| Multiple Linear Regression - Estimated Regression Equation |
| Y[t] = + 218.876252554515 -5.76855040693692X[t] + 72.7832532666989M1[t] + 87.6197783160123M2[t] + 64.8766418472774M3[t] + 44.7775949908746M4[t] + 20.7449417198273M5[t] + 55.9833505094106M6[t] + 47.7881528843493M7[t] + 25.6494118095783M8[t] + 17.0532314389814M9[t] -8.40513845351738M10[t] + 3.01280616186310M11[t] -0.540019448542279t + e[t] |
| Multiple Linear Regression - Ordinary Least Squares | |||||
| Variable | Parameter | S.D. | T-STAT H0: parameter = 0 | 2-tail p-value | 1-tail p-value |
| (Intercept) | 218.876252554515 | 28.618903 | 7.648 | 0 | 0 |
| X | -5.76855040693692 | 1.185888 | -4.8643 | 5e-06 | 2e-06 |
| M1 | 72.7832532666989 | 34.736143 | 2.0953 | 0.03889 | 0.019445 |
| M2 | 87.6197783160123 | 34.750363 | 2.5214 | 0.013409 | 0.006705 |
| M3 | 64.8766418472774 | 34.66935 | 1.8713 | 0.064482 | 0.032241 |
| M4 | 44.7775949908746 | 34.760825 | 1.2882 | 0.20092 | 0.10046 |
| M5 | 20.7449417198273 | 34.65118 | 0.5987 | 0.550858 | 0.275429 |
| M6 | 55.9833505094106 | 34.764824 | 1.6103 | 0.110749 | 0.055374 |
| M7 | 47.7881528843493 | 34.672869 | 1.3783 | 0.171466 | 0.085733 |
| M8 | 25.6494118095783 | 34.848826 | 0.736 | 0.463591 | 0.231796 |
| M9 | 17.0532314389814 | 34.934386 | 0.4882 | 0.626605 | 0.313302 |
| M10 | -8.40513845351738 | 34.790986 | -0.2416 | 0.809636 | 0.404818 |
| M11 | 3.01280616186310 | 35.630359 | 0.0846 | 0.932797 | 0.466399 |
| t | -0.540019448542279 | 0.248155 | -2.1761 | 0.032106 | 0.016053 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.557723806345547 |
| R-squared | 0.311055844164565 |
| Adjusted R-squared | 0.213705039535645 |
| F-TEST (value) | 3.19520568268790 |
| F-TEST (DF numerator) | 13 |
| F-TEST (DF denominator) | 92 |
| p-value | 0.000544869943113202 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 71.1801908095377 |
| Sum Squared Residuals | 466128.999858761 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 235.1 | 285.350935965737 | -50.2509359657371 |
| 2 | 280.7 | 299.647441566506 | -18.9474415665060 |
| 3 | 264.6 | 270.595735242292 | -5.99573524229156 |
| 4 | 240.7 | 261.493769751221 | -20.7937697512207 |
| 5 | 201.4 | 231.152546624694 | -29.7525466246944 |
| 6 | 240.8 | 271.619486372672 | -30.819486372672 |
| 7 | 241.1 | 268.652819706005 | -27.5528197060054 |
| 8 | 223.8 | 257.511159996566 | -33.711159996566 |
| 9 | 206.1 | 248.374960177427 | -42.2749601774268 |
| 10 | 174.7 | 222.376570836386 | -47.6765708363858 |
| 11 | 203.3 | 239.023046410161 | -35.7230464101609 |
| 12 | 220.5 | 258.544422427503 | -38.0444224275032 |
| 13 | 299.5 | 336.556206652597 | -37.0562066525968 |
| 14 | 347.4 | 373.926913881116 | -26.5269138811156 |
| 15 | 338.3 | 379.486509998523 | -41.1865099985229 |
| 16 | 327.7 | 318.467590845019 | 9.23240915498054 |
| 17 | 351.6 | 282.357817311556 | 69.242182688444 |
| 18 | 396.6 | 322.824757059534 | 73.775242940466 |
| 19 | 438.8 | 331.395191206741 | 107.404808793259 |
| 20 | 395.6 | 297.179329869554 | 98.420670130446 |
| 21 | 363.5 | 253.431827608793 | 110.068172391207 |
| 22 | 378.8 | 285.118942337121 | 93.6810576628785 |
| 23 | 357 | 244.079913841527 | 112.920086158473 |
| 24 | 369 | 240.527088231122 | 128.472911768878 |
