| Multiple Linear Regression - Estimated Regression Equation |
| APPLE[t] = -167.424814295902 -4.30135459798218e-07VOLUME[t] -8.7281919063852REV.GROWTH[t] + 8.83841129074743MICROSOFT[t] -0.668738093829939CONS.CONF[t] + 6.27872053212584M1[t] + 10.5105860530226M2[t] + 15.0431505457878M3[t] + 18.1188764739719M4[t] + 24.7843160355318M5[t] + 17.5713482106206M6[t] + 22.3168235770649M7[t] + 19.8568271551398M8[t] + 21.4874096649532M9[t] + 3.79266552398289M10[t] + 0.0655665756245166M11[t] + 1.54972876039673t + 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) | -167.424814295902 | 19.521004 | -8.5766 | 0 | 0 |
| VOLUME | -4.30135459798218e-07 | 0 | -1.6745 | 0.09715 | 0.048575 |
| REV.GROWTH | -8.7281919063852 | 10.288069 | -0.8484 | 0.398253 | 0.199126 |
| MICROSOFT | 8.83841129074743 | 0.832748 | 10.6135 | 0 | 0 |
| CONS.CONF | -0.668738093829939 | 0.160171 | -4.1751 | 6.4e-05 | 3.2e-05 |
| M1 | 6.27872053212584 | 11.415391 | 0.55 | 0.58353 | 0.291765 |
| M2 | 10.5105860530226 | 11.063574 | 0.95 | 0.344394 | 0.172197 |
| M3 | 15.0431505457878 | 11.009187 | 1.3664 | 0.174872 | 0.087436 |
| M4 | 18.1188764739719 | 10.957164 | 1.6536 | 0.101343 | 0.050671 |
| M5 | 24.7843160355318 | 11.040727 | 2.2448 | 0.026983 | 0.013492 |
| M6 | 17.5713482106206 | 10.992791 | 1.5984 | 0.1131 | 0.05655 |
| M7 | 22.3168235770649 | 10.983927 | 2.0318 | 0.044829 | 0.022415 |
| M8 | 19.8568271551398 | 11.066657 | 1.7943 | 0.075788 | 0.037894 |
| M9 | 21.4874096649532 | 10.957483 | 1.961 | 0.052663 | 0.026331 |
| M10 | 3.79266552398289 | 11.329386 | 0.3348 | 0.738505 | 0.369252 |
| M11 | 0.0655665756245166 | 11.145967 | 0.0059 | 0.995318 | 0.497659 |
| t | 1.54972876039673 | 0.147584 | 10.5007 | 0 | 0 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.957710226610275 |
| R-squared | 0.917208878153904 |
| Adjusted R-squared | 0.903962298658528 |
| F-TEST (value) | 69.241186260507 |
| F-TEST (DF numerator) | 16 |
| F-TEST (DF denominator) | 100 |
| p-value | 0 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 23.5449579349573 |
| Sum Squared Residuals | 55436.5044158911 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 10.81 | -29.1289346330788 | 39.9389346330788 |
| 2 | 9.12 | -21.8629293042175 | 30.9829293042175 |
| 3 | 11.03 | -37.8618195587563 | 48.8918195587563 |
| 4 | 12.74 | 15.8191941614227 | -3.07919416142274 |
| 5 | 9.98 | 28.4414830991174 | -18.4614830991174 |
| 6 | 11.62 | 33.9882169765273 | -22.3682169765273 |
| 7 | 9.4 | 17.6408173547178 | -8.24081735471784 |
| 8 | 9.27 | -11.1474465044169 | 20.4174465044169 |
| 9 | 7.76 | -19.8369714406765 | 27.5969714406765 |
| 10 | 8.78 | -7.83100248695104 | 16.6110024869510 |
| 11 | 10.65 | 12.807800388855 | -2.15780038885499 |
| 12 | 10.95 | 15.4526920100371 | -4.50269201003714 |
| 13 | 12.36 | 12.1036487574918 | 0.256351242508247 |
