Multiple Linear Regression - Estimated Regression Equation |
time_spent_seconds[t] = + 13965.9689635504 + 41.5257437746151page_views[t] + 87.6324851128416number_course_compenium_views[t] + 264.049531452567`number_logins `[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) | 13965.9689635504 | 5912.472191 | 2.3621 | 0.019548 | 0.009774 |
page_views | 41.5257437746151 | 14.600243 | 2.8442 | 0.00512 | 0.00256 |
number_course_compenium_views | 87.6324851128416 | 39.904251 | 2.1961 | 0.029733 | 0.014867 |
`number_logins ` | 264.049531452567 | 139.384746 | 1.8944 | 0.060235 | 0.030118 |
Multiple Linear Regression - Regression Statistics | |
Multiple R | 0.89676311271242 |
R-squared | 0.804184080321668 |
Adjusted R-squared | 0.799988024899989 |
F-TEST (value) | 191.652397193546 |
F-TEST (DF numerator) | 3 |
F-TEST (DF denominator) | 140 |
p-value | 0 |
Multiple Linear Regression - Residual Statistics | |
Residual Standard Deviation | 34574.6752426963 |
Sum Squared Residuals | 167357143539.308 |
Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
1 | 159261 | 164134.977139941 | -4873.97713994132 |
2 | 189672 | 146413.485638944 | 43258.5143610562 |
3 | 7215 | 33001.3422625473 | -25786.3422625473 |
4 | 129098 | 190875.209312069 | -61777.2093120689 |
5 | 230632 | 295057.101449757 | -64425.1014497566 |
6 | 515038 | 538764.307317687 | -23726.3073176869 |
7 | 180745 | 154556.456591341 | 26188.5434086593 |
8 | 185559 | 140536.934607416 | 45022.0653925845 |
9 | 154581 | 157989.565176967 | -3408.56517696738 |
10 | 298001 | 249743.711200641 | 48257.2887993589 |
11 | 121844 | 170137.776769436 | -48293.7767694356 |
12 | 184039 | 180709.876683045 | 3329.12331695534 |
13 | 100324 | 174193.588241037 | -73869.5882410366 |
14 | 220269 | 272119.757077762 | -51850.757077762 |
15 | 168265 | 126765.055950735 | 41499.9440492651 |
16 | 154647 | 143372.803744121 | 11274.196255879 |
17 | 142018 | 139705.599408206 | 2312.40059179431 |
18 | 79030 | 113490.919994838 | -34460.9199948379 |
19 | 167047 | 229192.009593541 | -62145.0095935413 |
20 | 27997 | 69817.6269087207 | -41820.6269087207 |
21 | 73019 | 105137.360346349 | -32118.3603463486 |
22 | 241082 | 230987.715802067 | 10094.2841979334 |
23 | 195820 | 162322.899713902 | 33497.1002860978 |
24 | 142001 | 182700.761298015 | -40699.7612980148 |
25 | 145433 | 163890.114588957 | -18457.1145889568 |
26 | 183744 | 145011.7332736 | 38732.2667263998 |
27 | 202357 | 202522.355097559 | -165.355097559215 |
28 | 199532 | 129954.973549821 | 69577.0264501792 |
29 | 354924 | 238428.541358521 | 116495.458641479 |
30 | 192399 | 190578.371068977 | 1820.62893102312 |
31 | 182286 | 138453.418569208 | 43832.5814307923 |
32 | 181590 | 140976.401660531 | 40613.5983394688 |
33 | 133801 | 197527.287888722 | -63726.2878887224 |
34 | 233686 | 255122.179441816 | -21436.1794418163 |
35 | 219428 | 196132.361791898 | 23295.6382081016 |
36 | 0 | 14271.5442387776 | -14271.5442387776 |
37 | 223044 | 203906.358493903 | 19137.6415060973 |
38 | 100129 | 143972.870903286 | -43843.8709032857 |