| 25 | 464.8 | 295.464670828468 | 169.335329171532 |
| 26 | 479.1 | 298.224075615365 | 180.875924384635 |
| 27 | 431.3 | 286.478020511962 | 144.821979488038 |
| 28 | 366.5 | 271.607504613954 | 94.8924953860464 |
| 29 | 326.3 | 258.571932708238 | 67.7280672917621 |
| 30 | 355.1 | 258.659019607657 | 96.4409803923426 |
| 31 | 331.6 | 272.998004161802 | 58.6019958381985 |
| 32 | 261.3 | 238.782142824614 | 22.5178571753857 |
| 33 | 249 | 229.645943005475 | 19.3540569945248 |
| 34 | 205.5 | 226.721755292182 | -21.2217552921819 |
| 35 | 235.6 | 243.368230865957 | -7.76823086595698 |
| 36 | 240.9 | 234.046854848615 | 6.85314515138534 |
| 37 | 264.9 | 306.290088666771 | -41.3900886667714 |
| 38 | 253.8 | 303.280943046732 | -49.4809430467316 |
| 39 | 232.3 | 274.229236722517 | -41.9292367225174 |
| 40 | 193.8 | 270.895821638383 | -77.0958216383833 |
| 41 | 177 | 280.934451360415 | -103.934451360415 |
| 42 | 213.2 | 315.632840701456 | -102.432840701456 |
| 43 | 207.2 | 306.897623627853 | -99.6976236278526 |
| 44 | 180.6 | 278.450312697602 | -97.8503126976024 |
| 45 | 188.6 | 292.388314506211 | -103.788314506211 |
| 46 | 175.4 | 231.778622723548 | -56.3786227235483 |
| 47 | 199 | 248.425098297323 | -49.4250982973235 |
| 48 | 179.6 | 221.798071059170 | -42.1980710591704 |
| 49 | 225.8 | 270.967103249579 | -45.1671032495794 |
| 50 | 234 | 291.032159257287 | -57.0321592572873 |
| 51 | 200.2 | 285.054654560821 | -84.8546545608209 |
| 52 | 183.6 | 258.647037848939 | -75.047037848939 |
| 53 | 178.2 | 245.611465943223 | -67.4114659432232 |
| 54 | 203.2 | 257.235653656517 | -54.0356536565166 |
| 55 | 208.5 | 248.500436582913 | -40.000436582913 |
| 56 | 191.8 | 225.821676059600 | -34.0216760595996 |
| 57 | 172.8 | 216.685476240461 | -43.8854762404605 |
| 58 | 148 | 167.612885271672 | -19.6128852716718 |
| 59 | 159.4 | 184.259360845447 | -24.8593608454469 |
| 60 | 154.5 | 232.623488897474 | -78.1234888974739 |
| 61 | 213.2 | 264.486869867072 | -51.2868698670721 |
| 62 | 196.4 | 267.246274653969 | -70.8462746539692 |
| 63 | 182.8 | 255.500219550566 | -72.7002195505658 |
| 64 | 176.4 | 217.55550202481 | -41.1555020248101 |
| 65 | 153.6 | 192.982829305220 | -39.3828293052205 |
| 66 | 173.2 | 233.449769053198 | -60.2497690531985 |
| 67 | 171 | 236.251652793469 | -65.2516527934687 |
| 68 | 151.2 | 219.341442677092 | -68.1414426770923 |
| 69 | 161.9 | 210.205242857953 | -48.3052428579532 |
| 70 | 157.2 | 178.438303109975 | -21.2383031099752 |
| 71 | 201.7 | 229.696081125372 | -27.9960811253719 |
| 72 | 236.4 | 203.069053887219 | 33.3309461127812 |
| 73 | 356.1 | 286.849388519249 | 69.2506114807507 |
| 74 | 398.3 | 283.840242899210 | 114.459757100790 |
| 75 | 403.7 | 260.557086981932 | 143.142913018068 |
| 76 | 384.6 | 262.992222304735 | 121.607777695265 |
| 77 | 365.8 | 249.956650399019 | 115.843349600981 |
| 78 | 368.1 | 296.192140553934 | 71.9078594460658 |
| 79 | 367.9 | 298.994024294204 | 68.9059757057955 |
| 80 | 347 | 264.778162957017 | 82.2218370429828 |
| 81 | 343.3 | 244.104862324004 | 99.1951376759957 |
| 82 | 292.9 | 264.254876238459 | 28.6451237615414 |
| 83 | 311.5 | 303.975553439981 | 7.52444656001858 |
| 84 | 300.9 | 317.728379050387 | -16.8283790503868 |
| 85 | 366.9 | 361.128860833859 | 5.77113916614109 |
| 86 | 356.9 | 398.499568062378 | -41.5995680623776 |
