Multiple Linear Regression - Estimated Regression Equation |
KnowingPeople[t] = + 0.725680871464287 -0.0675593352860248FindingFriends[t] + 0.387096838191507Popularity[t] + 0.27399933524668Liked[t] + 0.670538732124844`Celebrity `[t] -0.00187723512719696t + 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) | 0.725680871464287 | 1.803242 | 0.4024 | 0.68794 | 0.34397 |
FindingFriends | -0.0675593352860248 | 0.122209 | -0.5528 | 0.581212 | 0.290606 |
Popularity | 0.387096838191507 | 0.098004 | 3.9498 | 0.00012 | 6e-05 |
Liked | 0.27399933524668 | 0.126403 | 2.1677 | 0.031762 | 0.015881 |
`Celebrity ` | 0.670538732124844 | 0.200407 | 3.3459 | 0.001037 | 0.000518 |
t | -0.00187723512719696 | 0.004821 | -0.3894 | 0.697525 | 0.348762 |
Multiple Linear Regression - Regression Statistics | |
Multiple R | 0.653361596228413 |
R-squared | 0.426881375426139 |
Adjusted R-squared | 0.407777421273677 |
F-TEST (value) | 22.3451842492579 |
F-TEST (DF numerator) | 5 |
F-TEST (DF denominator) | 150 |
p-value | 1.11022302462516e-16 |
Multiple Linear Regression - Residual Statistics | |
Residual Standard Deviation | 2.66394071596264 |
Sum Squared Residuals | 1064.48702072453 |
Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
1 | 14 | 10.4513987286897 | 3.54860127131033 |
2 | 8 | 11.4710614549067 | -3.47106145490674 |
3 | 12 | 14.2581301427910 | -2.25813014279098 |
4 | 7 | 12.0665243873886 | -5.06652438738857 |
5 | 10 | 10.2783560732208 | -0.278356073220814 |
6 | 7 | 9.84847571490158 | -2.84847571490158 |
7 | 16 | 15.9370193311672 | 0.0629806688328206 |
8 | 11 | 9.07997012695083 | 1.92002987304917 |
9 | 14 | 11.0613814121382 | 2.93861858786181 |
10 | 6 | 9.70776667430223 | -3.70776667430223 |
11 | 16 | 12.4845229149442 | 3.51547708505585 |
12 | 11 | 11.4617316623214 | -0.461731662321422 |
13 | 16 | 12.1312630478748 | 3.86873695212525 |
14 | 12 | 8.43339370447926 | 3.56660629552074 |
15 | 7 | 11.5949806216145 | -4.59498062161446 |
16 | 13 | 9.83914592231627 | 3.16085407768373 |
17 | 11 | 11.0652486484939 | -0.0652486484939305 |
18 | 15 | 13.7753154424055 | 1.22468455759449 |
19 | 7 | 8.96597804353583 | -1.96597804353583 |
20 | 9 | 8.23394946728007 | 0.766050532719934 |
21 | 7 | 9.23935895878203 | -2.23935895878203 |
22 | 14 | 14.5514427369664 | -0.551442736966389 |
23 | 15 | 10.2901040085901 | 4.70989599140993 |
24 | 7 | 10.2112248794902 | -3.2112248794902 |
25 | 15 | 12.8726174554891 | 2.12738254451094 |
26 | 17 | 14.1473943995794 | 2.85260560042056 |
27 | 15 | 12.2194755321814 | 2.78052446781864 |
28 | 14 | 12.3535868561819 | 1.6464131438181 |
29 | 14 | 12.9546890178935 | 1.04531098210648 |
30 | 8 | 12.5703468272331 | -4.57034682723309 |
31 | 8 | 9.89830173662333 | -1.89830173662333 |
32 | 14 | 12.8909405359126 | 1.10905946408744 |
33 | 14 | 14.0761369770897 | -0.0761369770896918 |
34 | 8 | 10.6235917016642 | -2.62359170166418 |
35 | 11 | 9.0292847785165 | 1.97071522148349 |
36 | 16 | 14.2417195512523 | 1.75828044874770 |
37 | 10 | 12.6238956280730 | -2.62389562807305 |
38 | 8 | 9.87108664938803 | -1.87108664938803 |
