| Multiple Linear Regression - Estimated Regression Equation |
| x[t] = + 7.53923727288653 + 0.826888794540061y0[t] + 0.069050797530038y1[t] -0.0217694593981442y2[t] + 2.53073445567753M1[t] + 1.28398056947326M2[t] + 6.14157249017446M3[t] -0.388146101513589M4[t] + 4.19313623427351M5[t] + 1.84968635378636M6[t] -2.19663690001674M7[t] -0.985667763809098M8[t] + 3.69010557347512M9[t] + 9.24640884194022M10[t] + 4.94710351660652M11[t] -0.0551774169632081t + 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) | 7.53923727288653 | 6.662794 | 1.1315 | 0.260866 | 0.130433 |
| y0 | 0.826888794540061 | 0.106434 | 7.769 | 0 | 0 |
| y1 | 0.069050797530038 | 0.137621 | 0.5017 | 0.617085 | 0.308543 |
| y2 | -0.0217694593981442 | 0.107522 | -0.2025 | 0.840015 | 0.420007 |
| M1 | 2.53073445567753 | 5.31012 | 0.4766 | 0.634824 | 0.317412 |
| M2 | 1.28398056947326 | 5.35786 | 0.2396 | 0.811157 | 0.405579 |
| M3 | 6.14157249017446 | 5.335442 | 1.1511 | 0.252778 | 0.126389 |
| M4 | -0.388146101513589 | 5.338231 | -0.0727 | 0.9422 | 0.4711 |
| M5 | 4.19313623427351 | 5.307446 | 0.79 | 0.4316 | 0.2158 |
| M6 | 1.84968635378636 | 5.374224 | 0.3442 | 0.731525 | 0.365762 |
| M7 | -2.19663690001674 | 5.299369 | -0.4145 | 0.679499 | 0.339749 |
| M8 | -0.985667763809098 | 5.381707 | -0.1832 | 0.855096 | 0.427548 |
| M9 | 3.69010557347512 | 5.439081 | 0.6784 | 0.499251 | 0.249626 |
| M10 | 9.24640884194022 | 5.488148 | 1.6848 | 0.095532 | 0.047766 |
| M11 | 4.94710351660652 | 5.450876 | 0.9076 | 0.366551 | 0.183276 |
| t | -0.0551774169632081 | 0.041184 | -1.3398 | 0.183725 | 0.091863 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.903067366036784 |
| R-squared | 0.815530667600615 |
| Adjusted R-squared | 0.78444033067937 |
| F-TEST (value) | 26.2310012807659 |
| F-TEST (DF numerator) | 15 |
| F-TEST (DF denominator) | 89 |
| p-value | 0 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 10.8315560323775 |
| Sum Squared Residuals | 10441.7119413455 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 108.8235294 | 107.566092217664 | 1.25743718233622 |
| 2 | 111.7647059 | 104.110260547263 | 7.65444535273689 |
| 3 | 117.6470588 | 111.013554713815 | 6.63350408618513 |
| 4 | 111.7647059 | 109.559828809105 | 2.20487709089501 |
| 5 | 120.5882353 | 109.564035366087 | 11.0241999339127 |
| 6 | 102.9411765 | 113.927248856071 | -10.9860723560715 |
| 7 | 114.7058824 | 95.9709203917174 | 18.7349620082826 |
| 8 | 114.7058824 | 105.44418864151 | 9.26169375848992 |
| 9 | 117.6470588 | 111.261313816976 | 6.38574498302432 |
| 10 | 111.7647059 | 118.938354188982 | -7.17364828898211 |
| 11 | 97.05882353 | 109.922910324241 | -12.8640867942415 |
| 12 | 94.11764706 | 92.2902910657738 | 1.82735599422621 |
| 13 | 82.35294118 | 91.4464249752709 | -9.09348379527088 |
| 14 | 82.35294118 | 80.5334387371093 | 1.81950244289065 |
| 15 | 85.29411765 | 84.5875187388735 | 0.706598911126541 |
| 16 | 85.29411765 | 80.6907598830159 | 4.60335776698413 |
| 17 | 73.52941176 | 85.4199553827698 | -11.8905436227698 |
| 18 | 61.76470588 | 73.2291967920726 | -11.4644909120726 |
| 19 | 32.35294118 | 58.5872303336638 | -26.2342891536638 |
| 20 | 20.58823529 | 34.8665123583125 | -14.2782770683125 |
| 21 | 50 | 27.9842102848179 | 22.0157897151821 |
