| Multiple Linear Regression - Estimated Regression Equation |
| APPLE[t] = -135.571134934426 -37.2940667049397REV.GROWTH[t] + 82.8825039379301IPHONE[t] + 94.3952766372327IPAD[t] -4.24484261111306e-07VOLUME[t] + 5.42889693785601MICROSOFT[t] + 1.55788173789371t + 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) | -135.571134934426 | 10.076876 | -13.4537 | 0 | 0 |
| REV.GROWTH | -37.2940667049397 | 5.857235 | -6.3672 | 0 | 0 |
| IPHONE | 82.8825039379301 | 9.656002 | 8.5835 | 0 | 0 |
| IPAD | 94.3952766372327 | 11.31239 | 8.3444 | 0 | 0 |
| VOLUME | -4.24484261111306e-07 | 0 | -3.2062 | 0.001761 | 0.000881 |
| MICROSOFT | 5.42889693785601 | 0.432367 | 12.5562 | 0 | 0 |
| t | 1.55788173789371 | 0.060936 | 25.5659 | 0 | 0 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.984175061462104 |
| R-squared | 0.968600551603937 |
| Adjusted R-squared | 0.966887854418697 |
| F-TEST (value) | 565.541042486335 |
| F-TEST (DF numerator) | 6 |
| F-TEST (DF denominator) | 110 |
| p-value | 0 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 13.825177056523 |
| Sum Squared Residuals | 21024.9072708631 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 10.81 | -1.84667793521922 | 12.6566779352192 |
| 2 | 9.12 | -0.380059443336055 | 9.50005944333605 |
| 3 | 11.03 | -9.86698634304 | 20.89698634304 |
| 4 | 12.74 | 16.2114341468063 | -3.47143414680626 |
| 5 | 9.98 | 24.3000695622086 | -14.3200695622086 |
| 6 | 11.62 | 33.7296190769224 | -22.1096190769224 |
| 7 | 9.4 | 21.1581910253492 | -11.7581910253492 |
| 8 | 9.27 | 5.7402738692424 | 3.52972613075760 |
| 9 | 7.76 | -7.89544288708221 | 15.6554428870822 |
| 10 | 8.78 | -12.3879604007992 | 21.1679604007992 |
| 11 | 10.65 | 3.41940384523453 | 7.23059615476547 |
| 12 | 10.95 | 9.85665153285738 | 1.09334846714262 |
| 13 | 12.36 | 15.0199185293727 | -2.65991852937268 |
| 14 | 10.85 | 4.77310541613089 | 6.0768945838691 |
| 15 | 11.84 | 13.1241879786353 | -1.28418797863533 |
| 16 | 12.14 | -0.528463175381171 | 12.6684631753812 |
| 17 | 11.65 | -1.65263148682238 | 13.3026314868224 |
| 18 | 8.86 | 5.72186494219079 | 3.13813505780921 |
| 19 | 7.63 | -7.31173305339089 | 14.9417330533909 |
| 20 | 7.38 | -1.2399986580129 | 8.6199986580129 |
| 21 | 7.25 | -11.8080215792552 | 19.0580215792552 |
| 22 | 8.03 | 7.75290909348487 | 0.277090906515132 |
| 23 | 7.75 | 19.4403792240644 | -11.6903792240644 |
| 24 | 7.16 | 8.15147642419003 | -0.991476424190035 |
| 25 | 7.18 | 2.41381543655743 | 4.76618456344257 |
| 26 | 7.51 | 5.36127858115479 | 2.14872141884521 |
| 27 | 7.07 | 9.49002887100075 | -2.42002887100075 |
| 28 | 7.11 | 10.5869777475078 | -3.47697774750779 |
| 29 | 8.98 | 5.8271607948525 | 3.1528392051475 |
| 30 | 9.53 | 15.3986677860078 | -5.86866778600776 |
| 31 | 10.54 | 17.0365377482095 | -6.49653774820952 |
| 32 | 11.31 | 19.5870103737277 | -8.27701037372772 |