39 | 14 | 12.5267986608028 | 1.47320133919718 |
40 | 16 | 15.1787486781150 | 0.821251321884969 |
41 | 13 | 12.8425816934539 | 0.157418306546089 |
42 | 5 | 10.8708644355084 | -5.8708644355084 |
43 | 8 | 6.86666214199667 | 1.13333785800333 |
44 | 10 | 8.96685149471294 | 1.03314850528706 |
45 | 8 | 11.4673422384099 | -3.46734223840995 |
46 | 13 | 14.6194865968585 | -1.61948659685849 |
47 | 15 | 13.6636287356731 | 1.33637126432689 |
48 | 6 | 7.98020471026484 | -1.98020471026484 |
49 | 12 | 10.2891002246400 | 1.71089977536002 |
50 | 16 | 13.2605877448577 | 2.73941225514233 |
51 | 5 | 11.2754219894159 | -6.27542198941592 |
52 | 15 | 9.3798367368874 | 5.6201632631126 |
53 | 12 | 11.6493217986664 | 0.350678201333629 |
54 | 8 | 9.15451914340162 | -1.15451914340162 |
55 | 13 | 12.0782023342623 | 0.921797665737714 |
56 | 14 | 11.4372500933241 | 2.56274990667588 |
57 | 12 | 10.2388566232059 | 1.76114337679405 |
58 | 16 | 14.6095383842727 | 1.39046161572731 |
59 | 10 | 8.41961350929533 | 1.58038649070466 |
60 | 15 | 15.1506465342577 | -0.150646534257749 |
61 | 8 | 7.80974359194821 | 0.190256408051787 |
62 | 16 | 13.8513527674125 | 2.14864723258753 |
63 | 19 | 12.7299611912670 | 6.27003880873303 |
64 | 14 | 14.1891569676908 | -0.189156967690781 |
65 | 6 | 10.1201837979302 | -4.1201837979302 |
66 | 13 | 12.1251120831491 | 0.874887916850856 |
67 | 15 | 11.3584837303256 | 3.64151626967441 |
68 | 7 | 11.4602614394566 | -4.46026143945656 |
69 | 13 | 13.1771159480839 | -0.177115948083903 |
70 | 4 | 4.29500204999677 | -0.295002049996772 |
71 | 14 | 12.5703820809907 | 1.42961791900931 |
72 | 13 | 11.7267518341945 | 1.27324816580554 |
73 | 11 | 11.2922395932169 | -0.292239593216950 |
74 | 14 | 13.1206957723848 | 0.87930422761524 |
75 | 12 | 12.1396806933183 | -0.139680693318250 |
76 | 15 | 12.002684787619 | 2.99731521238100 |
77 | 14 | 10.9887101498343 | 3.01128985016574 |
78 | 13 | 11.5986289263839 | 1.40137107361614 |
79 | 8 | 11.7041686296174 | -3.70416862961742 |
80 | 6 | 6.44244121896844 | -0.44244121896844 |
81 | 7 | 8.44273762152912 | -1.44273762152912 |
82 | 13 | 12.8969717297083 | 0.103028270291697 |
83 | 13 | 13.6532951591377 | -0.653295159137705 |
84 | 11 | 10.4040538334189 | 0.59594616658106 |
85 | 5 | 10.0872709780445 | -5.08727097804453 |
86 | 12 | 11.6423537658143 | 0.35764623418567 |
87 | 8 | 8.72522855194161 | -0.725228551941614 |
88 | 11 | 12.1954145808913 | -1.19541458089128 |
89 | 14 | 15.4833035537605 | -1.48330355376054 |
90 | 9 | 9.65469235524489 | -0.65469235524489 |
91 | 10 | 13.6382772781201 | -3.63827727812013 |
92 | 13 | 11.8140133549802 | 1.18598664501978 |
93 | 16 | 15.0116958810876 | 0.988304118912432 |
94 | 16 | 13.2653037404760 | 2.73469625952397 |
95 | 11 | 11.0900385881168 | -0.0900385881167627 |
96 | 8 | 9.301870273949 | -1.30187027394900 |
97 | 4 | 10.7526721736120 | -6.75267217361196 |
98 | 7 | 7.51182472465405 | -0.511824724654047 |
99 | 14 | 11.7201088210146 | 2.27989117898542 |
100 | 11 | 12.3447279827578 | -1.34472798275778 |
