| Multiple Linear Regression - Estimated Regression Equation |
| Y[t] = + 47.471123246113 + 29.2155921501706X[t] + 8.03850118189862M1[t] + 10.4251146884086M2[t] + 15.7017281949185M3[t] + 18.4533417014284M4[t] + 24.8059552079383M5[t] + 30.4325687144482M6[t] + 31.6191822209582M7[t] + 28.1407957274681M8[t] + 20.6054092339780M9[t] + 16.2785054481103M10[t] + 8.97400784350905M11[t] + 1.75338649349008t + 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) | 47.471123246113 | 18.709349 | 2.5373 | 0.01267 | 0.006335 |
| X | 29.2155921501706 | 15.931636 | 1.8338 | 0.06957 | 0.034785 |
| M1 | 8.03850118189862 | 22.607477 | 0.3556 | 0.722891 | 0.361446 |
| M2 | 10.4251146884086 | 22.602693 | 0.4612 | 0.645604 | 0.322802 |
| M3 | 15.7017281949185 | 22.599407 | 0.6948 | 0.488754 | 0.244377 |
| M4 | 18.4533417014284 | 22.59762 | 0.8166 | 0.416039 | 0.208019 |
| M5 | 24.8059552079383 | 22.597333 | 1.0977 | 0.274878 | 0.137439 |
| M6 | 30.4325687144482 | 22.598545 | 1.3467 | 0.181045 | 0.090523 |
| M7 | 31.6191822209582 | 22.601256 | 1.399 | 0.164817 | 0.082408 |
| M8 | 28.1407957274681 | 22.605465 | 1.2449 | 0.216006 | 0.108003 |
| M9 | 20.6054092339780 | 22.611173 | 0.9113 | 0.364269 | 0.182134 |
| M10 | 16.2785054481103 | 23.234101 | 0.7006 | 0.485114 | 0.242557 |
| M11 | 8.97400784350905 | 23.241452 | 0.3861 | 0.700204 | 0.350102 |
| t | 1.75338649349008 | 0.184073 | 9.5255 | 0 | 0 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.82910426940108 |
| R-squared | 0.687413889539099 |
| Adjusted R-squared | 0.647961273655685 |
| F-TEST (value) | 17.4237848149399 |
| F-TEST (DF numerator) | 13 |
| F-TEST (DF denominator) | 103 |
| p-value | 0 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 49.1780861158411 |
| Sum Squared Residuals | 249103.867863759 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 100.01 | 57.2630109215018 | 42.7469890784982 |
| 2 | 103.84 | 61.4030109215014 | 42.4369890784986 |
| 3 | 104.48 | 68.4330109215018 | 36.0469890784982 |
| 4 | 95.43 | 72.9380109215016 | 22.4919890784984 |
| 5 | 104.8 | 81.0440109215017 | 23.7559890784983 |
| 6 | 108.64 | 88.4240109215017 | 20.2159890784983 |
| 7 | 105.65 | 91.3640109215017 | 14.2859890784983 |
| 8 | 108.42 | 89.6390109215017 | 18.7809890784983 |
| 9 | 115.35 | 83.8570109215017 | 31.4929890784983 |
| 10 | 113.64 | 81.283493629124 | 32.356506370876 |
| 11 | 115.24 | 75.7323825180129 | 39.5076174819871 |
| 12 | 100.33 | 68.511761167994 | 31.818238832006 |
| 13 | 101.29 | 78.3036488433826 | 22.9863511566174 |
| 14 | 104.48 | 82.4436488433828 | 22.0363511566172 |
| 15 | 99.26 | 89.4736488433826 | 9.78635115661737 |
| 16 | 100.11 | 93.9786488433826 | 6.13135115661735 |
| 17 | 103.52 | 102.084648843383 | 1.43535115661736 |
| 18 | 101.18 | 109.464648843383 | -8.28464884338262 |
| 19 | 96.39 | 112.404648843383 | -16.0146488433826 |