| 33 | 10.36 | 25.9698675883417 | -15.6098675883417 |
| 34 | 11.44 | 13.7406253192194 | -2.30062531921941 |
| 35 | 10.45 | 14.1530836966933 | -3.70308369669331 |
| 36 | 10.69 | 23.1368037282697 | -12.4468037282697 |
| 37 | 11.28 | 26.2303743534748 | -14.9503743534748 |
| 38 | 11.96 | 24.6963341445026 | -12.7363341445026 |
| 39 | 13.52 | 15.6315737801965 | -2.1115737801965 |
| 40 | 12.89 | 23.2421146563013 | -10.3521146563013 |
| 41 | 14.03 | 27.8867405032036 | -13.8567405032036 |
| 42 | 16.27 | 37.5734376135357 | -21.3034376135357 |
| 43 | 16.17 | 35.3512234844053 | -19.1812234844053 |
| 44 | 17.25 | 33.4727940591584 | -16.2227940591584 |
| 45 | 19.38 | 36.4844624980662 | -17.1044624980662 |
| 46 | 26.2 | 19.316496152646 | 6.883503847354 |
| 47 | 33.53 | 28.1604220454955 | 5.36957795450454 |
| 48 | 32.2 | 31.43421705302 | 0.76578294698 |
| 49 | 38.45 | 22.7703877754533 | 15.6796122245467 |
| 50 | 44.86 | 22.3523243917955 | 22.5076756082045 |
| 51 | 41.67 | 26.1068036791131 | 15.5631963208869 |
| 52 | 36.06 | 27.5082911167019 | 8.55170888329805 |
| 53 | 39.76 | 36.7871109091136 | 2.97288909088642 |
| 54 | 36.81 | 35.1023260685505 | 1.70767393144954 |
| 55 | 42.65 | 47.2903618455625 | -4.64036184556252 |
| 56 | 46.89 | 59.5843350884178 | -12.6943350884178 |
| 57 | 53.61 | 50.1631043131735 | 3.44689568682654 |
| 58 | 57.59 | 43.6521952787594 | 13.9378047212406 |
| 59 | 67.82 | 59.4101634304881 | 8.4098365695119 |
| 60 | 71.89 | 53.6301329708807 | 18.2598670291193 |
| 61 | 75.51 | 69.0358564045775 | 6.47414359542254 |
| 62 | 68.49 | 65.9725305167898 | 2.51746948321016 |
| 63 | 62.72 | 69.370004997769 | -6.65000499776898 |
| 64 | 70.39 | 58.7171974560556 | 11.6728025439444 |
| 65 | 59.77 | 58.2384828088655 | 1.53151719113453 |
| 66 | 57.27 | 61.8225710069717 | -4.55257100697166 |
| 67 | 67.96 | 63.3791261722705 | 4.58087382772945 |
| 68 | 67.85 | 75.3805654033086 | -7.53056540330859 |
| 69 | 76.98 | 83.6188873036833 | -6.63888730368326 |
| 70 | 81.08 | 98.3356890132253 | -17.2556890132253 |
| 71 | 91.66 | 103.283791827428 | -11.6237918274284 |
| 72 | 84.84 | 104.389944081900 | -19.5499440818997 |
| 73 | 85.73 | 104.268435379488 | -18.5384353794884 |
| 74 | 84.61 | 102.388313691616 | -17.778313691616 |
| 75 | 92.91 | 102.725535484698 | -9.81553548469795 |
| 76 | 99.8 | 113.225786787996 | -13.4257867879957 |
| 77 | 121.19 | 116.882370561592 | 4.30762943840814 |
| 78 | 122.04 | 130.111062870974 | -8.07106287097412 |
| 79 | 131.76 | 132.467610116814 | -0.707610116813713 |
| 80 | 138.48 | 135.187640930615 | 3.29235906938450 |
| 81 | 153.47 | 139.936448384227 | 13.5335516157732 |
| 82 | 189.95 | 184.638233836221 | 5.31176616377888 |
| 83 | 182.22 | 166.583013069025 | 15.6369869309755 |
| 84 | 198.08 | 184.622074743113 | 13.4579252568868 |
| 85 | 135.36 | 160.058171638852 | -24.6981716388521 |
| 86 | 125.02 | 141.143819410509 | -16.1238194105086 |
