| Multiple Linear Regression - Estimated Regression Equation |
| APPLE[t] = -148.389379308089 -7.06273178125015e-07VOLUME[t] -18.2064906878529REV.GROWTH[t] + 6.83287017871576MICROSOFT[t] + 0.0189694137186282NASDAQ[t] + 82.2743167281702INFLATION[t] -0.611219563554504CONS.CONF[t] + 1.65811032276012t + 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) | -148.389379308089 | 17.626702 | -8.4184 | 0 | 0 |
| VOLUME | -7.06273178125015e-07 | 0 | -2.7448 | 0.007083 | 0.003542 |
| REV.GROWTH | -18.2064906878529 | 11.098972 | -1.6404 | 0.10381 | 0.051905 |
| MICROSOFT | 6.83287017871576 | 1.127517 | 6.0601 | 0 | 0 |
| NASDAQ | 0.0189694137186282 | 0.014423 | 1.3152 | 0.191204 | 0.095602 |
| INFLATION | 82.2743167281702 | 218.096923 | 0.3772 | 0.706731 | 0.353365 |
| CONS.CONF | -0.611219563554504 | 0.17777 | -3.4383 | 0.00083 | 0.000415 |
| t | 1.65811032276012 | 0.175297 | 9.4589 | 0 | 0 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.953327788951627 |
| R-squared | 0.908833873187398 |
| Adjusted R-squared | 0.902979167795763 |
| F-TEST (value) | 155.231358777832 |
| F-TEST (DF numerator) | 7 |
| F-TEST (DF denominator) | 109 |
| p-value | 0 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 23.6651650789451 |
| Sum Squared Residuals | 61044.364165296 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 10.81 | -7.25629719972853 | 18.0662971997285 |
| 2 | 9.12 | -11.8938172664146 | 21.0138172664146 |
| 3 | 11.03 | -35.9471560679178 | 46.9771560679178 |
| 4 | 12.74 | 8.00592163519933 | 4.73407836480067 |
| 5 | 9.98 | 15.6435116393184 | -5.66351163931843 |
| 6 | 11.62 | 25.9664908898376 | -14.3464908898376 |
| 7 | 9.4 | 7.30583886604361 | 2.09416113395639 |
| 8 | 9.27 | -14.0289816713552 | 23.2989816713552 |
| 9 | 7.76 | -27.9641625344846 | 35.7241625344846 |
| 10 | 8.78 | -6.28813727547428 | 15.0681372754743 |
| 11 | 10.65 | 18.348086752952 | -7.698086752952 |
| 12 | 10.95 | 20.5019083917910 | -9.55190839179096 |
| 13 | 12.36 | 13.7159467430930 | -1.35594674309297 |
| 14 | 10.85 | -1.66783320853261 | 12.5178332085326 |
| 15 | 11.84 | 2.39855802678801 | 9.441441973212 |
| 16 | 12.14 | -18.9773771404354 | 31.1173771404354 |
| 17 | 11.65 | -23.4477382787103 | 35.0977382787103 |
| 18 | 8.86 | -15.9944636090714 | 24.8544636090714 |
| 19 | 7.63 | -28.338082547479 | 35.968082547479 |
| 20 | 7.38 | -18.3397337339018 | 25.7197337339018 |
| 21 | 7.25 | -34.6075664130422 | 41.8575664130422 |
| 22 | 8.03 | 3.76377701645388 | 4.26622298354612 |
| 23 | 7.75 | 18.3074055892636 | -10.5574055892636 |
| 24 | 7.16 | 3.84585997289421 | 3.31414002710579 |
| 25 | 7.18 | -5.50795310910591 | 12.6879531091059 |
| 26 | 7.51 | 7.55899679398066 | -0.0489967939806604 |
| 27 | 7.07 | 14.7729373320439 | -7.70293733204385 |
| 28 | 7.11 | 7.11171336524198 | -0.00171336524197807 |
| 29 | 8.98 | 0.727710762624938 | 8.25228923737506 |