| 20 | 97.56 | 110.679648843383 | -13.1196488433827 |
| 21 | 96.39 | 104.897648843383 | -8.50764884338265 |
| 22 | 85.1 | 102.324131551005 | -17.2241315510050 |
| 23 | 79.77 | 96.7730204398938 | -17.0030204398938 |
| 24 | 79.13 | 89.5523990898749 | -10.4223990898749 |
| 25 | 80.84 | 99.3442867652635 | -18.5042867652635 |
| 26 | 82.75 | 103.484286765264 | -20.7342867652636 |
| 27 | 92.55 | 110.514286765264 | -17.9642867652636 |
| 28 | 96.6 | 115.019286765264 | -18.4192867652636 |
| 29 | 96.92 | 123.125286765264 | -26.2052867652636 |
| 30 | 95.32 | 130.505286765264 | -35.1852867652635 |
| 31 | 98.52 | 133.445286765264 | -34.9252867652636 |
| 32 | 100.22 | 131.720286765264 | -31.5002867652636 |
| 33 | 104.91 | 125.938286765264 | -21.0282867652636 |
| 34 | 103.1 | 123.364769472886 | -20.2647694728859 |
| 35 | 97.13 | 117.813658361775 | -20.6836583617748 |
| 36 | 103.42 | 110.593037011756 | -7.17303701175578 |
| 37 | 111.72 | 120.384924687144 | -8.66492468714446 |
| 38 | 118.11 | 124.524924687145 | -6.41492468714453 |
| 39 | 111.62 | 131.554924687144 | -19.9349246871445 |
| 40 | 100.22 | 136.059924687144 | -35.8399246871445 |
| 41 | 102.03 | 144.165924687144 | -42.1359246871445 |
| 42 | 105.76 | 151.545924687144 | -45.7859246871445 |
| 43 | 107.68 | 154.485924687144 | -46.8059246871445 |
| 44 | 110.77 | 152.760924687144 | -41.9909246871445 |
| 45 | 105.44 | 146.978924687144 | -41.5389246871445 |
| 46 | 112.26 | 144.405407394767 | -32.1454073947668 |
| 47 | 114.07 | 138.854296283656 | -24.7842962836557 |
| 48 | 117.9 | 131.633674933637 | -13.7336749336367 |
| 49 | 124.72 | 141.425562609025 | -16.7055626090254 |
| 50 | 126.42 | 145.565562609025 | -19.1455626090255 |
| 51 | 134.73 | 152.595562609025 | -17.8655626090254 |
| 52 | 135.79 | 157.100562609025 | -21.3105626090254 |
| 53 | 143.36 | 165.206562609025 | -21.8465626090254 |
| 54 | 140.37 | 172.586562609025 | -32.2165626090254 |
| 55 | 144.74 | 175.526562609025 | -30.7865626090254 |
| 56 | 151.98 | 173.801562609025 | -21.8215626090254 |
| 57 | 150.92 | 168.019562609025 | -17.0995626090254 |
| 58 | 163.38 | 165.446045316648 | -2.06604531664770 |
| 59 | 154.43 | 159.894934205537 | -5.4649342055366 |
| 60 | 146.66 | 152.674312855518 | -6.01431285551764 |
| 61 | 157.95 | 162.466200530906 | -4.51620053090632 |
| 62 | 162.1 | 166.606200530906 | -4.50620053090638 |
| 63 | 180.42 | 173.636200530906 | 6.78379946909365 |
| 64 | 179.57 | 178.141200530906 | 1.42879946909366 |
| 65 | 171.58 | 186.247200530906 | -14.6672005309063 |
| 66 | 185.43 | 193.627200530906 | -8.19720053090631 |
| 67 | 190.64 | 196.567200530906 | -5.92720053090635 |
| 68 | 203 | 194.842200530906 | 8.15779946909364 |
| 69 | 202.36 | 189.060200530906 | 13.2997994690937 |
| 70 | 193.41 | 186.486683238529 | 6.92331676147138 |
| 71 | 186.17 | 180.935572127418 | 5.23442787258247 |