| 87 | 329.7 | 375.2164121451 | -45.5164121451003 |
| 88 | 316.2 | 343.040245026282 | -26.8402450262815 |
| 89 | 269 | 301.161921085881 | -32.1619210858812 |
| 90 | 289.3 | 330.091760019985 | -40.7917600199853 |
| 91 | 266.2 | 315.587992539445 | -49.3879925394448 |
| 92 | 253.6 | 258.29792957451 | -4.69792957450991 |
| 93 | 233.8 | 249.161729755371 | -15.3617297553708 |
| 94 | 228.4 | 228.931890821267 | -0.531890821266662 |
| 95 | 253.6 | 228.272715174231 | 25.327284825769 |
| 96 | 260.1 | 253.56264159851 | 6.53735840148978 |
| 97 | 306.6 | 325.805875416667 | -19.2058754166669 |
| 98 | 309.2 | 340.102381017438 | -30.902381017438 |
| 99 | 309.5 | 305.282124286287 | 4.21787571371313 |
| 100 | 271 | 255.800305946657 | 15.1996940533427 |
| 101 | 279.9 | 260.070385261752 | 19.8296147382477 |
| 102 | 317.9 | 271.694572975046 | 46.2054270249543 |
| 103 | 298.4 | 251.422255087568 | 46.9777449124317 |
| 104 | 246.7 | 211.437843343444 | 35.2621566565559 |
| 105 | 227.3 | 202.301643524305 | 24.9983564756950 |
| 106 | 209.1 | 164.76615336939 | 44.3338466306099 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 17 | 0.0549004408152914 | 0.109800881630583 | 0.945099559184709 |
| 18 | 0.0363109861130886 | 0.0726219722261773 | 0.963689013886911 |
| 19 | 0.0639557594486578 | 0.127911518897316 | 0.936044240551342 |
| 20 | 0.0329152156562201 | 0.0658304313124402 | 0.96708478434378 |
| 21 | 0.0161375839653802 | 0.0322751679307604 | 0.98386241603462 |
| 22 | 0.0218710273464834 | 0.0437420546929668 | 0.978128972653517 |
| 23 | 0.0118705339783835 | 0.023741067956767 | 0.988129466021616 |
| 24 | 0.00740071641294905 | 0.0148014328258981 | 0.99259928358705 |
| 25 | 0.00680839083581213 | 0.0136167816716243 | 0.993191609164188 |
| 26 | 0.0103027968179452 | 0.0206055936358903 | 0.989697203182055 |
| 27 | 0.0183422885454350 | 0.0366845770908699 | 0.981657711454565 |
| 28 | 0.0498162766406857 | 0.0996325532813714 | 0.950183723359314 |
| 29 | 0.140893991409397 | 0.281787982818794 | 0.859106008590603 |
| 30 | 0.265635686465602 | 0.531271372931203 | 0.734364313534398 |
| 31 | 0.504106041532474 | 0.991787916935052 | 0.495893958467526 |
| 32 | 0.717782685688492 | 0.564434628623016 | 0.282217314311508 |
| 33 | 0.8305378786584 | 0.338924242683198 | 0.169462121341599 |
| 34 | 0.90604358139581 | 0.187912837208377 | 0.0939564186041887 |
| 35 | 0.943936128651175 | 0.112127742697649 | 0.0560638713488247 |
| 36 | 0.963744579017965 | 0.0725108419640706 | 0.0362554209820353 |
| 37 | 0.983732220372201 | 0.0325355592555979 | 0.0162677796277990 |
| 38 | 0.99271544703113 | 0.0145691059377419 | 0.00728455296887096 |
| 39 | 0.994229884548512 | 0.0115402309029762 | 0.00577011545148811 |
| 40 | 0.996123912089796 | 0.00775217582040715 | 0.00387608791020357 |
| 41 | 0.998139675463463 | 0.00372064907307369 | 0.00186032453653684 |
| 42 | 0.998897052834993 | 0.00220589433001504 | 0.00110294716500752 |
| 43 | 0.99914294982267 | 0.00171410035466215 | 0.000857050177331075 |
| 44 | 0.999118472352052 | 0.00176305529589614 | 0.000881527647948072 |
| 45 | 0.999022452209016 | 0.00195509558196790 | 0.000977547790983951 |
| 46 | 0.998459943492454 | 0.00308011301509179 | 0.00154005650754589 |
| 47 | 0.99762390799464 | 0.0047521840107195 | 0.00237609200535975 |
