| Multiple Linear Regression - Estimated Regression Equation |
| time[t] = + 2157.90726732853 + 767.839567658183logins[t] + 1071.55386082128bloggedcomputations[t] + 1176.79467718521reviewedcompendiums[t] + 0.389289788168592compendiumcharacters[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) | 2157.90726732853 | 8164.47634 | 0.2643 | 0.791937 | 0.395968 |
| logins | 767.839567658183 | 119.437879 | 6.4288 | 0 | 0 |
| bloggedcomputations | 1071.55386082128 | 195.769413 | 5.4736 | 0 | 0 |
| reviewedcompendiums | 1176.79467718521 | 482.515663 | 2.4389 | 0.015994 | 0.007997 |
| compendiumcharacters | 0.389289788168592 | 0.186035 | 2.0926 | 0.038207 | 0.019103 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.870757004737581 |
| R-squared | 0.758217761299564 |
| Adjusted R-squared | 0.751259999034803 |
| F-TEST (value) | 108.974370271278 |
| F-TEST (DF numerator) | 4 |
| F-TEST (DF denominator) | 139 |
| p-value | 0 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 38089.2875375281 |
| Sum Squared Residuals | 201660341691.192 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 158258 | 151079.333812532 | 7178.66618746751 |
| 2 | 186930 | 139344.437077399 | 47585.5629226013 |
| 3 | 7215 | 16532.9788537397 | -9317.97885373969 |
| 4 | 129098 | 170734.637794057 | -41636.6377940567 |
| 5 | 230587 | 243989.564889364 | -13402.5648893643 |
| 6 | 508313 | 440116.469868079 | 68196.5301319207 |
| 7 | 180745 | 151617.829181134 | 29127.170818866 |
| 8 | 185559 | 183070.354232017 | 2488.64576798277 |
| 9 | 154581 | 140358.415152141 | 14222.5848478591 |
| 10 | 290658 | 199995.554102206 | 90662.4458977936 |
| 11 | 121844 | 160964.950279642 | -39120.9502796424 |
| 12 | 184039 | 192483.222891355 | -8444.22289135491 |
| 13 | 100324 | 160783.641883574 | -60459.6418835738 |
| 14 | 209427 | 222063.584987314 | -12636.584987314 |
| 15 | 167592 | 137228.771221374 | 30363.2287786262 |
| 16 | 154593 | 174970.824569164 | -20377.8245691639 |
| 17 | 142018 | 201521.438905733 | -59503.4389057329 |
| 18 | 77855 | 75724.3754919574 | 2130.62450804262 |
| 19 | 167047 | 205465.395694137 | -38418.3956941375 |
| 20 | 27997 | 76427.8532013248 | -48430.8532013248 |
| 21 | 70824 | 88879.567972782 | -18055.567972782 |
| 22 | 241082 | 252145.252272063 | -11063.2522720631 |
| 23 | 195820 | 143308.577221568 | 52511.4227784322 |
| 24 | 141899 | 159242.928136699 | -17343.9281366989 |
| 25 | 145433 | 159808.888560871 | -14375.8885608715 |
| 26 | 180241 | 115226.402019133 | 65014.5979808669 |
| 27 | 202232 | 242583.578993027 | -40351.5789930267 |
| 28 | 190230 | 211926.815884804 | -21696.8158848042 |
| 29 | 354924 | 228800.108959087 | 126123.891040913 |
| 30 | 192399 | 130033.659113262 | 62365.3408867379 |
| 31 | 182286 | 147770.522552693 | 34515.4774473073 |
| 32 | 181590 | 138990.971816426 | 42599.0281835745 |
| 33 | 133801 | 188623.058522797 | -54822.0585227966 |
| 34 | 233686 | 230074.756815623 | 3611.24318437741 |
| 35 | 219428 | 154190.204980914 | 65237.7950190857 |
| 36 | 0 | 2925.74683498669 | -2925.74683498669 |