| 30 | 9.53 | 14.5055971361330 | -4.97559713613304 |
| 31 | 10.54 | 25.7610561328307 | -15.2210561328307 |
| 32 | 11.31 | 27.4719510025171 | -16.1619510025171 |
| 33 | 10.36 | 37.4505056793357 | -27.0905056793357 |
| 34 | 11.44 | 26.1257305101077 | -14.6857305101077 |
| 35 | 10.45 | 20.3567994669585 | -9.90679946695851 |
| 36 | 10.69 | 32.8196379052649 | -22.1296379052649 |
| 37 | 11.28 | 31.8784521117184 | -20.5984521117184 |
| 38 | 11.96 | 34.33606389021 | -22.37606389021 |
| 39 | 13.52 | 20.5235594591247 | -7.00355945912474 |
| 40 | 12.89 | 26.8274749188411 | -13.9374749188411 |
| 41 | 14.03 | 35.2727695470326 | -21.2427695470326 |
| 42 | 16.27 | 41.7302900552444 | -25.4602900552444 |
| 43 | 16.17 | 35.10920895656 | -18.93920895656 |
| 44 | 17.25 | 36.0721675869396 | -18.8221675869396 |
| 45 | 19.38 | 41.7793624298572 | -22.3993624298572 |
| 46 | 26.2 | 32.2492387747191 | -6.04923877471913 |
| 47 | 33.53 | 45.3859719600091 | -11.8559719600091 |
| 48 | 32.2 | 45.1794136375662 | -12.9794136375662 |
| 49 | 38.45 | 25.0629517745891 | 13.3870482254109 |
| 50 | 44.86 | 25.7593296484485 | 19.1006703515515 |
| 51 | 41.67 | 33.0273529483209 | 8.6426470516791 |
| 52 | 36.06 | 36.4939573251818 | -0.433957325181782 |
| 53 | 39.76 | 48.6278629707337 | -8.8678629707337 |
| 54 | 36.81 | 44.4741283007009 | -7.66412830070093 |
| 55 | 42.65 | 58.8100399117758 | -16.1600399117758 |
| 56 | 46.89 | 73.2396907361254 | -26.3496907361254 |
| 57 | 53.61 | 71.7884825284871 | -18.1784825284871 |
| 58 | 57.59 | 64.2220932111743 | -6.63209321117433 |
| 59 | 67.82 | 78.7661913964846 | -10.9461913964846 |
| 60 | 71.89 | 67.3788372262097 | 4.51116277379034 |
| 61 | 75.51 | 75.2996189284124 | 0.210381071587573 |
| 62 | 68.49 | 73.388425385918 | -4.89842538591805 |
| 63 | 62.72 | 75.4018417627668 | -12.6818417627668 |
| 64 | 70.39 | 56.8285475247992 | 13.5614524752008 |
| 65 | 59.77 | 58.8596137559758 | 0.910386244024246 |
| 66 | 57.27 | 61.9524316798376 | -4.68243167983759 |
| 67 | 67.96 | 62.8315910583938 | 5.12840894160617 |
| 68 | 67.85 | 83.9814792821416 | -16.1314792821416 |
| 69 | 76.98 | 89.8955146736437 | -12.9155146736437 |
| 70 | 81.08 | 109.265356797849 | -28.1853567978494 |
| 71 | 91.66 | 116.701207254884 | -25.0412072548836 |
| 72 | 84.84 | 113.857358290331 | -29.0173582903314 |
| 73 | 85.73 | 109.96614092045 | -24.2361409204501 |
| 74 | 84.61 | 109.945971681826 | -25.3359716818258 |
| 75 | 92.91 | 112.423071766595 | -19.5130717665951 |
| 76 | 99.8 | 130.308730431090 | -30.5087304310903 |
| 77 | 121.19 | 133.981578404424 | -12.7915784044244 |
| 78 | 122.04 | 121.849847856193 | 0.190152143807101 |
| 79 | 131.76 | 111.721525241619 | 20.0384747583807 |
| 80 | 138.48 | 120.123245557877 | 18.3567544421226 |
| 81 | 153.47 | 131.945434721764 | 21.5245652782355 |
| 82 | 189.95 | 187.238258055067 | 2.71174194493264 |
