| Multiple Linear Regression - Estimated Regression Equation |
| Y[t] = + 8.2339349299459 -2.78755263787447X[t] + 1.31883197290955Y1[t] -0.154452435378261Y2[t] -0.256484237853682Y3[t] -3.13382616025963M1[t] + 0.968052253349415M2[t] -0.053936219421836M3[t] -4.64989216064404M4[t] -7.24376686972142M5[t] -8.614266794937M6[t] -9.13615037441491M7[t] -4.51485066691514M8[t] -3.88401004887181M9[t] + 2.93988204549788M10[t] -1.78358143139068M11[t] + 0.210428913856814t + 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) | 8.2339349299459 | 5.156068 | 1.5969 | 0.113532 | 0.056766 |
| X | -2.78755263787447 | 4.438695 | -0.628 | 0.531472 | 0.265736 |
| Y1 | 1.31883197290955 | 0.099241 | 13.2891 | 0 | 0 |
| Y2 | -0.154452435378261 | 0.169109 | -0.9133 | 0.363333 | 0.181666 |
| Y3 | -0.256484237853682 | 0.101598 | -2.5245 | 0.013209 | 0.006605 |
| M1 | -3.13382616025963 | 5.920954 | -0.5293 | 0.597822 | 0.298911 |
| M2 | 0.968052253349415 | 5.912037 | 0.1637 | 0.870274 | 0.435137 |
| M3 | -0.053936219421836 | 5.941597 | -0.0091 | 0.992776 | 0.496388 |
| M4 | -4.64989216064404 | 5.938704 | -0.783 | 0.435546 | 0.217773 |
| M5 | -7.24376686972142 | 5.945821 | -1.2183 | 0.226067 | 0.113033 |
| M6 | -8.614266794937 | 5.966356 | -1.4438 | 0.152015 | 0.076008 |
| M7 | -9.13615037441491 | 6.213281 | -1.4704 | 0.144684 | 0.072342 |
| M8 | -4.51485066691514 | 6.224649 | -0.7253 | 0.470003 | 0.235002 |
| M9 | -3.88401004887181 | 6.191525 | -0.6273 | 0.531929 | 0.265965 |
| M10 | 2.93988204549788 | 6.124509 | 0.48 | 0.632294 | 0.316147 |
| M11 | -1.78358143139068 | 6.125483 | -0.2912 | 0.77154 | 0.38577 |
| t | 0.210428913856814 | 0.070131 | 3.0005 | 0.003426 | 0.001713 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.989709517238206 |
| R-squared | 0.979524928511882 |
| Adjusted R-squared | 0.976147597132399 |
| F-TEST (value) | 290.029262293389 |
| F-TEST (DF numerator) | 16 |
| F-TEST (DF denominator) | 97 |
| p-value | 0 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 12.8403394174577 |
| Sum Squared Residuals | 15992.8086864852 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 95.43 | 101.412772695707 | -5.98277269570738 |
| 2 | 104.8 | 92.7084664787205 | 12.0915335212795 |
| 3 | 108.64 | 105.488007133916 | 3.15199286608399 |
| 4 | 105.65 | 107.040757915604 | -1.39075791560419 |
| 5 | 108.42 | 97.7176498608426 | 10.7023501391574 |
| 6 | 115.35 | 99.6876567228661 | 15.6623432771339 |
| 7 | 113.64 | 108.854762254693 | 4.78523774530708 |
| 8 | 115.24 | 109.650471486348 | 5.58952851365186 |
| 9 | 100.33 | 111.088550071074 | -10.7585500710744 |
| 10 | 101.29 | 98.650550513344 | 2.63944948665595 |
| 11 | 104.48 | 97.2961056752295 | 7.18389432477054 |
| 12 | 99.26 | 107.173095662494 | -7.91309566249369 |
| 13 | 100.11 | 96.6264673803068 | 3.48353261969316 |