| 87 | 143.5 | 150.621058883214 | -7.12105888321359 |
| 88 | 173.95 | 147.501750927209 | 26.4482490727914 |
| 89 | 188.75 | 151.199183794940 | 37.5508162050602 |
| 90 | 167.44 | 147.884565957664 | 19.5554340423359 |
| 91 | 158.95 | 158.308455075103 | 0.64154492489666 |
| 92 | 169.53 | 172.613448181149 | -3.08344818114924 |
| 93 | 113.66 | 162.40727701238 | -48.7472770123799 |
| 94 | 107.59 | 104.063049811504 | 3.52695018849571 |
| 95 | 92.67 | 104.729954864742 | -12.0599548647424 |
| 96 | 85.35 | 107.006126630859 | -21.6561266308588 |
| 97 | 90.13 | 96.5042308956197 | -6.37423089561974 |
| 98 | 89.31 | 96.2510887168013 | -6.94108871680126 |
| 99 | 105.12 | 110.034459121488 | -4.91445912148766 |
| 100 | 125.83 | 130.397175013295 | -4.56717501329474 |
| 101 | 135.81 | 137.351886988535 | -1.54188698853532 |
| 102 | 142.43 | 152.537077115678 | -10.1070771156777 |
| 103 | 163.39 | 143.609541498539 | 19.7804585014609 |
| 104 | 168.21 | 153.557081288762 | 14.652918711238 |
| 105 | 185.35 | 159.279311080191 | 26.0706889198091 |
| 106 | 188.5 | 181.532071854196 | 6.96792814580446 |
| 107 | 199.91 | 195.390755871801 | 4.51924412819882 |
| 108 | 210.73 | 201.285451050902 | 9.44454894909804 |
| 109 | 192.06 | 193.188295120410 | -1.12829512041048 |
| 110 | 204.62 | 202.152421621502 | 2.46757837849789 |
| 111 | 235 | 207.729715548465 | 27.2702844515350 |
| 112 | 261.09 | 278.580727939982 | -17.4907279399820 |
| 113 | 256.88 | 250.440566821516 | 6.4394331784842 |
| 114 | 251.53 | 239.363406876082 | 12.1665931239181 |
| 115 | 257.25 | 263.808754455495 | -6.55875445549526 |
| 116 | 243.1 | 258.209884478188 | -15.1098844781881 |
| 117 | 283.75 | 263.106967017295 | 20.6430329827046 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 10 | 0.00183744251006878 | 0.00367488502013756 | 0.998162557489931 |
| 11 | 0.000221701776074290 | 0.000443403552148581 | 0.999778298223926 |
| 12 | 2.33451928969247e-05 | 4.66903857938493e-05 | 0.999976654807103 |
| 13 | 3.57336492022593e-06 | 7.14672984045185e-06 | 0.99999642663508 |
| 14 | 3.06394047470637e-07 | 6.12788094941273e-07 | 0.999999693605953 |
| 15 | 4.99561525194126e-08 | 9.99123050388253e-08 | 0.999999950043847 |
| 16 | 1.14323401640995e-08 | 2.2864680328199e-08 | 0.99999998856766 |
| 17 | 1.29516620423317e-09 | 2.59033240846633e-09 | 0.999999998704834 |
| 18 | 1.491772056436e-09 | 2.983544112872e-09 | 0.999999998508228 |
| 19 | 6.20292343774259e-10 | 1.24058468754852e-09 | 0.999999999379708 |
| 20 | 1.52498801236632e-10 | 3.04997602473264e-10 | 0.999999999847501 |
| 21 | 3.0768729007166e-11 | 6.1537458014332e-11 | 0.999999999969231 |
| 22 | 5.92714862149371e-12 | 1.18542972429874e-11 | 0.999999999994073 |
| 23 | 1.24953074855443e-12 | 2.49906149710886e-12 | 0.99999999999875 |
| 24 | 2.04536285972470e-13 | 4.09072571944941e-13 | 0.999999999999795 |
| 25 | 3.06688200595873e-14 | 6.13376401191747e-14 | 0.99999999999997 |
