| Multiple Linear Regression - Estimated Regression Equation |
| Y[t] = -53.6518988484805 + 389.313447739161X[t] + 1.06481823529856Y1[t] -0.253504368502961Y2[t] -0.202623347892135Y3[t] + 0.390229059988102Y4[t] + 0.938161684005079t + 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) | -53.6518988484805 | 278.585629 | -0.1926 | 0.847747 | 0.423874 |
| X | 389.313447739161 | 203.330778 | 1.9147 | 0.058937 | 0.029469 |
| Y1 | 1.06481823529856 | 0.100807 | 10.563 | 0 | 0 |
| Y2 | -0.253504368502961 | 0.151694 | -1.6712 | 0.098412 | 0.049206 |
| Y3 | -0.202623347892135 | 0.15203 | -1.3328 | 0.186207 | 0.093103 |
| Y4 | 0.390229059988102 | 0.104855 | 3.7216 | 0.000357 | 0.000178 |
| t | 0.938161684005079 | 3.285311 | 0.2856 | 0.775916 | 0.387958 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.97728926035259 |
| R-squared | 0.955094298400514 |
| Adjusted R-squared | 0.951886748286265 |
| F-TEST (value) | 297.764419691423 |
| F-TEST (DF numerator) | 6 |
| F-TEST (DF denominator) | 84 |
| p-value | 0 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 493.393695460646 |
| Sum Squared Residuals | 20448736.4525063 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 7969 | 8256.82388074314 | -287.823880743136 |
| 2 | 8758 | 8005.85087479543 | 752.149125204573 |
| 3 | 8693 | 9006.6588719542 | -313.658871954206 |
| 4 | 8271 | 8593.00983883832 | -322.009838838315 |
| 5 | 7790 | 7889.59715653553 | -99.5971565355306 |
| 6 | 7769 | 7806.39783649278 | -37.3978364927831 |
| 7 | 8170 | 7967.0525803967 | 202.947419603304 |
| 8 | 8209 | 8333.09161319512 | -124.091613195121 |
| 9 | 9395 | 8090.45734673754 | 1304.54265326246 |
| 10 | 9260 | 9254.93649234952 | 5.06350765048006 |
| 11 | 9018 | 8960.04755371115 | 57.9524462888555 |
| 12 | 8501 | 8512.43043494026 | -11.4304349402629 |
| 13 | 8500 | 8514.37144326396 | -14.3714432639594 |
| 14 | 9649 | 8641.6604723202 | 1007.3395276798 |
| 15 | 9319 | 9876.64912907386 | -557.64912907386 |
| 16 | 8830 | 9033.37495303348 | -203.374953033483 |
| 17 | 8436 | 8364.06898347442 | 71.931016525579 |
| 18 | 8169 | 8584.67129137948 | -415.671291379477 |
| 19 | 8269 | 8371.49093275211 | -102.490932752115 |
| 20 | 7945 | 8435.60817309158 | -490.608173091585 |
| 21 | 9144 | 7966.54497394045 | 1177.45502605955 |
| 22 | 8770 | 9201.88212133634 | -431.882121336345 |
| 23 | 8834 | 8605.2993958995 | 228.700604100497 |
| 24 | 7837 | 8399.8169489039 | -562.816948903907 |
| 25 | 7792 | 7866.57282544846 | -74.572825448457 |
| 26 | 8616 | 7913.42445924083 | 702.575540759168 |
| 27 | 8518 | 9030.17068108118 | -512.170681081177 |
| 28 | 7940 | 8337.9287339065 | -397.928733906492 |
| 29 | 7545 | 7563.72343733864 | -18.7234373386381 |
| 30 | 7531 | 7631.98975459805 | -100.989754598051 |
| 31 | 7665 | 7797.02853374937 | -132.028533749366 |
| 32 | 7599 | 7798.68522586669 | -199.685225866689 |
| 33 | 8444 | 7544.07204681678 | 899.927953183218 |
| 34 | 8549 | 8428.89817019188 | 120.101829808118 |
| 35 | 7986 | 8393.09489019652 | -407.09489019652 |
| 36 | 7335 | 7570.95057978656 | -235.950579786559 |
| 37 | 7287 | 7329.88313391964 | -42.8831339196438 |
| 38 | 7870 | 7599.79236036677 | 270.207639633231 |
| 39 | 7839 | 8145.89660162245 | -306.896601622452 |
| 40 | 7327 | 7721.71915382154 | -394.719153821543 |
| 41 | 7259 | 7048.46860775574 | 210.531392244264 |
| 42 | 6964 | 7340.57823187068 | -376.578231870675 |
| 43 | 7271 | 7136.27936446095 | 134.720635539050 |
| 44 | 6956 | 7352.88162203274 | -396.881622032741 |
| 45 | 7608 | 6973.81451001628 | 634.185489983719 |
| 46 | 7692 | 7571.545096694 | 120.454903305999 |
| 47 | 7255 | 7680.26981788152 | -425.269817881525 |
