| Multiple Linear Regression - Estimated Regression Equation |
| time[t] = + 12596.2715491371 + 628.18936080481shared[t] + 705.033283660071blogs[t] + 1246.1156014661reviews[t] -0.0405178790839649CWcharacters[t] + 1.53493060361547Cwseconds[t] + 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) | 12596.2715491371 | 7630.275459 | 1.6508 | 0.101048 | 0.050524 |
| shared | 628.18936080481 | 1369.971712 | 0.4585 | 0.647285 | 0.323642 |
| blogs | 705.033283660071 | 190.070996 | 3.7093 | 3e-04 | 0.00015 |
| reviews | 1246.1156014661 | 450.602532 | 2.7654 | 0.006463 | 0.003231 |
| CWcharacters | -0.0405178790839649 | 0.191724 | -0.2113 | 0.832938 | 0.416469 |
| Cwseconds | 1.53493060361547 | 0.182918 | 8.3914 | 0 | 0 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.891445464184305 |
| R-squared | 0.79467501561477 |
| Adjusted R-squared | 0.78723570458632 |
| F-TEST (value) | 106.82105003752 |
| F-TEST (DF numerator) | 5 |
| F-TEST (DF denominator) | 138 |
| p-value | 0 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 35641.6560390247 |
| Sum Squared Residuals | 175305215038.172 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 159261 | 106084.828418904 | 53176.1715810962 |
| 2 | 189672 | 205593.20852754 | -15921.2085275399 |
| 3 | 7215 | 15499.4957415749 | -8284.49574157492 |
| 4 | 129098 | 136868.428859962 | -7770.42885996223 |
| 5 | 230632 | 213526.749010695 | 17105.2509893052 |
| 6 | 515038 | 439099.502929993 | 75938.4970700072 |
| 7 | 180745 | 179159.363633477 | 1585.63636652258 |
| 8 | 185559 | 211866.093266756 | -26307.0932667561 |
| 9 | 154581 | 146653.991935995 | 7927.00806400542 |
| 10 | 298001 | 245882.782355949 | 52118.2176440513 |
| 11 | 121844 | 143408.530192624 | -21564.530192624 |
| 12 | 184039 | 219090.196841107 | -35051.1968411074 |
| 13 | 100324 | 119902.717565042 | -19578.7175650421 |
| 14 | 217742 | 199199.952829379 | 18542.0471706206 |
| 15 | 168265 | 146864.117102087 | 21400.8828979125 |
| 16 | 154647 | 154413.899996071 | 233.100003928596 |
| 17 | 142018 | 206603.825933241 | -64585.8259332412 |
| 18 | 79030 | 41705.5548061807 | 37324.4451938193 |
| 19 | 167047 | 179171.97643207 | -12124.9764320696 |
| 20 | 27997 | 61593.8692016377 | -33596.8692016377 |
| 21 | 73019 | 75133.3473441603 | -2114.34734416027 |
| 22 | 241082 | 265362.447791246 | -24280.4477912456 |
| 23 | 195820 | 96033.4024687835 | 99786.5975312165 |
| 24 | 142001 | 146635.384899626 | -4634.3848996264 |
| 25 | 145433 | 155006.288320843 | -9573.28832084275 |
| 26 | 183744 | 138418.564567337 | 45325.4354326634 |
| 27 | 202232 | 175031.380081868 | 27200.6199181319 |
| 28 | 199532 | 266735.283709493 | -67203.2837094925 |
| 29 | 354924 | 271083.682296754 | 83840.3177032461 |
| 30 | 192399 | 194693.936761746 | -2294.93676174552 |
| 31 | 182286 | 154697.196313508 | 27588.8036864918 |
| 32 | 181590 | 183509.566539163 | -1919.56653916319 |
| 33 | 133801 | 129846.748363034 | 3954.25163696601 |
| 34 | 233686 | 139176.253243317 | 94509.7467566833 |
| 35 | 219428 | 230805.062838719 | -11377.0628387191 |