101 | 17 | 15.0642373353560 | 1.93576266464398 |
102 | 15 | 14.7208014296961 | 0.279198570303885 |
103 | 17 | 13.9610711212291 | 3.03892887877095 |
104 | 5 | 9.6865278400635 | -4.6865278400635 |
105 | 4 | 5.48243599973087 | -1.48243599973087 |
106 | 10 | 14.8160775448898 | -4.81607754488981 |
107 | 11 | 8.90670245829889 | 2.09329754170110 |
108 | 15 | 14.6734424099608 | 0.326557590039212 |
109 | 10 | 8.78985048509968 | 1.21014951490032 |
110 | 9 | 9.93518932320208 | -0.935189323202077 |
111 | 12 | 11.2884639936695 | 0.71153600633051 |
112 | 15 | 12.8758803963089 | 2.12411960369114 |
113 | 7 | 11.5461302497212 | -4.54613024972121 |
114 | 13 | 13.2535421996619 | -0.253542199661895 |
115 | 12 | 14.5832998700977 | -2.58329987009773 |
116 | 14 | 13.8175414058299 | 0.182458594170141 |
117 | 14 | 13.7481048354166 | 0.251895164583363 |
118 | 8 | 12.3587420798253 | -4.35874207982527 |
119 | 15 | 12.9701566887792 | 2.02984331122077 |
120 | 12 | 11.146762654195 | 0.85323734580499 |
121 | 12 | 10.5771317426455 | 1.42286825735455 |
122 | 16 | 11.8135469160655 | 4.18645308393454 |
123 | 9 | 8.81854991966438 | 0.181450080335623 |
124 | 15 | 12.5061143396657 | 2.49388566033429 |
125 | 15 | 13.7330869543991 | 1.26691304560094 |
126 | 6 | 11.512283634381 | -5.512283634381 |
127 | 14 | 15.6184086188877 | -1.61840861888772 |
128 | 15 | 11.9050685610048 | 3.09493143899524 |
129 | 10 | 11.389792431952 | -1.38979243195199 |
130 | 6 | 5.2677052448926 | 0.732294755107398 |
131 | 14 | 15.6108996783789 | -1.61089967837893 |
132 | 12 | 13.1264094703565 | -1.12640947035652 |
133 | 8 | 10.6024092504761 | -2.60240925047612 |
134 | 11 | 12.7613413236404 | -1.76134132364042 |
135 | 13 | 13.3272177649356 | -0.327217764935585 |
136 | 9 | 10.5489732157375 | -1.5489732157375 |
137 | 15 | 13.0039257917757 | 1.99607420822429 |
138 | 13 | 7.66519648715405 | 5.33480351284595 |
139 | 15 | 15.1420955124395 | -0.142095512439505 |
140 | 14 | 11.6211210131723 | 2.37887898682771 |
141 | 16 | 10.6071463753875 | 5.39285362461246 |
142 | 14 | 12.5398834426622 | 1.46011655733781 |
143 | 14 | 12.5191210901617 | 1.48087890983832 |
144 | 10 | 7.20269130579918 | 2.79730869420082 |
145 | 10 | 10.5320780995927 | -0.532078099592727 |
146 | 4 | 11.0295253170462 | -7.02952531704618 |
147 | 8 | 9.92447434394383 | -1.92447434394383 |
148 | 15 | 11.4386508467131 | 3.5613491532869 |
149 | 16 | 13.3684958084409 | 2.63150419155915 |
150 | 12 | 15.3012328757155 | -3.30123287571551 |
151 | 12 | 12.9870870586816 | -0.987087058681607 |
152 | 15 | 14.9009390085829 | 0.099060991417052 |
153 | 9 | 9.14932970403997 | -0.149329704039975 |
154 | 12 | 13.3135714651461 | -1.31357146514607 |
155 | 14 | 12.4221368889928 | 1.57786311100720 |
156 | 11 | 9.51190971947658 | 1.48809028052342 |
Goldfeld-Quandt test for Heteroskedasticity | |||
p-values | Alternative Hypothesis | ||
breakpoint index | greater | 2-sided | less |
9 | 0.672993749575081 | 0.654012500849837 | 0.327006250424919 |
10 | 0.642495655047936 | 0.715008689904129 | 0.357504344952064 |