| 83 | 182.22 | 164.040710945616 | 18.1792890543843 |
| 84 | 198.08 | 186.919658987854 | 11.1603410121462 |
| 85 | 135.36 | 143.895211762662 | -8.5352117626616 |
| 86 | 125.02 | 127.024258859856 | -2.00425885985605 |
| 87 | 143.5 | 145.916186263863 | -2.41618626386300 |
| 88 | 173.95 | 158.356273936138 | 15.593726063862 |
| 89 | 188.75 | 169.170903623261 | 19.579096376739 |
| 90 | 167.44 | 164.906415959316 | 2.53358404068357 |
| 91 | 158.95 | 149.027997297698 | 9.92200270230243 |
| 92 | 169.53 | 164.99220641348 | 4.53779358651994 |
| 93 | 113.66 | 140.975753105341 | -27.3157531053406 |
| 94 | 107.59 | 114.694156140423 | -7.10415614042257 |
| 95 | 92.67 | 109.629811992367 | -16.9598119923669 |
| 96 | 85.35 | 117.941860679225 | -32.5918606792251 |
| 97 | 90.13 | 123.718469444614 | -33.5884694446144 |
| 98 | 89.31 | 109.429071953966 | -20.1190719539663 |
| 99 | 105.12 | 128.092141566345 | -22.9721415663454 |
| 100 | 125.83 | 137.798060082971 | -11.9680600829715 |
| 101 | 135.81 | 138.888140749212 | -3.07814074921229 |
| 102 | 142.43 | 161.471995142760 | -19.0419951427598 |
| 103 | 163.39 | 170.969958455698 | -7.57995845569842 |
| 104 | 168.21 | 180.631328480647 | -12.4213284806473 |
| 105 | 185.35 | 189.909342094546 | -4.55934209454584 |
| 106 | 188.5 | 199.505779171235 | -11.0057791712348 |
| 107 | 199.91 | 220.124438930834 | -20.2144389308344 |
| 108 | 210.73 | 227.941368013672 | -17.2113680136724 |
| 109 | 192.06 | 198.723587232262 | -6.66358723226224 |
| 110 | 204.62 | 218.857212908644 | -14.2372129086437 |
| 111 | 235 | 225.424100221957 | 9.57589977804273 |
| 112 | 261.09 | 229.312975872687 | 31.7770241273128 |
| 113 | 256.88 | 184.458348804666 | 72.4216511953336 |
| 114 | 251.53 | 172.698121670036 | 78.8318783299642 |
| 115 | 257.25 | 197.816228826709 | 59.4337711732909 |
| 116 | 243.1 | 188.297365141005 | 54.802634858995 |
| 117 | 283.75 | 200.922235375498 | 82.8277646245023 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 11 | 0.00027663772149865 | 0.0005532754429973 | 0.999723362278501 |
| 12 | 1.32118051307657e-05 | 2.64236102615314e-05 | 0.99998678819487 |
| 13 | 6.18289109599182e-07 | 1.23657821919836e-06 | 0.99999938171089 |
| 14 | 2.52697611101983e-08 | 5.05395222203965e-08 | 0.99999997473024 |
| 15 | 2.62517295006229e-09 | 5.25034590012458e-09 | 0.999999997374827 |
| 16 | 3.52460288704446e-10 | 7.04920577408892e-10 | 0.99999999964754 |
| 17 | 1.90491888485377e-11 | 3.80983776970755e-11 | 0.99999999998095 |
| 18 | 1.64813992186741e-11 | 3.29627984373482e-11 | 0.999999999983519 |
| 19 | 1.57505323327944e-12 | 3.15010646655888e-12 | 0.999999999998425 |
| 20 | 1.13852461647358e-13 | 2.27704923294717e-13 | 0.999999999999886 |
| 21 | 1.22924062596919e-14 | 2.45848125193837e-14 | 0.999999999999988 |
| 22 | 1.62993357055265e-15 | 3.2598671411053e-15 | 0.999999999999998 |
| 23 | 9.85205552349464e-17 | 1.97041110469893e-16 | 1 |