| 36 | 0 | 12596.2715491372 | -12596.2715491372 |
| 37 | 223044 | 142778.632713085 | 80265.3672869152 |
| 38 | 100129 | 111077.320119248 | -10948.3201192476 |
| 39 | 136733 | 146589.835945681 | -9856.83594568139 |
| 40 | 249965 | 313077.777378089 | -63112.7773780885 |
| 41 | 242379 | 209675.119635742 | 32703.8803642577 |
| 42 | 145794 | 141319.588025528 | 4474.41197447243 |
| 43 | 96404 | 126635.74752937 | -30231.74752937 |
| 44 | 195891 | 174048.673008636 | 21842.3269913637 |
| 45 | 117156 | 142483.522627564 | -25327.5226275642 |
| 46 | 157787 | 151338.639796037 | 6448.36020396298 |
| 47 | 81293 | 130920.119158678 | -49627.1191586783 |
| 48 | 237435 | 170567.109275637 | 66867.8907243633 |
| 49 | 233155 | 214999.896829139 | 18155.1031708611 |
| 50 | 160344 | 162988.994378856 | -2644.99437885574 |
| 51 | 48188 | 70301.1937600542 | -22113.1937600542 |
| 52 | 161922 | 165361.585761567 | -3439.58576156725 |
| 53 | 307432 | 256146.070457506 | 51285.9295424944 |
| 54 | 235223 | 171681.512966648 | 63541.4870333524 |
| 55 | 195583 | 197041.173172537 | -1458.17317253744 |
| 56 | 146061 | 143646.060889412 | 2414.93911058827 |
| 57 | 208834 | 158472.537505684 | 50361.4624943157 |
| 58 | 93764 | 103827.313357816 | -10063.3133578163 |
| 59 | 151985 | 179252.194965681 | -27267.1949656812 |
| 60 | 190545 | 127894.129940377 | 62650.8700596233 |
| 61 | 148922 | 154654.769139028 | -5732.76913902812 |
| 62 | 132856 | 130510.212618686 | 2345.7873813137 |
| 63 | 129561 | 149381.109295861 | -19820.1092958613 |
| 64 | 112718 | 159349.879841673 | -46631.8798416728 |
| 65 | 160930 | 127298.509490532 | 33631.4905094676 |
| 66 | 99184 | 154180.064085273 | -54996.0640852734 |
| 67 | 192535 | 279264.200235584 | -86729.2002355842 |
| 68 | 138708 | 189549.259099163 | -50841.2590991629 |
| 69 | 114408 | 164346.426904888 | -49938.4269048883 |
| 70 | 31970 | 48422.3229027151 | -16452.3229027151 |
| 71 | 225558 | 165407.82236269 | 60150.1776373101 |
| 72 | 137011 | 127716.504507112 | 9294.49549288812 |
| 73 | 113612 | 158668.801962438 | -45056.8019624379 |
| 74 | 108641 | 96396.0221154304 | 12244.9778845696 |
| 75 | 162203 | 191829.460355803 | -29626.4603558028 |
| 76 | 100098 | 87520.752060844 | 12577.2479391561 |
| 77 | 174768 | 195867.752214714 | -21099.7522147135 |
| 78 | 158459 | 231016.411423704 | -72557.4114237037 |
| 79 | 80934 | 85666.2889508226 | -4732.28895082257 |
| 80 | 84971 | 118745.645674419 | -33774.6456744195 |
| 81 | 80545 | 135600.358942127 | -55055.3589421265 |
| 82 | 287191 | 170018.726176771 | 117172.273823229 |
| 83 | 62974 | 105296.753635454 | -42322.7536354542 |
| 84 | 134091 | 139422.270120662 | -5331.2701206619 |
| 85 | 75555 | 83047.162795553 | -7492.16279555299 |
| 86 | 162154 | 144129.791385036 | 18024.2086149641 |
| 87 | 226638 | 212641.14175808 | 13996.8582419195 |
| 88 | 115019 | 123223.283196727 | -8204.28319672714 |
| 89 | 108749 | 115847.354915272 | -7098.3549152719 |
| 90 | 155537 | 146539.69865274 | 8997.30134726031 |
| 91 | 153133 | 176852.658827991 | -23719.6588279913 |
