| Multiple Linear Regression - Estimated Regression Equation |
| APPLE[t] = -127.447605621375 -31.2727304377682REV.GROWTH[t] + 63.5049184403004IPHONE[t] + 105.207064497490IPAD[t] -3.07859516993699e-07VOLUME[t] + 6.18588427968051MICROSOFT[t] -0.254623501864903CONS.CONF[t] + 1.43045995687761t + 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) | -127.447605621375 | 11.410672 | -11.1692 | 0 | 0 |
| REV.GROWTH | -31.2727304377682 | 6.348574 | -4.9259 | 3e-06 | 2e-06 |
| IPHONE | 63.5049184403004 | 12.18411 | 5.2121 | 1e-06 | 0 |
| IPAD | 105.207064497490 | 12.285426 | 8.5636 | 0 | 0 |
| VOLUME | -3.07859516993699e-07 | 0 | -2.0578 | 0.041991 | 0.020995 |
| MICROSOFT | 6.18588427968051 | 0.59431 | 10.4085 | 0 | 0 |
| CONS.CONF | -0.254623501864903 | 0.101085 | -2.5189 | 0.013223 | 0.006611 |
| t | 1.43045995687761 | 0.085539 | 16.7229 | 0 | 0 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.982398930477056 |
| R-squared | 0.965107658602464 |
| Adjusted R-squared | 0.96286686603565 |
| F-TEST (value) | 430.699241373587 |
| F-TEST (DF numerator) | 7 |
| F-TEST (DF denominator) | 109 |
| p-value | 0 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 14.6405651902178 |
| Sum Squared Residuals | 23363.730250703 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 10.81 | -3.52890799709945 | 14.3389079970995 |
| 2 | 9.12 | -2.37587868159683 | 11.4958786815968 |
| 3 | 11.03 | -14.7838284836713 | 25.8138284836713 |
| 4 | 12.74 | 17.6437538075877 | -4.9037538075877 |
| 5 | 9.98 | 23.5361700648615 | -13.5561700648615 |
| 6 | 11.62 | 33.4029313768821 | -21.7829313768821 |
| 7 | 9.4 | 19.2480998684049 | -9.8480998684049 |
| 8 | 9.27 | 0.722720458997381 | 8.54727954100262 |
| 9 | 7.76 | -9.82154601818074 | 17.5815460181807 |
| 10 | 8.78 | -6.01938261112203 | 14.7993826111220 |
| 11 | 10.65 | 11.3114112451014 | -0.661411245101382 |
| 12 | 10.95 | 15.6321331960253 | -4.68213319602528 |
| 13 | 12.36 | 17.9465498433878 | -5.5865498433878 |
| 14 | 10.85 | 6.6941598770169 | 4.1558401229831 |
| 15 | 11.84 | 10.8301890139226 | 1.00981098607745 |
| 16 | 12.14 | -5.15283070868816 | 17.2928307086882 |
| 17 | 11.65 | -7.34007995615426 | 18.9900799561543 |
| 18 | 8.86 | 2.74519727835277 | 6.11480272164722 |
| 19 | 7.63 | -10.3008758903133 | 17.9308758903133 |
| 20 | 7.38 | -3.86895080909082 | 11.2489508090908 |
| 21 | 7.25 | -15.8410614651273 | 23.0910614651273 |
| 22 | 8.03 | 10.6875903640670 | -2.65759036406703 |
| 23 | 7.75 | 21.8926442087696 | -14.1426442087696 |
| 24 | 7.16 | 9.7012945910789 | -2.54129459107890 |
| 25 | 7.18 | 2.85635482396577 | 4.32364517603423 |
| 26 | 7.51 | 8.94928716407582 | -1.43928716407582 |
| 27 | 7.07 | 14.0319077973756 | -6.9619077973756 |
| 28 | 7.11 | 12.1886840265273 | -5.0786840265273 |
| 29 | 8.98 | 6.6437961713321 | 2.3362038286679 |
| 30 | 9.53 | 15.7779379773051 | -6.24793797730507 |