39 | 145864 | 160775.640284192 | -14911.6402841922 |
40 | 249965 | 189937.89098797 | 60027.1090120298 |
41 | 242379 | 197947.274607983 | 44431.7253920174 |
42 | 145794 | 155826.809526527 | -10032.8095265267 |
43 | 96404 | 94870.6872262151 | 1533.31277378489 |
44 | 195891 | 194755.482744519 | 1135.51725548135 |
45 | 117156 | 114682.493727047 | 2473.50627295268 |
46 | 157787 | 116508.704779446 | 41278.2952205543 |
47 | 81293 | 71930.3199260433 | 9362.68007395669 |
48 | 237435 | 205042.233142227 | 32392.7668577733 |
49 | 233155 | 197366.843746426 | 35788.1562535742 |
50 | 160344 | 221330.600176307 | -60986.6001763067 |
51 | 48188 | 66647.9546960516 | -18459.9546960516 |
52 | 161922 | 154905.420125233 | 7016.57987476714 |
53 | 307432 | 211370.333945036 | 96061.6660549642 |
54 | 235223 | 178547.128712406 | 56675.8712875942 |
55 | 195583 | 169454.634885515 | 26128.365114485 |
56 | 146061 | 146806.666092391 | -745.666092391205 |
57 | 208834 | 151239.985291414 | 57594.0147085865 |
58 | 93764 | 87417.2903802748 | 6346.70961972515 |
59 | 151985 | 117162.314694648 | 34822.6853053518 |
60 | 193222 | 239945.119498343 | -46723.1194983426 |
61 | 148922 | 143019.579017773 | 5902.4209822271 |
62 | 132856 | 191399.079414269 | -58543.0794142686 |
63 | 129561 | 117066.714957018 | 12494.2850429815 |
64 | 112718 | 113075.795481439 | -357.795481438563 |
65 | 160930 | 111819.150552249 | 49110.849447751 |
66 | 99184 | 114367.99860861 | -15183.9986086099 |
67 | 192535 | 171724.201664364 | 20810.7983356361 |
68 | 138708 | 229159.282518118 | -90451.2825181179 |
69 | 114408 | 93200.6200672772 | 21207.3799327228 |
70 | 31970 | 40896.3458151051 | -8926.34581510513 |
71 | 225558 | 247070.35247403 | -21512.3524740304 |
72 | 139220 | 124994.094205512 | 14225.9057944876 |
73 | 113612 | 133823.526735709 | -20211.5267357094 |
74 | 108641 | 139894.916084113 | -31253.9160841132 |
75 | 162203 | 200501.906084319 | -38298.9060843193 |
76 | 100098 | 124023.454617215 | -23925.4546172151 |
77 | 174768 | 184728.395441262 | -9960.3954412623 |
78 | 158459 | 216912.800494502 | -58453.800494502 |
79 | 80934 | 91105.0639774006 | -10171.0639774006 |
80 | 84971 | 118571.08513413 | -33600.0851341302 |
81 | 80545 | 89431.9508508799 | -8886.95085087988 |
82 | 287191 | 192908.530252382 | 94282.4697476183 |
83 | 62974 | 86688.1782894788 | -23714.1782894788 |
84 | 134091 | 133889.843678969 | 201.156321031037 |
85 | 75555 | 98452.5589617587 | -22897.5589617587 |
86 | 162154 | 150578.030094685 | 11575.9699053147 |
87 | 226638 | 238934.933984135 | -12296.9339841353 |
88 | 115367 | 118465.663506696 | -3098.66350669622 |
89 | 108749 | 123013.133028115 | -14264.1330281149 |
90 | 155537 | 144788.123970882 | 10748.8760291178 |
91 | 153133 | 159631.615112706 | -6498.61511270635 |
92 | 165618 | 183996.198128702 | -18378.198128702 |
93 | 151517 | 116585.515652277 | 34931.4843477235 |
94 | 133686 | 130217.887022134 | 3468.11297786598 |
95 | 61342 | 97891.1785462072 | -36549.1785462072 |