| 22 | 70.58823529 | 57.6335106957213 | 12.9547245942787 |
| 23 | 76.47058824 | 72.5902261112744 | 3.88036212872557 |
| 24 | 79.41176471 | 73.2333527664178 | 6.17841194358217 |
| 25 | 73.52941176 | 78.0989220812656 | -4.56951032126561 |
| 26 | 76.47058824 | 72.007973975433 | 4.46261426456703 |
| 27 | 73.52941176 | 78.7722053689506 | -5.24279360895062 |
| 28 | 70.58823529 | 70.0864297115538 | 0.501805578446237 |
| 29 | 64.70588235 | 71.913390360985 | -7.20750801098503 |
| 30 | 64.70588235 | 64.511648572953 | 0.194233777047068 |
| 31 | 64.70588235 | 60.0679945620729 | 4.63788778792709 |
| 32 | 61.76470588 | 61.3518419248102 | 0.412863955189781 |
| 33 | 50 | 63.5404119793233 | -13.5404119793233 |
| 34 | 47.05882353 | 59.1103437866636 | -12.0515202566636 |
| 35 | 35.29411765 | 51.5755006765849 | -16.2813830265849 |
| 36 | 20.58823529 | 36.8981369858392 | -16.3099016958392 |
| 37 | 41.17647059 | 26.4652301852713 | 14.7112404047287 |
| 38 | 47.05882353 | 41.4281383326729 | 5.63068519732714 |
| 39 | 44.11764706 | 52.8363777441776 | -8.71873068417762 |
| 40 | 35.29411765 | 43.7774422791358 | -8.48332462913585 |
| 41 | 41.17647059 | 40.6763233761131 | 0.500147213886919 |
| 42 | 58.82352941 | 42.5965038892347 | 16.2270255207653 |
| 43 | 29.41176471 | 53.6854230404153 | -24.2736583304153 |
| 44 | 55.88235294 | 31.6114439436683 | 24.2709089963316 |
| 45 | 55.88235294 | 55.7051999164809 | 0.177153023519054 |
| 46 | 64.70588235 | 63.674419213818 | 1.031463136182 |
| 47 | 70.58823529 | 66.0397636732268 | 4.5484716167732 |
| 48 | 64.70588235 | 66.5108062140631 | -1.80492386406311 |
| 49 | 61.76470588 | 64.3364092177825 | -2.57170333778247 |
| 50 | 55.88235294 | 60.068215243454 | -4.18586230345405 |
| 51 | 73.52941176 | 59.931543078139 | 13.5978686818609 |
| 52 | 61.76470588 | 67.5966489242215 | -5.83194304422145 |
| 53 | 67.64705882 | 63.7412495088871 | 3.90580931111286 |
| 54 | 67.64705882 | 65.0101446888536 | 2.63691413114641 |
| 55 | 55.88235294 | 61.5709364669332 | -5.68858352693322 |
| 56 | 52.94117647 | 52.8705690794532 | 0.0706073905468203 |
| 57 | 55.88235294 | 54.246776810246 | 1.63557612975403 |
| 58 | 55.88235294 | 62.2329492336114 | -6.35059629361144 |
| 59 | 64.70588235 | 58.145584893991 | 6.56029745600893 |
| 60 | 67.64705882 | 60.3753537360986 | 7.27170508390143 |
| 61 | 58.82352941 | 65.892208383411 | -7.06867897341103 |
| 62 | 41.17647059 | 57.3052065985106 | -16.1287360085106 |
| 63 | 41.17647059 | 46.8421663428646 | -5.66569575286456 |
| 64 | 41.17647059 | 39.2308103138721 | 1.94566027612786 |
| 65 | 44.11764706 | 44.1410821631747 | -0.0234351031746805 |
| 66 | 32.35294118 | 44.1744807315322 | -11.8215395515322 |
| 67 | 50 | 30.5479671784644 | 19.4520328215356 |
| 68 | 47.05882353 | 45.4195239470895 | 1.63929958291055 |
| 69 | 58.82352941 | 49.0827487741688 | 9.74078063583118 |
| 70 | 70.58823529 | 63.7247205774936 | 6.86351471250644 |
| 71 | 67.64705882 | 69.974731443895 | -2.32767262389501 |
| 72 | 58.82352941 | 63.096675681252 | -4.27314627125194 |
| 73 | 61.76470588 | 57.8169532546267 | 3.94775262537328 |
| 74 | 55.88235294 | 58.4018038962233 | -2.51945095622334 |
| 75 | 67.64705882 | 58.735340714515 | 8.91171810548505 |
| 76 | 67.64705882 | 61.4083391854887 | 6.23871963451133 |
| 77 | 67.64705882 | 66.8748620715258 | 0.772196748474231 |