11 | 0.50849608424266 | 0.98300783151468 | 0.49150391575734 |
12 | 0.428900278991959 | 0.857800557983918 | 0.571099721008041 |
13 | 0.77539832153592 | 0.449203356928159 | 0.224601678464079 |
14 | 0.711597944838265 | 0.576804110323469 | 0.288402055161735 |
15 | 0.90906323987734 | 0.181873520245319 | 0.0909367601226594 |
16 | 0.873843565201118 | 0.252312869597764 | 0.126156434798882 |
17 | 0.824057662731802 | 0.351884674536397 | 0.175942337268198 |
18 | 0.810564421013917 | 0.378871157972165 | 0.189435578986083 |
19 | 0.807924998670845 | 0.38415000265831 | 0.192075001329155 |
20 | 0.77275070121581 | 0.454498597568381 | 0.227249298784190 |
21 | 0.892691966214902 | 0.214616067570196 | 0.107308033785098 |
22 | 0.856085109932638 | 0.287829780134723 | 0.143914890067362 |
23 | 0.903959419399131 | 0.192081161201738 | 0.096040580600869 |
24 | 0.927599754361027 | 0.144800491277945 | 0.0724002456389724 |
25 | 0.911549014314716 | 0.176901971370567 | 0.0884509856852835 |
26 | 0.894505825454754 | 0.210988349090492 | 0.105494174545246 |
27 | 0.871248731251911 | 0.257502537496177 | 0.128751268748088 |
28 | 0.837229887187749 | 0.325540225624502 | 0.162770112812251 |
29 | 0.797503809742895 | 0.40499238051421 | 0.202496190257105 |
30 | 0.886354914746792 | 0.227290170506416 | 0.113645085253208 |
31 | 0.86197821969575 | 0.276043560608501 | 0.138021780304251 |
32 | 0.827902386787547 | 0.344195226424905 | 0.172097613212453 |
33 | 0.792334896330018 | 0.415330207339963 | 0.207665103669982 |
34 | 0.803796913801174 | 0.392406172397653 | 0.196203086198826 |
35 | 0.770603245923423 | 0.458793508153154 | 0.229396754076577 |
36 | 0.741652032180247 | 0.516695935639505 | 0.258347967819753 |
37 | 0.772171400000452 | 0.455657199999096 | 0.227828599999548 |
38 | 0.744809590131499 | 0.510380819737002 | 0.255190409868501 |
39 | 0.708681963079524 | 0.582636073840952 | 0.291318036920476 |
40 | 0.661948674442302 | 0.676102651115397 | 0.338051325557699 |
41 | 0.610228142274341 | 0.779543715451319 | 0.389771857725659 |
42 | 0.733843490546386 | 0.532313018907227 | 0.266156509453614 |
43 | 0.699309009587014 | 0.601381980825972 | 0.300690990412986 |
44 | 0.654760551812696 | 0.690478896374608 | 0.345239448187304 |
45 | 0.692726885268272 | 0.614546229463456 | 0.307273114731728 |
46 | 0.656776111549387 | 0.686447776901226 | 0.343223888450613 |
47 | 0.643608755817373 | 0.712782488365253 | 0.356391244182627 |
48 | 0.613670855754704 | 0.772658288490592 | 0.386329144245296 |
49 | 0.577893877320781 | 0.844212245358439 | 0.422106122679219 |
50 | 0.567314268655629 | 0.865371462688742 | 0.432685731344371 |
51 | 0.782361523665034 | 0.435276952669933 | 0.217638476334966 |
52 | 0.880797870101772 | 0.238404259796456 | 0.119202129898228 |
53 | 0.854438619948492 | 0.291122760103017 | 0.145561380051508 |
54 | 0.834714512104977 | 0.330570975790046 | 0.165285487895023 |
55 | 0.810990383923116 | 0.378019232153767 | 0.189009616076884 |
56 | 0.808470648005543 | 0.383058703988914 | 0.191529351994457 |
57 | 0.787485109128471 | 0.425029781743058 | 0.212514890871529 |