| 37 | 223044 | 155368.956224738 | 67675.0437752618 |
| 38 | 100129 | 114024.519201963 | -13895.519201963 |
| 39 | 136733 | 138778.340547318 | -2045.34054731789 |
| 40 | 249965 | 216296.306295175 | 33668.6937048252 |
| 41 | 242379 | 214385.149768955 | 27993.8502310454 |
| 42 | 145794 | 144283.908263564 | 1510.09173643634 |
| 43 | 96404 | 112596.20457326 | -16192.2045732604 |
| 44 | 195891 | 183540.817476129 | 12350.1825238706 |
| 45 | 115335 | 152722.943576719 | -37387.9435767193 |
| 46 | 157787 | 158718.623765815 | -931.62376581478 |
| 47 | 81293 | 101316.514583708 | -20023.5145837078 |
| 48 | 224049 | 197063.891359778 | 26985.1086402221 |
| 49 | 223789 | 188469.582091662 | 35319.417908338 |
| 50 | 160344 | 166331.474191723 | -5987.47419172348 |
| 51 | 48188 | 71104.613996103 | -22916.613996103 |
| 52 | 152206 | 183256.251039522 | -31050.2510395218 |
| 53 | 294283 | 195255.395860464 | 99027.6041395363 |
| 54 | 235223 | 171268.795617902 | 63954.2043820976 |
| 55 | 195583 | 169382.07153607 | 26200.92846393 |
| 56 | 145942 | 108424.626807335 | 37517.3731926648 |
| 57 | 208834 | 155345.907494733 | 53488.0925052672 |
| 58 | 93764 | 88818.8039343937 | 4945.1960656063 |
| 59 | 151985 | 165374.95884951 | -13389.9588495105 |
| 60 | 190545 | 180003.78321458 | 10541.2167854201 |
| 61 | 148922 | 150473.166073853 | -1551.1660738532 |
| 62 | 132856 | 150678.424836467 | -17822.424836467 |
| 63 | 124234 | 142967.085732219 | -18733.0857322188 |
| 64 | 112718 | 127240.61026388 | -14522.6102638796 |
| 65 | 160930 | 96857.2918444143 | 64072.7081555857 |
| 66 | 99184 | 126197.055157805 | -27013.055157805 |
| 67 | 182022 | 200633.503425842 | -18611.5034258419 |
| 68 | 138708 | 192685.465239683 | -53977.4652396832 |
| 69 | 114408 | 147957.245570271 | -33549.245570271 |
| 70 | 31970 | 45364.2359566139 | -13394.2359566139 |
| 71 | 225558 | 178692.172190082 | 46865.8278099176 |
| 72 | 137011 | 133125.810856868 | 3885.18914313171 |
| 73 | 113612 | 187201.365095941 | -73589.3650959414 |
| 74 | 108641 | 140450.0592067 | -31809.0592067001 |
| 75 | 162203 | 215807.61109424 | -53604.61109424 |
| 76 | 100098 | 106797.291075565 | -6699.29107556503 |
| 77 | 174768 | 195234.266841887 | -20466.2668418867 |
| 78 | 158459 | 214882.393983205 | -56423.3939832049 |
| 79 | 80934 | 79571.1173337311 | 1362.88266626886 |
| 80 | 84971 | 146035.087092059 | -61064.0870920595 |
| 81 | 80545 | 159183.685511271 | -78638.6855112714 |
| 82 | 287191 | 153952.87777878 | 133238.12222122 |
| 83 | 62974 | 83421.6372105522 | -20447.6372105522 |
| 84 | 130982 | 122121.206509579 | 8860.79349042108 |
| 85 | 75555 | 106806.179542089 | -31251.1795420886 |
| 86 | 162154 | 127248.039476403 | 34905.9605235971 |
| 87 | 224670 | 297176.656489142 | -72506.6564891421 |
| 88 | 115019 | 185921.57411247 | -70902.57411247 |
| 89 | 105038 | 139822.743018554 | -34784.7430185541 |
| 90 | 155537 | 130868.110468685 | 24668.8895313146 |
| 91 | 153133 | 144748.748853688 | 8384.25114631152 |
| 92 | 165577 | 199236.067638484 | -33659.0676384838 |
| 93 | 151517 | 131724.6435167 | 19792.3564833004 |