| 31 | 10.54 | 19.8397332947637 | -9.2997332947637 |
| 32 | 11.31 | 20.9957139825741 | -9.68571398257413 |
| 33 | 10.36 | 29.4382477747903 | -19.0782477747903 |
| 34 | 11.44 | 16.2156299359501 | -4.7756299359501 |
| 35 | 10.45 | 13.2784400100617 | -2.82844001006168 |
| 36 | 10.69 | 23.3112816912528 | -12.6212816912528 |
| 37 | 11.28 | 25.4657791781929 | -14.1857791781930 |
| 38 | 11.96 | 24.6191535860914 | -12.6591535860914 |
| 39 | 13.52 | 15.4448586505344 | -1.92485865053439 |
| 40 | 12.89 | 22.2606125802211 | -9.37061258022111 |
| 41 | 14.03 | 26.0841719071735 | -12.0541719071735 |
| 42 | 16.27 | 35.1675202936904 | -18.8975202936904 |
| 43 | 16.17 | 32.7013162963232 | -16.5313162963232 |
| 44 | 17.25 | 31.4207303475529 | -14.1707303475529 |
| 45 | 19.38 | 35.0443972499164 | -15.6643972499164 |
| 46 | 26.2 | 22.8848860454895 | 3.31511395451047 |
| 47 | 33.53 | 33.1612244447935 | 0.368775555206526 |
| 48 | 32.2 | 33.0845786737927 | -0.884578673792687 |
| 49 | 38.45 | 25.7643971001291 | 12.6856028998709 |
| 50 | 44.86 | 23.8263941330568 | 21.0336058669432 |
| 51 | 41.67 | 25.1827287537761 | 16.4872712462239 |
| 52 | 36.06 | 30.0091705588186 | 6.05082944118137 |
| 53 | 39.76 | 36.7826357675184 | 2.97736423248156 |
| 54 | 36.81 | 33.1157651827117 | 3.69423481728828 |
| 55 | 42.65 | 45.2637148966472 | -2.61371489664724 |
| 56 | 46.89 | 57.7743583255711 | -10.8843583255711 |
| 57 | 53.61 | 52.4525593932198 | 1.15744060678020 |
| 58 | 57.59 | 48.2019671476843 | 9.3880328523157 |
| 59 | 67.82 | 60.8228179415662 | 6.99718205843374 |
| 60 | 71.89 | 52.3830217578948 | 19.5069782421052 |
| 61 | 75.51 | 68.4886969517907 | 7.0213030482093 |
| 62 | 68.49 | 65.160640794458 | 3.32935920554197 |
| 63 | 62.72 | 67.4001322308557 | -4.68013223085572 |
| 64 | 70.39 | 53.5266426166795 | 16.8633573833205 |
| 65 | 59.77 | 51.8555183802917 | 7.9144816197083 |
| 66 | 57.27 | 55.8500004459759 | 1.41999955402413 |
| 67 | 67.96 | 58.2115104043816 | 9.74848959561838 |
| 68 | 67.85 | 72.5453326358316 | -4.69533263583160 |
| 69 | 76.98 | 80.7872560193313 | -3.80725601933125 |
| 70 | 81.08 | 95.1196855081471 | -14.0396855081471 |
| 71 | 91.66 | 100.509494642391 | -8.8494946423906 |
| 72 | 84.84 | 101.472422097319 | -16.6324220973192 |
| 73 | 85.73 | 117.321247612044 | -31.5912476120443 |
| 74 | 84.61 | 110.607139940152 | -25.9971399401515 |
| 75 | 92.91 | 111.286586907601 | -18.3765869076007 |
| 76 | 99.8 | 127.600608604569 | -27.800608604569 |
| 77 | 121.19 | 131.769344260362 | -10.5793442603624 |
| 78 | 122.04 | 123.505275038774 | -1.46527503877421 |
| 79 | 131.76 | 122.745569565414 | 9.0144304345864 |
| 80 | 138.48 | 126.285730425114 | 12.1942695748859 |
| 81 | 153.47 | 133.135127577878 | 20.3348724221221 |
| 82 | 189.95 | 182.338880576993 | 7.61111942300712 |
| 83 | 182.22 | 164.908258181345 | 17.3117418186554 |