| 14 | 103.52 | 102.047838878667 | 1.47216112133292 |
| 15 | 101.18 | 106.941059498899 | -5.7610594988989 |
| 16 | 96.39 | 98.7247712481097 | -2.33477124810969 |
| 17 | 97.56 | 89.5109277503564 | 8.04907224964357 |
| 18 | 96.39 | 91.2338904293413 | 5.15610957065868 |
| 19 | 85.1 | 90.4272525053426 | -5.32725250534263 |
| 20 | 79.77 | 80.2499909436541 | -0.479990943654141 |
| 21 | 79.13 | 76.1057406136558 | 3.02425938634423 |
| 22 | 80.84 | 86.0149476851543 | -5.17494768515434 |
| 23 | 82.75 | 85.2230263422002 | -2.47302634220016 |
| 24 | 92.55 | 89.6360420034344 | 2.91395799656558 |
| 25 | 96.6 | 98.903605893243 | -2.30360589324292 |
| 26 | 96.92 | 106.553663949985 | -9.63366394998497 |
| 27 | 95.32 | 103.025052728154 | -7.70505272815356 |
| 28 | 98.52 | 95.4412086015044 | 3.07879139849559 |
| 29 | 100.22 | 97.4430740600865 | 2.77692593991354 |
| 30 | 104.91 | 98.4411443900294 | 6.46885560997061 |
| 31 | 103.1 | 103.231692976079 | -0.131692976079254 |
| 32 | 97.13 | 104.515930600194 | -7.38593060019425 |
| 33 | 103.42 | 96.5604210863252 | 6.85957891367475 |
| 34 | 111.72 | 113.276512713876 | -1.55651271387623 |
| 35 | 118.11 | 120.269488607451 | -2.15948860745096 |
| 36 | 111.62 | 127.795594189851 | -16.1755941898513 |
| 37 | 100.22 | 113.197207203013 | -12.9772072030128 |
| 38 | 102.03 | 101.838292065030 | 0.191707934970322 |
| 39 | 105.76 | 106.839158844064 | -1.0791588440641 |
| 40 | 107.68 | 110.017236479149 | -2.33723647914866 |
| 41 | 110.77 | 109.125604017438 | 1.64439598256163 |
| 42 | 105.44 | 110.787488919250 | -5.3474889192496 |
| 43 | 112.26 | 102.476952076023 | 9.7830479239773 |
| 44 | 114.07 | 116.333809938221 | -2.26380993822070 |
| 45 | 117.9 | 119.875860719567 | -1.97586071956749 |
| 46 | 124.72 | 129.932526773841 | -5.21252677384082 |
| 47 | 126.42 | 133.358136968038 | -6.9381369680383 |
| 48 | 134.73 | 135.558461426973 | -0.828461426972701 |
| 49 | 135.79 | 141.582766233143 | -5.79276623314308 |
| 50 | 143.36 | 145.573512509548 | -2.21351250954844 |
| 51 | 140.37 | 152.450407387494 | -12.0804073874943 |
| 52 | 144.74 | 142.680494533191 | 2.05950546680902 |
| 53 | 151.98 | 144.580571560814 | 7.3994284391862 |
| 54 | 150.92 | 153.060774761900 | -2.14077476189966 |
| 55 | 163.38 | 149.112286453435 | 14.2677135465648 |
| 56 | 154.43 | 168.683435156685 | -14.2534351566851 |
| 57 | 146.66 | 156.068554478357 | -9.4085544783566 |
| 58 | 157.95 | 151.042106750054 | 6.90789324994557 |
| 59 | 162.1 | 164.914314512851 | -2.81431451285103 |
| 60 | 180.42 | 172.630592078376 | 7.78940792162427 |
| 61 | 179.57 | 190.331511923488 | -10.7615119234880 |
| 62 | 171.58 | 189.628833870758 | -18.0488338707582 |
| 63 | 185.43 | 173.712300180889 | 11.7176998191114 |
| 64 | 190.64 | 189.044682539168 | 1.59531746083159 |
| 65 | 203 | 193.442494153269 | 9.55750584673143 |
