| Multiple Linear Regression - Estimated Regression Equation |
| Time_spent[t] = + 12451.3838000746 + 63.8044698696514page_views[t] + 168.300011480851Logins[t] + 0.401031286233873Writing[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) | 12451.3838000746 | 5910.215393 | 2.1068 | 0.036923 | 0.018461 |
| page_views | 63.8044698696514 | 6.352575 | 10.0439 | 0 | 0 |
| Logins | 168.300011480851 | 136.772977 | 1.2305 | 0.220571 | 0.110286 |
| Writing | 0.401031286233873 | 0.158508 | 2.53 | 0.012512 | 0.006256 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.897248374941655 |
| R-squared | 0.805054646335441 |
| Adjusted R-squared | 0.800877245899772 |
| F-TEST (value) | 192.716656861863 |
| F-TEST (DF numerator) | 3 |
| F-TEST (DF denominator) | 140 |
| p-value | 0 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 34081.665147442 |
| Sum Squared Residuals | 162618385891.131 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 158258 | 148698.710703669 | 9559.28929633127 |
| 2 | 186930 | 144189.777767258 | 42740.2222327417 |
| 3 | 7215 | 28301.9097420137 | -21086.9097420137 |
| 4 | 129098 | 184917.069595143 | -55819.0695951428 |
| 5 | 230587 | 276657.888968268 | -46070.8889682683 |
| 6 | 508313 | 551647.701366131 | -43334.7013661311 |
| 7 | 180745 | 149754.336283893 | 30990.6637161066 |
| 8 | 185559 | 141905.241101461 | 43653.7588985394 |
| 9 | 154581 | 151935.751716503 | 2645.24828349689 |
| 10 | 290658 | 237738.334938705 | 52919.6650612948 |
| 11 | 121844 | 169220.772020514 | -47376.7720205139 |
| 12 | 184039 | 182027.060230357 | 2011.93976964263 |
| 13 | 100324 | 154278.287458054 | -53954.2874580536 |
| 14 | 209427 | 245666.736112151 | -36239.7361121509 |
| 15 | 167592 | 127296.884702931 | 40295.1152970686 |
| 16 | 154593 | 150498.977620307 | 4094.02237969288 |
| 17 | 142018 | 165514.449112405 | -23496.4491124047 |
| 18 | 77855 | 106528.519566893 | -28673.5195668932 |
| 19 | 167047 | 222915.304551508 | -55868.3045515081 |
| 20 | 27997 | 84167.1441616494 | -56170.1441616494 |
| 21 | 73019 | 93549.630476984 | -20530.630476984 |
| 22 | 241082 | 241587.137108957 | -505.137108956562 |
| 23 | 195820 | 153066.515561131 | 42753.4844388692 |
| 24 | 141899 | 179186.845164688 | -37287.8451646877 |
| 25 | 145433 | 159355.182824641 | -13922.182824641 |
| 26 | 180241 | 134851.754780542 | 45389.2452194584 |
| 27 | 202232 | 195630.452744169 | 6601.54725583111 |
| 28 | 190230 | 134557.57171032 | 55672.4282896801 |
| 29 | 354924 | 244316.688796192 | 110607.311203808 |
| 30 | 192399 | 170684.156559617 | 21714.843440383 |
| 31 | 182286 | 141223.508542189 | 41062.491457811 |
| 32 | 181590 | 135595.355877073 | 45994.6441229266 |
| 33 | 133801 | 202135.581608614 | -68334.5816086144 |
| 34 | 233686 | 253477.197649601 | -19791.197649601 |
| 35 | 219428 | 190414.981749205 | 29013.0182507948 |
| 36 | 0 | 12683.4882814251 | -12683.4882814251 |
| 37 | 223044 | 171425.815772483 | 51618.1842275169 |
| 38 | 100129 | 136881.607599741 | -36752.6075997411 |
| 39 | 136733 | 175362.662336015 | -38629.6623360155 |
