.345e+06 1.358 0.174703
as.factor(sqft_living)6070 1.516e+06 7.880e+05 1.924 0.054403 .
as.factor(sqft_living)6210 2.857e+06 1.086e+06 2.632 0.008521 **
as.factor(sqft_living)6390 2.824e+06 1.219e+06 2.317 0.020536 *
as.factor(sqft_living)6430 4.434e+06 7.487e+05 5.923 3.48e-09 ***
as.factor(sqft_living)6490 1.666e+06 7.878e+05 2.115 0.034491 *
as.factor(sqft_living)6500 2.314e+06 1.129e+06 2.049 0.040518 *
as.factor(sqft_living)6630 2.618e+06 2.942e+06 0.890 0.373526
as.factor(sqft_living)6640 1.920e+06 7.942e+05 2.417 0.015705 *
as.factor(sqft_living)6900 1.163e+06 7.907e+05 1.471 0.141429
as.factor(sqft_living)6980 2.523e+06 1.301e+06 1.939 0.052606 .
as.factor(sqft_living)7050 5.136e+06 2.545e+06 2.018 0.043638 *
as.factor(sqft_living)7270 2.135e+06 1.097e+06 1.946 0.051713 .
as.factor(sqft_living)7320 1.293e+06 7.684e+05 1.683 0.092440 .
as.factor(sqft_living)8020 6.344e+03 1.019e+06 0.006 0.995035
as.factor(sqft_living)8670 2.547e+06 1.027e+06 2.480 0.013195 *
as.factor(sqft_living)9640 4.157e+06 1.033e+06 4.023 5.87e-05 ***
as.factor(sqft_living)10040 6.763e+06 8.138e+05 8.311 < 2e-16 ***
as.factor(sqft_living)13540 2.215e+06 1.031e+06 2.148 0.031821 *
as.factor(bathrooms)0.75 -4.312e+04 7.234e+05 -0.060 0.952469
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as.factor(bathrooms)1.75 3.327e+04 6.979e+05 0.048 0.961977
as.factor(bathrooms)2 1.117e+05 6.980e+05 0.160 0.872830
as.factor(bathrooms)2.25 7.671e+04 6.980e+05 0.110 0.912493
as.factor(bathrooms)2.5 7.881e+04 6.974e+05 0.113 0.910041
as.factor(bathrooms)2.75 6.091e+04 6.979e+05 0.087 0.930453
as.factor(bathrooms)3 2.938e+04 6.958e+05 0.042 0.966324
as.factor(bathrooms)3.25 2.224e+05 7.004e+05 0.318 0.750859
as.factor(bathrooms)3.5 8.463e+04 7.010e+05 0.121 0.903915
as.factor(bathrooms)3.75 2.074e+04 7.113e+05 0.029 0.976736
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as.factor(bathrooms)4.25 1.245e+05 7.377e+05 0.169 0.865988
as.factor(bathrooms)4.5 -1.259e+05 7.442e+05 -0.169 0.865635
as.factor(bathrooms)4.75 -5.046e+05 1.189e+06 -0.425 0.671205
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as.factor(bathrooms)5.25 -1.965e+05 8.949e+05 -0.220 0.826212
as.factor(bathrooms)5.5 -1.464e+06 2.531e+06 -0.579 0.562958
as.factor(bathrooms)5.75 NA NA NA NA
as.factor(bathrooms)6.25 NA NA NA NA
as.factor(bathrooms)6.5 NA NA NA NA
as.factor(bathrooms)6.75 NA NA NA NA
as.factor(bathrooms)8 NA NA NA NA
as.factor(view)1 7.458e+04 7.933e+04 0.940 0.347217
as.factor(view)2 8.512e+04 4.753e+04 1.791 0.073428 .
