Tabel Durbin-Watson (dL dan dU)

Batas bawah (dL) dan batas atas (dU) statistik Durbin-Watson. Contoh: n = 40, k = 2 → dL = 1,3908, dU = 1,6000.

nk = 1k = 2k = 3k = 4k = 5k = 6
dLdUdLdUdLdUdLdUdLdUdLdU
60.61021.40010.37752.12820.27253.0045––––––
70.69951.35630.46721.89640.28242.54670.20153.2504––––
80.76291.33240.55911.77710.36742.28660.21882.84700.15493.4169––
90.82431.31990.62911.69930.45482.12820.29572.58810.17433.06660.12283.5342
100.87911.31970.69721.64130.52532.01630.37602.41360.24272.82170.14203.2308
110.92731.32410.75801.60440.59481.92800.44412.28330.31552.64460.20253.0045
120.97081.33140.81221.57940.65761.86400.51202.17660.37962.50610.26812.8320
131.00971.34040.86121.56210.71471.81590.57452.09430.44452.38970.32772.6920
141.04501.35030.90541.55070.76671.77880.63212.02960.50522.29590.38902.5716
151.07701.36050.94551.54320.81401.75010.68521.97730.56202.21980.44712.4715
161.10621.37090.98201.53860.85721.72770.73401.93510.61502.15670.50222.3881
171.13291.38121.01541.53610.89681.71010.77901.90050.66412.10410.55422.3175
181.15761.39131.04611.53530.93311.69610.82041.87190.70982.06000.60302.2575
191.18041.40121.07431.53550.96661.68510.85881.84810.75232.02260.64872.2061
201.20151.41071.10041.53670.99761.67630.89421.82830.79181.99080.69152.1619
211.22121.42001.12461.53851.02621.66940.92721.81160.82861.96350.73152.1235
221.23951.42891.14711.54081.05291.66400.95781.79740.86281.94000.76902.0902
231.25671.43751.16811.54351.07781.65970.98641.78550.89491.91960.80412.0609
241.27281.44571.18781.54641.10101.65651.01311.77530.92491.90180.83712.0352
251.28791.45371.20631.54951.12281.65401.03811.76660.95301.88630.86802.0125
261.30221.46141.22361.55281.14321.65221.06161.75910.97941.87270.89721.9924
271.31571.46881.23991.55621.16241.65101.08361.75271.00421.86080.92461.9745
281.32841.47591.25531.55961.18051.65021.10441.74731.02761.85020.95051.9585
291.34051.48281.26991.56311.19761.64991.12411.74261.04971.84090.97501.9442
301.35201.48941.28371.56661.21381.64981.14261.73861.07061.83260.99811.9313
311.36301.49571.29691.57011.22911.65001.16021.73521.09041.82521.02011.9198
321.37341.50191.30931.57361.24371.65051.17691.73231.10921.81871.04091.9093
331.38331.50781.32121.57701.25761.65111.19271.72981.12701.81281.06061.8999
341.39281.51361.33251.58041.27071.65191.20781.72771.14391.80761.07941.8913
351.40191.51911.34331.58381.28331.65281.22211.72591.16011.80291.09731.8835
361.41061.52451.35371.58721.29531.65391.23581.72451.17551.79871.11441.8764
371.41901.52971.36351.59041.30681.65501.24891.72331.19011.79501.13071.8700
381.42701.53471.37301.59371.31771.65621.26141.72231.20421.79161.14631.8641
391.43471.53961.38211.59691.32831.65751.27341.72151.21761.78861.16121.8587
401.44211.54441.39081.60001.33841.65891.28481.72091.23051.78591.17541.8538
411.44931.54891.39921.60311.34801.66031.29581.72051.24281.78351.18911.8493
421.45621.55341.40731.60611.35731.66171.30641.72021.25461.78141.20221.8451
431.46281.55771.41511.60911.36631.66321.31651.72001.26601.77941.21481.8413
441.46921.56191.42261.61201.37491.66471.32631.72001.27691.77771.22691.8378
451.47541.56601.42981.61481.38321.66621.33571.72001.28741.77621.23851.8346
461.48141.57001.43681.61761.39121.66771.34481.72011.29761.77481.24971.8317
471.48721.57391.44351.62041.39891.66921.35351.72031.30731.77361.26051.8290
481.49281.57761.45001.62311.40641.67081.36191.72061.31671.77251.27091.8265
491.49821.58131.45631.62571.41361.67231.37011.72101.32581.77161.28091.8241
501.50351.58491.46251.62831.42061.67381.37791.72131.33461.77081.29061.8220
511.50861.58831.46841.63091.42731.67541.38551.72181.34301.77001.29991.8201
521.51351.59171.47411.63341.43391.67691.39291.72231.35121.76941.30901.8183
531.51831.59511.47971.63581.44021.67851.40001.72281.35921.76891.31771.8166
541.52301.59831.48511.63831.44641.68001.40691.72341.36691.76841.32621.8151
551.52761.60141.49031.64061.45231.68151.41361.72401.37431.76811.33441.8137
561.53201.60451.49541.64291.45811.68301.42011.72461.38151.76781.34241.8124
571.53631.60751.50041.64521.46371.68451.42641.72531.38851.76751.35011.8112
581.54051.61051.50521.64751.46921.68601.43251.72591.39531.76731.35761.8101
591.54451.61341.50991.64971.47451.68741.43851.72661.40191.76721.36481.8091
601.54851.61621.51441.65181.47961.68891.44431.72731.40831.76711.37191.8082
611.55241.61891.51891.65401.48471.69041.44991.72811.41461.76711.37871.8073
621.55621.62161.52321.65601.48961.69181.45541.72881.42061.76711.38541.8065