| 94 | 133686 | 115064.475819457 | 18621.524180543 |
| 95 | 58128 | 88277.6688252233 | -30149.6688252233 |
| 96 | 245196 | 212278.238835871 | 32917.7611641285 |
| 97 | 195576 | 214714.392478766 | -19138.3924787661 |
| 98 | 19349 | 27995.2606720053 | -8646.26067200526 |
| 99 | 225371 | 169887.588571841 | 55483.4114281586 |
| 100 | 152796 | 152354.102268301 | 441.897731699127 |
| 101 | 59117 | 54986.9852877012 | 4130.01471229877 |
| 102 | 91762 | 114753.596933694 | -22991.5969336937 |
| 103 | 127987 | 145089.671079797 | -17102.6710797966 |
| 104 | 113552 | 111255.827002216 | 2296.17299778389 |
| 105 | 85338 | 91521.9845301186 | -6183.98453011864 |
| 106 | 27676 | 42296.4312548954 | -14620.4312548954 |
| 107 | 147984 | 174545.900092804 | -26561.9000928038 |
| 108 | 122417 | 96539.6297360345 | 25877.3702639655 |
| 109 | 0 | 2157.90726732851 | -2157.90726732851 |
| 110 | 91529 | 143659.421492828 | -52130.4214928275 |
| 111 | 107205 | 119106.897327095 | -11901.8973270946 |
| 112 | 144664 | 129738.813427882 | 14925.1865721184 |
| 113 | 136540 | 149653.645050537 | -13113.6450505369 |
| 114 | 76656 | 124197.084701901 | -47541.0847019009 |
| 115 | 3616 | 5997.10510561942 | -2381.10510561942 |
| 116 | 0 | 2157.90726732851 | -2157.90726732851 |
| 117 | 183065 | 115050.802536424 | 68014.1974635762 |
| 118 | 144636 | 203614.836343716 | -58978.8363437163 |
| 119 | 152826 | 149938.098989121 | 2887.90101087898 |
| 120 | 113273 | 112008.506124355 | 1264.49387564518 |
| 121 | 43410 | 26507.145656665 | 16902.854343335 |
| 122 | 175774 | 182621.193494794 | -6847.19349479441 |
| 123 | 95401 | 95804.349167137 | -403.349167136987 |
| 124 | 118893 | 160536.75491307 | -41643.7549130698 |
| 125 | 60493 | 62933.1815677853 | -2440.18156778533 |
| 126 | 19764 | 26680.3049033557 | -6916.3049033557 |
| 127 | 164062 | 128809.476169224 | 35252.523830776 |
| 128 | 132696 | 104881.386719574 | 27814.6132804263 |
| 129 | 155088 | 147681.396477818 | 7406.60352218191 |
| 130 | 11796 | 12493.6065914439 | -697.606591443877 |
| 131 | 10674 | 9068.46337625217 | 1605.53662374783 |
| 132 | 142261 | 147321.187951635 | -5060.18795163544 |
| 133 | 6836 | 5638.22064748827 | 1197.77935251173 |
| 134 | 154206 | 147638.894133899 | 6567.10586610108 |
| 135 | 5118 | 9819.19527440947 | -4701.19527440947 |
| 136 | 40248 | 29842.2435519604 | 10405.7564480396 |
| 137 | 0 | 2157.90726732851 | -2157.90726732851 |
| 138 | 122641 | 118700.521289604 | 3940.47871039625 |
| 139 | 88837 | 108512.287630841 | -19675.2876308412 |
| 140 | 7131 | 5229.26553796126 | 1901.73446203874 |
| 141 | 9056 | 18463.1023717033 | -9407.10237170329 |
| 142 | 76611 | 59786.5891269167 | 16824.4108730833 |
| 143 | 132697 | 134273.271274347 | -1576.27127434687 |
| 144 | 100681 | 69998.7318681033 | 30682.2681318967 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 8 | 0.268613237813534 | 0.537226475627067 | 0.731386762186466 |
| 9 | 0.156667562733839 | 0.313335125467679 | 0.843332437266161 |
| 10 | 0.376666259840516 | 0.753332519681032 | 0.623333740159484 |