96 | 245196 | 205129.678089208 | 40066.3219107923 |
97 | 195576 | 158899.83147322 | 36676.1685267797 |
98 | 19349 | 32266.1807052808 | -12917.1807052808 |
99 | 225371 | 212095.275299028 | 13275.7247009724 |
100 | 153213 | 188060.379235976 | -34847.3792359763 |
101 | 59117 | 75316.154334614 | -16199.154334614 |
102 | 91762 | 94023.2775751938 | -2261.27757519382 |
103 | 136769 | 118857.110102113 | 17911.8898978869 |
104 | 114798 | 104232.756493014 | 10565.2435069864 |
105 | 85338 | 78245.6815283251 | 7092.31847167491 |
106 | 27676 | 61525.1040570688 | -33849.1040570688 |
107 | 153535 | 123309.272581918 | 30225.7274180817 |
108 | 122417 | 94145.3981028521 | 28271.6018971479 |
109 | 0 | 13965.9689635505 | -13965.9689635505 |
110 | 91529 | 96440.3937916296 | -4911.3937916296 |
111 | 107205 | 111300.658731925 | -4095.65873192487 |
112 | 144664 | 123362.995196286 | 21301.0048037138 |
113 | 146445 | 132310.580415073 | 14134.4195849272 |
114 | 76656 | 91787.9210429079 | -15131.9210429079 |
115 | 3616 | 19752.0794268131 | -16136.0794268131 |
116 | 0 | 13965.9689635505 | -13965.9689635505 |
117 | 183088 | 106509.643036561 | 76578.3569634389 |
118 | 144677 | 151264.57786065 | -6587.5778606499 |
119 | 159104 | 173555.642516886 | -14451.6425168862 |
120 | 113273 | 87400.1654001177 | 25872.8345998823 |
121 | 43410 | 76878.6243707496 | -33468.6243707496 |
122 | 175774 | 152439.90496252 | 23334.0950374804 |
123 | 95401 | 87230.1022657524 | 8170.89773424758 |
124 | 134837 | 168364.459670515 | -33527.4596705148 |
125 | 60493 | 70131.3213305313 | -9638.32133053125 |
126 | 19764 | 35541.8367002097 | -15777.8367002097 |
127 | 164062 | 154423.310896294 | 9638.68910370612 |
128 | 132696 | 103388.604242285 | 29307.3957577154 |
129 | 155367 | 144248.089816391 | 11118.9101836086 |
130 | 11796 | 33895.9714768395 | -22099.9714768395 |
131 | 10674 | 23303.8096452596 | -12629.8096452596 |
132 | 142261 | 129294.896884958 | 12966.1031150424 |
133 | 6836 | 17424.6303889086 | -10588.6303889086 |
134 | 162563 | 161201.981770599 | 1361.01822940097 |
135 | 5118 | 17027.993707119 | -11909.993707119 |
136 | 40248 | 56153.0989554383 | -15905.0989554384 |
137 | 0 | 13965.9689635505 | -13965.9689635505 |
138 | 122641 | 100202.670039672 | 22438.3299603278 |
139 | 88837 | 101764.085279975 | -12927.0852799752 |
140 | 7131 | 20751.8294331513 | -13620.8294331513 |
141 | 9056 | 37176.4975552323 | -28120.4975552323 |
142 | 76611 | 81872.6485332414 | -5261.64853324143 |
143 | 132697 | 101846.293404401 | 30850.7065955987 |
144 | 100681 | 102892.787007349 | -2211.78700734923 |
Goldfeld-Quandt test for Heteroskedasticity | |||
p-values | Alternative Hypothesis | ||
breakpoint index | greater | 2-sided | less |
7 | 0.851533436140308 | 0.296933127719384 | 0.148466563859692 |
8 | 0.796213177976408 | 0.407573644047184 | 0.203786822023592 |
9 | 0.797197561612175 | 0.405604876775649 | 0.202802438387825 |
10 | 0.838678806807724 | 0.322642386384551 | 0.161321193192276 |
11 | 0.844908025412393 | 0.310183949175213 | 0.155091974587607 |
