| Multiple Linear Regression - Estimated Regression Equation |
| Y[t] = + 126.383760683761 -49.8978632478632X[t] -19.5698836657170M1[t] -24.5135158051825M2[t] + 0.285709198209129M3[t] -48.4007800841134M4[t] -50.5301265092932M5[t] -5.49975579975582M6[t] -10.3552927011260M7[t] -9.92785239451906M8[t] -26.7667226292227M9[t] -20.9555928639262M10[t] -16.0277964319631M11[t] + 0.272203568036901t + 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) | 126.383760683761 | 4.924358 | 25.665 | 0 | 0 |
| X | -49.8978632478632 | 4.442725 | -11.2314 | 0 | 0 |
| M1 | -19.5698836657170 | 5.841073 | -3.3504 | 0.001367 | 0.000684 |
| M2 | -24.5135158051825 | 5.838375 | -4.1987 | 8.6e-05 | 4.3e-05 |
| M3 | 0.285709198209129 | 5.836432 | 0.049 | 0.961112 | 0.480556 |
| M4 | -48.4007800841134 | 5.835244 | -8.2946 | 0 | 0 |
| M5 | -50.5301265092932 | 5.834812 | -8.6601 | 0 | 0 |
| M6 | -5.49975579975582 | 6.084279 | -0.9039 | 0.369477 | 0.184738 |
| M7 | -10.3552927011260 | 6.085009 | -1.7018 | 0.093729 | 0.046864 |
| M8 | -9.92785239451906 | 6.060242 | -1.6382 | 0.106367 | 0.053183 |
| M9 | -26.7667226292227 | 6.057693 | -4.4186 | 4e-05 | 2e-05 |
| M10 | -20.9555928639262 | 6.055871 | -3.4604 | 0.000974 | 0.000487 |
| M11 | -16.0277964319631 | 6.054778 | -2.6471 | 0.010242 | 0.005121 |
| t | 0.272203568036901 | 0.066434 | 4.0973 | 0.000122 | 6.1e-05 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.917996846433517 |
| R-squared | 0.842718210061882 |
| Adjusted R-squared | 0.81026323753497 |
| F-TEST (value) | 25.9657656269178 |
| F-TEST (DF numerator) | 13 |
| F-TEST (DF denominator) | 63 |
| p-value | 0 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 10.4865511345852 |
| Sum Squared Residuals | 6927.96854599104 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 105.7 | 107.086080586081 | -1.38608058608068 |
| 2 | 105.7 | 102.414652014652 | 3.28534798534793 |
| 3 | 111.1 | 127.486080586081 | -16.3860805860806 |
| 4 | 82.4 | 79.0717948717949 | 3.32820512820513 |
| 5 | 60 | 77.2146520146519 | -17.2146520146519 |
| 6 | 107.3 | 122.517226292226 | -15.2172262922263 |
| 7 | 99.3 | 117.933892958893 | -18.6338929588929 |
| 8 | 113.5 | 118.633536833537 | -5.13353683353683 |
| 9 | 108.9 | 102.066870166870 | 6.83312983312984 |
| 10 | 100.2 | 108.150203500204 | -7.95020350020353 |
| 11 | 103.9 | 113.350203500203 | -9.45020350020345 |
| 12 | 138.7 | 129.650203500204 | 9.04979649979646 |
| 13 | 120.2 | 110.352523402523 | 9.84747659747661 |
| 14 | 100.2 | 105.681094831095 | -5.48109483109483 |
| 15 | 143.2 | 130.752523402523 | 12.4474765974766 |
| 16 | 70.9 | 82.3382376882377 | -11.4382376882377 |
| 17 | 85.2 | 80.4810948310949 | 4.71890516890516 |
| 18 | 133 | 125.783669108669 | 7.2163308913309 |
| 19 | 136.6 | 121.200335775336 | 15.3996642246642 |
| 20 | 117.9 | 121.899979649980 | -3.99997964997965 |
| 21 | 106.3 | 105.333312983313 | 0.966687016687016 |
| 22 | 122.3 | 111.416646316646 | 10.8833536833537 |
| 23 | 125.5 | 116.616646316646 | 8.88335368335368 |