| 14 | 10.85 | 0.620794122307112 | 10.2292058776929 |
| 15 | 11.84 | 5.72395740774698 | 6.11604259225302 |
| 16 | 12.14 | -16.5775122145614 | 28.7175122145614 |
| 17 | 11.65 | -14.085937921687 | 25.735937921687 |
| 18 | 8.86 | -6.10756959535391 | 14.9675695953539 |
| 19 | 7.63 | -16.8562599716215 | 24.4862599716215 |
| 20 | 7.38 | -9.78485602718028 | 17.1648560271803 |
| 21 | 7.25 | -25.4985835759382 | 32.7485835759382 |
| 22 | 8.03 | 1.23196201938234 | 6.79803798061766 |
| 23 | 7.75 | 11.3812859040640 | -3.63128590406404 |
| 24 | 7.16 | -5.31966796601335 | 12.4796679660134 |
| 25 | 7.18 | -11.7249246568766 | 18.9049246568766 |
| 26 | 7.51 | 4.96057352962864 | 2.54942647037136 |
| 27 | 7.07 | 17.2899390327428 | -10.2199390327428 |
| 28 | 7.11 | 14.7279488222825 | -7.61794882228247 |
| 29 | 8.98 | 12.2329173121377 | -3.25291731213772 |
| 30 | 9.53 | 17.5267717732773 | -7.99677177327729 |
| 31 | 10.54 | 33.4039351298877 | -22.8639351298877 |
| 32 | 11.31 | 30.6567552749443 | -19.3467552749443 |
| 33 | 10.36 | 45.3067025210455 | -34.9467025210455 |
| 34 | 11.44 | 13.0754575258651 | -1.63545752586509 |
| 35 | 10.45 | 1.34700980675375 | 9.10299019324625 |
| 36 | 10.69 | 15.3627618198796 | -4.67276181987964 |
| 37 | 11.28 | 20.3781618147631 | -9.09816181476312 |
| 38 | 11.96 | 25.2728146088783 | -13.3128146088783 |
| 39 | 13.52 | 16.2860072990066 | -2.76600729900657 |
| 40 | 12.89 | 27.5456874102571 | -14.6556874102571 |
| 41 | 14.03 | 39.0887992601857 | -25.0587992601857 |
| 42 | 16.27 | 41.4498449447815 | -25.1798449447815 |
| 43 | 16.17 | 43.7135139851325 | -27.5435139851325 |
| 44 | 17.25 | 41.0322112286433 | -23.7822112286433 |
| 45 | 19.38 | 47.9575666891021 | -28.5775666891021 |
| 46 | 26.2 | 26.9848384046912 | -0.784838404691183 |
| 47 | 33.53 | 37.5638539443876 | -4.03385394438765 |
| 48 | 32.2 | 33.7655396498255 | -1.56553964982551 |
| 49 | 38.45 | 27.1047709883906 | 11.3452290116094 |
| 50 | 44.86 | 28.2152262679419 | 16.6447737320581 |
| 51 | 41.67 | 34.4560788646183 | 7.2139211353817 |
| 52 | 36.06 | 47.4625291208946 | -11.4025291208946 |
| 53 | 39.76 | 61.4918559914739 | -21.7318559914739 |
| 54 | 36.81 | 47.5662944562746 | -10.7562944562746 |
| 55 | 42.65 | 63.3982633935495 | -20.7482633935495 |
| 56 | 46.89 | 77.702976868646 | -30.812976868646 |
| 57 | 53.61 | 76.7894369524919 | -23.1794369524919 |
| 58 | 57.59 | 56.2951178397668 | 1.29488216023321 |
| 59 | 67.82 | 66.0204213227497 | 1.79957867725034 |
| 60 | 71.89 | 51.718786966296 | 20.1712130337040 |
| 61 | 75.51 | 68.8686566886356 | 6.64134331136439 |
| 62 | 68.49 | 69.071756514849 | -0.581756514848956 |
| 63 | 62.72 | 74.8427344024244 | -12.1227344024244 |
| 64 | 70.39 | 53.2307715219882 | 17.1592284780118 |
| 65 | 59.77 | 58.454383717183 | 1.31561628281696 |
