Multiple Linear Regression - Estimated Regression Equation |
time[t] = + 11489.3212413663 + 158.305304711761comp[t] + 998.640799783652blog[t] -1782.2058980465review[t] + 886.630562666766fbm[t] + 0.965385019668044charac[t] -52.6499459504649t + 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) | 11489.3212413663 | 6404.995375 | 1.7938 | 0.07505 | 0.037525 |
comp | 158.305304711761 | 60.832624 | 2.6023 | 0.010279 | 0.005139 |
blog | 998.640799783652 | 161.413108 | 6.1869 | 0 | 0 |
review | -1782.2058980465 | 803.985513 | -2.2167 | 0.028292 | 0.014146 |
fbm | 886.630562666766 | 228.836011 | 3.8745 | 0.000165 | 8.2e-05 |
charac | 0.965385019668044 | 0.18498 | 5.2189 | 1e-06 | 0 |
t | -52.6499459504649 | 46.511184 | -1.132 | 0.259618 | 0.129809 |
Multiple Linear Regression - Regression Statistics | |
Multiple R | 0.856216044194739 |
R-squared | 0.733105914336488 |
Adjusted R-squared | 0.721417122263633 |
F-TEST (value) | 62.7187060704943 |
F-TEST (DF numerator) | 6 |
F-TEST (DF denominator) | 137 |
p-value | 0 |
Multiple Linear Regression - Residual Statistics | |
Residual Standard Deviation | 19992.1039782133 |
Sum Squared Residuals | 54756738342.1699 |
Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
1 | 63031 | 53992.2522045717 | 9038.74779542831 |
2 | 66751 | 63181.2068949121 | 3569.79310508793 |
3 | 7176 | 12863.4195912143 | -5687.41959121431 |
4 | 78306 | 89070.390409156 | -10764.390409156 |
5 | 137944 | 119257.054812903 | 18686.9451870969 |
6 | 261308 | 228129.067675008 | 33178.9323249922 |
7 | 69266 | 66476.1920038006 | 2789.80799619941 |
8 | 80226 | 87919.8402354819 | -7693.84023548188 |
9 | 73226 | 73492.4087720934 | -266.408772093367 |
10 | 178519 | 113403.66889252 | 65115.3311074795 |
11 | 66476 | 89746.2033774511 | -23270.2033774511 |
12 | 98606 | 102256.534977582 | -3650.53497758203 |
13 | 50001 | 48429.9903302722 | 1571.00966972783 |
14 | 91093 | 99354.9230277774 | -8261.9230277774 |
15 | 73884 | 66260.1618854851 | 7623.83811451489 |
16 | 72961 | 71936.6852519044 | 1024.3147480956 |
17 | 69388 | 131279.242165411 | -61891.2421654114 |
18 | 15629 | 24702.1977552815 | -9073.19775528155 |
19 | 71693 | 108244.917632334 | -36551.9176323342 |
20 | 19920 | 59651.7864294824 | -39731.7864294824 |
21 | 39403 | 38163.0218671497 | 1239.97813285027 |
22 | 99933 | 123339.188993024 | -23406.1889930238 |
23 | 56088 | 40990.6072423565 | 15097.3927576435 |
24 | 62006 | 73719.9754998732 | -11713.9754998732 |
25 | 81665 | 72679.8236416484 | 8985.17635835164 |
26 | 65223 | 59796.9695297346 | 5426.03047026538 |
27 | 88794 | 85657.5605141219 | 3136.43948587812 |
28 | 90642 | 80791.19688541 | 9850.80311459003 |
29 | 203699 | 135316.213967927 | 68382.7860320725 |
30 | 99340 | 59218.6465346436 | 40121.3534653564 |
31 | 56695 | 61696.1942235063 | -5001.1942235063 |
32 | 108143 | 84418.1575515073 | 23724.8424484927 |
33 | 58313 | 69194.9730478232 | -10881.9730478232 |
34 | 29101 | 43325.281020385 | -14224.281020385 |