| 24 | 148.4 | 132.916646316646 | 15.4833536833537 |
| 25 | 126.3 | 113.618966218966 | 12.6810337810338 |
| 26 | 99.6 | 108.947537647538 | -9.34753764753764 |
| 27 | 140.4 | 134.018966218966 | 6.3810337810338 |
| 28 | 80.3 | 85.6046805046805 | -5.30468050468051 |
| 29 | 92.6 | 83.7475376475377 | 8.85246235246234 |
| 30 | 138.5 | 129.050111925112 | 9.44988807488808 |
| 31 | 110.9 | 124.466778591779 | -13.5667785917786 |
| 32 | 119.6 | 125.166422466422 | -5.56642246642248 |
| 33 | 105 | 108.599755799756 | -3.5997557997558 |
| 34 | 109 | 114.683089133089 | -5.68308913308913 |
| 35 | 129.4 | 119.883089133089 | 9.51691086691087 |
| 36 | 148.6 | 136.183089133089 | 12.4169108669108 |
| 37 | 101.4 | 116.885409035409 | -15.485409035409 |
| 38 | 134.8 | 112.213980463980 | 22.5860195360196 |
| 39 | 143.7 | 137.285409035409 | 6.41459096459096 |
| 40 | 81.6 | 88.8711233211233 | -7.27112332112333 |
| 41 | 90.3 | 87.0139804639805 | 3.28601953601952 |
| 42 | 141.5 | 132.316554741555 | 9.18344525844527 |
| 43 | 140.7 | 127.733221408221 | 12.9667785917786 |
| 44 | 140.2 | 128.432865282865 | 11.7671347171347 |
| 45 | 100.2 | 111.866198616199 | -11.6661986161986 |
| 46 | 125.7 | 117.949531949532 | 7.75046805046806 |
| 47 | 119.6 | 123.149531949532 | -3.54953194953197 |
| 48 | 134.7 | 139.449531949532 | -4.74953194953197 |
| 49 | 109 | 120.151851851852 | -11.1518518518518 |
| 50 | 116.3 | 115.480423280423 | 0.81957671957673 |
| 51 | 146.9 | 140.551851851852 | 6.34814814814816 |
| 52 | 97.4 | 92.1375661375661 | 5.26243386243387 |
| 53 | 89.4 | 90.2804232804233 | -0.880423280423285 |
| 54 | 132.1 | 135.582997557998 | -3.48299755799756 |
| 55 | 139.8 | 130.999664224664 | 8.80033577533578 |
| 56 | 129 | 131.699308099308 | -2.6993080993081 |
| 57 | 112.5 | 115.132641432641 | -2.63264143264143 |
| 58 | 121.9 | 121.215974765975 | 0.684025234025239 |
| 59 | 121.7 | 126.415974765975 | -4.71597476597477 |
| 60 | 123.1 | 142.715974765975 | -19.6159747659748 |
| 61 | 131.6 | 123.418294668295 | 8.18170533170535 |
| 62 | 119.3 | 118.746866096866 | 0.553133903133916 |
| 63 | 132.5 | 143.818294668295 | -11.3182946682947 |
| 64 | 98.3 | 95.404008954009 | 2.89599104599105 |
| 65 | 85.1 | 93.5468660968661 | -8.44686609686611 |
| 66 | 131.7 | 138.849440374440 | -7.14944037444039 |
| 67 | 129.3 | 134.266107041107 | -4.96610704110704 |
| 68 | 90.7 | 85.0678876678877 | 5.63211233211233 |
| 69 | 78.6 | 68.501221001221 | 10.098778998779 |
| 70 | 68.9 | 74.5845543345543 | -5.68455433455433 |
| 71 | 79.1 | 79.7845543345543 | -0.684554334554351 |
| 72 | 83.5 | 96.0845543345543 | -12.5845543345543 |
| 73 | 74.1 | 76.7868742368742 | -2.68687423687422 |
| 74 | 59.7 | 72.1154456654457 | -12.4154456654457 |
| 75 | 93.3 | 97.1868742368742 | -3.88687423687423 |
| 76 | 61.3 | 48.7725885225885 | 12.5274114774115 |
| 77 | 56.6 | 46.9154456654457 | 9.68455433455432 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 17 | 0.936205566026584 | 0.127588867946832 | 0.063794433973416 |
| 18 | 0.909276935731682 | 0.181446128536636 | 0.090723064268318 |