12 | 0.77756012075874 | 0.444879758482519 | 0.22243987924126 |
13 | 0.732477392488282 | 0.535045215023435 | 0.267522607511718 |
14 | 0.700036549494316 | 0.599926901011367 | 0.299963450505684 |
15 | 0.706009903358776 | 0.587980193282448 | 0.293990096641224 |
16 | 0.740204120168091 | 0.519591759663817 | 0.259795879831909 |
17 | 0.729882148047268 | 0.540235703905463 | 0.270117851952732 |
18 | 0.70253290455333 | 0.59493419089334 | 0.29746709544667 |
19 | 0.834003713327625 | 0.331992573344751 | 0.165996286672375 |
20 | 0.862975825370829 | 0.274048349258342 | 0.137024174629171 |
21 | 0.82671414769106 | 0.34657170461788 | 0.17328585230894 |
22 | 0.789354519661157 | 0.421290960677686 | 0.210645480338843 |
23 | 0.857220248305802 | 0.285559503388395 | 0.142779751694197 |
24 | 0.891537854477222 | 0.216924291045556 | 0.108462145522778 |
25 | 0.861068061997059 | 0.277863876005881 | 0.138931938002941 |
26 | 0.862442859879503 | 0.275114280240995 | 0.137557140120497 |
27 | 0.883290106415779 | 0.233419787168441 | 0.116709893584221 |
28 | 0.945116981655515 | 0.10976603668897 | 0.0548830183444848 |
29 | 0.999057904483847 | 0.0018841910323055 | 0.00094209551615275 |
30 | 0.998551986386585 | 0.00289602722682894 | 0.00144801361341447 |
31 | 0.998669342955412 | 0.00266131408917559 | 0.0013306570445878 |
32 | 0.998713270839566 | 0.00257345832086822 | 0.00128672916043411 |
33 | 0.99942349850734 | 0.00115300298532092 | 0.00057650149266046 |
34 | 0.999213841071949 | 0.00157231785610105 | 0.000786158928050526 |
35 | 0.998917469691589 | 0.00216506061682199 | 0.00108253030841099 |
36 | 0.998512518715147 | 0.00297496256970615 | 0.00148748128485308 |
37 | 0.998066367619436 | 0.00386726476112871 | 0.00193363238056436 |
38 | 0.998450587179079 | 0.00309882564184127 | 0.00154941282092064 |
39 | 0.997851640754677 | 0.00429671849064615 | 0.00214835924532307 |
40 | 0.998898256598235 | 0.00220348680352945 | 0.00110174340176473 |
41 | 0.999060156428465 | 0.00187968714306926 | 0.000939843571534631 |
42 | 0.998609437603347 | 0.00278112479330696 | 0.00139056239665348 |
43 | 0.997897483094529 | 0.00420503381094249 | 0.00210251690547125 |
44 | 0.996864070507985 | 0.0062718589840307 | 0.00313592949201535 |
45 | 0.995406324900629 | 0.00918735019874218 | 0.00459367509937109 |
46 | 0.996135664598018 | 0.00772867080396453 | 0.00386433540198227 |
47 | 0.994506401930426 | 0.0109871961391483 | 0.00549359806957415 |
48 | 0.994097486350929 | 0.0118050272981412 | 0.00590251364907062 |
49 | 0.993998366475866 | 0.0120032670482685 | 0.00600163352413424 |
50 | 0.99716035687557 | 0.00567928624886058 | 0.00283964312443029 |
51 | 0.99632656310817 | 0.00734687378366041 | 0.00367343689183021 |
52 | 0.994748496845373 | 0.0105030063092534 | 0.00525150315462669 |
53 | 0.999564119951148 | 0.000871760097703748 | 0.000435880048851874 |
54 | 0.999790676021169 | 0.00041864795766213 | 0.000209323978831065 |
55 | 0.999748968319188 | 0.000502063361624053 | 0.000251031680812026 |
56 | 0.999607348180676 | 0.000785303638648661 | 0.000392651819324331 |