| 78 | 67.64705882 | 64.2201234870896 | 3.42693533291036 |
| 79 | 79.41176471 | 60.1186228163233 | 19.2931418936767 |
| 80 | 76.47058824 | 71.0025180070682 | 5.46807023293176 |
| 81 | 50 | 74.0034503859922 | -24.0034503859922 |
| 82 | 70.58823529 | 57.1571415688206 | 13.4310937211794 |
| 83 | 76.47058824 | 68.0630524798642 | 8.40753576013584 |
| 84 | 70.58823529 | 69.9227077486253 | 0.665527541374659 |
| 85 | 79.41176471 | 67.4921994577806 | 11.9195652522194 |
| 86 | 79.41176471 | 72.9521089540444 | 6.4596557559556 |
| 87 | 76.47058824 | 78.4918508449737 | -2.02126260497373 |
| 88 | 70.58823529 | 69.2828455050576 | 1.30538978494244 |
| 89 | 67.64705882 | 68.7418081030667 | -1.09474928306669 |
| 90 | 67.64705882 | 63.5690015990042 | 4.07805722099579 |
| 91 | 70.58823529 | 59.3924659910184 | 11.1957692989816 |
| 92 | 50 | 63.0443113978172 | -13.0443113978172 |
| 93 | 61.76470588 | 50.843816838413 | 10.920889041587 |
| 94 | 55.88235294 | 64.5873842648895 | -8.70503132488945 |
| 95 | 64.70588235 | 56.6294068669222 | 8.07647548307782 |
| 96 | 64.70588235 | 58.2609110819302 | 6.4449712680698 |
| 97 | 52.94117647 | 61.4737955069276 | -8.53261903692764 |
| 98 | 47.05882353 | 50.2516772752893 | -3.19285374528927 |
| 99 | 41.17647059 | 49.3776777236911 | -8.20120713369113 |
| 100 | 35.29411765 | 37.7786601085497 | -2.48454245854970 |
| 101 | 41.17647059 | 37.1625877773905 | 4.01388281260949 |
| 102 | 47.05882353 | 39.3498866931887 | 7.70893683681133 |
| 103 | 23.52941176 | 40.6466745593912 | -17.1172627993912 |
| 104 | 8.823529412 | 22.6243848622709 | -13.8008554502709 |
| 105 | 0 | 13.3320711635821 | -13.3320711635821 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 19 | 0.281912121595811 | 0.563824243191622 | 0.71808787840419 |
| 20 | 0.18450624501164 | 0.36901249002328 | 0.81549375498836 |
| 21 | 0.9132219186573 | 0.173556162685399 | 0.0867780813426997 |
| 22 | 0.936220565501796 | 0.127558868996409 | 0.0637794344982045 |
| 23 | 0.906653814772452 | 0.186692370455096 | 0.0933461852275478 |
| 24 | 0.860546698720898 | 0.278906602558204 | 0.139453301279102 |
| 25 | 0.841262036971209 | 0.317475926057582 | 0.158737963028791 |
| 26 | 0.8093909114126 | 0.3812181771748 | 0.1906090885874 |
| 27 | 0.74109545406589 | 0.51780909186822 | 0.25890454593411 |
| 28 | 0.683409932501212 | 0.633180134997576 | 0.316590067498788 |
| 29 | 0.610487165534414 | 0.779025668931173 | 0.389512834465586 |
| 30 | 0.647512695327753 | 0.704974609344493 | 0.352487304672246 |
| 31 | 0.596562630194958 | 0.806874739610085 | 0.403437369805042 |
| 32 | 0.518677674644713 | 0.962644650710574 | 0.481322325355287 |
| 33 | 0.61662644631183 | 0.766747107376341 | 0.383373553688171 |
| 34 | 0.573743166103369 | 0.852513667793262 | 0.426256833896631 |
| 35 | 0.591186459533412 | 0.817627080933175 | 0.408813540466588 |
| 36 | 0.672702523555652 | 0.654594952888696 | 0.327297476444348 |
| 37 | 0.808790714569878 | 0.382418570860245 | 0.191209285430122 |
| 38 | 0.785094086263103 | 0.429811827473794 | 0.214905913736897 |
| 39 | 0.748816100835349 | 0.502367798329302 | 0.251183899164651 |
| 40 | 0.71022031164688 | 0.57955937670624 | 0.28977968835312 |
| 41 | 0.67579130411968 | 0.64841739176064 | 0.32420869588032 |