35 | 113060 | 76943.7855916598 | 36116.2144083402 |
36 | 0 | 9593.92318714956 | -9593.92318714956 |
37 | 65773 | 41800.7726514754 | 23972.2273485246 |
38 | 67047 | 82555.6803698381 | -15508.6803698381 |
39 | 41953 | 84397.6054984044 | -42444.6054984044 |
40 | 109835 | 130297.110681854 | -20462.1106818541 |
41 | 86584 | 90014.9331590008 | -3430.93315900078 |
42 | 59588 | 58061.9837863741 | 1526.01621362591 |
43 | 40064 | 54822.947137437 | -14758.947137437 |
44 | 70227 | 78328.4000409084 | -8101.40004090839 |
45 | 60437 | 86462.9365714865 | -26025.9365714865 |
46 | 47000 | 35705.593620853 | 11294.406379147 |
47 | 40295 | 36292.1730139892 | 4002.82698601075 |
48 | 103397 | 82617.8983444013 | 20779.1016555987 |
49 | 78982 | 77835.6272619876 | 1146.37273801243 |
50 | 60206 | 66152.7336717985 | -5946.73367179854 |
51 | 39887 | 29666.57984591 | 10220.42015409 |
52 | 49791 | 46499.2095473598 | 3291.79045264016 |
53 | 129283 | 81769.6973069214 | 47513.3026930786 |
54 | 104816 | 77090.6459287719 | 27725.3540712281 |
55 | 101395 | 96955.6614312554 | 4439.3385687446 |
56 | 72824 | 52514.1530547869 | 20309.8469452131 |
57 | 76018 | 65111.4354162438 | 10906.5645837562 |
58 | 33891 | 38955.4727517325 | -5064.47275173246 |
59 | 62164 | 73976.9876906732 | -11812.9876906732 |
60 | 28266 | 41661.7493060307 | -13395.7493060307 |
61 | 35093 | 41405.0618580813 | -6312.06185808134 |
62 | 35252 | 48139.0798084682 | -12887.0798084682 |
63 | 36977 | 54345.546913134 | -17368.546913134 |
64 | 42406 | 46442.7048737424 | -4036.70487374237 |
65 | 56353 | 41622.8914383707 | 14730.1085616293 |
66 | 58817 | 72098.7316619135 | -13281.7316619135 |
67 | 76053 | 93077.361278796 | -17024.361278796 |
68 | 70872 | 86089.6544838365 | -15217.6544838365 |
69 | 42372 | 58108.9043300536 | -15736.9043300536 |
70 | 19144 | 19361.2552443755 | -217.255244375533 |
71 | 114177 | 83123.9736145892 | 31053.0263854108 |
72 | 53544 | 55117.8808251584 | -1573.88082515843 |
73 | 51379 | 81031.1352583095 | -29652.1352583095 |
74 | 40756 | 56342.6507128495 | -15586.6507128495 |
75 | 46956 | 75240.1923741913 | -28284.1923741913 |
76 | 17799 | 22637.8871080703 | -4838.88710807035 |
77 | 71154 | 69615.2927417207 | 1538.70725827928 |
78 | 58305 | 78392.2708172123 | -20087.2708172123 |
79 | 27454 | 41271.7911277122 | -13817.7911277122 |
80 | 34323 | 58974.8505558128 | -24651.8505558128 |
81 | 44761 | 68604.2745807003 | -23843.2745807003 |
82 | 113862 | 51319.0903326323 | 62542.9096673677 |
83 | 35027 | 26320.1582429055 | 8706.84175709452 |
84 | 62396 | 65727.801980106 | -3331.80198010599 |
85 | 29613 | 43557.2190133282 | -13944.2190133282 |
86 | 65559 | 51738.6159357303 | 13820.3840642697 |
87 | 110811 | 89567.6029865071 | 21243.3970134929 |
88 | 27883 | 42743.002293892 | -14860.002293892 |
89 | 40181 | 48574.2063403702 | -8393.20634037015 |
90 | 53398 | 57784.791275072 | -4386.79127507196 |
91 | 56435 | 56061.3351462598 | 373.664853740196 |
92 | 77283 | 88374.3583791358 | -11091.3583791358 |