| 66 | 202.36 | 204.226182444478 | -1.86618244447761 |
| 67 | 193.41 | 199.825360335701 | -6.41536033570145 |
| 68 | 186.17 | 189.782247178288 | -3.61224717828812 |
| 69 | 192.24 | 182.621672435185 | 9.61832756481513 |
| 70 | 209.6 | 201.075073079901 | 8.52492692009854 |
| 71 | 206.41 | 220.376381165894 | -13.9663811658941 |
| 72 | 209.82 | 213.925163915622 | -4.10516391562168 |
| 73 | 230.37 | 211.539120596557 | 18.8308794034428 |
| 74 | 235.8 | 243.244926881428 | -7.44492688142766 |
| 75 | 232.07 | 245.546016137308 | -13.4760161373078 |
| 76 | 244.64 | 230.131818038993 | 14.5081819610074 |
| 77 | 242.19 | 243.509488315661 | -1.31948831566053 |
| 78 | 217.48 | 238.133498065163 | -20.6534980651629 |
| 79 | 209.39 | 202.388106945803 | 7.00189305419727 |
| 80 | 211.73 | 200.995390967259 | 10.7346090327406 |
| 81 | 221 | 212.509973035343 | 8.4900269646575 |
| 82 | 203.11 | 233.483405217892 | -30.3734052178917 |
| 83 | 214.71 | 203.344519466974 | 11.3654805330260 |
| 84 | 224.19 | 221.022525881986 | 3.16747411801425 |
| 85 | 238.04 | 233.39851050358 | 4.64148949641999 |
| 86 | 238.36 | 251.537214409355 | -13.1772144093545 |
| 87 | 246.24 | 246.577044276929 | -0.337044276929331 |
| 88 | 259.87 | 248.982181722497 | 10.8878182775033 |
| 89 | 249.97 | 263.275255571139 | -13.3052555711394 |
| 90 | 266.48 | 244.932465539483 | 21.5475344605167 |
| 91 | 282.98 | 264.428125694898 | 18.5518743051019 |
| 92 | 306.31 | 291.009766115919 | 15.3002338840814 |
| 93 | 301.73 | 313.048812987219 | -11.3188129872186 |
| 94 | 314.62 | 306.207518317559 | 8.41248168244122 |
| 95 | 332.62 | 313.417842770237 | 19.2021572297628 |
| 96 | 355.51 | 338.334634545201 | 17.1753654547993 |
| 97 | 370.32 | 359.513075495955 | 10.8069245040452 |
| 98 | 408.13 | 375.205151815036 | 32.9248481849636 |
| 99 | 433.58 | 416.100264379409 | 17.4797356205907 |
| 100 | 440.51 | 435.640632918327 | 4.86936708167322 |
| 101 | 386.29 | 428.768209181745 | -42.478209181745 |
| 102 | 342.84 | 348.503189368683 | -5.66318936868292 |
| 103 | 254.97 | 297.485460758025 | -42.5154607580250 |
| 104 | 203.42 | 207.048957613432 | -3.62895761343153 |
| 105 | 170.09 | 164.620414573275 | 5.4695854267254 |
| 106 | 174.03 | 158.197358948378 | 15.8326410516218 |
| 107 | 167.85 | 177.250184491125 | -9.40018449112482 |
| 108 | 177.01 | 179.033890296064 | -2.02389029606416 |
| 109 | 188.19 | 188.134962075007 | 0.0550379249930264 |
| 110 | 211.2 | 207.362099141473 | 3.83790085852747 |
| 111 | 240.91 | 232.820689432938 | 8.08931056706187 |
| 112 | 230.26 | 261.196216003458 | -30.9362160034576 |
| 113 | 251.25 | 234.276725528649 | 16.9732744713511 |
| 114 | 241.66 | 254.823709358807 | -13.1637093588072 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 20 | 0.0453334140488965 | 0.090666828097793 | 0.954666585951103 |