| 72 | 192.24 | 173.714950777399 | 18.5250492226014 |
| 73 | 209.6 | 183.506838452787 | 26.0931615472128 |
| 74 | 206.41 | 187.646838452787 | 18.7631615472127 |
| 75 | 209.82 | 194.676838452787 | 15.1431615472127 |
| 76 | 230.37 | 199.181838452787 | 31.1881615472127 |
| 77 | 235.8 | 207.287838452787 | 28.5121615472128 |
| 78 | 232.07 | 214.667838452787 | 17.4021615472127 |
| 79 | 244.64 | 217.607838452787 | 27.0321615472127 |
| 80 | 242.19 | 215.882838452787 | 26.3071615472128 |
| 81 | 217.48 | 210.100838452787 | 7.37916154721275 |
| 82 | 209.39 | 207.527321160410 | 1.86267883959044 |
| 83 | 211.73 | 201.976210049298 | 9.75378995070157 |
| 84 | 221 | 194.755588699279 | 26.2444113007205 |
| 85 | 203.11 | 204.547476374668 | -1.43747637466814 |
| 86 | 214.71 | 208.687476374668 | 6.02252362533179 |
| 87 | 224.19 | 215.717476374668 | 8.47252362533183 |
| 88 | 238.04 | 220.222476374668 | 17.8175236253318 |
| 89 | 238.36 | 228.328476374668 | 10.0315236253318 |
| 90 | 246.24 | 235.708476374668 | 10.5315236253318 |
| 91 | 259.87 | 238.648476374668 | 21.2215236253318 |
| 92 | 249.97 | 236.923476374668 | 13.0465236253318 |
| 93 | 266.48 | 231.141476374668 | 35.3385236253318 |
| 94 | 282.98 | 228.567959082290 | 54.4120409177096 |
| 95 | 306.31 | 223.016847971179 | 83.2931520288207 |
| 96 | 301.73 | 245.011818771331 | 56.718181228669 |
| 97 | 314.62 | 254.803706446720 | 59.8162935532803 |
| 98 | 332.62 | 258.943706446720 | 73.6762935532802 |
| 99 | 355.51 | 265.973706446720 | 89.5362935532803 |
| 100 | 370.32 | 270.478706446720 | 99.8412935532803 |
| 101 | 408.13 | 278.58470644672 | 129.545293553280 |
| 102 | 433.58 | 285.96470644672 | 147.615293553280 |
| 103 | 440.51 | 288.90470644672 | 151.605293553280 |
| 104 | 386.29 | 287.17970644672 | 99.1102935532803 |
| 105 | 342.84 | 281.39770644672 | 61.4422935532802 |
| 106 | 254.97 | 278.824189154342 | -23.8541891543421 |
| 107 | 203.42 | 273.273078043231 | -69.853078043231 |
| 108 | 170.09 | 266.052456693212 | -95.962456693212 |
| 109 | 174.03 | 275.844344368601 | -101.814344368601 |
| 110 | 167.85 | 279.984344368601 | -112.134344368601 |
| 111 | 177.01 | 287.014344368601 | -110.004344368601 |
| 112 | 188.19 | 291.519344368601 | -103.329344368601 |
| 113 | 211.2 | 299.625344368601 | -88.4253443686007 |
| 114 | 240.91 | 307.005344368601 | -66.0953443686007 |
| 115 | 230.26 | 309.945344368601 | -79.6853443686007 |
| 116 | 251.25 | 308.220344368601 | -56.9703443686007 |
| 117 | 241.66 | 302.438344368601 | -60.7783443686007 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 17 | 0.000274435732045288 | 0.000548871464090576 | 0.999725564267955 |
| 18 | 4.56351542180012e-05 | 9.12703084360024e-05 | 0.999954364845782 |
| 19 | 7.97251293144967e-06 | 1.59450258628993e-05 | 0.999992027487069 |
| 20 | 1.46627834597354e-06 | 2.93255669194708e-06 | 0.999998533721654 |