93 | 71738 | 55083.4326085045 | 16654.5673914955 |
94 | 48503 | 49829.5806849795 | -1326.58068497953 |
95 | 25214 | 31567.8245639877 | -6353.82456398767 |
96 | 119424 | 69983.3879337105 | 49440.6120662895 |
97 | 79201 | 95871.3685606863 | -16670.3685606863 |
98 | 19349 | 23664.5052596452 | -4315.50525964516 |
99 | 78760 | 54747.740529223 | 24012.259470777 |
100 | 54133 | 39786.2309920099 | 14346.7690079901 |
101 | 21623 | 16617.8850669693 | 5005.11493303065 |
102 | 25497 | 52615.4835178412 | -27118.4835178412 |
103 | 69535 | 54721.9566762828 | 14813.0433237172 |
104 | 30709 | 28248.8818201903 | 2460.11817980975 |
105 | 37043 | 29685.3177865718 | 7357.68221342818 |
106 | 24716 | 5717.32790673527 | 18998.6720932647 |
107 | 54865 | 79918.3015703765 | -25053.3015703765 |
108 | 27246 | 18155.0795567102 | 9090.92044328982 |
109 | 0 | 5750.47713276562 | -5750.47713276562 |
110 | 38814 | 49482.4071251334 | -10668.4071251334 |
111 | 27646 | 50956.5053366955 | -23310.5053366955 |
112 | 65373 | 65276.4391905936 | 96.5608094063615 |
113 | 43021 | 67725.767646466 | -24704.767646466 |
114 | 43116 | 49335.2429621308 | -6219.24296213082 |
115 | 3058 | 5434.57745706284 | -2376.57745706284 |
116 | 0 | 5381.92751111237 | -5381.92751111237 |
117 | 96347 | 75133.3929769757 | 21213.6070230243 |
118 | 48626 | 55789.2050098966 | -7163.20500989662 |
119 | 73073 | 42283.7693211288 | 30789.2306788712 |
120 | 45266 | 61677.0267291209 | -16411.0267291209 |
121 | 43410 | 25644.8191063372 | 17765.1808936628 |
122 | 83842 | 89023.0873550641 | -5181.08735506412 |
123 | 39296 | 39336.4372973149 | -40.4372973149055 |
124 | 38490 | 44686.8272046868 | -6196.82720468678 |
125 | 39841 | 29002.9790640556 | 10838.0209359444 |
126 | 19764 | 23256.2457190565 | -3492.2457190565 |
127 | 59975 | 69498.2065821565 | -9523.20658215648 |
128 | 64589 | 48060.7050105423 | 16528.2949894577 |
129 | 63339 | 77906.3743466647 | -14567.3743466647 |
130 | 11796 | 6448.40453782201 | 5347.59546217799 |
131 | 7627 | 5700.31545483772 | 1926.68454516228 |
132 | 68998 | 42255.0610248012 | 26742.9389751988 |
133 | 6836 | 3496.19905546677 | 3339.80094453323 |
134 | 33365 | 31756.7192309157 | 1608.2807690843 |
135 | 5118 | 9533.08784168356 | -4415.08784168356 |
136 | 20898 | 13235.989364361 | 7662.01063563896 |
137 | 0 | 4276.27864615261 | -4276.27864615261 |
138 | 42690 | 44145.5474679492 | -1455.54746794923 |
139 | 14507 | 15396.5005432571 | -889.500543257135 |
140 | 7131 | 4118.32880830121 | 3012.67119169879 |
141 | 4194 | 4698.90008119779 | -504.900081197792 |
142 | 21416 | 32508.2776465339 | -11092.2776465339 |
143 | 30591 | 31672.5502514645 | -1081.5502514645 |
144 | 42419 | 32702.8896807762 | 9716.11031922377 |
Goldfeld-Quandt test for Heteroskedasticity | |||
p-values | Alternative Hypothesis | ||
breakpoint index | greater | 2-sided | less |
10 | 0.748145984486609 | 0.503708031026782 | 0.251854015513391 |
11 | 0.89829172782934 | 0.20341654434132 | 0.10170827217066 |