57 | 0.999820217965619 | 0.000359564068761462 | 0.000179782034380731 |
58 | 0.999721711757758 | 0.000556576484482983 | 0.000278288242241492 |
59 | 0.99972329886059 | 0.000553402278820448 | 0.000276701139410224 |
60 | 0.99979921284632 | 0.000401574307359007 | 0.000200787153679503 |
61 | 0.999688513672911 | 0.00062297265417843 | 0.000311486327089215 |
62 | 0.999872233574422 | 0.000255532851155052 | 0.000127766425577526 |
63 | 0.999808206246103 | 0.000383587507794113 | 0.000191793753897057 |
64 | 0.999698876783135 | 0.000602246433730874 | 0.000301123216865437 |
65 | 0.999820605462697 | 0.000358789074606954 | 0.000179394537303477 |
66 | 0.999744737167821 | 0.000510525664358686 | 0.000255262832179343 |
67 | 0.999690303008771 | 0.000619393982458476 | 0.000309696991229238 |
68 | 0.999988488067239 | 2.30238655212474e-05 | 1.15119327606237e-05 |
69 | 0.999984890671464 | 3.02186570723634e-05 | 1.51093285361817e-05 |
70 | 0.999975782527718 | 4.84349445645018e-05 | 2.42174722822509e-05 |
71 | 0.999973473765006 | 5.30524699887588e-05 | 2.65262349943794e-05 |
72 | 0.999959552210355 | 8.08955792894085e-05 | 4.04477896447043e-05 |
73 | 0.999946742562267 | 0.000106514875466779 | 5.32574377333893e-05 |
74 | 0.999946139332165 | 0.000107721335669282 | 5.38606678346409e-05 |
75 | 0.999966897124946 | 6.6205750107573e-05 | 3.31028750537865e-05 |
76 | 0.99996237324274 | 7.52535145194007e-05 | 3.76267572597003e-05 |
77 | 0.999951199170114 | 9.7601659772213e-05 | 4.88008298861065e-05 |
78 | 0.999995720312777 | 8.55937444648144e-06 | 4.27968722324072e-06 |
79 | 0.999992937285386 | 1.41254292282643e-05 | 7.06271461413216e-06 |
80 | 0.999993714770284 | 1.25704594324994e-05 | 6.28522971624969e-06 |
81 | 0.999989106992396 | 2.17860152082235e-05 | 1.08930076041117e-05 |
82 | 0.999999889892746 | 2.20214507584187e-07 | 1.10107253792093e-07 |
83 | 0.999999865669261 | 2.68661478082407e-07 | 1.34330739041203e-07 |
84 | 0.999999737098204 | 5.25803591106028e-07 | 2.62901795553014e-07 |
85 | 0.999999637001971 | 7.25996058246046e-07 | 3.62998029123023e-07 |
86 | 0.999999297187827 | 1.40562434700607e-06 | 7.02812173503033e-07 |
87 | 0.999999388173813 | 1.22365237338991e-06 | 6.11826186694956e-07 |
88 | 0.99999912650768 | 1.74698464017803e-06 | 8.73492320089017e-07 |
89 | 0.999998763346678 | 2.47330664333002e-06 | 1.23665332166501e-06 |
90 | 0.999998074473865 | 3.85105226973924e-06 | 1.92552613486962e-06 |
91 | 0.999996331752484 | 7.33649503266342e-06 | 3.66824751633171e-06 |
92 | 0.999997541425044 | 4.91714991112949e-06 | 2.45857495556474e-06 |
93 | 0.999998084398616 | 3.83120276725964e-06 | 1.91560138362982e-06 |
94 | 0.999996363351226 | 7.27329754786327e-06 | 3.63664877393164e-06 |
95 | 0.999996587200455 | 6.82559908991721e-06 | 3.4127995449586e-06 |
96 | 0.99999572440808 | 8.55118384083403e-06 | 4.27559192041701e-06 |
97 | 0.999995450611434 | 9.09877713240821e-06 | 4.5493885662041e-06 |
98 | 0.999991513621133 | 1.69727577339799e-05 | 8.48637886698993e-06 |