| 26 | 4.02178632379643e-15 | 8.04357264759286e-15 | 0.999999999999996 |
| 27 | 5.12363086958004e-16 | 1.02472617391601e-15 | 1 |
| 28 | 8.25869525370473e-17 | 1.65173905074095e-16 | 1 |
| 29 | 1.31391125362607e-17 | 2.62782250725215e-17 | 1 |
| 30 | 2.64437799253747e-18 | 5.28875598507493e-18 | 1 |
| 31 | 8.21112760528427e-19 | 1.64222552105685e-18 | 1 |
| 32 | 3.93703941330233e-19 | 7.87407882660466e-19 | 1 |
| 33 | 4.98655682266382e-20 | 9.97311364532763e-20 | 1 |
| 34 | 1.13171744512182e-20 | 2.26343489024365e-20 | 1 |
| 35 | 1.57490029718757e-21 | 3.14980059437513e-21 | 1 |
| 36 | 1.75390705503886e-22 | 3.50781411007772e-22 | 1 |
| 37 | 1.88841144413662e-23 | 3.77682288827324e-23 | 1 |
| 38 | 3.87563321155669e-24 | 7.75126642311337e-24 | 1 |
| 39 | 1.7293354905297e-24 | 3.4586709810594e-24 | 1 |
| 40 | 2.69867380319165e-25 | 5.3973476063833e-25 | 1 |
| 41 | 2.15078301058695e-25 | 4.30156602117390e-25 | 1 |
| 42 | 1.41470135371147e-25 | 2.82940270742293e-25 | 1 |
| 43 | 3.15113342762535e-26 | 6.3022668552507e-26 | 1 |
| 44 | 3.51971520483203e-26 | 7.03943040966405e-26 | 1 |
| 45 | 1.69748712789882e-25 | 3.39497425579764e-25 | 1 |
| 46 | 7.60230415310389e-25 | 1.52046083062078e-24 | 1 |
| 47 | 2.74856515629569e-23 | 5.49713031259138e-23 | 1 |
| 48 | 1.05799555590122e-22 | 2.11599111180244e-22 | 1 |
| 49 | 2.20560275968689e-23 | 4.41120551937378e-23 | 1 |
| 50 | 3.81051658080217e-21 | 7.62103316160435e-21 | 1 |
| 51 | 2.59551611897551e-17 | 5.19103223795103e-17 | 1 |
| 52 | 7.79378756131742e-18 | 1.55875751226348e-17 | 1 |
| 53 | 1.38105003906226e-16 | 2.76210007812453e-16 | 1 |
| 54 | 5.58918046771283e-16 | 1.11783609354257e-15 | 1 |
| 55 | 3.89120820240851e-14 | 7.78241640481702e-14 | 0.999999999999961 |
| 56 | 3.23708955538501e-12 | 6.47417911077001e-12 | 0.999999999996763 |
| 57 | 1.49382775109723e-10 | 2.98765550219446e-10 | 0.999999999850617 |
| 58 | 9.03685216239956e-10 | 1.80737043247991e-09 | 0.999999999096315 |
| 59 | 5.63542187985485e-08 | 1.12708437597097e-07 | 0.999999943645781 |
| 60 | 9.28718361348122e-06 | 1.85743672269624e-05 | 0.999990712816387 |
| 61 | 1.35288877163936e-05 | 2.70577754327873e-05 | 0.999986471112284 |
| 62 | 1.19435497790641e-05 | 2.38870995581281e-05 | 0.99998805645022 |
| 63 | 7.19605565097034e-06 | 1.43921113019407e-05 | 0.99999280394435 |
| 64 | 1.17923595068115e-05 | 2.3584719013623e-05 | 0.999988207640493 |
| 65 | 9.34631721159982e-06 | 1.86926344231996e-05 | 0.999990653682788 |
| 66 | 5.54126474165325e-06 | 1.10825294833065e-05 | 0.999994458735258 |
| 67 | 1.24272568588675e-05 | 2.48545137177350e-05 | 0.999987572743141 |
| 68 | 1.06868432795311e-05 | 2.13736865590622e-05 | 0.99998931315672 |
| 69 | 1.22541230389465e-05 | 2.4508246077893e-05 | 0.999987745876961 |
| 70 | 8.78298240488041e-06 | 1.75659648097608e-05 | 0.999991217017595 |