12 | 0.827983181597481 | 0.344033636805038 | 0.172016818402519 |
13 | 0.752398489769843 | 0.495203020460314 | 0.247601510230157 |
14 | 0.839137871760219 | 0.321724256479562 | 0.160862128239781 |
15 | 0.769156465412538 | 0.461687069174924 | 0.230843534587462 |
16 | 0.706526694319837 | 0.586946611360327 | 0.293473305680163 |
17 | 0.981235123939862 | 0.0375297521202758 | 0.0187648760601379 |
18 | 0.970931781915066 | 0.0581364361698685 | 0.0290682180849343 |
19 | 0.974514525277999 | 0.0509709494440029 | 0.0254854747220014 |
20 | 0.977567378243615 | 0.0448652435127695 | 0.0224326217563847 |
21 | 0.980799482808634 | 0.0384010343827317 | 0.0192005171913658 |
22 | 0.974018993783847 | 0.0519620124323055 | 0.0259810062161527 |
23 | 0.980622522304269 | 0.0387549553914628 | 0.0193774776957314 |
24 | 0.972679669484143 | 0.0546406610317132 | 0.0273203305158566 |
25 | 0.981390115605672 | 0.0372197687886559 | 0.018609884394328 |
26 | 0.976155396809783 | 0.0476892063804333 | 0.0238446031902166 |
27 | 0.970323484943156 | 0.059353030113688 | 0.029676515056844 |
28 | 0.969848237163514 | 0.0603035256729727 | 0.0301517628364864 |
29 | 0.999395955226405 | 0.00120808954718945 | 0.000604044773594725 |
30 | 0.999820501026468 | 0.000358997947063078 | 0.000179498973531539 |
31 | 0.999698315410219 | 0.000603369179561311 | 0.000301684589780655 |
32 | 0.999678750605867 | 0.000642498788266976 | 0.000321249394133488 |
33 | 0.999655054851005 | 0.000689890297990051 | 0.000344945148995026 |
34 | 0.999557559781152 | 0.000884880437695057 | 0.000442440218847528 |
35 | 0.999798088251677 | 0.000403823496646096 | 0.000201911748323048 |
36 | 0.999715520015215 | 0.000568959969570414 | 0.000284479984785207 |
37 | 0.999730854110119 | 0.000538291779761914 | 0.000269145889880957 |
38 | 0.99968699485398 | 0.000626010292040485 | 0.000313005146020243 |
39 | 0.999953730091663 | 9.25398166743852e-05 | 4.62699083371926e-05 |
40 | 0.999960074366038 | 7.98512679231146e-05 | 3.99256339615573e-05 |
41 | 0.99993319038953 | 0.00013361922093963 | 6.68096104698152e-05 |
42 | 0.999888474240421 | 0.000223051519157389 | 0.000111525759578695 |
43 | 0.999852226611709 | 0.000295546776581993 | 0.000147773388290997 |
44 | 0.999765884927175 | 0.000468230145650098 | 0.000234115072825049 |
45 | 0.999785735040299 | 0.000428529919401207 | 0.000214264959700604 |
46 | 0.999725742085726 | 0.00054851582854782 | 0.00027425791427391 |
47 | 0.999584308682437 | 0.000831382635125713 | 0.000415691317562857 |
48 | 0.999645058853246 | 0.000709882293507613 | 0.000354941146753807 |
49 | 0.999441096013502 | 0.0011178079729962 | 0.000558903986498098 |
50 | 0.999186529196834 | 0.00162694160633093 | 0.000813470803165465 |
51 | 0.998913064753175 | 0.00217387049365061 | 0.00108693524682531 |
52 | 0.998365795538374 | 0.00326840892325106 | 0.00163420446162553 |
53 | 0.999842369655399 | 0.00031526068920289 | 0.000157630344601445 |
54 | 0.999945336414686 | 0.000109327170628197 | 5.46635853140987e-05 |