| 21 | 1.15894958300442e-06 | 2.31789916600884e-06 | 0.999998841050417 |
| 22 | 2.23395829906392e-06 | 4.46791659812783e-06 | 0.9999977660417 |
| 23 | 3.62575293254753e-06 | 7.25150586509505e-06 | 0.999996374247067 |
| 24 | 8.3507134585288e-07 | 1.67014269170576e-06 | 0.999999164928654 |
| 25 | 1.41006894240002e-07 | 2.82013788480004e-07 | 0.999999858993106 |
| 26 | 2.3473061863232e-08 | 4.6946123726464e-08 | 0.999999976526938 |
| 27 | 4.69234905624935e-09 | 9.3846981124987e-09 | 0.99999999530765 |
| 28 | 1.78166766397197e-09 | 3.56333532794395e-09 | 0.999999998218332 |
| 29 | 3.35716477220309e-10 | 6.71432954440617e-10 | 0.999999999664284 |
| 30 | 5.39253076050422e-11 | 1.07850615210084e-10 | 0.999999999946075 |
| 31 | 1.31515389333556e-11 | 2.63030778667113e-11 | 0.999999999986849 |
| 32 | 2.85612006558114e-12 | 5.71224013116228e-12 | 0.999999999997144 |
| 33 | 6.7122422994813e-13 | 1.34244845989626e-12 | 0.999999999999329 |
| 34 | 2.383381794753e-13 | 4.766763589506e-13 | 0.999999999999762 |
| 35 | 4.99473028280626e-14 | 9.98946056561252e-14 | 0.99999999999995 |
| 36 | 5.81390115915307e-14 | 1.16278023183061e-13 | 0.999999999999942 |
| 37 | 1.45086669253644e-13 | 2.90173338507287e-13 | 0.999999999999855 |
| 38 | 2.66258535816818e-13 | 5.32517071633636e-13 | 0.999999999999734 |
| 39 | 1.07664687666786e-13 | 2.15329375333572e-13 | 0.999999999999892 |
| 40 | 2.18339443086272e-14 | 4.36678886172544e-14 | 0.999999999999978 |
| 41 | 4.17473788040758e-15 | 8.34947576081516e-15 | 0.999999999999996 |
| 42 | 8.95158320562925e-16 | 1.79031664112585e-15 | 1 |
| 43 | 2.26142220583709e-16 | 4.52284441167417e-16 | 1 |
| 44 | 5.78393912593834e-17 | 1.15678782518767e-16 | 1 |
| 45 | 1.08088894302196e-17 | 2.16177788604391e-17 | 1 |
| 46 | 3.10145538010868e-18 | 6.20291076021736e-18 | 1 |
| 47 | 1.28053798966470e-18 | 2.56107597932940e-18 | 1 |
| 48 | 1.02229840148895e-18 | 2.04459680297790e-18 | 1 |
| 49 | 9.03835324941757e-19 | 1.80767064988351e-18 | 1 |
| 50 | 4.73554254443513e-19 | 9.47108508887027e-19 | 1 |
| 51 | 5.90284583743365e-19 | 1.18056916748673e-18 | 1 |
| 52 | 1.06309076366634e-18 | 2.12618152733269e-18 | 1 |
| 53 | 2.22582565382329e-18 | 4.45165130764658e-18 | 1 |
| 54 | 2.51453061830056e-18 | 5.02906123660112e-18 | 1 |
| 55 | 4.32544597199891e-18 | 8.65089194399782e-18 | 1 |
| 56 | 9.34677257035783e-18 | 1.86935451407157e-17 | 1 |
| 57 | 1.16029251890089e-17 | 2.32058503780177e-17 | 1 |
| 58 | 4.70455430969171e-17 | 9.40910861938343e-17 | 1 |
| 59 | 6.47087971969078e-17 | 1.29417594393816e-16 | 1 |
| 60 | 4.25762382359724e-17 | 8.51524764719448e-17 | 1 |
| 61 | 3.1949867275225e-17 | 6.389973455045e-17 | 1 |
| 62 | 2.26502340451146e-17 | 4.53004680902293e-17 | 1 |
| 63 | 5.4936819069854e-17 | 1.09873638139708e-16 | 1 |
| 64 | 1.34198046833590e-16 | 2.68396093667179e-16 | 1 |