| 11 | 0.625420610052774 | 0.749158779894451 | 0.374579389947226 |
| 12 | 0.632068862639463 | 0.735862274721075 | 0.367931137360537 |
| 13 | 0.598342087765081 | 0.803315824469838 | 0.401657912234919 |
| 14 | 0.546803081400072 | 0.906393837199855 | 0.453196918599928 |
| 15 | 0.459446318045273 | 0.918892636090546 | 0.540553681954727 |
| 16 | 0.471039259560755 | 0.94207851912151 | 0.528960740439245 |
| 17 | 0.725864467330996 | 0.548271065338007 | 0.274135532669004 |
| 18 | 0.733172586728005 | 0.533654826543989 | 0.266827413271995 |
| 19 | 0.684981119210051 | 0.630037761579897 | 0.315018880789949 |
| 20 | 0.635401802472399 | 0.729196395055202 | 0.364598197527601 |
| 21 | 0.563116292679519 | 0.873767414640961 | 0.43688370732048 |
| 22 | 0.540186472607651 | 0.919627054784698 | 0.459813527392349 |
| 23 | 0.712605249507667 | 0.574789500984666 | 0.287394750492333 |
| 24 | 0.65690774397666 | 0.686184512046681 | 0.34309225602334 |
| 25 | 0.601199317381856 | 0.797601365236289 | 0.398800682618144 |
| 26 | 0.723623045697618 | 0.552753908604764 | 0.276376954302382 |
| 27 | 0.722367008286805 | 0.55526598342639 | 0.277632991713195 |
| 28 | 0.682174250565835 | 0.63565149886833 | 0.317825749434165 |
| 29 | 0.964373375465835 | 0.0712532490683299 | 0.0356266245341649 |
| 30 | 0.973321014447092 | 0.0533579711058168 | 0.0266789855529084 |
| 31 | 0.97106995076847 | 0.0578600984630591 | 0.0289300492315295 |
| 32 | 0.969612983821101 | 0.0607740323577972 | 0.0303870161788986 |
| 33 | 0.985372019506304 | 0.029255960987391 | 0.0146279804936955 |
| 34 | 0.97941961830774 | 0.0411607633845205 | 0.0205803816922603 |
| 35 | 0.986069409745712 | 0.0278611805085752 | 0.0139305902542876 |
| 36 | 0.980455778159681 | 0.0390884436806371 | 0.0195442218403186 |
| 37 | 0.989536689368686 | 0.0209266212626289 | 0.0104633106313144 |
| 38 | 0.985903515327316 | 0.0281929693453679 | 0.014096484672684 |
| 39 | 0.980455123112095 | 0.039089753775809 | 0.0195448768879045 |
| 40 | 0.977317933169718 | 0.0453641336605646 | 0.0226820668302823 |
| 41 | 0.973493297703639 | 0.0530134045927218 | 0.0265067022963609 |
| 42 | 0.96416682367593 | 0.0716663526481392 | 0.0358331763240696 |
| 43 | 0.959249085374318 | 0.0815018292513646 | 0.0407509146256823 |
| 44 | 0.948563320217531 | 0.102873359564938 | 0.0514366797824691 |
| 45 | 0.951621083851159 | 0.0967578322976826 | 0.0483789161488413 |
| 46 | 0.937079986644735 | 0.12584002671053 | 0.0629200133552652 |
| 47 | 0.924341175767753 | 0.151317648464494 | 0.0756588242322469 |
| 48 | 0.916274209368878 | 0.167451581262244 | 0.0837257906311218 |
| 49 | 0.914306667662151 | 0.171386664675699 | 0.0856933323378493 |
| 50 | 0.895387377286685 | 0.20922524542663 | 0.104612622713315 |
| 51 | 0.879710523320198 | 0.240578953359604 | 0.120289476679802 |
| 52 | 0.876369731810329 | 0.247260536379343 | 0.123630268189671 |
| 53 | 0.971485441379363 | 0.0570291172412743 | 0.0285145586206372 |
| 54 | 0.985198340142212 | 0.0296033197155771 | 0.0148016598577885 |
| 55 | 0.982924028238145 | 0.0341519435237099 | 0.0170759717618549 |