55 | 0.99993739418716 | 0.000125211625679069 | 6.26058128395346e-05 |
56 | 0.999949292263657 | 0.000101415472685645 | 5.07077363428226e-05 |
57 | 0.999959215528425 | 8.15689431496465e-05 | 4.07844715748232e-05 |
58 | 0.999935086538146 | 0.000129826923708578 | 6.49134618542892e-05 |
59 | 0.999915589630383 | 0.000168820739234593 | 8.44103696172967e-05 |
60 | 0.99988407406206 | 0.000231851875879392 | 0.000115925937939696 |
61 | 0.99983853012137 | 0.000322939757259055 | 0.000161469878629528 |
62 | 0.999817034018936 | 0.000365931962128035 | 0.000182965981064017 |
63 | 0.999845886796605 | 0.000308226406789825 | 0.000154113203394912 |
64 | 0.999757272363483 | 0.000485455273033059 | 0.00024272763651653 |
65 | 0.999751259231532 | 0.000497481536935929 | 0.000248740768467964 |
66 | 0.999655793334099 | 0.000688413331801558 | 0.000344206665900779 |
67 | 0.999555876227571 | 0.000888247544857538 | 0.000444123772428769 |
68 | 0.999778063441068 | 0.000443873117864112 | 0.000221936558932056 |
69 | 0.999707203725435 | 0.000585592549129767 | 0.000292796274564883 |
70 | 0.999567348378033 | 0.000865303243933441 | 0.00043265162196672 |
71 | 0.999610256599398 | 0.000779486801203807 | 0.000389743400601904 |
72 | 0.999427760629599 | 0.00114447874080142 | 0.000572239370400711 |
73 | 0.999514394987881 | 0.000971210024237672 | 0.000485605012118836 |
74 | 0.999528332110793 | 0.000943335778414537 | 0.000471667889207269 |
75 | 0.999830335529665 | 0.000339328940670376 | 0.000169664470335188 |
76 | 0.999867400154054 | 0.00026519969189271 | 0.000132599845946355 |
77 | 0.99983282067691 | 0.00033435864617944 | 0.00016717932308972 |
78 | 0.999790988355062 | 0.000418023289875097 | 0.000209011644937548 |
79 | 0.999842953343605 | 0.000314093312790684 | 0.000157046656395342 |
80 | 0.999819426699017 | 0.000361146601965859 | 0.000180573300982929 |
81 | 0.99982844254291 | 0.000343114914180766 | 0.000171557457090383 |
82 | 0.999999917838008 | 1.64323984406658e-07 | 8.21619922033288e-08 |
83 | 0.999999868826389 | 2.62347221016578e-07 | 1.31173610508289e-07 |
84 | 0.999999836099772 | 3.27800456604794e-07 | 1.63900228302397e-07 |
85 | 0.999999827235123 | 3.45529754689068e-07 | 1.72764877344534e-07 |
86 | 0.999999709966655 | 5.80066689136708e-07 | 2.90033344568354e-07 |
87 | 0.999999810944286 | 3.78111427256323e-07 | 1.89055713628161e-07 |
88 | 0.999999882056276 | 2.35887447975915e-07 | 1.17943723987957e-07 |
89 | 0.999999766838469 | 4.66323062677581e-07 | 2.3316153133879e-07 |
90 | 0.999999747802039 | 5.0439592210111e-07 | 2.52197961050555e-07 |
91 | 0.99999957982031 | 8.40359380168547e-07 | 4.20179690084274e-07 |
92 | 0.999999265358665 | 1.46928266972103e-06 | 7.34641334860515e-07 |
93 | 0.999999224139041 | 1.55172191906271e-06 | 7.75860959531356e-07 |
94 | 0.999998414559997 | 3.17088000646141e-06 | 1.58544000323071e-06 |
95 | 0.999996882420199 | 6.23515960222308e-06 | 3.11757980111154e-06 |
96 | 0.999999321898678 | 1.3562026438032e-06 | 6.78101321901598e-07 |