58 | 0.756917348986921 | 0.486165302026157 | 0.243082651013079 |
59 | 0.72865260634877 | 0.54269478730246 | 0.27134739365123 |
60 | 0.688717555037758 | 0.622564889924484 | 0.311282444962242 |
61 | 0.648896562962073 | 0.702206874075855 | 0.351103437037927 |
62 | 0.635645828242656 | 0.728708343514688 | 0.364354171757344 |
63 | 0.807019411778625 | 0.385961176442749 | 0.192980588221375 |
64 | 0.77429120912167 | 0.45141758175666 | 0.22570879087833 |
65 | 0.83142835004005 | 0.3371432999199 | 0.16857164995995 |
66 | 0.802602745147945 | 0.39479450970411 | 0.197397254852055 |
67 | 0.832467716634208 | 0.335064566731584 | 0.167532283365792 |
68 | 0.881461440553534 | 0.237077118892932 | 0.118538559446466 |
69 | 0.856327874692653 | 0.287344250614694 | 0.143672125307347 |
70 | 0.829731777690764 | 0.340536444618472 | 0.170268222309236 |
71 | 0.80551860922803 | 0.388962781543939 | 0.194481390771970 |
72 | 0.77834317473687 | 0.443313650526261 | 0.221656825263130 |
73 | 0.746657499136332 | 0.506685001727337 | 0.253342500863668 |
74 | 0.726840351819517 | 0.546319296360967 | 0.273159648180483 |
75 | 0.688999098470906 | 0.622001803058187 | 0.311000901529093 |
76 | 0.708006039775724 | 0.583987920448552 | 0.291993960224276 |
77 | 0.725968085269886 | 0.548063829460229 | 0.274031914730114 |
78 | 0.699615374432004 | 0.600769251135992 | 0.300384625567996 |
79 | 0.741491067741814 | 0.517017864516372 | 0.258508932258186 |
80 | 0.70383488791249 | 0.592330224175021 | 0.296165112087511 |
81 | 0.677106288900781 | 0.645787422198438 | 0.322893711099219 |
82 | 0.633469313628138 | 0.733061372743724 | 0.366530686371862 |
83 | 0.595925027095157 | 0.808149945809686 | 0.404074972904843 |
84 | 0.55811060828776 | 0.88377878342448 | 0.44188939171224 |
85 | 0.707407220228597 | 0.585185559542806 | 0.292592779771403 |
86 | 0.668550156753092 | 0.662899686493816 | 0.331449843246908 |
87 | 0.627609439072175 | 0.74478112185565 | 0.372390560927825 |
88 | 0.589728601791803 | 0.820542796416395 | 0.410271398208197 |
89 | 0.557797133917057 | 0.884405732165886 | 0.442202866082943 |
90 | 0.512986333074871 | 0.974027333850258 | 0.487013666925129 |
91 | 0.5474242256197 | 0.9051515487606 | 0.4525757743803 |
92 | 0.539024509195157 | 0.921950981609687 | 0.460975490804843 |
93 | 0.503953008816759 | 0.992093982366482 | 0.496046991183241 |
94 | 0.507070088792487 | 0.985859822415027 | 0.492929911207513 |
95 | 0.458586737129305 | 0.91717347425861 | 0.541413262870695 |
96 | 0.423766588937372 | 0.847533177874744 | 0.576233411062628 |
97 | 0.623543846758856 | 0.752912306482288 | 0.376456153241144 |
98 | 0.580905840150339 | 0.838188319699323 | 0.419094159849661 |
99 | 0.581886770602418 | 0.836226458795164 | 0.418113229397582 |
100 | 0.54394524172895 | 0.9121095165421 | 0.45605475827105 |
101 | 0.534712900278224 | 0.930574199443553 | 0.465287099721776 |
102 | 0.488075491649375 | 0.97615098329875 | 0.511924508350625 |
103 | 0.571582589804618 | 0.856834820390764 | 0.428417410195382 |
104 | 0.717860395548497 | 0.564279208903007 | 0.282139604451503 |