| 92 | 165618 | 194749.348043468 | -29131.3480434679 |
| 93 | 151517 | 154940.178484419 | -3423.17848441886 |
| 94 | 133686 | 113349.03299575 | 20336.9670042504 |
| 95 | 61342 | 84386.1779736232 | -23044.1779736232 |
| 96 | 245196 | 230332.211084082 | 14863.7889159178 |
| 97 | 195576 | 201585.129756452 | -6009.12975645154 |
| 98 | 19349 | 37591.4762162751 | -18242.4762162751 |
| 99 | 225371 | 138528.030687483 | 86842.9693125174 |
| 100 | 152796 | 151440.821825621 | 1355.17817437862 |
| 101 | 59117 | 39685.9550398066 | 19431.0449601934 |
| 102 | 91762 | 122446.910122554 | -30684.9101225538 |
| 103 | 136769 | 125866.744521551 | 10902.2554784491 |
| 104 | 114798 | 113736.761771039 | 1061.23822896127 |
| 105 | 85338 | 90773.9513808633 | -5435.95138086334 |
| 106 | 27676 | 37302.2897639738 | -9626.2897639738 |
| 107 | 153535 | 192464.993127216 | -38929.9931272162 |
| 108 | 122417 | 74499.4222830614 | 47917.5777169386 |
| 109 | 0 | 12596.2715491372 | -12596.2715491372 |
| 110 | 91529 | 126510.148505845 | -34981.1485058453 |
| 111 | 107205 | 84930.2075989474 | 22274.7924010526 |
| 112 | 144664 | 154004.428358427 | -9340.42835842667 |
| 113 | 136540 | 139579.684872173 | -3039.68487217302 |
| 114 | 76656 | 104224.636960233 | -27568.636960233 |
| 115 | 3616 | 12596.2715491372 | -8980.27154913717 |
| 116 | 0 | 12596.2715491372 | -12596.2715491372 |
| 117 | 183065 | 162007.542401297 | 21057.4575987029 |
| 118 | 144677 | 196462.557748849 | -51785.557748849 |
| 119 | 159104 | 123289.612904188 | 35814.3870958116 |
| 120 | 113273 | 122130.173680782 | -8857.17368078221 |
| 121 | 43410 | 18684.8940123382 | 24725.1059876618 |
| 122 | 175774 | 193051.200288675 | -17277.2002886747 |
| 123 | 95401 | 103353.191599568 | -7952.19159956824 |
| 124 | 134837 | 137708.22319426 | -2871.22319425968 |
| 125 | 60493 | 38028.4249395303 | 22464.5750604697 |
| 126 | 19764 | 37771.2222110746 | -18007.2222110746 |
| 127 | 164062 | 153699.482519901 | 10362.5174800991 |
| 128 | 132696 | 116405.015416725 | 16290.9845832748 |
| 129 | 155367 | 142258.075968438 | 13108.9240315616 |
| 130 | 11796 | 15793.5360357294 | -3997.53603572943 |
| 131 | 10674 | 12596.2715491372 | -1922.27154913716 |
| 132 | 142261 | 135292.924010586 | 6968.07598941384 |
| 133 | 6836 | 13842.3871506033 | -7006.38715060328 |
| 134 | 162563 | 147262.536036978 | 15300.4639630218 |
| 135 | 5118 | 16121.4379674375 | -11003.4379674375 |
| 136 | 40248 | 32856.61304029 | 7391.38695970998 |
| 137 | 0 | 12596.2715491372 | -12596.2715491372 |
| 138 | 122641 | 111979.671667077 | 10661.3283329226 |
| 139 | 88837 | 130288.610695587 | -41451.6106955866 |
| 140 | 7131 | 13224.460909942 | -6093.46090994198 |
| 141 | 9056 | 19543.1127829079 | -10487.1127829079 |
| 142 | 76611 | 61569.342977424 | 15041.657022576 |
| 143 | 132697 | 157113.68299444 | -24416.6829944399 |
| 144 | 100681 | 118419.100211437 | -17738.1002114372 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 9 | 0.284892400272545 | 0.569784800545091 | 0.715107599727455 |
| 10 | 0.427942644734763 | 0.855885289469525 | 0.572057355265237 |