631.55991.62431.52741.65811.49431.69321.46071.72961.42651.76711.39181.8058
641.56351.62681.53151.66011.49901.69461.46591.73031.43221.76721.39811.8052
651.56701.62941.53551.66211.50351.69601.47091.73111.43781.76731.40431.8046
661.57041.63181.53951.66401.50791.69741.47581.73191.44331.76741.41021.8041
671.57381.63431.54331.66601.51221.69881.48061.73271.44861.76761.41601.8036
681.57711.63661.54701.66781.51641.70011.48531.73351.45371.76781.42171.8032
691.58031.63901.55071.66971.52051.70151.48991.73421.45881.76801.42721.8028
701.58341.64131.55421.67151.52451.70281.49431.73501.46371.76831.43261.8024
711.58651.64351.55771.67331.52841.70411.49871.73581.46851.76851.43791.8021
721.58951.64571.56111.67511.53231.70541.50291.73661.47321.76881.44301.8019
731.59241.64791.56451.67681.53601.70671.50711.73741.47771.76911.44801.8016
741.59531.65001.56771.67851.53971.70791.51111.73821.48221.76941.45291.8014
751.59811.65211.57091.68021.54321.70921.51511.73901.48661.76971.45771.8013
761.60091.65411.57401.68191.54671.71041.51901.73981.49091.77011.46231.8011
771.60361.65611.57711.68351.55021.71171.52281.74061.49501.77041.46691.8010
781.60631.65811.58011.68511.55351.71291.52651.74141.49911.77081.47141.8009
791.60891.66011.58301.68671.55681.71411.53011.74221.50311.77121.47571.8009
801.61141.66201.58591.68821.56001.71531.53371.74301.50701.77161.48001.8008
811.61391.66381.58871.68981.56321.71641.53721.74381.51091.77201.48421.8008
821.61641.66571.59151.69131.56631.71761.54061.74461.51461.77241.48831.8008
831.61881.66751.59421.69281.56931.71871.54401.74541.51831.77281.49231.8008
841.62121.66931.59691.69421.57231.71991.54721.74621.52191.77321.49621.8008
851.62351.67101.59951.69571.57521.72101.55051.74701.52541.77361.50001.8009
861.62581.67281.60211.69711.57801.72211.55361.74781.52891.77401.50381.8009
871.62801.67451.60461.69851.58081.72321.55671.74851.53221.77451.50751.8010
881.63021.67611.60711.69991.58361.72431.55971.74931.53561.77491.51111.8011
891.63241.67781.60951.70131.58631.72541.56271.75011.53881.77541.51461.8012
901.63451.67941.61191.70261.58891.72641.56561.75081.54201.77581.51811.8013
911.63661.68101.61431.70401.59151.72751.56851.75161.54521.77621.52151.8015
921.63871.68261.61661.70531.59411.72851.57131.75231.54821.77671.52491.8016
931.64071.68411.61881.70661.59661.72951.57411.75311.55131.77721.52821.8018
941.64271.68571.62111.70781.59911.73061.57681.75381.55421.77761.53141.8019
951.64471.68721.62331.70911.60151.73161.57951.75461.55721.77811.53461.8021
961.64661.68871.62541.71031.60391.73261.58211.75531.56001.77851.53771.8023
971.64851.69011.62751.71161.60621.73351.58471.75601.56281.77901.54071.8025
981.65041.69161.62961.71281.60861.73451.58721.75671.56561.77951.54371.8027
991.65221.69301.63171.71401.61081.73551.58971.75751.56831.77991.54671.8029
1001.65401.69441.63371.71521.61311.73641.59221.75821.57101.78041.54961.8031
1051.66271.70111.64331.72091.62371.74111.60381.76171.58371.78271.56341.8042
1101.67081.70741.65231.72621.63361.74541.61461.76511.59541.78511.57611.8054
1151.67831.71331.66061.73131.64271.74961.62461.76831.60631.78741.58781.8068
1201.68531.71891.66841.73611.65131.75361.63391.77151.61641.78961.59871.8081
1251.69191.72411.67571.74061.65921.75741.64261.77451.62581.79191.60891.8096
1301.69811.72911.68251.74491.66671.76101.65081.77741.63461.79411.61841.8110
1351.70401.73381.68891.74901.67381.76451.65841.78021.64291.79621.62721.8125
1401.70951.73821.69501.75291.68041.76781.66561.78301.65071.79841.63561.8140
1451.71471.74251.70081.75661.68661.77101.67241.78561.65801.80041.64341.8154
1501.71971.74651.70621.76021.69251.77411.67881.78811.66491.80241.65081.8169
1551.72441.75041.71131.76361.69821.77701.68481.79061.67141.80441.65781.8184
1601.72891.75401.71631.76681.70351.77981.69061.79301.67761.80631.66441.8198
1651.73321.75761.72091.76991.70851.78251.69601.79521.68341.80811.67071.8212
1701.73731.76091.72541.77291.71341.78511.70121.79751.68901.81001.67671.8226
1751.74121.76421.72961.77581.71801.78761.70621.79961.69431.81171.68241.8240
1801.74491.76731.73371.77861.72241.79011.71091.80171.69941.81351.68781.8254
1851.74851.77021.73761.78131.72661.79241.71541.80371.70421.81511.69301.8267
1901.75201.77311.74131.78381.73061.79471.71981.80571.70891.81681.69791.8280
1951.75531.77591.74491.78631.73441.79691.72391.80761.71331.81841.70261.8293
2001.75841.77851.74831.78871.73821.79901.72791.80941.71751.81991.70711.8306