as.factor(view)3 1.660e+05 7.014e+04 2.367 0.017968 *
as.factor(view)4 2.754e+05 1.070e+05 2.573 0.010114 *
as.factor(sqft_above)380 NA NA NA NA
as.factor(sqft_above)420 NA NA NA NA
as.factor(sqft_above)430 NA NA NA NA
as.factor(sqft_above)490 NA NA NA NA
as.factor(sqft_above)520 NA NA NA NA
as.factor(sqft_above)550 -1.774e+06 2.163e+06 -0.820 0.412337
as.factor(sqft_above)560 NA NA NA NA
as.factor(sqft_above)580 NA NA NA NA
as.factor(sqft_above)590 -1.763e+06 2.114e+06 -0.834 0.404365
as.factor(sqft_above)610 -1.484e+06 2.160e+06 -0.687 0.492088
as.factor(sqft_above)620 NA NA NA NA
as.factor(sqft_above)630 -1.749e+06 2.121e+06 -0.825 0.409687
as.factor(sqft_above)650 -1.696e+06 2.112e+06 -0.803 0.421999
as.factor(sqft_above)660 NA NA NA NA
as.factor(sqft_above)670 -1.528e+06 2.150e+06 -0.711 0.477370
as.factor(sqft_above)680 -1.948e+06 2.162e+06 -0.901 0.367664
as.factor(sqft_above)690 -1.522e+06 2.144e+06 -0.710 0.477848
as.factor(sqft_above)700 -1.600e+06 2.106e+06 -0.759 0.447623
as.factor(sqft_above)710 NA NA NA NA
as.factor(sqft_above)720 -1.584e+06 2.071e+06 -0.765 0.444535
as.factor(sqft_above)730 -1.615e+06 2.132e+06 -0.758 0.448703
as.factor(sqft_above)740 -1.582e+06 2.077e+06 -0.762 0.446371
as.factor(sqft_above)750 -1.477e+06 2.107e+06 -0.701 0.483420
as.factor(sqft_above)760 -1.902e+06 2.068e+06 -0.920 0.357824
as.factor(sqft_above)770 -1.475e+06 2.065e+06 -0.714 0.475345
as.factor(sqft_above)780 -1.438e+06 2.064e+06 -0.696 0.486166
as.factor(sqft_above)790 -1.636e+06 2.081e+06 -0.786 0.431908
as.factor(sqft_above)798 NA NA NA NA
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as.factor(sqft_above)806 NA NA NA NA
as.factor(sqft_above)810 -1.462e+06 2.077e+06 -0.704 0.481584
as.factor(sqft_above)820 -1.518e+06 2.048e+06 -0.741 0.458794
as.factor(sqft_above)830 -1.526e+06 2.043e+06 -0.747 0.455309
as.factor(sqft_above)840 -1.689e+06 2.044e+06 -0.827 0.408554
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as.factor(sqft_above)860 -1.474e+06 2.031e+06 -0.726 0.468047
as.factor(sqft_above)870 -1.363e+06 2.040e+06 -0.668 0.504230
as.factor(sqft_above)880 -1.489e+06 2.032e+06 -0.733 0.463773
as.factor(sqft_above)890 -1.489e+06 2.043e+06 -0.729 0.466285
as.factor(sqft_above)900 -1.423e+06 2.028e+06 -0.702 0.482869
as.factor(sqft_above)910 -1.420e+06 2.030e+06 -0.700 0.484165
as.factor(sqft_above)920 -1.497e+06 2.023e+06 -0.740 0.459316
as.factor(sqft_above)930 -1.533e+06 2.024e+06 -0.758 0.448734
as.factor(sqft_above)940 -1.527e+06 2.019e+06 -0.756 0.449471
as.factor(sqft_above)944 NA NA NA NA
as.factor(sqft_above)950 -1.419e+06 2.013e+06 -0.705 0.480954
as.factor(sqft_above)960 -1.444e+06 2.010e+06 -0.718 0.472585
as.factor(sqft_above)970 -1.434e+06 2.012e+06 -0.713 0.476099
as.factor(sqft_above)980 -1.446e+06 2.007e+06 -0.721 0.471120
as.factor(sqft_above)990 -1.497e+06 2.015e+06 -0.743 0.457627
as.factor(sqft_above)995 -1.210e+06 1.984e+06 -0.610 0.542173
as.factor(sqft_above)1000 -1.380e+06 2.001e+06 -0.690 0.490429
as.factor(sqft_above)1010 -1.366e+06 1.999e+06 -0.683 0.494469
as.factor(sqft_above)1020 -1.502e+06 1.999e+06 -0.751 0.452512
as.factor(sqft_above)1030 -1.418e+06 1.996e+06 -0.710 0.477511
as.factor(sqft_above)1040 -1.461e+06 1.994e+06 -0.733 0.463832
as.factor(sqft_above)1050 -1.345e+06 1.991e+06 -0.675 0.499406
as.factor(sqft_above)1060 -1.422e+06 1.989e+06 -0.715 0.474524
as.factor(sqft_above)1068 NA NA NA NA
as.factor(sqft_above)1070 -1.443e+06 1.988e+06 -0.726 0.467938
as.factor(sqft_above)1080 -1.267e+06 1.983e+06 -0.639 0.522859
as.factor(sqft_above)1088 NA NA NA NA
as.factor(sqft_above)1090 -1.364e+06 1.981e+06 -0.689 0.491022
as.factor(sqft_above)1092 NA NA NA NA
as.factor(sqft_above)1100 -1.373e+06 1.979e+06 -0.694 0.487787
as.factor(sqft_above)1105 NA NA NA NA
as.factor(sqft_above)1110 -1.474e+06 1.978e+06 -0.745 0.456094
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as.factor(sqft_above)1954 NA NA NA NA
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as.factor(sqft_above)1982 NA NA NA NA
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as.factor(sqft_above)1995 NA NA NA NA
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as.factor(sqft_above)2009 NA NA NA NA
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as.factor(sqft_above)2015 NA NA NA NA
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as.factor(sqft_basement)410 6.414e+05 3.294e+05 1.947 0.051608 .
