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
VariableParameterS.D.T-STAT
H0: parameter = 0
2-tail p-value1-tail p-value
(Intercept)13965.96896355045912.4721912.36210.0195480.009774
page_views41.525743774615114.6002432.84420.005120.00256
number_course_compenium_views87.632485112841639.9042512.19610.0297330.014867
`number_logins `264.049531452567139.3847461.89440.0602350.030118


Multiple Linear Regression - Regression Statistics
Multiple R0.89676311271242
R-squared0.804184080321668
Adjusted R-squared0.799988024899989
F-TEST (value)191.652397193546
F-TEST (DF numerator)3
F-TEST (DF denominator)140
p-value0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation34574.6752426963
Sum Squared Residuals167357143539.308


Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolation
Forecast
Residuals
Prediction Error
1159261164134.977139941-4873.97713994132
2189672146413.48563894443258.5143610562
3721533001.3422625473-25786.3422625473
4129098190875.209312069-61777.2093120689
5230632295057.101449757-64425.1014497566
6515038538764.307317687-23726.3073176869
7180745154556.45659134126188.5434086593
8185559140536.93460741645022.0653925845
9154581157989.565176967-3408.56517696738
10298001249743.71120064148257.2887993589
11121844170137.776769436-48293.7767694356
12184039180709.8766830453329.12331695534
13100324174193.588241037-73869.5882410366
14220269272119.757077762-51850.757077762
15168265126765.05595073541499.9440492651
16154647143372.80374412111274.196255879
17142018139705.5994082062312.40059179431
1879030113490.919994838-34460.9199948379
19167047229192.009593541-62145.0095935413
202799769817.6269087207-41820.6269087207
2173019105137.360346349-32118.3603463486
22241082230987.71580206710094.2841979334
23195820162322.89971390233497.1002860978
24142001182700.761298015-40699.7612980148
25145433163890.114588957-18457.1145889568
26183744145011.733273638732.2667263998
27202357202522.355097559-165.355097559215
28199532129954.97354982169577.0264501792
29354924238428.541358521116495.458641479
30192399190578.3710689771820.62893102312
31182286138453.41856920843832.5814307923
32181590140976.40166053140613.5983394688
33133801197527.287888722-63726.2878887224
34233686255122.179441816-21436.1794418163
35219428196132.36179189823295.6382081016
36014271.5442387776-14271.5442387776
37223044203906.35849390319137.6415060973
38100129143972.870903286-43843.8709032857
39145864160775.640284192-14911.6402841922
40249965189937.8909879760027.1090120298
41242379197947.27460798344431.7253920174
42145794155826.809526527-10032.8095265267
439640494870.68722621511533.31277378489
44195891194755.4827445191135.51725548135
45117156114682.4937270472473.50627295268
46157787116508.70477944641278.2952205543
478129371930.31992604339362.68007395669
48237435205042.23314222732392.7668577733
49233155197366.84374642635788.1562535742
50160344221330.600176307-60986.6001763067
514818866647.9546960516-18459.9546960516
52161922154905.4201252337016.57987476714
53307432211370.33394503696061.6660549642
54235223178547.12871240656675.8712875942
55195583169454.63488551526128.365114485
56146061146806.666092391-745.666092391205
57208834151239.98529141457594.0147085865
589376487417.29038027486346.70961972515
59151985117162.31469464834822.6853053518
60193222239945.119498343-46723.1194983426
61148922143019.5790177735902.4209822271
62132856191399.079414269-58543.0794142686
63129561117066.71495701812494.2850429815
64112718113075.795481439-357.795481438563
65160930111819.15055224949110.849447751
6699184114367.99860861-15183.9986086099
67192535171724.20166436420810.7983356361
68138708229159.282518118-90451.2825181179
6911440893200.620067277221207.3799327228
703197040896.3458151051-8926.34581510513
71225558247070.35247403-21512.3524740304
72139220124994.09420551214225.9057944876
73113612133823.526735709-20211.5267357094
74108641139894.916084113-31253.9160841132
75162203200501.906084319-38298.9060843193
76100098124023.454617215-23925.4546172151
77174768184728.395441262-9960.3954412623
78158459216912.800494502-58453.800494502
798093491105.0639774006-10171.0639774006
8084971118571.08513413-33600.0851341302
818054589431.9508508799-8886.95085087988
82287191192908.53025238294282.4697476183
836297486688.1782894788-23714.1782894788
84134091133889.843678969201.156321031037
857555598452.5589617587-22897.5589617587
86162154150578.03009468511575.9699053147
87226638238934.933984135-12296.9339841353
88115367118465.663506696-3098.66350669622
89108749123013.133028115-14264.1330281149
90155537144788.12397088210748.8760291178
91153133159631.615112706-6498.61511270635
92165618183996.198128702-18378.198128702
93151517116585.51565227734931.4843477235
94133686130217.8870221343468.11297786598
956134297891.1785462072-36549.1785462072
96245196205129.67808920840066.3219107923
97195576158899.8314732236676.1685267797
981934932266.1807052808-12917.1807052808
99225371212095.27529902813275.7247009724