| 48 | 0.996475997864928 | 0.007048004270143 | 0.0035240021350715 |
| 49 | 0.994496883957106 | 0.0110062320857874 | 0.00550311604289372 |
| 50 | 0.991899637256719 | 0.0162007254865629 | 0.00810036274328144 |
| 51 | 0.989738582202752 | 0.020522835594496 | 0.010261417797248 |
| 52 | 0.986393963216154 | 0.0272120735676923 | 0.0136060367838462 |
| 53 | 0.98133996480988 | 0.0373200703802411 | 0.0186600351901205 |
| 54 | 0.973358508071665 | 0.0532829838566699 | 0.0266414919283350 |
| 55 | 0.96165446558797 | 0.0766910688240583 | 0.0383455344120292 |
| 56 | 0.946090752451017 | 0.107818495097966 | 0.0539092475489831 |
| 57 | 0.92683513157189 | 0.146329736856220 | 0.0731648684281102 |
| 58 | 0.902028267296547 | 0.195943465406905 | 0.0979717327034525 |
| 59 | 0.870796419491457 | 0.258407161017087 | 0.129203580508543 |
| 60 | 0.853362647900062 | 0.293274704199877 | 0.146637352099938 |
| 61 | 0.826767731301562 | 0.346464537396875 | 0.173232268698438 |
| 62 | 0.815062408827885 | 0.369875182344229 | 0.184937591172115 |
| 63 | 0.826204117947216 | 0.347591764105567 | 0.173795882052784 |
| 64 | 0.82508351885913 | 0.349832962281738 | 0.174916481140869 |
| 65 | 0.83630468824285 | 0.327390623514299 | 0.163695311757149 |
| 66 | 0.872922909869041 | 0.254154180261918 | 0.127077090130959 |
| 67 | 0.919050103779685 | 0.161899792440630 | 0.0809498962203148 |
| 68 | 0.967813321401707 | 0.0643733571965862 | 0.0321866785982931 |
| 69 | 0.990783983976596 | 0.0184320320468091 | 0.00921601602340454 |
| 70 | 0.998607853644344 | 0.00278429271131179 | 0.00139214635565590 |
| 71 | 0.999896347579425 | 0.00020730484114984 | 0.00010365242057492 |
| 72 | 0.999996463938058 | 7.07212388487722e-06 | 3.53606194243861e-06 |
| 73 | 0.999998929040771 | 2.14191845724132e-06 | 1.07095922862066e-06 |
| 74 | 0.999999044499815 | 1.91100036922173e-06 | 9.55500184610863e-07 |
| 75 | 0.999998983162347 | 2.03367530644486e-06 | 1.01683765322243e-06 |
| 76 | 0.999997931716107 | 4.13656778587572e-06 | 2.06828389293786e-06 |
| 77 | 0.999995280523164 | 9.43895367233078e-06 | 4.71947683616539e-06 |
| 78 | 0.999992138242528 | 1.57235149438238e-05 | 7.8617574719119e-06 |
| 79 | 0.999976154639054 | 4.76907218924849e-05 | 2.38453609462424e-05 |
| 80 | 0.999934156408777 | 0.000131687182445854 | 6.58435912229268e-05 |
| 81 | 0.999918006950827 | 0.000163986098345271 | 8.19930491726355e-05 |
| 82 | 0.999899525727278 | 0.000200948545444922 | 0.000100474272722461 |
| 83 | 0.999780411249424 | 0.000439177501153056 | 0.000219588750576528 |
| 84 | 0.999401065629427 | 0.00119786874114685 | 0.000598934370573425 |
| 85 | 0.99962213832565 | 0.00075572334870044 | 0.00037786167435022 |
| 86 | 0.999550195705711 | 0.000899608588577075 | 0.000449804294288537 |
| 87 | 0.997963625567745 | 0.00407274886450936 | 0.00203637443225468 |
| 88 | 0.996421649743654 | 0.00715670051269202 | 0.00357835025634601 |
| 89 | 0.984054826271862 | 0.0318903474562761 | 0.0159451737281380 |
| Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
| Description | # significant tests | % significant tests | OK/NOK |
| 1% type I error level | 28 | 0.383561643835616 | NOK |
| 5% type I error level | 45 | 0.616438356164384 | NOK |
| 10% type I error level | 52 | 0.712328767123288 | NOK |