| 56 | 0.984539529269822 | 0.0309209414603567 | 0.0154604707301784 |
| 57 | 0.990040399993307 | 0.0199192000133863 | 0.00995960000669313 |
| 58 | 0.986260497066769 | 0.0274790058664628 | 0.0137395029332314 |
| 59 | 0.982566145763273 | 0.0348677084734549 | 0.0174338542367274 |
| 60 | 0.977013141164746 | 0.0459737176705079 | 0.022986858835254 |
| 61 | 0.969546133408538 | 0.0609077331829236 | 0.0304538665914618 |
| 62 | 0.961573344624301 | 0.0768533107513988 | 0.0384266553756994 |
| 63 | 0.954314926336832 | 0.091370147326336 | 0.045685073663168 |
| 64 | 0.943730521359863 | 0.112538957280273 | 0.0562694786401366 |
| 65 | 0.965141605443159 | 0.0697167891136813 | 0.0348583945568406 |
| 66 | 0.962013443774117 | 0.0759731124517655 | 0.0379865562258827 |
| 67 | 0.955776015536915 | 0.0884479689261691 | 0.0442239844630845 |
| 68 | 0.963088619306347 | 0.0738227613873057 | 0.0369113806936529 |
| 69 | 0.961032807639756 | 0.0779343847204874 | 0.0389671923602437 |
| 70 | 0.954204340941285 | 0.0915913181174299 | 0.045795659058715 |
| 71 | 0.971180540882944 | 0.0576389182341119 | 0.028819459117056 |
| 72 | 0.965588956531966 | 0.0688220869360689 | 0.0344110434680344 |
| 73 | 0.982579708776446 | 0.0348405824471076 | 0.0174202912235538 |
| 74 | 0.979613163753732 | 0.0407736724925357 | 0.0203868362462678 |
| 75 | 0.983177642281897 | 0.0336447154362064 | 0.0168223577181032 |
| 76 | 0.979180734091643 | 0.0416385318167145 | 0.0208192659083573 |
| 77 | 0.973099844612108 | 0.0538003107757838 | 0.0269001553878919 |
| 78 | 0.976698575927709 | 0.0466028481445816 | 0.0233014240722908 |
| 79 | 0.969216369758292 | 0.0615672604834165 | 0.0307836302417083 |
| 80 | 0.983696976137023 | 0.0326060477259548 | 0.0163030238629774 |
| 81 | 0.994403289063818 | 0.0111934218723642 | 0.0055967109361821 |
| 82 | 0.99999206451781 | 1.58709643790531e-05 | 7.93548218952653e-06 |
| 83 | 0.999991429063964 | 1.71418720722065e-05 | 8.57093603610324e-06 |
| 84 | 0.999985047131016 | 2.99057379685047e-05 | 1.49528689842523e-05 |
| 85 | 0.999985877140407 | 2.82457191856828e-05 | 1.41228595928414e-05 |
| 86 | 0.9999858655113 | 2.82689773994839e-05 | 1.41344886997419e-05 |
| 87 | 0.999994437101803 | 1.11257963949215e-05 | 5.56289819746077e-06 |
| 88 | 0.999999744895485 | 5.10209029155207e-07 | 2.55104514577603e-07 |
| 89 | 0.999999793919162 | 4.1216167576961e-07 | 2.06080837884805e-07 |
| 90 | 0.999999773293557 | 4.53412885461272e-07 | 2.26706442730636e-07 |
| 91 | 0.999999698400291 | 6.03199417787197e-07 | 3.01599708893598e-07 |
| 92 | 0.999999556184288 | 8.87631423772758e-07 | 4.43815711886379e-07 |
| 93 | 0.99999929465813 | 1.41068374090667e-06 | 7.05341870453333e-07 |
| 94 | 0.999999059060586 | 1.88187882872825e-06 | 9.40939414364125e-07 |
| 95 | 0.99999880568179 | 2.38863642061365e-06 | 1.19431821030682e-06 |
| 96 | 0.999998395126307 | 3.20974738660764e-06 | 1.60487369330382e-06 |
| 97 | 0.999997237937101 | 5.52412579720847e-06 | 2.76206289860423e-06 |
| 98 | 0.999994694063157 | 1.06118736859278e-05 | 5.30593684296391e-06 |