| 48 | 6804 | 6939.55546706389 | -135.555467063888 |
| 49 | 6655 | 6808.45099955334 | -153.450999553342 |
| 50 | 7341 | 6886.38735844056 | 454.612641559439 |
| 51 | 7602 | 7576.41601113087 | 25.5839888691315 |
| 52 | 7086 | 7535.56530821606 | -449.565308216059 |
| 53 | 6625 | 6723.7488737145 | -98.7488737145055 |
| 54 | 6272 | 6579.42652442540 | -307.426524425395 |
| 55 | 6576 | 6527.75279509811 | 48.2472049018884 |
| 56 | 6491 | 6833.93391081884 | -342.933910818836 |
| 57 | 7649 | 6558.92763962897 | 1090.07236037103 |
| 58 | 7400 | 7615.12483317645 | -215.124833176446 |
| 59 | 6913 | 7193.2178143519 | -280.217814351898 |
| 60 | 6532 | 6470.90477624466 | 61.0952237553373 |
| 61 | 6486 | 6691.94228283222 | -205.942282832224 |
| 62 | 7295 | 6741.99450457856 | 553.005495421444 |
| 63 | 7556 | 7503.18976290293 | 52.810237097074 |
| 64 | 7088 | 7826.9172997677 | -738.917299767692 |
| 65 | 6952 | 7081.48306194851 | -129.48306194851 |
| 66 | 6773 | 7319.05660382183 | -546.056603821826 |
| 67 | 6917 | 7360.5464069742 | -443.546406974206 |
| 68 | 7371 | 7405.12525174213 | -34.1252517421308 |
| 69 | 8221 | 7836.18469030156 | 384.815309698436 |
| 70 | 7953 | 8528.09860485466 | -575.098604854659 |
| 71 | 8027 | 7992.3887509464 | 34.6112490536075 |
| 72 | 7287 | 8144.99678032757 | -857.996780327568 |
| 73 | 8076 | 7725.2078828464 | 350.792117153598 |
| 74 | 8933 | 8634.30534905233 | 298.694650947671 |
| 75 | 9433 | 9526.59601951766 | -93.5960195176592 |
| 76 | 9479 | 9394.05072916581 | 84.949270834186 |
| 77 | 9199 | 9451.46086460913 | -252.460864609126 |
| 78 | 9469 | 9375.70334992214 | 93.2966500778647 |
| 79 | 10015 | 9920.9175143086 | 94.0824856914075 |
| 80 | 10999 | 10509.4853271391 | 489.51467286094 |
| 81 | 13009 | 11255.8188064267 | 1753.18119357332 |
| 82 | 13699 | 13142.3228207016 | 556.677179298449 |
| 83 | 13895 | 13382.1254764783 | 512.874523521749 |
| 84 | 13248 | 13393.5624637788 | -145.562463778832 |
| 85 | 13973 | 13300.4266715286 | 672.573328471395 |
| 86 | 15095 | 14466.9192554304 | 628.08074456959 |
| 87 | 15201 | 15686.3750117986 | -485.375011798626 |
| 88 | 14823 | 15116.3718759299 | -293.371875929857 |
| 89 | 14538 | 14743.5099537661 | -205.509953766094 |
| 90 | 14547 | 14953.1585001142 | -406.158500114213 |
| 91 | 14407 | 15153.8846768012 | -746.884676801216 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 10 | 0.89397314128492 | 0.21205371743016 | 0.10602685871508 |
| 11 | 0.849365868015715 | 0.301268263968569 | 0.150634131984284 |
| 12 | 0.755306292890817 | 0.489387414218366 | 0.244693707109183 |
| 13 | 0.652137005127738 | 0.695725989744524 | 0.347862994872262 |
| 14 | 0.77444569325223 | 0.451108613495541 | 0.225554306747771 |
| 15 | 0.738235159624512 | 0.523529680750975 | 0.261764840375488 |
| 16 | 0.66478216632633 | 0.670435667347339 | 0.335217833673669 |
| 17 | 0.596921190440057 | 0.806157619119887 | 0.403078809559943 |
| 18 | 0.618192849933302 | 0.763614300133397 | 0.381807150066698 |
| 19 | 0.570772653239892 | 0.858454693520216 | 0.429227346760108 |
| 20 | 0.627715914800387 | 0.744568170399225 | 0.372284085199613 |
| 21 | 0.751877938258775 | 0.496244123482449 | 0.248122061741225 |
| 22 | 0.736210621559769 | 0.527578756880463 | 0.263789378440231 |
| 23 | 0.680341472728478 | 0.639317054543045 | 0.319658527271522 |
| 24 | 0.721687433539776 | 0.556625132920447 | 0.278312566460224 |
| 25 | 0.688404155625863 | 0.623191688748274 | 0.311595844374137 |
| 26 | 0.705944359045618 | 0.588111281908764 | 0.294055640954382 |
| 27 | 0.690154432924912 | 0.619691134150176 | 0.309845567075088 |
| 28 | 0.69432536453812 | 0.611349270923761 | 0.305674635461880 |
| 29 | 0.65374174914022 | 0.69251650171956 | 0.34625825085978 |