| 24 | 8.05964884453112e-18 | 1.61192976890622e-17 | 1 |
| 25 | 1.19283679518757e-18 | 2.38567359037513e-18 | 1 |
| 26 | 3.06554929894651e-19 | 6.13109859789302e-19 | 1 |
| 27 | 3.65319242510013e-20 | 7.30638485020025e-20 | 1 |
| 28 | 7.62891516151882e-21 | 1.52578303230376e-20 | 1 |
| 29 | 1.98339526256844e-21 | 3.96679052513689e-21 | 1 |
| 30 | 5.45257125979069e-22 | 1.09051425195814e-21 | 1 |
| 31 | 9.93543838435353e-23 | 1.98708767687071e-22 | 1 |
| 32 | 1.81163750547319e-23 | 3.62327501094637e-23 | 1 |
| 33 | 2.36978147368201e-24 | 4.73956294736403e-24 | 1 |
| 34 | 1.95322666949359e-25 | 3.90645333898717e-25 | 1 |
| 35 | 2.72452494956233e-26 | 5.44904989912465e-26 | 1 |
| 36 | 2.55197001591057e-27 | 5.10394003182115e-27 | 1 |
| 37 | 1.87001595046548e-28 | 3.74003190093096e-28 | 1 |
| 38 | 1.26037464609739e-29 | 2.52074929219479e-29 | 1 |
| 39 | 7.98055063650405e-30 | 1.59611012730081e-29 | 1 |
| 40 | 3.58711932288152e-30 | 7.17423864576304e-30 | 1 |
| 41 | 5.95626010672981e-30 | 1.19125202134596e-29 | 1 |
| 42 | 9.45641009499601e-30 | 1.89128201899920e-29 | 1 |
| 43 | 4.52361170611147e-30 | 9.04722341222295e-30 | 1 |
| 44 | 2.12069982473014e-29 | 4.24139964946028e-29 | 1 |
| 45 | 1.00046488107864e-27 | 2.00092976215728e-27 | 1 |
| 46 | 1.68171575568683e-26 | 3.36343151137367e-26 | 1 |
| 47 | 3.26126345211141e-24 | 6.52252690422283e-24 | 1 |
| 48 | 5.5963568993283e-24 | 1.11927137986566e-23 | 1 |
| 49 | 1.42366175256984e-24 | 2.84732350513969e-24 | 1 |
| 50 | 9.2074053761228e-22 | 1.84148107522456e-21 | 1 |
| 51 | 1.66390484630104e-18 | 3.32780969260208e-18 | 1 |
| 52 | 7.71090430554334e-19 | 1.54218086110867e-18 | 1 |
| 53 | 8.61408178715721e-18 | 1.72281635743144e-17 | 1 |
| 54 | 1.13945183337120e-17 | 2.27890366674241e-17 | 1 |
| 55 | 1.58869958305457e-15 | 3.17739916610915e-15 | 0.999999999999998 |
| 56 | 8.12692986791222e-14 | 1.62538597358244e-13 | 0.999999999999919 |
| 57 | 1.09244669772712e-11 | 2.18489339545423e-11 | 0.999999999989076 |
| 58 | 1.75361428704096e-10 | 3.50722857408192e-10 | 0.999999999824638 |
| 59 | 6.80901079946783e-08 | 1.36180215989357e-07 | 0.999999931909892 |
| 60 | 8.1482859241526e-06 | 1.62965718483052e-05 | 0.999991851714076 |
| 61 | 4.95780565604735e-05 | 9.9156113120947e-05 | 0.99995042194344 |
| 62 | 8.15463841357615e-05 | 0.000163092768271523 | 0.999918453615864 |
| 63 | 5.13341323143487e-05 | 0.000102668264628697 | 0.999948665867686 |
| 64 | 5.16580006943093e-05 | 0.000103316001388619 | 0.999948341999306 |
| 65 | 3.92578576286463e-05 | 7.85157152572926e-05 | 0.999960742142371 |
| 66 | 2.67171750013388e-05 | 5.34343500026776e-05 | 0.999973282824999 |
| 67 | 0.000133574397831221 | 0.000267148795662442 | 0.999866425602169 |
| 68 | 0.000259886032146504 | 0.000519772064293007 | 0.999740113967853 |
| 69 | 0.000588593631742839 | 0.00117718726348568 | 0.999411406368257 |