| 40 | 249965 | 197727.50114432 | 52237.4988556798 |
| 41 | 242379 | 196783.71733831 | 45595.2826616905 |
| 42 | 145794 | 148595.160229632 | -2801.160229632 |
| 43 | 96404 | 114325.617506652 | -17921.6175066524 |
| 44 | 195891 | 188873.195661252 | 7017.80433874804 |
| 45 | 117156 | 126395.701231608 | -9239.70123160757 |
| 46 | 157787 | 119134.872753296 | 38652.1272467043 |
| 47 | 81293 | 74948.4350002821 | 6344.56499971787 |
| 48 | 224049 | 190259.466660633 | 33789.5333393672 |
| 49 | 223789 | 196858.206410423 | 26930.7935895772 |
| 50 | 160344 | 207193.430050267 | -46849.4300502667 |
| 51 | 48188 | 68108.5704179511 | -19920.5704179511 |
| 52 | 152206 | 154889.733999639 | -2683.73399963902 |
| 53 | 294283 | 211097.860539292 | 83185.1394607076 |
| 54 | 235223 | 169110.881976189 | 66112.1180238111 |
| 55 | 195583 | 155945.344011993 | 39637.6559880067 |
| 56 | 145942 | 140168.278801488 | 5773.72119851214 |
| 57 | 208834 | 157238.917569004 | 51595.0824309959 |
| 58 | 93764 | 89712.1958927507 | 4051.80410724927 |
| 59 | 151985 | 112748.883961363 | 39236.1160386375 |
| 60 | 190545 | 230716.314962184 | -40171.3149621843 |
| 61 | 148922 | 143596.447740902 | 5325.55225909819 |
| 62 | 132856 | 172201.873319811 | -39345.8733198107 |
| 63 | 126107 | 130645.033799997 | -4538.0337999973 |
| 64 | 112718 | 108173.768071921 | 4544.23192807949 |
| 65 | 160930 | 107585.806345506 | 53344.1936544945 |
| 66 | 99184 | 115870.24864515 | -16686.2486451498 |
| 67 | 182022 | 198271.718182474 | -16249.718182474 |
| 68 | 138708 | 220124.214489403 | -81416.2144894031 |
| 69 | 114408 | 115138.558281578 | -730.558281577747 |
| 70 | 31970 | 38336.490784843 | -6366.49078484301 |
| 71 | 225558 | 221107.420458037 | 4450.57954196339 |
| 72 | 137011 | 129506.815513444 | 7504.18448655615 |
| 73 | 113612 | 136827.201121849 | -23215.2011218486 |
| 74 | 108641 | 133060.961152082 | -24419.9611520816 |
| 75 | 162203 | 229833.43276493 | -67630.4327649304 |
| 76 | 100098 | 119893.183411818 | -19795.1834118178 |
| 77 | 174768 | 183158.986400797 | -8390.98640079723 |
| 78 | 158459 | 220934.42919548 | -62475.4291954802 |
| 79 | 80934 | 89787.4677805704 | -8853.46778057039 |
| 80 | 84971 | 120078.57124646 | -35107.5712464597 |
| 81 | 80545 | 99887.8473281931 | -19342.8473281931 |
| 82 | 287191 | 178564.350462307 | 108626.649537693 |
| 83 | 62974 | 83767.0067959258 | -20793.0067959258 |
| 84 | 130982 | 127865.774849611 | 3116.22515038883 |
| 85 | 75555 | 91562.5658871859 | -16007.5658871859 |
| 86 | 162154 | 153842.946678492 | 8311.05332150818 |
| 87 | 226638 | 242600.230985879 | -15962.2309858789 |
| 88 | 115019 | 116897.961239049 | -1878.96123904857 |
| 89 | 105038 | 122378.332924708 | -17340.3329247077 |
| 90 | 155537 | 134768.98529744 | 20768.0147025603 |
| 91 | 153133 | 162476.818331335 | -9343.81833133542 |
| 92 | 165577 | 198030.475783246 | -32453.475783246 |
| 93 | 151517 | 115744.84531795 | 35772.1546820499 |
| 94 | 133686 | 130647.16676626 | 3038.83323374011 |
| 95 | 58128 | 92741.2025400168 | -34613.2025400168 |
| 96 | 245196 | 202972.255743397 | 42223.7442566025 |