| 84 | 198.08 | 181.806106516856 | 16.2738934831442 |
| 85 | 135.36 | 158.600532567402 | -23.2405325674016 |
| 86 | 125.02 | 136.913798436335 | -11.8937984363352 |
| 87 | 143.5 | 149.279735341508 | -5.77973534150823 |
| 88 | 173.95 | 148.651987313169 | 25.2980126868310 |
| 89 | 188.75 | 152.730378957901 | 36.0196210420988 |
| 90 | 167.44 | 150.627090531793 | 16.8129094682072 |
| 91 | 158.95 | 153.985976269473 | 4.964023730527 |
| 92 | 169.53 | 166.533537595656 | 2.99646240434364 |
| 93 | 113.66 | 157.411974154532 | -43.751974154532 |
| 94 | 107.59 | 112.346326078964 | -4.75632607896362 |
| 95 | 92.67 | 107.350128115044 | -14.6801281150444 |
| 96 | 85.35 | 109.241734896144 | -23.8917348961441 |
| 97 | 90.13 | 105.699584728280 | -15.5695847282803 |
| 98 | 89.31 | 98.5717858659368 | -9.26178586593684 |
| 99 | 105.12 | 113.273341476923 | -8.15334147692337 |
| 100 | 125.83 | 128.771285845827 | -2.94128584582696 |
| 101 | 135.81 | 132.215022215934 | 3.59497778406606 |
| 102 | 142.43 | 151.202637790153 | -8.77263779015328 |
| 103 | 163.39 | 145.161943758117 | 18.2280562418828 |
| 104 | 168.21 | 153.634935091603 | 14.5750649083966 |
| 105 | 185.35 | 160.704186121382 | 24.6458138786181 |
| 106 | 188.5 | 182.531107940535 | 5.96889205946534 |
| 107 | 199.91 | 196.378935616161 | 3.53106438383950 |
| 108 | 210.73 | 202.551797220621 | 8.17820277937923 |
| 109 | 192.06 | 191.044373971335 | 1.01562602866539 |
| 110 | 204.62 | 201.789564394526 | 2.83043560547424 |
| 111 | 235 | 206.004460059641 | 28.9955399403592 |
| 112 | 261.09 | 281.497277100175 | -20.4072771001755 |
| 113 | 256.88 | 249.885062486601 | 6.99493751339883 |
| 114 | 251.53 | 238.084736740704 | 13.4452632592964 |
| 115 | 257.25 | 265.108249436415 | -7.85824943641501 |
| 116 | 243.1 | 255.863746085701 | -12.7637460857006 |
| 117 | 283.75 | 263.158280425202 | 20.5917195747977 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 11 | 0.00172421722144613 | 0.00344843444289225 | 0.998275782778554 |
| 12 | 0.000159014550034780 | 0.000318029100069559 | 0.999840985449965 |
| 13 | 2.19781136117100e-05 | 4.39562272234199e-05 | 0.999978021886388 |
| 14 | 1.80747137492613e-06 | 3.61494274985226e-06 | 0.999998192528625 |
| 15 | 1.48095854095045e-07 | 2.96191708190091e-07 | 0.999999851904146 |
| 16 | 1.62403183391325e-08 | 3.24806366782649e-08 | 0.999999983759682 |
| 17 | 1.3352375949971e-09 | 2.6704751899942e-09 | 0.999999998664762 |
| 18 | 3.13486898889623e-09 | 6.26973797779245e-09 | 0.99999999686513 |
| 19 | 9.65149427177646e-10 | 1.93029885435529e-09 | 0.99999999903485 |
| 20 | 1.37234468248636e-10 | 2.74468936497273e-10 | 0.999999999862766 |
| 21 | 2.50893382217956e-11 | 5.01786764435912e-11 | 0.99999999997491 |
| 22 | 2.80766423512544e-12 | 5.61532847025089e-12 | 0.999999999997192 |
| 23 | 2.83281012592729e-13 | 5.66562025185459e-13 | 0.999999999999717 |