| 66 | 57.27 | 56.1779314592343 | 1.09206854076566 |
| 67 | 67.96 | 66.077489829688 | 1.88251017031203 |
| 68 | 67.85 | 85.6368170614178 | -17.7868170614178 |
| 69 | 76.98 | 96.8473018730144 | -19.8673018730144 |
| 70 | 81.08 | 96.5646572599 | -15.4846572599 |
| 71 | 91.66 | 99.9915897284772 | -8.33158972847717 |
| 72 | 84.84 | 99.4434417737356 | -14.6034417737356 |
| 73 | 85.73 | 107.742314508485 | -22.0123145084845 |
| 74 | 84.61 | 101.362023352933 | -16.7520233529330 |
| 75 | 92.91 | 107.279193279517 | -14.3691932795170 |
| 76 | 99.8 | 130.430002832845 | -30.6300028328452 |
| 77 | 121.19 | 141.937008363237 | -20.7470083632374 |
| 78 | 122.04 | 123.507306046263 | -1.46730604626286 |
| 79 | 131.76 | 119.604966151996 | 12.1550338480041 |
| 80 | 138.48 | 123.584783515897 | 14.8952164841034 |
| 81 | 153.47 | 136.380498835399 | 17.0895011646011 |
| 82 | 189.95 | 184.374081452730 | 5.57591854727027 |
| 83 | 182.22 | 157.593166659243 | 24.6268333407566 |
| 84 | 198.08 | 180.179466815272 | 17.9005331847278 |
| 85 | 135.36 | 151.444911624608 | -16.0849116246079 |
| 86 | 125.02 | 127.552761331245 | -2.53276133124544 |
| 87 | 143.5 | 152.419301067743 | -8.91930106774267 |
| 88 | 173.95 | 163.407098659772 | 10.5429013402276 |
| 89 | 188.75 | 176.900514929889 | 11.8494850701110 |
| 90 | 167.44 | 168.277653301704 | -0.837653301703739 |
| 91 | 158.95 | 155.784767286365 | 3.16523271363483 |
| 92 | 169.53 | 168.650480585262 | 0.879519414737732 |
| 93 | 113.66 | 156.068556343813 | -42.4085563438126 |
| 94 | 107.59 | 113.744518120294 | -6.15451812029398 |
| 95 | 92.67 | 100.310998012182 | -7.64099801218243 |
| 96 | 85.35 | 104.266506063077 | -18.9165060630770 |
| 97 | 90.13 | 115.575994244093 | -25.4459942440925 |
| 98 | 89.31 | 102.575169337853 | -13.2651693378535 |
| 99 | 105.12 | 127.117420713788 | -21.9974207137881 |
| 100 | 125.83 | 139.387273796008 | -13.5572737960081 |
| 101 | 135.81 | 146.178344363205 | -10.3683443632049 |
| 102 | 142.43 | 167.312791478231 | -24.8827914782306 |
| 103 | 163.39 | 175.964235147452 | -12.5742351474520 |
| 104 | 168.21 | 182.912081270901 | -14.7020812709006 |
| 105 | 185.35 | 194.518521350729 | -9.16852135072932 |
| 106 | 188.5 | 194.720369864322 | -6.22036986432195 |
| 107 | 199.91 | 209.643874233287 | -9.73387423328692 |
| 108 | 210.73 | 217.020472867890 | -6.29047286789028 |
| 109 | 192.06 | 196.505400663489 | -4.44540066348926 |
| 110 | 204.62 | 218.581810238581 | -13.9618102385807 |
| 111 | 235 | 226.827187491169 | 8.17281250883057 |
| 112 | 261.09 | 236.567005889091 | 24.5229941109093 |
| 113 | 256.88 | 196.160630885258 | 60.7193691147421 |
| 114 | 251.53 | 174.100759159062 | 77.4292408409384 |
| 115 | 257.25 | 206.968271692833 | 50.2817283071672 |
| 116 | 243.1 | 190.026196725886 | 53.0738032741138 |