| 71 | 8.91214064254e-06 | 1.782428128508e-05 | 0.999991087859357 |
| 72 | 5.50865263933336e-06 | 1.10173052786667e-05 | 0.99999449134736 |
| 73 | 6.98837987428219e-06 | 1.39767597485644e-05 | 0.999993011620126 |
| 74 | 5.39700697586155e-06 | 1.07940139517231e-05 | 0.999994602993024 |
| 75 | 5.04801482752983e-06 | 1.00960296550597e-05 | 0.999994951985173 |
| 76 | 6.62599306604586e-06 | 1.32519861320917e-05 | 0.999993374006934 |
| 77 | 2.92018662947762e-05 | 5.84037325895524e-05 | 0.999970798133705 |
| 78 | 2.87037939978037e-05 | 5.74075879956074e-05 | 0.999971296206002 |
| 79 | 1.65305372166246e-05 | 3.30610744332492e-05 | 0.999983469462783 |
| 80 | 1.05129880064772e-05 | 2.10259760129543e-05 | 0.999989487011994 |
| 81 | 1.10570455164677e-05 | 2.21140910329355e-05 | 0.999988942954483 |
| 82 | 1.38435489755978e-05 | 2.76870979511957e-05 | 0.999986156451024 |
| 83 | 9.68483644631961e-06 | 1.93696728926392e-05 | 0.999990315163554 |
| 84 | 1.24526463326877e-05 | 2.49052926653753e-05 | 0.999987547353667 |
| 85 | 0.0013646328552896 | 0.0027292657105792 | 0.99863536714471 |
| 86 | 0.0030291421046581 | 0.0060582842093162 | 0.996970857895342 |
| 87 | 0.00271337754516137 | 0.00542675509032275 | 0.997286622454839 |
| 88 | 0.00597407406837167 | 0.0119481481367433 | 0.994025925931628 |
| 89 | 0.0566824672887657 | 0.113364934577531 | 0.943317532711234 |
| 90 | 0.114284051818924 | 0.228568103637848 | 0.885715948181076 |
| 91 | 0.232054378645432 | 0.464108757290863 | 0.767945621354568 |
| 92 | 0.868290833755197 | 0.263418332489606 | 0.131709166244803 |
| 93 | 0.96799608903622 | 0.0640078219275609 | 0.0320039109637805 |
| 94 | 0.964812783652517 | 0.070374432694965 | 0.0351872163474825 |
| 95 | 0.950786445848101 | 0.0984271083037974 | 0.0492135541518987 |
| 96 | 0.938005463879672 | 0.123989072240657 | 0.0619945361203283 |
| 97 | 0.904898228057825 | 0.190203543884351 | 0.0951017719421755 |
| 98 | 0.87326221647838 | 0.25347556704324 | 0.12673778352162 |
| 99 | 0.85068771586579 | 0.298624568268419 | 0.149312284134210 |
| 100 | 0.797050191324409 | 0.405899617351182 | 0.202949808675591 |
| 101 | 0.804009903576664 | 0.391980192846672 | 0.195990096423336 |
| 102 | 0.766350529209496 | 0.467298941581008 | 0.233649470790504 |
| 103 | 0.743422009420212 | 0.513155981159577 | 0.256577990579788 |
| 104 | 0.652044394741462 | 0.695911210517075 | 0.347955605258538 |
| 105 | 0.591396326010698 | 0.817207347978604 | 0.408603673989302 |
| 106 | 0.509771215925727 | 0.980457568148546 | 0.490228784074273 |
| 107 | 0.409437985865344 | 0.818875971730689 | 0.590562014134655 |
| Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
| Description | # significant tests | % significant tests | OK/NOK |
| 1% type I error level | 78 | 0.795918367346939 | NOK |
| 5% type I error level | 79 | 0.806122448979592 | NOK |
| 10% type I error level | 82 | 0.836734693877551 | NOK |