| 11 | 0.49952841783611 | 0.99905683567222 | 0.50047158216389 |
| 12 | 0.630280448130017 | 0.739439103739966 | 0.369719551869983 |
| 13 | 0.538609538176207 | 0.922780923647585 | 0.461390461823793 |
| 14 | 0.470960817625965 | 0.94192163525193 | 0.529039182374035 |
| 15 | 0.379533249993902 | 0.759066499987803 | 0.620466750006098 |
| 16 | 0.312286363538508 | 0.624572727077017 | 0.687713636461492 |
| 17 | 0.51899174989462 | 0.96201650021076 | 0.48100825010538 |
| 18 | 0.497060427498437 | 0.994120854996874 | 0.502939572501563 |
| 19 | 0.419210511036891 | 0.838421022073783 | 0.580789488963109 |
| 20 | 0.353467288799439 | 0.706934577598879 | 0.64653271120056 |
| 21 | 0.28328075432541 | 0.566561508650821 | 0.71671924567459 |
| 22 | 0.249160503754033 | 0.498321007508067 | 0.750839496245967 |
| 23 | 0.843261967796628 | 0.313476064406745 | 0.156738032203373 |
| 24 | 0.79721715504366 | 0.40556568991268 | 0.20278284495634 |
| 25 | 0.753611196101134 | 0.492777607797732 | 0.246388803898866 |
| 26 | 0.783748866554157 | 0.432502266891687 | 0.216251133445843 |
| 27 | 0.755227509178513 | 0.489544981642973 | 0.244772490821487 |
| 28 | 0.847136806557542 | 0.305726386884917 | 0.152863193442458 |
| 29 | 0.900968457154822 | 0.198063085690356 | 0.0990315428451779 |
| 30 | 0.874907381298464 | 0.250185237403072 | 0.125092618701536 |
| 31 | 0.868230047675104 | 0.263539904649792 | 0.131769952324896 |
| 32 | 0.833761334815387 | 0.332477330369226 | 0.166238665184613 |
| 33 | 0.80241576140748 | 0.39516847718504 | 0.19758423859252 |
| 34 | 0.955613456443248 | 0.0887730871135031 | 0.0443865435567515 |
| 35 | 0.941628966333911 | 0.116742067332177 | 0.0583710336660886 |
| 36 | 0.926409899075523 | 0.147180201848954 | 0.073590100924477 |
| 37 | 0.971528107633522 | 0.0569437847329559 | 0.028471892366478 |
| 38 | 0.962194746458062 | 0.075610507083876 | 0.037805253541938 |
| 39 | 0.954489863170014 | 0.0910202736599724 | 0.0455101368299862 |
| 40 | 0.978274531941396 | 0.043450936117208 | 0.021725468058604 |
| 41 | 0.975393118578682 | 0.0492137628426353 | 0.0246068814213176 |
| 42 | 0.96658549228171 | 0.0668290154365796 | 0.0334145077182898 |
| 43 | 0.969294291206579 | 0.0614114175868428 | 0.0307057087934214 |
| 44 | 0.96217908649945 | 0.0756418270010995 | 0.0378209135005498 |
| 45 | 0.960031583742377 | 0.0799368325152454 | 0.0399684162576227 |
| 46 | 0.947894573801887 | 0.104210852396227 | 0.0521054261981133 |
| 47 | 0.953459104502803 | 0.093081790994394 | 0.046540895497197 |
| 48 | 0.973849984579637 | 0.052300030840725 | 0.0261500154203625 |
| 49 | 0.968370465762743 | 0.0632590684745132 | 0.0316295342372566 |
| 50 | 0.958453779731325 | 0.0830924405373504 | 0.0415462202686752 |
| 51 | 0.950836408001768 | 0.0983271839964646 | 0.0491635919982323 |
| 52 | 0.946293383383653 | 0.107413233232693 | 0.0537066166163467 |
| 53 | 0.964796265083747 | 0.0704074698325066 | 0.0352037349162533 |
| 54 | 0.983394615792362 | 0.0332107684152753 | 0.0166053842076377 |
| 55 | 0.977515106664006 | 0.0449697866719875 | 0.0224848933359937 |