99 | 0.999984070020845 | 3.18599583100421e-05 | 1.59299791550211e-05 |
100 | 0.99999014303287 | 1.97139342592327e-05 | 9.85696712961637e-06 |
101 | 0.999983505961506 | 3.29880769888866e-05 | 1.64940384944433e-05 |
102 | 0.999968646288719 | 6.270742256218e-05 | 3.135371128109e-05 |
103 | 0.999948207497123 | 0.000103585005753163 | 5.17925028765813e-05 |
104 | 0.999906433686141 | 0.000187132627717185 | 9.35663138585925e-05 |
105 | 0.999836887755163 | 0.000326224489674183 | 0.000163112244837091 |
106 | 0.999849019870409 | 0.000301960259181685 | 0.000150980129590843 |
107 | 0.999830694269703 | 0.000338611460594879 | 0.000169305730297439 |
108 | 0.999854724211512 | 0.000290551576976769 | 0.000145275788488385 |
109 | 0.999737885200746 | 0.000524229598508438 | 0.000262114799254219 |
110 | 0.999530853665982 | 0.000938292668036348 | 0.000469146334018174 |
111 | 0.999228595453255 | 0.00154280909348936 | 0.000771404546744681 |
112 | 0.998856454829107 | 0.00228709034178697 | 0.00114354517089349 |
113 | 0.998120081894732 | 0.00375983621053542 | 0.00187991810526771 |
114 | 0.997675313637544 | 0.00464937272491106 | 0.00232468636245553 |
115 | 0.996186047431053 | 0.00762790513789409 | 0.00381395256894705 |
116 | 0.993748384232929 | 0.012503231534143 | 0.0062516157670715 |
117 | 0.99987840327718 | 0.000243193445639626 | 0.000121596722819813 |
118 | 0.999872905728417 | 0.000254188543164988 | 0.000127094271582494 |
119 | 0.999982222814025 | 3.55543719506182e-05 | 1.77771859753091e-05 |
120 | 0.99998086000124 | 3.82799975192069e-05 | 1.91399987596035e-05 |
121 | 0.99998334418723 | 3.33116255399139e-05 | 1.66558127699569e-05 |
122 | 0.999958200193361 | 8.35996132772267e-05 | 4.17998066386134e-05 |
123 | 0.999898580346334 | 0.000202839307332079 | 0.000101419653666039 |
124 | 0.999984366872151 | 3.12662556979733e-05 | 1.56331278489866e-05 |
125 | 0.999972592886873 | 5.48142262546418e-05 | 2.74071131273209e-05 |
126 | 0.999926861539781 | 0.000146276920437242 | 7.31384602186212e-05 |
127 | 0.999801869793853 | 0.000396260412294499 | 0.000198130206147249 |
128 | 0.999955480091027 | 8.90398179470275e-05 | 4.45199089735138e-05 |
129 | 0.999856675536786 | 0.000286648926428576 | 0.000143324463214288 |
130 | 0.999657649324889 | 0.000684701350222002 | 0.000342350675111001 |
131 | 0.998969146415164 | 0.0020617071696713 | 0.00103085358483565 |
132 | 0.997007725189268 | 0.00598454962146338 | 0.00299227481073169 |
133 | 0.992012593306265 | 0.0159748133874693 | 0.00798740669373467 |
134 | 0.993240113021356 | 0.0135197739572871 | 0.00675988697864357 |
135 | 0.983556691563233 | 0.0328866168735336 | 0.0164433084367668 |
136 | 0.958900833003013 | 0.0821983339939741 | 0.0410991669969871 |
137 | 0.918955737485886 | 0.162088525028227 | 0.0810442625141135 |
Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
Description | # significant tests | % significant tests | OK/NOK |
1% type I error level | 99 | 0.755725190839695 | NOK |
5% type I error level | 107 | 0.816793893129771 | NOK |
10% type I error level | 108 | 0.824427480916031 | NOK |