| 117 | 283.75 | 203.03697045102 | 80.71302954898 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 20 | 0.000298062341214584 | 0.000596124682429168 | 0.999701937658785 |
| 21 | 2.10230122855614e-05 | 4.20460245711228e-05 | 0.999978976987714 |
| 22 | 1.64092555787285e-06 | 3.2818511157457e-06 | 0.999998359074442 |
| 23 | 1.3134321322866e-07 | 2.6268642645732e-07 | 0.999999868656787 |
| 24 | 7.44455761869434e-09 | 1.48891152373887e-08 | 0.999999992555442 |
| 25 | 7.72586811908547e-10 | 1.54517362381709e-09 | 0.999999999227413 |
| 26 | 7.01162955072654e-11 | 1.40232591014531e-10 | 0.999999999929884 |
| 27 | 3.94236890332904e-12 | 7.88473780665807e-12 | 0.999999999996058 |
| 28 | 3.23935930685226e-12 | 6.47871861370452e-12 | 0.99999999999676 |
| 29 | 2.92733709203219e-13 | 5.85467418406437e-13 | 0.999999999999707 |
| 30 | 4.10100907222039e-14 | 8.20201814444079e-14 | 0.99999999999996 |
| 31 | 1.62761385744920e-14 | 3.25522771489839e-14 | 0.999999999999984 |
| 32 | 3.16374958345142e-15 | 6.32749916690283e-15 | 0.999999999999997 |
| 33 | 2.28967388533605e-16 | 4.57934777067209e-16 | 1 |
| 34 | 2.34307109995582e-17 | 4.68614219991165e-17 | 1 |
| 35 | 2.35543625184074e-18 | 4.71087250368148e-18 | 1 |
| 36 | 2.01910832410829e-19 | 4.03821664821657e-19 | 1 |
| 37 | 5.47175796241618e-20 | 1.09435159248324e-19 | 1 |
| 38 | 5.57354219456846e-21 | 1.11470843891369e-20 | 1 |
| 39 | 1.01640108419724e-21 | 2.03280216839449e-21 | 1 |
| 40 | 9.93576426012005e-23 | 1.98715285202401e-22 | 1 |
| 41 | 1.82343342329803e-23 | 3.64686684659607e-23 | 1 |
| 42 | 7.36302382080744e-24 | 1.47260476416149e-23 | 1 |
| 43 | 8.04296570733289e-25 | 1.60859314146658e-24 | 1 |
| 44 | 2.52162742389229e-25 | 5.04325484778459e-25 | 1 |
| 45 | 4.81289543358371e-25 | 9.62579086716742e-25 | 1 |
| 46 | 8.94377176984187e-24 | 1.78875435396837e-23 | 1 |
| 47 | 9.2873509559074e-22 | 1.85747019118148e-21 | 1 |
| 48 | 1.32624221022531e-21 | 2.65248442045062e-21 | 1 |
| 49 | 2.25831446702500e-22 | 4.51662893405001e-22 | 1 |
| 50 | 1.86554228222619e-21 | 3.73108456445239e-21 | 1 |
| 51 | 6.44577065763044e-19 | 1.28915413152609e-18 | 1 |
| 52 | 1.27760077447776e-19 | 2.55520154895553e-19 | 1 |
| 53 | 7.99468666600866e-19 | 1.59893733320173e-18 | 1 |
| 54 | 1.39816679161453e-18 | 2.79633358322907e-18 | 1 |
| 55 | 2.90173885318732e-16 | 5.80347770637465e-16 | 1 |
| 56 | 1.04121122947437e-14 | 2.08242245894873e-14 | 0.99999999999999 |
| 57 | 9.4640665569416e-13 | 1.89281331138832e-12 | 0.999999999999054 |
| 58 | 1.09682883884725e-11 | 2.19365767769449e-11 | 0.999999999989032 |
| 59 | 4.69579445067328e-10 | 9.39158890134655e-10 | 0.99999999953042 |
| 60 | 1.13161093849961e-08 | 2.26322187699922e-08 | 0.99999998868389 |
| 61 | 2.77285856367914e-08 | 5.54571712735827e-08 | 0.999999972271414 |
| 62 | 2.26406705423354e-08 | 4.52813410846707e-08 | 0.99999997735933 |