| 97 | 195576 | 172039.088675953 | 23536.9113240473 |
| 98 | 19349 | 30261.397578658 | -10912.397578658 |
| 99 | 225371 | 201307.235214105 | 24063.7647858946 |
| 100 | 152796 | 162899.073007692 | -10103.0730076919 |
| 101 | 59117 | 62695.5063009185 | -3578.50630091848 |
| 102 | 91762 | 96982.4713212515 | -5220.47132125155 |
| 103 | 127987 | 114185.867638712 | 13801.1323612881 |
| 104 | 113552 | 103562.593924257 | 9989.40607574251 |
| 105 | 85338 | 77827.0333911201 | 7510.9666088799 |
| 106 | 27676 | 56524.2728691438 | -28848.2728691438 |
| 107 | 147984 | 127850.517062166 | 20133.4829378339 |
| 108 | 122417 | 95998.1604617647 | 26418.8395382353 |
| 109 | 0 | 12451.3838000746 | -12451.3838000746 |
| 110 | 91529 | 126245.469155008 | -34716.4691550076 |
| 111 | 107205 | 111128.981420995 | -3923.98142099482 |
| 112 | 144664 | 119458.293021585 | 25205.7069784146 |
| 113 | 136540 | 128636.980290603 | 7903.01970939714 |
| 114 | 76656 | 91680.794577121 | -15024.794577121 |
| 115 | 3616 | 18269.6325073116 | -14653.6325073116 |
| 116 | 0 | 12451.3838000746 | -12451.3838000746 |
| 117 | 183065 | 102634.307990436 | 80430.6920095644 |
| 118 | 144636 | 153915.085879747 | -9279.08587974696 |
| 119 | 156889 | 168982.947301365 | -12093.9473013645 |
| 120 | 113273 | 92966.9100080464 | 20306.0899919536 |
| 121 | 43410 | 66404.2295838159 | -22994.2295838159 |
| 122 | 175774 | 152817.51170544 | 22956.4882945604 |
| 123 | 95401 | 89451.3656011127 | 5949.63439888734 |
| 124 | 118893 | 157693.048230755 | -38800.0482307551 |
| 125 | 60493 | 78933.7634497229 | -18440.7634497229 |
| 126 | 19764 | 34961.9898091127 | -15197.9898091127 |
| 127 | 164062 | 149391.871828352 | 14670.1281716478 |
| 128 | 132696 | 100054.742892942 | 32641.2571070576 |
| 129 | 155367 | 144531.953761627 | 10835.0462383734 |
| 130 | 11796 | 30300.028190033 | -18504.028190033 |
| 131 | 10674 | 20218.921950628 | -9544.92195062804 |
| 132 | 142261 | 151767.279380432 | -9506.27938043208 |
| 133 | 6836 | 15572.2670991728 | -8736.26709917282 |
| 134 | 154206 | 159846.461593914 | -5640.46159391449 |
| 135 | 5118 | 15636.0715690425 | -10518.0715690425 |
| 136 | 40248 | 51016.1583972013 | -10768.1583972013 |
| 137 | 0 | 12451.3838000746 | -12451.3838000746 |
| 138 | 122641 | 100008.936747538 | 22632.0632524616 |
| 139 | 88837 | 126915.001438521 | -38078.0014385208 |
| 140 | 7131 | 18292.7459054397 | -11161.7459054397 |
| 141 | 9056 | 32334.3977694891 | -23278.3977694891 |
| 142 | 76611 | 79299.8288181788 | -2688.82881817884 |
| 143 | 132697 | 111990.338661892 | 20706.6613381082 |
| 144 | 100681 | 98254.6399974795 | 2426.36000252049 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 7 | 0.747001047446475 | 0.505997905107051 | 0.252998952553525 |
| 8 | 0.677240471366615 | 0.64551905726677 | 0.322759528633385 |
| 9 | 0.592246026087128 | 0.815507947825745 | 0.407753973912872 |
| 10 | 0.630071496307774 | 0.739857007384452 | 0.369928503692226 |
| 11 | 0.823912272365332 | 0.352175455269335 | 0.176087727634668 |
| 12 | 0.760206455862814 | 0.479587088274373 | 0.239793544137186 |