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as.factor(sqft_basement)990 1.503e+05 4.829e+05 0.311 0.755589
as.factor(sqft_basement)1000 2.607e+05 4.527e+05 0.576 0.564743
as.factor(sqft_basement)1010 9.473e+04 4.819e+05 0.197 0.844172
as.factor(sqft_basement)1020 2.563e+05 4.914e+05 0.522 0.602028
as.factor(sqft_basement)1030 1.771e+05 4.779e+05 0.370 0.711037
as.factor(sqft_basement)1040 4.627e+05 5.032e+05 0.920 0.357896
as.factor(sqft_basement)1050 4.179e+05 5.095e+05 0.820 0.412180
as.factor(sqft_basement)1060 9.498e+04 4.994e+05 0.190 0.849179
as.factor(sqft_basement)1070 1.516e+05 5.077e+05 0.299 0.765337
as.factor(sqft_basement)1080 5.776e+04 5.377e+05 0.107 0.914468
as.factor(sqft_basement)1090 2.352e+05 5.111e+05 0.460 0.645440
as.factor(sqft_basement)1100 1.521e+05 5.092e+05 0.299 0.765268
as.factor(sqft_basement)1110 2.184e+05 5.296e+05 0.412 0.680026
as.factor(sqft_basement)1120 2.251e+05 5.428e+05 0.415 0.678418
as.factor(sqft_basement)1130 3.945e+05 5.370e+05 0.735 0.462609
as.factor(sqft_basement)1140 1.750e+05 5.600e+05 0.312 0.754705
as.factor(sqft_basement)1150 1.363e+05 5.796e+05 0.235 0.814061
as.factor(sqft_basement)1160 2.251e+05 5.460e+05 0.412 0.680127
as.factor(sqft_basement)1170 5.005e+05 5.785e+05 0.865 0.386997
as.factor(sqft_basement)1180 2.573e+05 5.664e+05 0.454 0.649645
as.factor(sqft_basement)1190 3.325e+05 6.034e+05 0.551 0.581652
as.factor(sqft_basement)1200 2.222e+05 5.562e+05 0.399 0.689598
as.factor(sqft_basement)1210 4.831e+04 5.909e+05 0.082 0.934842
as.factor(sqft_basement)1220 3.143e+05 6.140e+05 0.512 0.608823
as.factor(sqft_basement)1230 4.437e+05 6.031e+05 0.736 0.462039
as.factor(sqft_basement)1250 1.712e+05 5.816e+05 0.294 0.768467
as.factor(sqft_basement)1260 2.728e+05 6.137e+05 0.444 0.656727
as.factor(sqft_basement)1270 1.524e+05 6.603e+05 0.231 0.817497
as.factor(sqft_basement)1280 4.578e+05 6.689e+05 0.684 0.493756
as.factor(sqft_basement)1284 NA NA NA NA
as.factor(sqft_basement)1290 4.750e+05 6.405e+05 0.742 0.458343
as.factor(sqft_basement)1300 1.016e+05 6.138e+05 0.166 0.868503
as.factor(sqft_basement)1310 3.216e+05 8.710e+05 0.369 0.711973
as.factor(sqft_basement)1320 3.083e+05 6.336e+05 0.487 0.626617
as.factor(sqft_basement)1330 1.991e+05 7.382e+05 0.270 0.787413
as.factor(sqft_basement)1340 3.249e+05 6.489e+05 0.501 0.616580
as.factor(sqft_basement)1350 3.066e+04 6.539e+05 0.047 0.962607
as.factor(sqft_basement)1360 -1.295e+05 6.657e+05 -0.195 0.845780
as.factor(sqft_basement)1370 3.211e+05 6.470e+05 0.496 0.619739
as.factor(sqft_basement)1380 2.119e+05 6.681e+05 0.317 0.751132
as.factor(sqft_basement)1400 1.937e+05 6.664e+05 0.291 0.771392
as.factor(sqft_basement)1420 3.507e+05 5.434e+05 0.645 0.518709
as.factor(sqft_basement)1430 NA NA NA NA
as.factor(sqft_basement)1440 2.427e+05 8.304e+05 0.292 0.770066