α = 5%; k = jumlah variabel independen (tidak termasuk konstanta).

Cara mengambil keputusan Durbin-Watson

KondisiKeputusan
0 < d < dLAda autokorelasi positif
dL ≤ d ≤ dUTidak dapat disimpulkan
dU < d < 4 − dUTidak ada autokorelasi
4 − dU ≤ d ≤ 4 − dLTidak dapat disimpulkan
4 − dL < d < 4Ada autokorelasi negatif

Contoh: n = 40, k = 2, d hitung = 1,85. Dari tabel dU = 1,6000 sehingga 4 − dU = 2,4000. Karena 1,6000 < 1,85 < 2,4000, tidak terjadi autokorelasi.

Bagaimana tabel ini dihitung?

Nilai dL dan dU adalah titik kritis 5% dari dua statistik pembatas Durbin-Watson (1950/1951), yang distribusinya dihitung eksak dengan integrasi numerik Imhof (1961) — metode yang sama dengan tabel Savin & White (1977). Hasilnya sama dengan tabel buku hingga 3 desimal. Regresi di kalkulator regresi berganda menghitung dL/dU ini otomatis.

Pertanyaan yang sering diajukan

Apa arti k pada tabel Durbin-Watson?

Jumlah variabel independen, tidak termasuk konstanta. Beberapa buku memakai k' untuk hal yang sama.

Bagaimana jika n saya tidak ada di tabel?

Gunakan kalkulator dL/dU di atas untuk n hingga 2.000.

Apakah uji DW wajib untuk data cross-section?

Secara teori autokorelasi relevan untuk data runtut waktu, namun banyak pedoman skripsi tetap mencantumkannya.

Apakah ada alternatif uji DW?

Run test, Breusch-Godfrey (LM test), atau Durbin h untuk model dengan lag variabel dependen.

Alat terkait

Seluruh nilai pada halaman ini dihitung langsung dari fungsi distribusi (bukan disalin dari buku), dengan ketelitian 4 desimal.