| 13 | 0.700488830577521 | 0.599022338844958 | 0.299511169422479 |
| 14 | 0.652096201191717 | 0.695807597616565 | 0.347903798808283 |
| 15 | 0.668888858374592 | 0.662222283250817 | 0.331111141625408 |
| 16 | 0.589646735189674 | 0.820706529620652 | 0.410353264810326 |
| 17 | 0.694323435667193 | 0.611353128665614 | 0.305676564332807 |
| 18 | 0.644548097702631 | 0.710903804594737 | 0.355451902297369 |
| 19 | 0.765023850988528 | 0.469952298022944 | 0.234976149011472 |
| 20 | 0.859646573313796 | 0.280706853372408 | 0.140353426686204 |
| 21 | 0.818704836846199 | 0.362590326307601 | 0.181295163153801 |
| 22 | 0.774647210211726 | 0.450705579576547 | 0.225352789788274 |
| 23 | 0.830412950626082 | 0.339174098747836 | 0.169587049373918 |
| 24 | 0.852132221744895 | 0.295735556510211 | 0.147867778255105 |
| 25 | 0.813369614206387 | 0.373260771587225 | 0.186630385793613 |
| 26 | 0.819563283582901 | 0.360873432834199 | 0.180436716417099 |
| 27 | 0.829662988690001 | 0.340674022619998 | 0.170337011309999 |
| 28 | 0.888895187570206 | 0.222209624859587 | 0.111104812429794 |
| 29 | 0.989839728398206 | 0.0203205432035883 | 0.0101602716017942 |
| 30 | 0.987041391267724 | 0.0259172174645511 | 0.0129586087322755 |
| 31 | 0.987492840758709 | 0.0250143184825824 | 0.0125071592412912 |
| 32 | 0.989140233782099 | 0.021719532435801 | 0.0108597662179005 |
| 33 | 0.997015051317814 | 0.00596989736437206 | 0.00298494868218603 |
| 34 | 0.995965518080146 | 0.00806896383970836 | 0.00403448191985418 |
| 35 | 0.99501330773884 | 0.00997338452232037 | 0.00498669226116018 |
| 36 | 0.993457232349276 | 0.0130855353014479 | 0.00654276765072393 |
| 37 | 0.995370378206935 | 0.00925924358612979 | 0.00462962179306489 |
| 38 | 0.995584023858653 | 0.00883195228269471 | 0.00441597614134735 |
| 39 | 0.996533061712241 | 0.00693387657551797 | 0.00346693828775899 |
| 40 | 0.997069676919724 | 0.00586064616055248 | 0.00293032308027624 |
| 41 | 0.997573635304221 | 0.00485272939155795 | 0.00242636469577898 |
| 42 | 0.996448511345274 | 0.00710297730945224 | 0.00355148865472612 |
| 43 | 0.996458631398059 | 0.00708273720388267 | 0.00354136860194134 |
| 44 | 0.994860040604041 | 0.0102799187919175 | 0.00513995939595873 |
| 45 | 0.993056370032591 | 0.0138872599348177 | 0.00694362996740884 |
| 46 | 0.993705282800226 | 0.0125894343995477 | 0.00629471719977383 |
| 47 | 0.991144073748227 | 0.017711852503547 | 0.0088559262517735 |
| 48 | 0.990880768481849 | 0.0182384630363018 | 0.00911923151815089 |
| 49 | 0.98922839246405 | 0.0215432150718991 | 0.0107716075359496 |
| 50 | 0.991987405169137 | 0.0160251896617263 | 0.00801259483086314 |
| 51 | 0.990237732616902 | 0.019524534766196 | 0.00976226738309801 |
| 52 | 0.986516447532008 | 0.0269671049359836 | 0.0134835524679918 |
| 53 | 0.997183335824589 | 0.00563332835082212 | 0.00281666417541106 |
| 54 | 0.999031825377718 | 0.00193634924456505 | 0.000968174622282524 |
| 55 | 0.999158922799364 | 0.00168215440127206 | 0.000841077200636032 |
| 56 | 0.998742124721762 | 0.00251575055647557 | 0.00125787527823778 |