| 19 | 0.929897883358947 | 0.140204233282106 | 0.0701021166410528 |
| 20 | 0.908172739003429 | 0.183654521993143 | 0.0918272609965713 |
| 21 | 0.898499146723534 | 0.203001706552931 | 0.101500853276466 |
| 22 | 0.857172475096707 | 0.285655049806586 | 0.142827524903293 |
| 23 | 0.801693569986058 | 0.396612860027884 | 0.198306430013942 |
| 24 | 0.768737405293272 | 0.462525189413455 | 0.231262594706728 |
| 25 | 0.739463688146475 | 0.521072623707051 | 0.260536311853525 |
| 26 | 0.831656895042687 | 0.336686209914627 | 0.168343104957313 |
| 27 | 0.770544937344607 | 0.458910125310787 | 0.229455062655393 |
| 28 | 0.763795091389755 | 0.47240981722049 | 0.236204908610245 |
| 29 | 0.700959485460333 | 0.598081029079334 | 0.299040514539667 |
| 30 | 0.630014875015923 | 0.739970249968154 | 0.369985124984077 |
| 31 | 0.801586915352753 | 0.396826169294494 | 0.198413084647247 |
| 32 | 0.804671622556693 | 0.390656754886614 | 0.195328377443307 |
| 33 | 0.80171463809524 | 0.396570723809522 | 0.198285361904761 |
| 34 | 0.813239154403094 | 0.373521691193812 | 0.186760845596906 |
| 35 | 0.763168966568306 | 0.473662066863387 | 0.236831033431694 |
| 36 | 0.790843489228378 | 0.418313021543244 | 0.209156510771622 |
| 37 | 0.931828670354126 | 0.136342659291748 | 0.0681713296458738 |
| 38 | 0.975716776179814 | 0.0485664476403719 | 0.0242832238201859 |
| 39 | 0.963319041889111 | 0.0733619162217775 | 0.0366809581108887 |
| 40 | 0.982987331120944 | 0.0340253377581117 | 0.0170126688790559 |
| 41 | 0.97367078553315 | 0.0526584289337013 | 0.0263292144668507 |
| 42 | 0.962397988308342 | 0.0752040233833155 | 0.0376020116916578 |
| 43 | 0.951565924991817 | 0.0968681500163655 | 0.0484340750081828 |
| 44 | 0.94240329715319 | 0.115193405693622 | 0.0575967028468108 |
| 45 | 0.975612864034739 | 0.0487742719305228 | 0.0243871359652614 |
| 46 | 0.96594026399974 | 0.0681194720005217 | 0.0340597360002608 |
| 47 | 0.952976443141558 | 0.0940471137168832 | 0.0470235568584416 |
| 48 | 0.95810115548702 | 0.0837976890259592 | 0.0418988445129796 |
| 49 | 0.98232551334649 | 0.0353489733070188 | 0.0176744866535094 |
| 50 | 0.969244673624392 | 0.0615106527512166 | 0.0307553263756083 |
| 51 | 0.967277844378397 | 0.0654443112432055 | 0.0327221556216028 |
| 52 | 0.949310673439072 | 0.101378653121856 | 0.0506893265609278 |
| 53 | 0.927095179739313 | 0.145809640521373 | 0.0729048202606866 |
| 54 | 0.89874850574942 | 0.20250298850116 | 0.10125149425058 |
| 55 | 0.837881916765228 | 0.324236166469544 | 0.162118083234772 |
| 56 | 0.763610018973827 | 0.472779962052346 | 0.236389981026173 |
| 57 | 0.711645894391059 | 0.576708211217883 | 0.288354105608941 |
| 58 | 0.634250022010307 | 0.731499955979386 | 0.365749977989693 |
| 59 | 0.48983381856805 | 0.9796676371361 | 0.51016618143195 |
| 60 | 0.3963426819236 | 0.7926853638472 | 0.6036573180764 |
| 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 | 4 | 0.090909090909091 | NOK |
| 10% type I error level | 13 | 0.295454545454545 | NOK |