as.factor(sqft_basement)1450 2.054e+05 7.363e+05 0.279 0.780302
as.factor(sqft_basement)1460 1.570e+05 7.198e+05 0.218 0.827365
as.factor(sqft_basement)1480 1.877e+05 8.074e+05 0.232 0.816165
as.factor(sqft_basement)1490 NA NA NA NA
as.factor(sqft_basement)1500 2.016e+05 7.078e+05 0.285 0.775756
as.factor(sqft_basement)1510 5.411e+05 7.355e+05 0.736 0.462032
as.factor(sqft_basement)1520 NA NA NA NA
as.factor(sqft_basement)1530 NA NA NA NA
as.factor(sqft_basement)1540 1.835e+05 7.525e+05 0.244 0.807300
as.factor(sqft_basement)1560 1.304e+06 1.116e+06 1.168 0.242913
as.factor(sqft_basement)1580 8.578e+05 8.264e+05 1.038 0.299328
as.factor(sqft_basement)1590 -1.429e+05 8.364e+05 -0.171 0.864334
as.factor(sqft_basement)1600 1.466e+05 7.965e+05 0.184 0.853985
as.factor(sqft_basement)1610 5.444e+04 1.128e+06 0.048 0.961499
as.factor(sqft_basement)1620 5.087e+05 1.060e+06 0.480 0.631422
as.factor(sqft_basement)1630 6.448e+05 9.597e+05 0.672 0.501744
as.factor(sqft_basement)1640 -2.784e+05 9.836e+05 -0.283 0.777140
as.factor(sqft_basement)1650 1.570e+05 1.028e+06 0.153 0.878600
as.factor(sqft_basement)1660 7.390e+05 9.464e+05 0.781 0.434898
as.factor(sqft_basement)1670 3.521e+05 8.882e+05 0.396 0.691802
as.factor(sqft_basement)1690 1.165e+06 9.064e+05 1.285 0.198801
as.factor(sqft_basement)1700 1.402e+05 9.670e+05 0.145 0.884710
as.factor(sqft_basement)1720 5.934e+05 1.007e+06 0.589 0.555833
as.factor(sqft_basement)1730 6.028e+05 1.007e+06 0.598 0.549651
as.factor(sqft_basement)1740 8.712e+05 9.961e+05 0.875 0.381842
as.factor(sqft_basement)1760 1.698e+06 1.392e+06 1.220 0.222589
as.factor(sqft_basement)1780 1.627e+05 1.092e+06 0.149 0.881574
as.factor(sqft_basement)1800 3.603e+05 1.527e+06 0.236 0.813460
as.factor(sqft_basement)1830 NA NA NA NA
as.factor(sqft_basement)1840 1.357e+06 1.609e+06 0.843 0.399090
as.factor(sqft_basement)1850 1.251e+06 1.143e+06 1.094 0.273880
as.factor(sqft_basement)1860 1.311e+06 1.607e+06 0.816 0.414804
as.factor(sqft_basement)1870 NA NA NA NA
as.factor(sqft_basement)1910 1.515e+06 1.210e+06 1.252 0.210612
as.factor(sqft_basement)1940 NA NA NA NA
as.factor(sqft_basement)1950 NA NA NA NA
as.factor(sqft_basement)2000 3.561e+05 1.264e+06 0.282 0.778106
as.factor(sqft_basement)2020 NA NA NA NA
as.factor(sqft_basement)2030 1.738e+06 1.473e+06 1.180 0.237994
as.factor(sqft_basement)2060 -1.675e+05 1.262e+06 -0.133 0.894448
as.factor(sqft_basement)2070 4.913e+05 1.207e+06 0.407 0.684074
as.factor(sqft_basement)2080 NA NA NA NA
as.factor(sqft_basement)2100 -1.362e+05 1.171e+06 -0.116 0.907366
as.factor(sqft_basement)2110 NA NA NA NA
as.factor(sqft_basement)2150 -8.512e+05 1.365e+06 -0.624 0.532807
as.factor(sqft_basement)2180 8.884e+05 1.426e+06 0.623 0.533317
as.factor(sqft_basement)2200 NA NA NA NA
as.factor(sqft_basement)2300 NA NA NA NA
as.factor(sqft_basement)2330 NA NA NA NA
as.factor(sqft_basement)2360 NA NA NA NA