| 57 | 0.99927187267075 | 0.00145625465849921 | 0.000728127329249607 |
| 58 | 0.998920686626462 | 0.00215862674707637 | 0.00107931337353819 |
| 59 | 0.999039967046064 | 0.00192006590787121 | 0.000960032953935605 |
| 60 | 0.999157540632279 | 0.00168491873544212 | 0.000842459367721059 |
| 61 | 0.998746691881092 | 0.00250661623781527 | 0.00125330811890763 |
| 62 | 0.998920046279213 | 0.00215990744157441 | 0.0010799537207872 |
| 63 | 0.998467542531352 | 0.00306491493729667 | 0.00153245746864834 |
| 64 | 0.997765708168168 | 0.00446858366366387 | 0.00223429183183193 |
| 65 | 0.998790337223587 | 0.00241932555282556 | 0.00120966277641278 |
| 66 | 0.998402044330218 | 0.00319591133956506 | 0.00159795566978253 |
| 67 | 0.997880900724713 | 0.00423819855057492 | 0.00211909927528746 |
| 68 | 0.999822560879735 | 0.000354878240529797 | 0.000177439120264899 |
| 69 | 0.999748813813755 | 0.000502372372489438 | 0.000251186186244719 |
| 70 | 0.99961638605482 | 0.000767227890359601 | 0.000383613945179801 |
| 71 | 0.999456182609863 | 0.00108763478027388 | 0.00054381739013694 |
| 72 | 0.999223064415832 | 0.00155387116833659 | 0.000776935584168294 |
| 73 | 0.999034335461636 | 0.00193132907672722 | 0.000965664538363609 |
| 74 | 0.999018531595301 | 0.00196293680939894 | 0.000981468404699471 |
| 75 | 0.999827172699008 | 0.000345654601983689 | 0.000172827300991845 |
| 76 | 0.999819744901242 | 0.000360510197516906 | 0.000180255098758453 |
| 77 | 0.999805624199917 | 0.000388751600166683 | 0.000194375800083342 |
| 78 | 0.99998283047383 | 3.43390523404583e-05 | 1.71695261702291e-05 |
| 79 | 0.999972743993669 | 5.45120126629222e-05 | 2.72560063314611e-05 |
| 80 | 0.999974953572822 | 5.00928543562229e-05 | 2.50464271781114e-05 |
| 81 | 0.999961213104276 | 7.75737914473687e-05 | 3.87868957236843e-05 |
| 82 | 0.999999847356879 | 3.05286241985206e-07 | 1.52643120992603e-07 |
| 83 | 0.999999807194423 | 3.85611153167976e-07 | 1.92805576583988e-07 |
| 84 | 0.99999962754464 | 7.4491071955234e-07 | 3.7245535977617e-07 |
| 85 | 0.999999435910573 | 1.12817885470007e-06 | 5.64089427350033e-07 |
| 86 | 0.999998907619156 | 2.18476168799694e-06 | 1.09238084399847e-06 |
| 87 | 0.999999038073929 | 1.92385214282379e-06 | 9.61926071411897e-07 |
| 88 | 0.999998556763424 | 2.8864731522809e-06 | 1.44323657614045e-06 |
| 89 | 0.999998036557006 | 3.92688598715108e-06 | 1.96344299357554e-06 |
| 90 | 0.999997096967681 | 5.80606463807555e-06 | 2.90303231903778e-06 |
| 91 | 0.999994648401826 | 1.07031963485626e-05 | 5.35159817428131e-06 |
| 92 | 0.999996973190366 | 6.05361926778209e-06 | 3.02680963389104e-06 |
| 93 | 0.999997657405638 | 4.68518872475407e-06 | 2.34259436237703e-06 |
| 94 | 0.999995484861657 | 9.03027668623093e-06 | 4.51513834311547e-06 |
| 95 | 0.999996066500007 | 7.86699998638495e-06 | 3.93349999319247e-06 |
| 96 | 0.999995616092178 | 8.7678156443802e-06 | 4.3839078221901e-06 |
| 97 | 0.99999431380248 | 1.13723950399379e-05 | 5.68619751996894e-06 |
| 98 | 0.999989356289784 | 2.12874204328216e-05 | 1.06437102164108e-05 |
| 99 | 0.999981347183437 | 3.73056331262017e-05 | 1.86528165631009e-05 |