| 42 | 0.78906703145489 | 0.421865937090222 | 0.210932968545111 |
| 43 | 0.906549919956668 | 0.186900160086664 | 0.0934500800433318 |
| 44 | 0.977763306352532 | 0.0444733872949371 | 0.0222366936474685 |
| 45 | 0.968537957517603 | 0.0629240849647939 | 0.0314620424823969 |
| 46 | 0.957071701294215 | 0.0858565974115703 | 0.0429282987057852 |
| 47 | 0.959974955952985 | 0.0800500880940293 | 0.0400250440470147 |
| 48 | 0.947048858906828 | 0.105902282186344 | 0.052951141093172 |
| 49 | 0.92894337917981 | 0.142113241640380 | 0.0710566208201902 |
| 50 | 0.904772417437276 | 0.190455165125448 | 0.095227582562724 |
| 51 | 0.92632473600099 | 0.147350527998020 | 0.0736752639990101 |
| 52 | 0.906654996777704 | 0.186690006444592 | 0.0933450032222958 |
| 53 | 0.880191652925728 | 0.239616694148544 | 0.119808347074272 |
| 54 | 0.85051406395176 | 0.298971872096479 | 0.149485936048240 |
| 55 | 0.860382225049478 | 0.279235549901043 | 0.139617774950522 |
| 56 | 0.820527352207334 | 0.358945295585331 | 0.179472647792666 |
| 57 | 0.772724599008706 | 0.454550801982589 | 0.227275400991294 |
| 58 | 0.74529164920571 | 0.509416701588579 | 0.254708350794290 |
| 59 | 0.71564289548234 | 0.56871420903532 | 0.28435710451766 |
| 60 | 0.675933266627741 | 0.648133466744518 | 0.324066733372259 |
| 61 | 0.649097689772367 | 0.701804620455265 | 0.350902310227632 |
| 62 | 0.737764240989278 | 0.524471518021444 | 0.262235759010722 |
| 63 | 0.73092320337295 | 0.538153593254099 | 0.269076796627049 |
| 64 | 0.692225551125105 | 0.615548897749791 | 0.307774448874896 |
| 65 | 0.638098244514466 | 0.723803510971068 | 0.361901755485534 |
| 66 | 0.754558785199003 | 0.490882429601993 | 0.245441214800997 |
| 67 | 0.777125424470976 | 0.445749151058049 | 0.222874575529024 |
| 68 | 0.718650018957375 | 0.56269996208525 | 0.281349981042625 |
| 69 | 0.766957758849959 | 0.466084482300082 | 0.233042241150041 |
| 70 | 0.754312118504878 | 0.491375762990244 | 0.245687881495122 |
| 71 | 0.704767300863245 | 0.590465398273511 | 0.295232699136755 |
| 72 | 0.733531237544996 | 0.532937524910007 | 0.266468762455004 |
| 73 | 0.718168203006991 | 0.563663593986018 | 0.281831796993009 |
| 74 | 0.724858687457771 | 0.550282625084458 | 0.275141312542229 |
| 75 | 0.658960143174935 | 0.68207971365013 | 0.341039856825065 |
| 76 | 0.583644724111087 | 0.832710551777826 | 0.416355275888913 |
| 77 | 0.497235746448333 | 0.994471492896666 | 0.502764253551667 |
| 78 | 0.511643381420781 | 0.976713237158439 | 0.488356618579219 |
| 79 | 0.466190166954649 | 0.932380333909297 | 0.533809833045351 |
| 80 | 0.52571823404574 | 0.94856353190852 | 0.47428176595426 |
| 81 | 0.745240709302363 | 0.509518581395274 | 0.254759290697637 |
| 82 | 0.655194423367866 | 0.689611153264268 | 0.344805576632134 |
| 83 | 0.556357603076589 | 0.887284793846823 | 0.443642396923411 |
| 84 | 0.609691108035881 | 0.780617783928239 | 0.390308891964119 |
| 85 | 0.466556175127239 | 0.933112350254479 | 0.533443824872761 |
| 86 | 0.311222016211226 | 0.622444032422452 | 0.688777983788774 |
| Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
| Description | # significant tests | % significant tests | OK/NOK |
| 1% type I error level | 0 | 0 | OK |
| 5% type I error level | 1 | 0.0147058823529412 | OK |
| 10% type I error level | 4 | 0.0588235294117647 | OK |