| 70 | 0.000702568829928276 | 0.00140513765985655 | 0.999297431170072 |
| 71 | 0.00109786777604698 | 0.00219573555209396 | 0.998902132223953 |
| 72 | 0.000772207890773714 | 0.00154441578154743 | 0.999227792109226 |
| 73 | 0.000870301131224275 | 0.00174060226244855 | 0.999129698868776 |
| 74 | 0.000548902296640388 | 0.00109780459328078 | 0.99945109770336 |
| 75 | 0.000492466571749745 | 0.00098493314349949 | 0.99950753342825 |
| 76 | 0.000592931765124049 | 0.00118586353024810 | 0.999407068234876 |
| 77 | 0.00215017485955428 | 0.00430034971910855 | 0.997849825140446 |
| 78 | 0.00666031708653628 | 0.0133206341730726 | 0.993339682913464 |
| 79 | 0.0187664262382322 | 0.0375328524764643 | 0.981233573761768 |
| 80 | 0.0678631639292491 | 0.135726327858498 | 0.93213683607075 |
| 81 | 0.369416524229525 | 0.73883304845905 | 0.630583475770475 |
| 82 | 0.59206434717558 | 0.81587130564884 | 0.40793565282442 |
| 83 | 0.669134932680944 | 0.661730134638112 | 0.330865067319056 |
| 84 | 0.973241352869706 | 0.0535172942605871 | 0.0267586471302936 |
| 85 | 0.969529782712866 | 0.0609404345742687 | 0.0304702172871344 |
| 86 | 0.96612510056239 | 0.067749798875218 | 0.033874899437609 |
| 87 | 0.959062738516025 | 0.0818745229679498 | 0.0409372614839749 |
| 88 | 0.967913954566471 | 0.0641720908670581 | 0.0320860454335290 |
| 89 | 0.972522940552008 | 0.0549541188959833 | 0.0274770594479916 |
| 90 | 0.986905380380195 | 0.0261892392396093 | 0.0130946196198046 |
| 91 | 0.982182236930125 | 0.0356355261397502 | 0.0178177630698751 |
| 92 | 0.997710690231105 | 0.00457861953778968 | 0.00228930976889484 |
| 93 | 0.996545440135187 | 0.00690911972962623 | 0.00345455986481312 |
| 94 | 0.995731214324004 | 0.00853757135199298 | 0.00426878567599649 |
| 95 | 0.994266267702411 | 0.0114674645951771 | 0.00573373229758854 |
| 96 | 0.991721645529233 | 0.0165567089415344 | 0.00827835447076718 |
| 97 | 0.984440351583452 | 0.0311192968330952 | 0.0155596484165476 |
| 98 | 0.973677681059196 | 0.0526446378816076 | 0.0263223189408038 |
| 99 | 0.96386822456361 | 0.072263550872781 | 0.0361317754363905 |
| 100 | 0.958327434381192 | 0.0833451312376168 | 0.0416725656188084 |
| 101 | 0.934119733111594 | 0.131760533776811 | 0.0658802668884057 |
| 102 | 0.884963201976872 | 0.230073596046256 | 0.115036798023128 |
| 103 | 0.824710689210805 | 0.35057862157839 | 0.175289310789195 |
| 104 | 0.729268926311728 | 0.541462147376544 | 0.270731073688272 |
| 105 | 0.87212375223441 | 0.255752495531179 | 0.127876247765589 |
| 106 | 0.971231455859265 | 0.0575370882814706 | 0.0287685441407353 |
| Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
| Description | # significant tests | % significant tests | OK/NOK |
| 1% type I error level | 70 | 0.729166666666667 | NOK |
| 5% type I error level | 77 | 0.802083333333333 | NOK |
| 10% type I error level | 87 | 0.90625 | NOK |