| 56 | 0.970390748418348 | 0.0592185031633045 | 0.0296092515816523 |
| 57 | 0.979673007045016 | 0.040653985909967 | 0.0203269929549835 |
| 58 | 0.973665939320663 | 0.052668121358673 | 0.0263340606793365 |
| 59 | 0.970298172273217 | 0.059403655453565 | 0.0297018277267825 |
| 60 | 0.981730532829734 | 0.0365389343405313 | 0.0182694671702656 |
| 61 | 0.975645262721819 | 0.0487094745563623 | 0.0243547372781811 |
| 62 | 0.9681623727288 | 0.063675254542401 | 0.0318376272712005 |
| 63 | 0.96265242882493 | 0.0746951423501397 | 0.0373475711750699 |
| 64 | 0.967778139534891 | 0.0644437209302176 | 0.0322218604651088 |
| 65 | 0.967568310047356 | 0.0648633799052885 | 0.0324316899526443 |
| 66 | 0.9791829767109 | 0.0416340465781983 | 0.0208170232890992 |
| 67 | 0.996449482585631 | 0.00710103482873722 | 0.00355051741436861 |
| 68 | 0.997491218175962 | 0.00501756364807603 | 0.00250878182403802 |
| 69 | 0.99835741258844 | 0.003285174823121 | 0.0016425874115605 |
| 70 | 0.997894390038358 | 0.00421121992328367 | 0.00210560996164184 |
| 71 | 0.99908001923644 | 0.00183996152712208 | 0.000919980763561041 |
| 72 | 0.998762163682696 | 0.00247567263460872 | 0.00123783631730436 |
| 73 | 0.999022582785031 | 0.00195483442993749 | 0.000977417214968745 |
| 74 | 0.998631015888054 | 0.00273796822389275 | 0.00136898411194638 |
| 75 | 0.998399590912955 | 0.00320081817409035 | 0.00160040908704518 |
| 76 | 0.99772327536156 | 0.00455344927687818 | 0.00227672463843909 |
| 77 | 0.996866303005586 | 0.0062673939888281 | 0.00313369699441405 |
| 78 | 0.999042601994736 | 0.00191479601052778 | 0.000957398005263888 |
| 79 | 0.998566128431344 | 0.00286774313731236 | 0.00143387156865618 |
| 80 | 0.998644386896605 | 0.00271122620679096 | 0.00135561310339548 |
| 81 | 0.999278679822978 | 0.00144264035404297 | 0.000721320177021483 |
| 82 | 0.999999214609375 | 1.57078125046379e-06 | 7.85390625231895e-07 |
| 83 | 0.999999737435097 | 5.2512980701824e-07 | 2.6256490350912e-07 |
| 84 | 0.999999482866864 | 1.03426627168867e-06 | 5.17133135844334e-07 |
| 85 | 0.999999052943367 | 1.89411326625033e-06 | 9.47056633125166e-07 |
| 86 | 0.999998484011314 | 3.03197737238208e-06 | 1.51598868619104e-06 |
| 87 | 0.99999765959056 | 4.68081888004436e-06 | 2.34040944002218e-06 |
| 88 | 0.99999563136656 | 8.73726687800672e-06 | 4.36863343900336e-06 |
| 89 | 0.99999367373265 | 1.26525346977139e-05 | 6.32626734885693e-06 |
| 90 | 0.99999013539002 | 1.9729219960154e-05 | 9.86460998007701e-06 |
| 91 | 0.999990878801912 | 1.82423961763339e-05 | 9.12119808816697e-06 |
| 92 | 0.999987030479292 | 2.59390414167908e-05 | 1.29695207083954e-05 |
| 93 | 0.999976096836395 | 4.78063272102767e-05 | 2.39031636051383e-05 |
| 94 | 0.999974329551067 | 5.13408978653302e-05 | 2.56704489326651e-05 |
| 95 | 0.999962338149705 | 7.53237005893938e-05 | 3.76618502946969e-05 |
| 96 | 0.999946119077713 | 0.000107761844574248 | 5.38809222871238e-05 |
| 97 | 0.999933673051343 | 0.000132653897313735 | 6.63269486568673e-05 |
| 98 | 0.999892073136753 | 0.00021585372649456 | 0.00010792686324728 |