| 99 | 0.999999124995611 | 1.75000877727658e-06 | 8.75004388638292e-07 |
| 100 | 0.999998179051811 | 3.64189637840346e-06 | 1.82094818920173e-06 |
| 101 | 0.999996344430306 | 7.3111393875153e-06 | 3.65556969375765e-06 |
| 102 | 0.999994301565313 | 1.13968693750102e-05 | 5.69843468750508e-06 |
| 103 | 0.999989576202929 | 2.08475941426055e-05 | 1.04237970713027e-05 |
| 104 | 0.999979388487945 | 4.12230241095518e-05 | 2.06115120547759e-05 |
| 105 | 0.999959944951847 | 8.0110096305224e-05 | 4.0055048152612e-05 |
| 106 | 0.999959495080293 | 8.10098394139021e-05 | 4.0504919706951e-05 |
| 107 | 0.999948697216958 | 0.000102605566084598 | 5.13027830422988e-05 |
| 108 | 0.999909640273418 | 0.000180719453164586 | 9.03597265822932e-05 |
| 109 | 0.999833206341426 | 0.000333587317146986 | 0.000166793658573493 |
| 110 | 0.999862578307239 | 0.000274843385521008 | 0.000137421692760504 |
| 111 | 0.99974102196631 | 0.000517956067380588 | 0.000258978033690294 |
| 112 | 0.999573887760011 | 0.00085222447997888 | 0.00042611223998944 |
| 113 | 0.999226854613331 | 0.00154629077333702 | 0.000773145386668508 |
| 114 | 0.999630666796664 | 0.000738666406672887 | 0.000369333203336444 |
| 115 | 0.999319671836175 | 0.0013606563276495 | 0.000680328163824752 |
| 116 | 0.998789010994989 | 0.00242197801002304 | 0.00121098900501152 |
| 117 | 0.99993727919887 | 0.00012544160226011 | 6.27208011300551e-05 |
| 118 | 0.999995196514796 | 9.60697040708558e-06 | 4.80348520354279e-06 |
| 119 | 0.999988851992512 | 2.22960149770233e-05 | 1.11480074885117e-05 |
| 120 | 0.999971341248743 | 5.73175025140912e-05 | 2.86587512570456e-05 |
| 121 | 0.999946656190132 | 0.000106687619736287 | 5.33438098681436e-05 |
| 122 | 0.999885262826648 | 0.000229474346703897 | 0.000114737173351948 |
| 123 | 0.99973779600993 | 0.000524407980140769 | 0.000262203990070384 |
| 124 | 0.999998252450833 | 3.49509833327638e-06 | 1.74754916663819e-06 |
| 125 | 0.999993822435683 | 1.23551286334856e-05 | 6.17756431674282e-06 |
| 126 | 0.999982574982681 | 3.48500346375726e-05 | 1.74250173187863e-05 |
| 127 | 0.999988882281667 | 2.22354366662537e-05 | 1.11177183331269e-05 |
| 128 | 0.99997359186983 | 5.28162603390993e-05 | 2.64081301695497e-05 |
| 129 | 0.999916077282096 | 0.000167845435808133 | 8.39227179040667e-05 |
| 130 | 0.999699509385902 | 0.000600981228196568 | 0.000300490614098284 |
| 131 | 0.999016737096911 | 0.0019665258061786 | 0.0009832629030893 |
| 132 | 0.998504422435538 | 0.00299115512892415 | 0.00149557756446208 |
| 133 | 0.994918102838977 | 0.0101637943220451 | 0.00508189716102256 |
| 134 | 0.997729796866708 | 0.00454040626658453 | 0.00227020313329227 |
| 135 | 0.993690748523714 | 0.0126185029525728 | 0.00630925147628641 |
| 136 | 0.995739143797369 | 0.0085217124052613 | 0.00426085620263065 |
| Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
| Description | # significant tests | % significant tests | OK/NOK |
| 1% type I error level | 53 | 0.410852713178295 | NOK |
| 5% type I error level | 77 | 0.596899224806202 | NOK |
| 10% type I error level | 99 | 0.767441860465116 | NOK |