100153213188060.379235976-34847.3792359763
1015911775316.154334614-16199.154334614
1029176294023.2775751938-2261.27757519382
103136769118857.11010211317911.8898978869
104114798104232.75649301410565.2435069864
1058533878245.68152832517092.31847167491
1062767661525.1040570688-33849.1040570688
107153535123309.27258191830225.7274180817
10812241794145.398102852128271.6018971479
109013965.9689635505-13965.9689635505
1109152996440.3937916296-4911.3937916296
111107205111300.658731925-4095.65873192487
112144664123362.99519628621301.0048037138
113146445132310.58041507314134.4195849272
1147665691787.9210429079-15131.9210429079
115361619752.0794268131-16136.0794268131
116013965.9689635505-13965.9689635505
117183088106509.64303656176578.3569634389
118144677151264.57786065-6587.5778606499
119159104173555.642516886-14451.6425168862
12011327387400.165400117725872.8345998823
1214341076878.6243707496-33468.6243707496
122175774152439.9049625223334.0950374804
1239540187230.10226575248170.89773424758
124134837168364.459670515-33527.4596705148
1256049370131.3213305313-9638.32133053125
1261976435541.8367002097-15777.8367002097
127164062154423.3108962949638.68910370612
128132696103388.60424228529307.3957577154
129155367144248.08981639111118.9101836086
1301179633895.9714768395-22099.9714768395
1311067423303.8096452596-12629.8096452596
132142261129294.89688495812966.1031150424
133683617424.6303889086-10588.6303889086
134162563161201.9817705991361.01822940097
135511817027.993707119-11909.993707119
1364024856153.0989554383-15905.0989554384
137013965.9689635505-13965.9689635505
138122641100202.67003967222438.3299603278
13988837101764.085279975-12927.0852799752
140713120751.8294331513-13620.8294331513
141905637176.4975552323-28120.4975552323
1427661181872.6485332414-5261.64853324143
143132697101846.29340440130850.7065955987
144100681102892.787007349-2211.78700734923


Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
70.8515334361403080.2969331277193840.148466563859692
80.7962131779764080.4075736440471840.203786822023592
90.7971975616121750.4056048767756490.202802438387825
100.8386788068077240.3226423863845510.161321193192276
110.8449080254123930.3101839491752130.155091974587607
120.777560120758740.4448797584825190.22243987924126
130.7324773924882820.5350452150234350.267522607511718
140.7000365494943160.5999269010113670.299963450505684
150.7060099033587760.5879801932824480.293990096641224
160.7402041201680910.5195917596638170.259795879831909
170.7298821480472680.5402357039054630.270117851952732
180.702532904553330.594934190893340.29746709544667
190.8340037133276250.3319925733447510.165996286672375
200.8629758253708290.2740483492583420.137024174629171
210.826714147691060.346571704617880.17328585230894
220.7893545196611570.4212909606776860.210645480338843
230.8572202483058020.2855595033883950.142779751694197
240.8915378544772220.2169242910455560.108462145522778
250.8610680619970590.2778638760058810.138931938002941
260.8624428598795030.2751142802409950.137557140120497
270.8832901064157790.2334197871684410.116709893584221
280.9451169816555150.109766036688970.0548830183444848
290.9990579044838470.00188419103230550.00094209551615275
300.9985519863865850.002896027226828940.00144801361341447
310.9986693429554120.002661314089175590.0013306570445878
320.9987132708395660.002573458320868220.00128672916043411
330.999423498507340.001153002985320920.00057650149266046
340.9992138410719490.001572317856101050.000786158928050526
350.9989174696915890.002165060616821990.00108253030841099
360.9985125187151470.002974962569706150.00148748128485308
370.9980663676194360.003867264761128710.00193363238056436
380.9984505871790790.003098825641841270.00154941282092064
390.9978516407546770.004296718490646150.00214835924532307
400.9988982565982350.002203486803529450.00110174340176473
410.9990601564284650.001879687143069260.000939843571534631
420.9986094376033470.002781124793306960.00139056239665348
430.9978974830945290.004205033810942490.00210251690547125
440.9968640705079850.00627185898403070.00313592949201535
450.9954063249006290.009187350198742180.00459367509937109
460.9961356645980180.007728670803964530.00386433540198227
470.9945064019304260.01098719613914830.00549359806957415
480.9940974863509290.01180502729814120.00590251364907062
490.9939983664758660.01200326704826850.00600163352413424
500.997160356875570.005679286248860580.00283964312443029
510.996326563108170.007346873783660410.00367343689183021
520.9947484968453730.01050300630925340.00525150315462669
530.9995641199511480.0008717600977037480.000435880048851874
540.9997906760211690.000418647957662130.000209323978831065
550.9997489683191880.0005020633616240530.000251031680812026
560.9996073481806760.0007853036386486610.000392651819324331
570.9998202179656190.0003595640687614620.000179782034380731
580.9997217117577580.0005565764844829830.000278288242241492