| 99 | 0.999999419247766 | 1.16150446768097e-06 | 5.80752233840484e-07 |
| 100 | 0.999998746780577 | 2.50643884618553e-06 | 1.25321942309277e-06 |
| 101 | 0.999998634670421 | 2.73065915711261e-06 | 1.3653295785563e-06 |
| 102 | 0.99999827034266 | 3.45931467842547e-06 | 1.72965733921274e-06 |
| 103 | 0.999997693733247 | 4.61253350701822e-06 | 2.30626675350911e-06 |
| 104 | 0.999995164402296 | 9.67119540812735e-06 | 4.83559770406368e-06 |
| 105 | 0.999990004775157 | 1.99904496850907e-05 | 9.99522484254535e-06 |
| 106 | 0.99998877329761 | 2.2453404779997e-05 | 1.12267023899985e-05 |
| 107 | 0.99998470498971 | 3.05900205778636e-05 | 1.52950102889318e-05 |
| 108 | 0.999991505301482 | 1.698939703632e-05 | 8.49469851816001e-06 |
| 109 | 0.99998364369613 | 3.2712607741134e-05 | 1.6356303870567e-05 |
| 110 | 0.99997836951648 | 4.32609670379942e-05 | 2.16304835189971e-05 |
| 111 | 0.999973910458352 | 5.2179083295266e-05 | 2.6089541647633e-05 |
| 112 | 0.999944854506355 | 0.000110290987290391 | 5.51454936451955e-05 |
| 113 | 0.999899128414983 | 0.000201743170033356 | 0.000100871585016678 |
| 114 | 0.999873232261147 | 0.000253535477706884 | 0.000126767738853442 |
| 115 | 0.999749834481262 | 0.000500331037476424 | 0.000250165518738212 |
| 116 | 0.999547741327872 | 0.000904517344255627 | 0.000452258672127814 |
| 117 | 0.999714761490347 | 0.000570477019306176 | 0.000285238509653088 |
| 118 | 0.999913575127646 | 0.000172849744707556 | 8.6424872353778e-05 |
| 119 | 0.999960803756 | 7.8392488001995e-05 | 3.91962440009975e-05 |
| 120 | 0.999907981153177 | 0.000184037693645399 | 9.20188468226996e-05 |
| 121 | 0.999921329615614 | 0.000157340768773032 | 7.86703843865159e-05 |
| 122 | 0.999837389215658 | 0.000325221568683249 | 0.000162610784341625 |
| 123 | 0.999611254032232 | 0.000777491935536685 | 0.000388745967768343 |
| 124 | 0.999997249017652 | 5.50196469510008e-06 | 2.75098234755004e-06 |
| 125 | 0.999991088429462 | 1.78231410767693e-05 | 8.91157053838467e-06 |
| 126 | 0.999982961494959 | 3.40770100824266e-05 | 1.70385050412133e-05 |
| 127 | 0.9999817699465 | 3.64601070012402e-05 | 1.82300535006201e-05 |
| 128 | 0.9999622604754 | 7.54790492008822e-05 | 3.77395246004411e-05 |
| 129 | 0.999862379004115 | 0.000275241991769916 | 0.000137620995884958 |
| 130 | 0.999489526347796 | 0.00102094730440894 | 0.000510473652204469 |
| 131 | 0.9984223896992 | 0.00315522060159788 | 0.00157761030079894 |
| 132 | 0.999986387232512 | 2.72255349750583e-05 | 1.36127674875291e-05 |
| 133 | 0.999902359981583 | 0.000195280036834326 | 9.76400184171631e-05 |
| 134 | 0.999629118420945 | 0.00074176315810983 | 0.000370881579054915 |
| 135 | 0.996851727116913 | 0.00629654576617485 | 0.00314827288308742 |
| Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
| Description | # significant tests | % significant tests | OK/NOK |
| 1% type I error level | 69 | 0.543307086614173 | NOK |
| 5% type I error level | 77 | 0.606299212598425 | NOK |
| 10% type I error level | 98 | 0.771653543307087 | NOK |