| 24 | 2.69761858333651e-14 | 5.39523716667302e-14 | 0.999999999999973 |
| 25 | 3.28126023589668e-15 | 6.56252047179336e-15 | 0.999999999999997 |
| 26 | 1.31474501457829e-15 | 2.62949002915658e-15 | 0.999999999999999 |
| 27 | 1.9454741347776e-16 | 3.8909482695552e-16 | 1 |
| 28 | 3.56554857552281e-17 | 7.13109715104562e-17 | 1 |
| 29 | 4.54223351745534e-18 | 9.08446703491068e-18 | 1 |
| 30 | 6.63375737407224e-19 | 1.32675147481445e-18 | 1 |
| 31 | 1.78327103826010e-19 | 3.56654207652019e-19 | 1 |
| 32 | 5.16697198107829e-20 | 1.03339439621566e-19 | 1 |
| 33 | 5.53281867035672e-21 | 1.10656373407134e-20 | 1 |
| 34 | 6.29894793638778e-22 | 1.25978958727756e-21 | 1 |
| 35 | 8.28006689157946e-23 | 1.65601337831589e-22 | 1 |
| 36 | 9.13322426216869e-24 | 1.82664485243374e-23 | 1 |
| 37 | 9.39441983003671e-25 | 1.87888396600734e-24 | 1 |
| 38 | 1.15967496837846e-25 | 2.31934993675693e-25 | 1 |
| 39 | 4.01945609348265e-26 | 8.0389121869653e-26 | 1 |
| 40 | 4.23126343457939e-27 | 8.46252686915878e-27 | 1 |
| 41 | 1.36030972393050e-27 | 2.72061944786100e-27 | 1 |
| 42 | 3.3214290653706e-28 | 6.6428581307412e-28 | 1 |
| 43 | 3.36045420458172e-29 | 6.72090840916343e-29 | 1 |
| 44 | 2.08562635539501e-29 | 4.17125271079001e-29 | 1 |
| 45 | 1.44923066830914e-28 | 2.89846133661828e-28 | 1 |
| 46 | 5.68034692032284e-27 | 1.13606938406457e-26 | 1 |
| 47 | 2.7182989075141e-24 | 5.4365978150282e-24 | 1 |
| 48 | 8.20410853305554e-24 | 1.64082170661111e-23 | 1 |
| 49 | 1.40402239460520e-24 | 2.80804478921041e-24 | 1 |
| 50 | 2.92331202474042e-22 | 5.84662404948083e-22 | 1 |
| 51 | 7.24764891310876e-19 | 1.44952978262175e-18 | 1 |
| 52 | 1.74916767799813e-19 | 3.49833535599627e-19 | 1 |
| 53 | 1.67359343272545e-18 | 3.3471868654509e-18 | 1 |
| 54 | 2.12142414982258e-18 | 4.24284829964517e-18 | 1 |
| 55 | 1.73938793648101e-16 | 3.47877587296201e-16 | 1 |
| 56 | 2.31020939931033e-14 | 4.62041879862065e-14 | 0.999999999999977 |
| 57 | 1.05605933130825e-11 | 2.1121186626165e-11 | 0.99999999998944 |
| 58 | 1.22265760983376e-10 | 2.44531521966752e-10 | 0.999999999877734 |
| 59 | 9.81743092417652e-09 | 1.96348618483530e-08 | 0.99999999018257 |
| 60 | 4.13254266885094e-07 | 8.26508533770188e-07 | 0.999999586745733 |
| 61 | 4.45090412790688e-07 | 8.90180825581376e-07 | 0.999999554909587 |
| 62 | 2.56446266192424e-07 | 5.12892532384848e-07 | 0.999999743553734 |
| 63 | 1.23683676775800e-07 | 2.47367353551601e-07 | 0.999999876316323 |
| 64 | 1.85246051944528e-07 | 3.70492103889057e-07 | 0.999999814753948 |
| 65 | 1.61049310624433e-07 | 3.22098621248867e-07 | 0.99999983895069 |
| 66 | 1.00732571483350e-07 | 2.01465142966699e-07 | 0.999999899267428 |
| 67 | 1.36442823570598e-07 | 2.72885647141197e-07 | 0.999999863557176 |
| 68 | 8.00211787586437e-08 | 1.60042357517287e-07 | 0.999999919978821 |
| 69 | 5.78413163239539e-08 | 1.15682632647908e-07 | 0.999999942158684 |