590.999723298860590.0005534022788204480.000276701139410224
600.999799212846320.0004015743073590070.000200787153679503
610.9996885136729110.000622972654178430.000311486327089215
620.9998722335744220.0002555328511550520.000127766425577526
630.9998082062461030.0003835875077941130.000191793753897057
640.9996988767831350.0006022464337308740.000301123216865437
650.9998206054626970.0003587890746069540.000179394537303477
660.9997447371678210.0005105256643586860.000255262832179343
670.9996903030087710.0006193939824584760.000309696991229238
680.9999884880672392.30238655212474e-051.15119327606237e-05
690.9999848906714643.02186570723634e-051.51093285361817e-05
700.9999757825277184.84349445645018e-052.42174722822509e-05
710.9999734737650065.30524699887588e-052.65262349943794e-05
720.9999595522103558.08955792894085e-054.04477896447043e-05
730.9999467425622670.0001065148754667795.32574377333893e-05
740.9999461393321650.0001077213356692825.38606678346409e-05
750.9999668971249466.6205750107573e-053.31028750537865e-05
760.999962373242747.52535145194007e-053.76267572597003e-05
770.9999511991701149.7601659772213e-054.88008298861065e-05
780.9999957203127778.55937444648144e-064.27968722324072e-06
790.9999929372853861.41254292282643e-057.06271461413216e-06
800.9999937147702841.25704594324994e-056.28522971624969e-06
810.9999891069923962.17860152082235e-051.08930076041117e-05
820.9999998898927462.20214507584187e-071.10107253792093e-07
830.9999998656692612.68661478082407e-071.34330739041203e-07
840.9999997370982045.25803591106028e-072.62901795553014e-07
850.9999996370019717.25996058246046e-073.62998029123023e-07
860.9999992971878271.40562434700607e-067.02812173503033e-07
870.9999993881738131.22365237338991e-066.11826186694956e-07
880.999999126507681.74698464017803e-068.73492320089017e-07
890.9999987633466782.47330664333002e-061.23665332166501e-06
900.9999980744738653.85105226973924e-061.92552613486962e-06
910.9999963317524847.33649503266342e-063.66824751633171e-06
920.9999975414250444.91714991112949e-062.45857495556474e-06
930.9999980843986163.83120276725964e-061.91560138362982e-06
940.9999963633512267.27329754786327e-063.63664877393164e-06
950.9999965872004556.82559908991721e-063.4127995449586e-06
960.999995724408088.55118384083403e-064.27559192041701e-06
970.9999954506114349.09877713240821e-064.5493885662041e-06
980.9999915136211331.69727577339799e-058.48637886698993e-06
990.9999840700208453.18599583100421e-051.59299791550211e-05
1000.999990143032871.97139342592327e-059.85696712961637e-06
1010.9999835059615063.29880769888866e-051.64940384944433e-05
1020.9999686462887196.270742256218e-053.135371128109e-05
1030.9999482074971230.0001035850057531635.17925028765813e-05
1040.9999064336861410.0001871326277171859.35663138585925e-05
1050.9998368877551630.0003262244896741830.000163112244837091
1060.9998490198704090.0003019602591816850.000150980129590843
1070.9998306942697030.0003386114605948790.000169305730297439
1080.9998547242115120.0002905515769767690.000145275788488385
1090.9997378852007460.0005242295985084380.000262114799254219
1100.9995308536659820.0009382926680363480.000469146334018174
1110.9992285954532550.001542809093489360.000771404546744681
1120.9988564548291070.002287090341786970.00114354517089349
1130.9981200818947320.003759836210535420.00187991810526771
1140.9976753136375440.004649372724911060.00232468636245553
1150.9961860474310530.007627905137894090.00381395256894705
1160.9937483842329290.0125032315341430.0062516157670715
1170.999878403277180.0002431934456396260.000121596722819813
1180.9998729057284170.0002541885431649880.000127094271582494
1190.9999822228140253.55543719506182e-051.77771859753091e-05
1200.999980860001243.82799975192069e-051.91399987596035e-05
1210.999983344187233.33116255399139e-051.66558127699569e-05
1220.9999582001933618.35996132772267e-054.17998066386134e-05
1230.9998985803463340.0002028393073320790.000101419653666039
1240.9999843668721513.12662556979733e-051.56331278489866e-05
1250.9999725928868735.48142262546418e-052.74071131273209e-05
1260.9999268615397810.0001462769204372427.31384602186212e-05
1270.9998018697938530.0003962604122944990.000198130206147249
1280.9999554800910278.90398179470275e-054.45199089735138e-05
1290.9998566755367860.0002866489264285760.000143324463214288
1300.9996576493248890.0006847013502220020.000342350675111001
1310.9989691464151640.00206170716967130.00103085358483565
1320.9970077251892680.005984549621463380.00299227481073169
1330.9920125933062650.01597481338746930.00798740669373467
1340.9932401130213560.01351977395728710.00675988697864357
1350.9835566915632330.03288661687353360.0164433084367668
1360.9589008330030130.08219833399397410.0410991669969871
1370.9189557374858860.1620885250282270.0810442625141135


Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level990.755725190839695NOK
5% type I error level1070.816793893129771NOK
10% type I error level1080.824427480916031NOK