105 | 0.705068588575037 | 0.589862822849926 | 0.294931411424963 |
106 | 0.74815371180075 | 0.503692576398502 | 0.251846288199251 |
107 | 0.724414659105042 | 0.551170681789917 | 0.275585340894958 |
108 | 0.703810904231639 | 0.592378191536722 | 0.296189095768361 |
109 | 0.666982575410507 | 0.666034849178986 | 0.333017424589493 |
110 | 0.618665995520391 | 0.762668008959217 | 0.381334004479608 |
111 | 0.576997070154409 | 0.846005859691181 | 0.423002929845591 |
112 | 0.633792687241786 | 0.732414625516428 | 0.366207312758214 |
113 | 0.692135460221124 | 0.615729079557753 | 0.307864539778876 |
114 | 0.643066896926194 | 0.713866206147612 | 0.356933103073806 |
115 | 0.60840603904613 | 0.78318792190774 | 0.39159396095387 |
116 | 0.555508204360359 | 0.888983591279283 | 0.444491795639641 |
117 | 0.50256329651968 | 0.99487340696064 | 0.49743670348032 |
118 | 0.522255846950964 | 0.955488306098071 | 0.477744153049036 |
119 | 0.498384865533384 | 0.996769731066767 | 0.501615134466616 |
120 | 0.461054472542074 | 0.922108945084147 | 0.538945527457926 |
121 | 0.411035987309852 | 0.822071974619704 | 0.588964012690148 |
122 | 0.438868748859365 | 0.877737497718731 | 0.561131251140635 |
123 | 0.380838949698585 | 0.761677899397169 | 0.619161050301415 |
124 | 0.384235931715124 | 0.768471863430249 | 0.615764068284876 |
125 | 0.33971331208871 | 0.67942662417742 | 0.66028668791129 |
126 | 0.534992216772501 | 0.930015566454998 | 0.465007783227499 |
127 | 0.475054605949401 | 0.950109211898802 | 0.524945394050599 |
128 | 0.516695581249197 | 0.966608837501607 | 0.483304418750803 |
129 | 0.455380064948302 | 0.910760129896604 | 0.544619935051698 |
130 | 0.399688426840368 | 0.799376853680735 | 0.600311573159632 |
131 | 0.340360904117779 | 0.680721808235558 | 0.659639095882221 |
132 | 0.295324989533931 | 0.590649979067862 | 0.704675010466069 |
133 | 0.313772846352729 | 0.627545692705457 | 0.686227153647271 |
134 | 0.278241525863858 | 0.556483051727717 | 0.721758474136142 |
135 | 0.228278951461775 | 0.45655790292355 | 0.771721048538225 |
136 | 0.298717716279923 | 0.597435432559847 | 0.701282283720077 |
137 | 0.23970907140185 | 0.4794181428037 | 0.76029092859815 |
138 | 0.257050882020855 | 0.51410176404171 | 0.742949117979145 |
139 | 0.254786331982826 | 0.509572663965652 | 0.745213668017174 |
140 | 0.211234043900898 | 0.422468087801796 | 0.788765956099102 |
141 | 0.295277023795257 | 0.590554047590514 | 0.704722976204743 |
142 | 0.264237938911651 | 0.528475877823301 | 0.73576206108835 |
143 | 0.200750198663441 | 0.401500397326883 | 0.799249801336559 |
144 | 0.216733051559074 | 0.433466103118148 | 0.783266948440926 |
145 | 0.141498546457949 | 0.282997092915898 | 0.858501453542051 |
146 | 0.66001393117389 | 0.67997213765222 | 0.33998606882611 |
147 | 0.545294136072753 | 0.909411727854493 | 0.454705863927247 |
Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
Description | # significant tests | % significant tests | OK/NOK |
1% type I error level | 0 | 0 | OK |
5% type I error level | 0 | 0 | OK |
10% type I error level | 0 | 0 | OK |