| 63 | 1.21880737176311e-08 | 2.43761474352623e-08 | 0.999999987811926 |
| 64 | 1.37858336903612e-08 | 2.75716673807225e-08 | 0.999999986214166 |
| 65 | 7.21431811323126e-09 | 1.44286362264625e-08 | 0.999999992785682 |
| 66 | 3.17745026574134e-09 | 6.35490053148268e-09 | 0.99999999682255 |
| 67 | 1.68933674434146e-09 | 3.37867348868292e-09 | 0.999999998310663 |
| 68 | 6.37325753804294e-10 | 1.27465150760859e-09 | 0.999999999362674 |
| 69 | 2.32560519979753e-10 | 4.65121039959507e-10 | 0.99999999976744 |
| 70 | 8.95938626215323e-11 | 1.79187725243065e-10 | 0.999999999910406 |
| 71 | 5.0587852257088e-11 | 1.01175704514176e-10 | 0.999999999949412 |
| 72 | 2.21416893512473e-11 | 4.42833787024946e-11 | 0.999999999977858 |
| 73 | 1.21613418981504e-11 | 2.43226837963008e-11 | 0.999999999987839 |
| 74 | 4.66958290754625e-12 | 9.33916581509249e-12 | 0.99999999999533 |
| 75 | 3.4537656171977e-12 | 6.9075312343954e-12 | 0.999999999996546 |
| 76 | 6.83441154359367e-12 | 1.36688230871873e-11 | 0.999999999993166 |
| 77 | 1.82677310352169e-10 | 3.65354620704339e-10 | 0.999999999817323 |
| 78 | 1.46059632304135e-09 | 2.92119264608271e-09 | 0.999999998539404 |
| 79 | 1.29112628497995e-08 | 2.5822525699599e-08 | 0.999999987088737 |
| 80 | 1.06272791761511e-07 | 2.12545583523021e-07 | 0.999999893727208 |
| 81 | 1.72609360441871e-06 | 3.45218720883741e-06 | 0.999998273906396 |
| 82 | 2.42790336043982e-05 | 4.85580672087964e-05 | 0.999975720966396 |
| 83 | 0.000110652464152783 | 0.000221304928305566 | 0.999889347535847 |
| 84 | 0.00248714269368214 | 0.00497428538736428 | 0.997512857306318 |
| 85 | 0.00169965019642761 | 0.00339930039285522 | 0.998300349803572 |
| 86 | 0.00171519202309680 | 0.00343038404619360 | 0.998284807976903 |
| 87 | 0.00173255273999131 | 0.00346510547998263 | 0.998267447260009 |
| 88 | 0.0144975911513671 | 0.0289951823027342 | 0.985502408848633 |
| 89 | 0.0524945685855242 | 0.104989137171048 | 0.947505431414476 |
| 90 | 0.112909635390278 | 0.225819270780557 | 0.887090364609722 |
| 91 | 0.157451085487678 | 0.314902170975357 | 0.842548914512322 |
| 92 | 0.962871427458067 | 0.0742571450838665 | 0.0371285725419332 |
| 93 | 0.984890666247923 | 0.0302186675041535 | 0.0151093337520767 |
| 94 | 0.974204228246163 | 0.0515915435076731 | 0.0257957717538365 |
| 95 | 0.953848227983957 | 0.0923035440320864 | 0.0461517720160432 |
| 96 | 0.920666898298993 | 0.158666203402014 | 0.079333101701007 |
| 97 | 0.82417167467208 | 0.35165665065584 | 0.17582832532792 |
| Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
| Description | # significant tests | % significant tests | OK/NOK |
| 1% type I error level | 68 | 0.871794871794872 | NOK |
| 5% type I error level | 70 | 0.897435897435897 | NOK |
| 10% type I error level | 73 | 0.935897435897436 | NOK |