| 30 | 0.607993994548525 | 0.78401201090295 | 0.392006005451475 |
| 31 | 0.55408374042737 | 0.891832519145259 | 0.445916259572629 |
| 32 | 0.502469663942555 | 0.99506067211489 | 0.497530336057445 |
| 33 | 0.622241180836077 | 0.755517638327846 | 0.377758819163923 |
| 34 | 0.568242019339213 | 0.863515961321574 | 0.431757980660787 |
| 35 | 0.52534079173257 | 0.94931841653486 | 0.47465920826743 |
| 36 | 0.481292951467691 | 0.962585902935383 | 0.518707048532309 |
| 37 | 0.427603131636863 | 0.855206263273726 | 0.572396868363137 |
| 38 | 0.399694667231359 | 0.799389334462718 | 0.600305332768641 |
| 39 | 0.348676660524961 | 0.697353321049922 | 0.651323339475039 |
| 40 | 0.320800189095517 | 0.641600378191034 | 0.679199810904483 |
| 41 | 0.287476969021716 | 0.574953938043432 | 0.712523030978284 |
| 42 | 0.262492012866358 | 0.524984025732716 | 0.737507987133642 |
| 43 | 0.226024042340609 | 0.452048084681218 | 0.77397595765939 |
| 44 | 0.202874303369910 | 0.405748606739821 | 0.79712569663009 |
| 45 | 0.259693546785521 | 0.519387093571043 | 0.740306453214479 |
| 46 | 0.228155587264774 | 0.456311174529548 | 0.771844412735226 |
| 47 | 0.193889963555326 | 0.387779927110651 | 0.806110036444674 |
| 48 | 0.161075876588869 | 0.322151753177738 | 0.838924123411131 |
| 49 | 0.133868031404317 | 0.267736062808634 | 0.866131968595683 |
| 50 | 0.169892077993099 | 0.339784155986199 | 0.8301079220069 |
| 51 | 0.151092715951951 | 0.302185431903902 | 0.848907284048049 |
| 52 | 0.123223595353424 | 0.246447190706848 | 0.876776404646576 |
| 53 | 0.0997625863640436 | 0.199525172728087 | 0.900237413635956 |
| 54 | 0.0829224912407482 | 0.165844982481496 | 0.917077508759252 |
| 55 | 0.0689352049322392 | 0.137870409864478 | 0.931064795067761 |
| 56 | 0.0552422614705541 | 0.110484522941108 | 0.944757738529446 |
| 57 | 0.208817550911718 | 0.417635101823436 | 0.791182449088282 |
| 58 | 0.165652001065968 | 0.331304002131936 | 0.834347998934032 |
| 59 | 0.129563105612798 | 0.259126211225595 | 0.870436894387202 |
| 60 | 0.097646599199982 | 0.195293198399964 | 0.902353400800018 |
| 61 | 0.0739698861465624 | 0.147939772293125 | 0.926030113853438 |
| 62 | 0.0803235098137166 | 0.160647019627433 | 0.919676490186283 |
| 63 | 0.0602377053478535 | 0.120475410695707 | 0.939762294652146 |
| 64 | 0.0439108511537503 | 0.0878217023075006 | 0.95608914884625 |
| 65 | 0.0371971982980791 | 0.0743943965961582 | 0.962802801701921 |
| 66 | 0.0247403661661561 | 0.0494807323323122 | 0.975259633833844 |
| 67 | 0.0158300688018093 | 0.0316601376036185 | 0.98416993119819 |
| 68 | 0.0117552434032038 | 0.0235104868064075 | 0.988244756596796 |
| 69 | 0.0199218704623624 | 0.0398437409247249 | 0.980078129537638 |
| 70 | 0.0151910671832110 | 0.0303821343664219 | 0.984808932816789 |
| 71 | 0.0119808024015595 | 0.0239616048031189 | 0.98801919759844 |
| 72 | 0.0244853440990360 | 0.0489706881980719 | 0.975514655900964 |
| 73 | 0.0288842706774096 | 0.0577685413548192 | 0.97111572932259 |
| 74 | 0.0256630102017726 | 0.0513260204035453 | 0.974336989798227 |
| 75 | 0.0187829291714798 | 0.0375658583429596 | 0.98121707082852 |
| 76 | 0.0174106903985939 | 0.0348213807971879 | 0.982589309601406 |
| 77 | 0.0275149278157864 | 0.0550298556315729 | 0.972485072184214 |
| 78 | 0.0286631397289115 | 0.0573262794578231 | 0.971336860271088 |
| 79 | 0.0956850900263294 | 0.191370180052659 | 0.90431490997367 |
| 80 | 0.572714803821567 | 0.854570392356867 | 0.427285196178433 |
| 81 | 0.520678982828234 | 0.958642034343532 | 0.479321017171766 |
| 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 | 9 | 0.125 | NOK |
| 10% type I error level | 15 | 0.208333333333333 | NOK |