as.factor(sqft_basement)2550 NA NA NA NA
as.factor(sqft_basement)2730 NA NA NA NA
as.factor(sqft_basement)2850 NA NA NA NA
as.factor(sqft_basement)4130 NA NA NA NA
as.factor(sqft_basement)4820 NA NA NA NA
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 509800 on 3479 degrees of freedom
Multiple R-squared: 0.3816, Adjusted R-squared: 0.1825
F-statistic: 1.916 on 1120 and 3479 DF, p-value: < 2.2e-16Model Regresi \[ Y_i = 4135000 - 35070(bedrooms) - 0.5909(sqft_lot) + 31260(floors) + 207700(waterfront) + 22740(condition) - 2041(yr_built) + 11.76(yr_renovated) + 80310(sqft_living) \]
4.2 Uji Linearitas
> plot(regresi$fitted.values, regresi$residuals)
> abline(h = 0, col = "blue")
Berdasarkan plot tersebut diketahui bahwa residual bersifat linear
4.3 Uji Normalitas
> qqnorm(regresi$residuals)
> qqline(regresi$residuals, col = "blue")
>
> shapiro.test(regresi$residuals)
Shapiro-Wilk normality test
data: regresi$residuals
W = 0.24901, p-value < 2.2e-16Berdasarkan uji normalitas diperoleh bahwa nilai p-value < \(\alpha\) sehingga dapat disimpulkan bahwa residual tidak menyebar secara normal
4.4 Uji Autokorelasi
> dwtest(regresi)
Durbin-Watson test
data: regresi
DW = 1.9944, p-value = 0.7604
alternative hypothesis: true autocorrelation is greater than 0Berdasarkan uji autokorelasi diperoleh bahwa nilai p-value > dari \(\alpha\) sehingga dapat disimpulkan bahwa data regresi tidak terdapat auto korelasi
4.5 Uji Non Multikolinearitas
> library(car)
> vif(regresi)
Error in vif.default(regresi): there are aliased coefficients in the modelModel tidak dapat dilakukan uji non multikolinearitas
4.6 Uji Homoskedastisitas
> plot(regresi$fitted.values, regresi$residuals)
> abline(h = 0, col = "red")
> bptest(regresi)
studentized Breusch-Pagan test
data: regresi
BP = 295.66, df = 1120, p-value = 1Berdasarkan uji homoskedastisitas diperoleh bahwa nilai p-value > dari \(\alpha\) maka terima \(H_0\) sehingga dapat disimpulkan bahwa terdapat homoskedastisitas
5. KESIMPULAN
Berdasarkan hasil analisis diatas diperoleh model regresi sebagai berikut: \[ Y_i = 4135000 - 35070(bedrooms) - 0.5909(sqft_lot) + 31260(floors) + 207700(waterfront) + 22740(condition) - 2041(yr_built) + 11.76(yr_renovated) + 80310(sqft_living) \] Model regresi diatas memenuhi asumsi linearitas, dan homoskedastisitas. Namun, asumsi tersebut tidak memenuhi asumsi normalitas, dan autokorelasi. Selain itu, model regresi tidak dapat dilakukan uji non multikolinearitas.
6. DAFTAR PUSTAKA
Agung, A. (2020). Analisis Regresi Linier: Teori, Aplikasi dan Contohnya. Penerbit Pustaka Mandiri.
Montgomery, D. C., & Peck, E. A. (2010). Introduction to linear regression analysis. John Wiley & Sons.
Sugiyono. 2004. Metode Penelitian Bisnis. Alfabeta. Bandung.
Prasetyo, P. (2020). Analisis Regresi Linier dan Regresi Logistik dengan SPSS 25 dan R. Penerbit Deepublish.