97 | 0.999998735744693 | 2.52851061470941e-06 | 1.2642553073547e-06 |
98 | 0.999997415800267 | 5.16839946669951e-06 | 2.58419973334975e-06 |
99 | 0.999996469103634 | 7.06179273211056e-06 | 3.53089636605528e-06 |
100 | 0.999995413007121 | 9.17398575786925e-06 | 4.58699287893462e-06 |
101 | 0.999992506356716 | 1.498728656737e-05 | 7.49364328368501e-06 |
102 | 0.999992945692889 | 1.41086142227926e-05 | 7.05430711139629e-06 |
103 | 0.999989274108047 | 2.14517839053427e-05 | 1.07258919526714e-05 |
104 | 0.999978728541446 | 4.25429171075635e-05 | 2.12714585537817e-05 |
105 | 0.999964472864727 | 7.10542705466741e-05 | 3.5527135273337e-05 |
106 | 0.999938966782781 | 0.000122066434437854 | 6.10332172189269e-05 |
107 | 0.999958216704061 | 8.35665918774764e-05 | 4.17832959387382e-05 |
108 | 0.999949468536439 | 0.0001010629271219 | 5.05314635609499e-05 |
109 | 0.999899185670443 | 0.000201628659113597 | 0.000100814329556799 |
110 | 0.999809457517036 | 0.000381084965927166 | 0.000190542482963583 |
111 | 0.999858628181127 | 0.000282743637744953 | 0.000141371818872477 |
112 | 0.999810822483618 | 0.000378355032763729 | 0.000189177516381865 |
113 | 0.999884126708294 | 0.000231746583412871 | 0.000115873291706435 |
114 | 0.999769349324518 | 0.000461301350963392 | 0.000230650675481696 |
115 | 0.999553565711279 | 0.000892868577442006 | 0.000446434288721003 |
116 | 0.9993157237732 | 0.00136855245360026 | 0.000684276226800129 |
117 | 0.999783618800828 | 0.000432762398343517 | 0.000216381199171759 |
118 | 0.999873025495774 | 0.00025394900845211 | 0.000126974504226055 |
119 | 0.999869312714939 | 0.000261374570121447 | 0.000130687285060723 |
120 | 0.999951014377794 | 9.79712444124171e-05 | 4.89856222062086e-05 |
121 | 0.999903297323996 | 0.000193405352007914 | 9.67026760039571e-05 |
122 | 0.999755556955389 | 0.000488886089221188 | 0.000244443044610594 |
123 | 0.999401914505642 | 0.00119617098871667 | 0.000598085494358334 |
124 | 0.998590193822016 | 0.00281961235596879 | 0.0014098061779844 |
125 | 0.99688799652047 | 0.00622400695905936 | 0.00311200347952968 |
126 | 0.994659020046092 | 0.0106819599078157 | 0.00534097995390783 |
127 | 0.989496215231671 | 0.0210075695366586 | 0.0105037847683293 |
128 | 0.989396633222932 | 0.0212067335541356 | 0.0106033667770678 |
129 | 0.991547992594454 | 0.016904014811092 | 0.00845200740554598 |
130 | 0.979794670161791 | 0.0404106596764182 | 0.0202053298382091 |
131 | 0.955788374920216 | 0.0884232501595674 | 0.0442116250797837 |
132 | 0.997261274276813 | 0.00547745144637359 | 0.00273872572318679 |
133 | 0.988446456154815 | 0.0231070876903699 | 0.0115535438451849 |
134 | 0.992703839717715 | 0.0145923205645703 | 0.00729616028228513 |
Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
Description | # significant tests | % significant tests | OK/NOK |
1% type I error level | 98 | 0.784 | NOK |
5% type I error level | 111 | 0.888 | NOK |
10% type I error level | 118 | 0.944 | NOK |