| 70 | 3.56849524634906e-08 | 7.13699049269812e-08 | 0.999999964315048 |
| 71 | 3.8648562224383e-08 | 7.7297124448766e-08 | 0.999999961351438 |
| 72 | 1.73534869044673e-08 | 3.47069738089345e-08 | 0.999999982646513 |
| 73 | 2.52776722879697e-08 | 5.05553445759394e-08 | 0.999999974722328 |
| 74 | 5.04973047241453e-08 | 1.00994609448291e-07 | 0.999999949502695 |
| 75 | 9.67122352617275e-08 | 1.93424470523455e-07 | 0.999999903287765 |
| 76 | 1.33861910882730e-06 | 2.67723821765460e-06 | 0.999998661380891 |
| 77 | 1.57740988663506e-05 | 3.15481977327011e-05 | 0.999984225901134 |
| 78 | 2.46213946203428e-05 | 4.92427892406855e-05 | 0.99997537860538 |
| 79 | 2.4582303951525e-05 | 4.916460790305e-05 | 0.999975417696048 |
| 80 | 3.40899336086989e-05 | 6.81798672173979e-05 | 0.999965910066391 |
| 81 | 0.000127239228766631 | 0.000254478457533263 | 0.999872760771233 |
| 82 | 0.000490047126749211 | 0.000980094253498421 | 0.99950995287325 |
| 83 | 0.000538176018742943 | 0.00107635203748589 | 0.999461823981257 |
| 84 | 0.00110638083506556 | 0.00221276167013111 | 0.998893619164934 |
| 85 | 0.0102738434999139 | 0.0205476869998278 | 0.989726156500086 |
| 86 | 0.0131379923817859 | 0.0262759847635718 | 0.986862007618214 |
| 87 | 0.0108092467227036 | 0.0216184934454073 | 0.989190753277296 |
| 88 | 0.0226841812674819 | 0.0453683625349638 | 0.977315818732518 |
| 89 | 0.122861266769115 | 0.245722533538229 | 0.877138733230885 |
| 90 | 0.198969279508304 | 0.397938559016608 | 0.801030720491696 |
| 91 | 0.335282160719634 | 0.670564321439268 | 0.664717839280366 |
| 92 | 0.91991594501348 | 0.160168109973038 | 0.0800840549865192 |
| 93 | 0.973629244576231 | 0.0527415108475374 | 0.0263707554237687 |
| 94 | 0.97249616939097 | 0.0550076612180592 | 0.0275038306090296 |
| 95 | 0.958866891065904 | 0.0822662178681917 | 0.0411331089340959 |
| 96 | 0.950376940360434 | 0.0992461192791326 | 0.0496230596395663 |
| 97 | 0.92586406548765 | 0.148271869024699 | 0.0741359345123494 |
| 98 | 0.888347990958069 | 0.223304018083862 | 0.111652009041931 |
| 99 | 0.852041150810986 | 0.295917698378029 | 0.147958849189014 |
| 100 | 0.794687609788068 | 0.410624780423864 | 0.205312390211932 |
| 101 | 0.80640443493608 | 0.38719113012784 | 0.19359556506392 |
| 102 | 0.765948155527825 | 0.46810368894435 | 0.234051844472175 |
| 103 | 0.712724314586299 | 0.574551370827401 | 0.287275685413701 |
| 104 | 0.604754486864996 | 0.790491026270008 | 0.395245513135004 |
| 105 | 0.51448896180029 | 0.97102207639942 | 0.48551103819971 |
| 106 | 0.408821795702961 | 0.817643591405922 | 0.591178204297039 |
| Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
| Description | # significant tests | % significant tests | OK/NOK |
| 1% type I error level | 74 | 0.770833333333333 | NOK |
| 5% type I error level | 78 | 0.8125 | NOK |
| 10% type I error level | 82 | 0.854166666666667 | NOK |