| 65 | 1.60201829192070e-16 | 3.20403658384140e-16 | 1 |
| 66 | 5.42507736824333e-16 | 1.08501547364867e-15 | 1 |
| 67 | 2.86324180675846e-15 | 5.72648361351691e-15 | 0.999999999999997 |
| 68 | 1.94459292182849e-14 | 3.88918584365698e-14 | 0.99999999999998 |
| 69 | 8.50181412539746e-14 | 1.70036282507949e-13 | 0.999999999999915 |
| 70 | 1.84491284437922e-13 | 3.68982568875843e-13 | 0.999999999999815 |
| 71 | 4.23992432527825e-13 | 8.47984865055649e-13 | 0.999999999999576 |
| 72 | 4.66926665911313e-13 | 9.33853331822626e-13 | 0.999999999999533 |
| 73 | 5.65914716072277e-13 | 1.13182943214455e-12 | 0.999999999999434 |
| 74 | 4.93719390967793e-13 | 9.87438781935585e-13 | 0.999999999999506 |
| 75 | 4.74622760678002e-13 | 9.49245521356004e-13 | 0.999999999999525 |
| 76 | 1.30782940530446e-12 | 2.61565881060892e-12 | 0.999999999998692 |
| 77 | 5.08310163718688e-12 | 1.01662032743738e-11 | 0.999999999994917 |
| 78 | 3.2024736795388e-11 | 6.4049473590776e-11 | 0.999999999967975 |
| 79 | 3.81877395603373e-10 | 7.63754791206745e-10 | 0.999999999618123 |
| 80 | 3.59399590826126e-09 | 7.18799181652252e-09 | 0.999999996406004 |
| 81 | 1.03675906267600e-07 | 2.07351812535201e-07 | 0.999999896324094 |
| 82 | 1.50480090936069e-06 | 3.00960181872138e-06 | 0.99999849519909 |
| 83 | 2.89383185352590e-05 | 5.78766370705181e-05 | 0.999971061681465 |
| 84 | 1.78851971396527e-05 | 3.57703942793055e-05 | 0.99998211480286 |
| 85 | 8.99001916723703e-06 | 1.79800383344741e-05 | 0.999991009980833 |
| 86 | 4.25132766164832e-06 | 8.50265532329663e-06 | 0.999995748672338 |
| 87 | 2.10241885470461e-06 | 4.20483770940923e-06 | 0.999997897581145 |
| 88 | 1.16302185079410e-06 | 2.32604370158820e-06 | 0.99999883697815 |
| 89 | 1.22619193211801e-06 | 2.45238386423603e-06 | 0.999998773808068 |
| 90 | 5.39590701415312e-06 | 1.07918140283062e-05 | 0.999994604092986 |
| 91 | 4.42258707027308e-05 | 8.84517414054617e-05 | 0.999955774129297 |
| 92 | 0.00212017673342080 | 0.00424035346684161 | 0.997879823266579 |
| 93 | 0.298313690288161 | 0.596627380576321 | 0.701686309711839 |
| 94 | 0.429010340756011 | 0.858020681512022 | 0.570989659243989 |
| 95 | 0.410178383127036 | 0.820356766254072 | 0.589821616872964 |
| 96 | 0.380411181516313 | 0.760822363032625 | 0.619588818483688 |
| 97 | 0.324948216852113 | 0.649896433704227 | 0.675051783147887 |
| 98 | 0.224034759041403 | 0.448069518082807 | 0.775965240958597 |
| 99 | 0.142387611127018 | 0.284775222254037 | 0.857612388872982 |
| 100 | 0.0826161993529477 | 0.165232398705895 | 0.917383800647052 |
| Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
| Description | # significant tests | % significant tests | OK/NOK |
| 1% type I error level | 76 | 0.904761904761905 | NOK |
| 5% type I error level | 76 | 0.904761904761905 | NOK |
| 10% type I error level | 76 | 0.904761904761905 | NOK |