| 100 | 0.999979773522905 | 4.04529541907932e-05 | 2.02264770953966e-05 |
| 101 | 0.999962791584514 | 7.44168309727881e-05 | 3.72084154863941e-05 |
| 102 | 0.999931856976973 | 0.000136286046054439 | 6.81430230272195e-05 |
| 103 | 0.999886164504236 | 0.000227670991527773 | 0.000113835495763886 |
| 104 | 0.999798433961747 | 0.000403132076506885 | 0.000201566038253442 |
| 105 | 0.999656617145965 | 0.000686765708069654 | 0.000343382854034827 |
| 106 | 0.999649847971953 | 0.000700304056094152 | 0.000350152028047076 |
| 107 | 0.999473709154079 | 0.00105258169184177 | 0.000526290845920884 |
| 108 | 0.999333497832707 | 0.00133300433458629 | 0.000666502167293144 |
| 109 | 0.99887446303799 | 0.00225107392402062 | 0.00112553696201031 |
| 110 | 0.998495366480388 | 0.0030092670392244 | 0.0015046335196122 |
| 111 | 0.997496601956344 | 0.00500679608731269 | 0.00250339804365634 |
| 112 | 0.996949474587492 | 0.00610105082501629 | 0.00305052541250814 |
| 113 | 0.995026845905065 | 0.00994630818987057 | 0.00497315409493528 |
| 114 | 0.992836810345895 | 0.01432637930821 | 0.007163189654105 |
| 115 | 0.988983512701664 | 0.0220329745966724 | 0.0110164872983362 |
| 116 | 0.983058714778346 | 0.033882570443308 | 0.016941285221654 |
| 117 | 0.999769487094127 | 0.0004610258117457 | 0.00023051290587285 |
| 118 | 0.999590295769471 | 0.000819408461058433 | 0.000409704230529216 |
| 119 | 0.999842109840205 | 0.00031578031958965 | 0.000157890159794825 |
| 120 | 0.999839876828666 | 0.000320246342667602 | 0.000160123171333801 |
| 121 | 0.999776541284769 | 0.000446917430461187 | 0.000223458715230594 |
| 122 | 0.999534299869395 | 0.000931400261210246 | 0.000465700130605123 |
| 123 | 0.999011987239905 | 0.00197602552018982 | 0.000988012760094912 |
| 124 | 0.999928000421259 | 0.000143999157481687 | 7.19995787408437e-05 |
| 125 | 0.999905988719781 | 0.000188022560438141 | 9.40112802190705e-05 |
| 126 | 0.999775282019772 | 0.000449435960456574 | 0.000224717980228287 |
| 127 | 0.999512390437373 | 0.000975219125252989 | 0.000487609562626494 |
| 128 | 0.999864639396799 | 0.000270721206401032 | 0.000135360603200516 |
| 129 | 0.999610555859173 | 0.000778888281653092 | 0.000389444140826546 |
| 130 | 0.999131671318249 | 0.00173665736350251 | 0.000868328681751257 |
| 131 | 0.997627254886599 | 0.0047454902268012 | 0.0023727451134006 |
| 132 | 0.997062760478729 | 0.00587447904254204 | 0.00293723952127102 |
| 133 | 0.992479939723353 | 0.0150401205532945 | 0.00752006027664727 |
| 134 | 0.98570123079322 | 0.0285975384135605 | 0.0142987692067803 |
| 135 | 0.966604217356458 | 0.0667915652870845 | 0.0333957826435422 |
| 136 | 0.925117326020378 | 0.149765347959244 | 0.0748826739796219 |
| 137 | 0.864075201756102 | 0.271849596487796 | 0.135924798243898 |
| Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
| Description | # significant tests | % significant tests | OK/NOK |
| 1% type I error level | 87 | 0.66412213740458 | NOK |
| 5% type I error level | 106 | 0.809160305343511 | NOK |
| 10% type I error level | 107 | 0.816793893129771 | NOK |