| 21 | 0.132146517318799 | 0.264293034637597 | 0.867853482681201 |
| 22 | 0.0613815041829615 | 0.122763008365923 | 0.938618495817038 |
| 23 | 0.0266070463657822 | 0.0532140927315645 | 0.973392953634218 |
| 24 | 0.0288401304807753 | 0.0576802609615505 | 0.971159869519225 |
| 25 | 0.0185471781070875 | 0.0370943562141750 | 0.981452821892912 |
| 26 | 0.008846946656842 | 0.017693893313684 | 0.991153053343158 |
| 27 | 0.00385348783260667 | 0.00770697566521335 | 0.996146512167393 |
| 28 | 0.00232835448045329 | 0.00465670896090659 | 0.997671645519547 |
| 29 | 0.000953661793598913 | 0.00190732358719783 | 0.9990463382064 |
| 30 | 0.000449876958391226 | 0.000899753916782453 | 0.99955012304161 |
| 31 | 0.000210584519787064 | 0.000421169039574128 | 0.999789415480213 |
| 32 | 8.51823470650232e-05 | 0.000170364694130046 | 0.999914817652935 |
| 33 | 0.000186529403287792 | 0.000373058806575584 | 0.999813470596712 |
| 34 | 8.92139617674816e-05 | 0.000178427923534963 | 0.999910786038233 |
| 35 | 3.93403388073272e-05 | 7.86806776146545e-05 | 0.999960659661193 |
| 36 | 3.04112315640955e-05 | 6.08224631281909e-05 | 0.999969588768436 |
| 37 | 2.11654226183901e-05 | 4.23308452367802e-05 | 0.999978834577382 |
| 38 | 8.15160369826621e-06 | 1.63032073965324e-05 | 0.999991848396302 |
| 39 | 3.29615346306019e-06 | 6.59230692612038e-06 | 0.999996703846537 |
| 40 | 1.25465090036378e-06 | 2.50930180072755e-06 | 0.9999987453491 |
| 41 | 4.67289266998663e-07 | 9.34578533997326e-07 | 0.999999532710733 |
| 42 | 2.95000903525589e-07 | 5.90001807051177e-07 | 0.999999704999097 |
| 43 | 5.39649364492355e-07 | 1.07929872898471e-06 | 0.999999460350635 |
| 44 | 2.06884131027377e-07 | 4.13768262054754e-07 | 0.99999979311587 |
| 45 | 1.32842073425841e-07 | 2.65684146851682e-07 | 0.999999867157927 |
| 46 | 5.23092811987071e-08 | 1.04618562397414e-07 | 0.99999994769072 |
| 47 | 1.86242268423776e-08 | 3.72484536847552e-08 | 0.999999981375773 |
| 48 | 1.49570299965968e-08 | 2.99140599931937e-08 | 0.99999998504297 |
| 49 | 5.77249094827321e-09 | 1.15449818965464e-08 | 0.999999994227509 |
| 50 | 2.09643833194607e-09 | 4.19287666389214e-09 | 0.999999997903562 |
| 51 | 1.06139821096093e-09 | 2.12279642192187e-09 | 0.999999998938602 |
| 52 | 4.33791066591454e-10 | 8.67582133182908e-10 | 0.99999999956621 |
| 53 | 1.83701044822566e-10 | 3.67402089645133e-10 | 0.999999999816299 |
| 54 | 6.67556747819397e-11 | 1.33511349563879e-10 | 0.999999999933244 |
| 55 | 2.08581137516617e-10 | 4.17162275033234e-10 | 0.999999999791419 |
| 56 | 1.98088590100397e-10 | 3.96177180200793e-10 | 0.999999999801911 |
| 57 | 1.09432664195203e-10 | 2.18865328390406e-10 | 0.999999999890567 |
| 58 | 4.49562827808727e-11 | 8.99125655617454e-11 | 0.999999999955044 |
| 59 | 1.45814737809445e-11 | 2.91629475618890e-11 | 0.999999999985419 |
| 60 | 4.52019976949899e-11 | 9.04039953899797e-11 | 0.999999999954798 |
| 61 | 2.11828810939198e-11 | 4.23657621878396e-11 | 0.999999999978817 |
| 62 | 5.12621614638768e-11 | 1.02524322927754e-10 | 0.999999999948738 |
| 63 | 4.39213263054836e-11 | 8.78426526109672e-11 | 0.999999999956079 |
| 64 | 1.44081979592520e-11 | 2.88163959185040e-11 | 0.999999999985592 |
| 65 | 1.51486431002012e-11 | 3.02972862004024e-11 | 0.999999999984851 |
| 66 | 5.81007907994128e-12 | 1.16201581598826e-11 | 0.99999999999419 |
| 67 | 5.38933377964112e-12 | 1.07786675592822e-11 | 0.99999999999461 |
| 68 | 2.75988606779933e-12 | 5.51977213559865e-12 | 0.99999999999724 |
| 69 | 1.09612517444718e-12 | 2.19225034889437e-12 | 0.999999999998904 |
| 70 | 7.59880062041359e-13 | 1.51976012408272e-12 | 0.99999999999924 |
| 71 | 6.03938972030396e-13 | 1.20787794406079e-12 | 0.999999999999396 |
| 72 | 2.34819556667122e-13 | 4.69639113334244e-13 | 0.999999999999765 |
| 73 | 1.04816815345052e-12 | 2.09633630690105e-12 | 0.999999999998952 |
| 74 | 4.30574411433484e-13 | 8.61148822866969e-13 | 0.99999999999957 |
| 75 | 4.25123086537252e-13 | 8.50246173074504e-13 | 0.999999999999575 |
| 76 | 2.92717081855446e-13 | 5.85434163710892e-13 | 0.999999999999707 |
| 77 | 4.19455363885615e-13 | 8.3891072777123e-13 | 0.99999999999958 |
| 78 | 1.76770749265684e-11 | 3.53541498531367e-11 | 0.999999999982323 |
| 79 | 1.36092624988806e-11 | 2.72185249977611e-11 | 0.99999999998639 |
| 80 | 5.06337921936045e-12 | 1.01267584387209e-11 | 0.999999999994937 |
| 81 | 1.99104136118746e-12 | 3.98208272237491e-12 | 0.99999999999801 |
| 82 | 1.00038474400529e-09 | 2.00076948801059e-09 | 0.999999998999615 |
| 83 | 5.74264429946464e-10 | 1.14852885989293e-09 | 0.999999999425736 |
| 84 | 2.18040686316066e-10 | 4.36081372632132e-10 | 0.99999999978196 |
| 85 | 1.96926047734112e-10 | 3.93852095468225e-10 | 0.999999999803074 |
| 86 | 4.43399715939075e-09 | 8.8679943187815e-09 | 0.999999995566003 |
| 87 | 1.00495890680825e-07 | 2.00991781361650e-07 | 0.99999989950411 |
| 88 | 4.44218850699269e-08 | 8.88437701398537e-08 | 0.999999955578115 |
| 89 | 1.10830577218266e-07 | 2.21661154436531e-07 | 0.999999889169423 |
| 90 | 1.70928354369139e-06 | 3.41856708738277e-06 | 0.999998290716456 |
| 91 | 9.77133956858552e-07 | 1.95426791371710e-06 | 0.999999022866043 |
| 92 | 2.01010035288756e-06 | 4.02020070577512e-06 | 0.999997989899647 |
| 93 | 1.12913093090125e-06 | 2.25826186180250e-06 | 0.99999887086907 |
| 94 | 0.000143470359089262 | 0.000286940718178525 | 0.99985652964091 |
| Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
| Description | # significant tests | % significant tests | OK/NOK |
| 1% type I error level | 68 | 0.906666666666667 | NOK |
| 5% type I error level | 70 | 0.933333333333333 | NOK |
| 10% type I error level | 73 | 0.973333333333333 | NOK |
