Multiple Linear Regression - Estimated Regression Equation |
Popularity[t] = + 1.04499634277405 + 0.119499232591395FindingFriends[t] + 0.241564101757528KnowingPeople[t] + 0.378018708974303Liked[t] + 0.607491789609728Celebrity[t] -0.0489828130821502B[t] + 0.174147430517712`2B`[t] + 0.508543630098061`3B`[t] -0.136999283939151Month[t] -0.00188085357862906t + 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) | 1.04499634277405 | 3.928053 | 0.266 | 0.790588 | 0.395294 |
FindingFriends | 0.119499232591395 | 0.096875 | 1.2335 | 0.219357 | 0.109678 |
KnowingPeople | 0.241564101757528 | 0.061926 | 3.9008 | 0.000146 | 7.3e-05 |
Liked | 0.378018708974303 | 0.098076 | 3.8543 | 0.000173 | 8.7e-05 |
Celebrity | 0.607491789609728 | 0.157196 | 3.8645 | 0.000167 | 8.3e-05 |
B | -0.0489828130821502 | 0.224347 | -0.2183 | 0.827473 | 0.413736 |
`2B` | 0.174147430517712 | 0.270802 | 0.6431 | 0.521181 | 0.26059 |
`3B` | 0.508543630098061 | 0.318646 | 1.596 | 0.112661 | 0.056331 |
Month | -0.136999283939151 | 0.40264 | -0.3403 | 0.734156 | 0.367078 |
t | -0.00188085357862906 | 0.00416 | -0.4522 | 0.651825 | 0.325912 |
Multiple Linear Regression - Regression Statistics | |
Multiple R | 0.717470503794907 |
R-squared | 0.514763923815717 |
Adjusted R-squared | 0.484852110900247 |
F-TEST (value) | 17.2093856454116 |
F-TEST (DF numerator) | 9 |
F-TEST (DF denominator) | 146 |
p-value | 0 |
Multiple Linear Regression - Residual Statistics | |
Residual Standard Deviation | 2.10772912266704 |
Sum Squared Residuals | 648.608219962662 |
Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
1 | 15 | 13.4991679358302 | 1.50083206416975 |
2 | 12 | 11.8981100087714 | 0.101889991228633 |
3 | 9 | 11.2935847722229 | -2.29358477222292 |
4 | 10 | 12.0768505287867 | -2.07685052878672 |
5 | 13 | 13.1972017006551 | -0.197201700655095 |
6 | 16 | 15.2319939102505 | 0.768006089749507 |
7 | 14 | 12.9323548805402 | 1.06764511945981 |
8 | 16 | 13.9216499103898 | 2.07835008961024 |
9 | 10 | 10.9960803593227 | -0.99608035932271 |
10 | 8 | 10.7774869517918 | -2.77748695179182 |
11 | 12 | 12.2534224487608 | -0.253422448760777 |
12 | 15 | 15.1206012967996 | -0.120601296799615 |
13 | 14 | 10.9134325266142 | 3.08656747338582 |
14 | 14 | 12.8294273946596 | 1.17057260534035 |
15 | 12 | 13.0880808678829 | -1.08808086788291 |
16 | 12 | 11.1902899797029 | 0.809710020297104 |
17 | 10 | 9.59770555485905 | 0.402294445140952 |
18 | 4 | 6.79756754087376 | -2.79756754087376 |
19 | 14 | 15.2815827522669 | -1.28158275226692 |
20 | 15 | 14.270888314854 | 0.72911168514603 |
21 | 16 | 13.3886064572321 | 2.61139354276794 |
22 | 12 | 10.7600502371897 | 1.23994976281025 |
23 | 12 | 12.1554714328047 | -0.155471432804706 |
24 | 12 | 11.3322488313704 | 0.667751168629633 |
25 | 12 | 11.5427480347434 | 0.457251965256588 |
26 | 12 | 12.3012178940586 | -0.301217894058612 |
27 | 11 | 8.46962533788692 | 2.53037466211308 |
28 | 11 | 13.110090528414 | -2.11009052841395 |
29 | 11 | 12.1549938067566 | -1.15499380675655 |
30 | 11 | 11.8038737203049 | -0.803873720304907 |
31 | 11 | 11.4519360188544 | -0.451936018854354 |
32 | 11 | 8.6474840743162 | 2.3525159256838 |
33 | 15 | 14.3690467642203 | 0.6309532357797 |
34 | 15 | 14.8623851352788 | 0.137614864721171 |
35 | 9 | 14.6068491588206 | -5.60684915882057 |
36 | 16 | 10.8330247477272 | 5.16697525227284 |
37 | 13 | 9.1808716662534 | 3.81912833374659 |
38 | 9 | 10.3709164058374 | -1.37091640583742 |
39 | 16 | 14.2333980566539 | 1.76660194334615 |
40 | 12 | 12.9016318251215 | -0.901631825121454 |
41 | 15 | 9.01596982045073 | 5.98403017954927 |
42 | 5 | 9.81670811647123 | -4.81670811647123 |
43 | 11 | 11.4096349362273 | -0.409634936227332 |
44 | 17 | 13.2472484232903 | 3.75275157670973 |
45 | 9 | 9.10604536654858 | -0.106045366548579 |
46 | 13 | 14.7177500231691 | -1.71775002316915 |
47 | 16 | 14.2203721878772 | 1.77962781212282 |
48 | 16 | 13.8209516141241 | 2.17904838587587 |
49 | 14 | 14.3483495841271 | -0.34834958412712 |
50 | 16 | 13.5435983667526 | 2.45640163324742 |
51 | 11 | 12.8177075336821 | -1.81770753368211 |
52 | 11 | 11.8786166688209 | -0.878616668820855 |
53 | 11 | 13.7454798740905 | -2.74547987409047 |
54 | 12 | 12.2263929114652 | -0.226392911465156 |
55 | 12 | 13.8219110758755 | -1.82191107587552 |
56 | 12 | 12.0787466070131 | -0.0787466070131064 |
57 | 14 | 13.7158698120011 | 0.284130187998901 |
58 | 10 | 10.8938292706448 | -0.893829270644781 |
59 | 9 | 9.36948662402635 | -0.369486624026354 |
60 | 12 | 12.2721352488986 | -0.272135248898609 |
61 | 10 | 10.0150315755398 | -0.0150315755398049 |
62 | 14 | 12.9817732388354 | 1.01822676116463 |
63 | 8 | 9.91845471742309 | -1.91845471742309 |
64 | 16 | 14.4858215406104 | 1.51417845938958 |
65 | 14 | 15.7326316930428 | -1.73263169304282 |
66 | 14 | 10.7303196129192 | 3.26968038708076 |
67 | 12 | 11.2259567009063 | 0.774043299093689 |
68 | 14 | 13.3732883951205 | 0.626711604879521 |
69 | 7 | 11.1119568444562 | -4.11195684445617 |
70 | 19 | 13.9160274426111 | 5.08397255738893 |
71 | 15 | 12.8356176170298 | 2.16438238297024 |
72 | 8 | 11.2358065245671 | -3.23580652456709 |
73 | 10 | 14.2688825796494 | -4.26888257964936 |
74 | 13 | 12.9157668620937 | 0.0842331379063024 |
75 | 13 | 11.3430448027132 | 1.65695519728685 |
76 | 10 | 10.4753560056011 | -0.475356005601079 |
77 | 12 | 9.1508164416875 | 2.8491835583125 |
78 | 15 | 17.4307739990282 | -2.43077399902825 |
79 | 7 | 11.1523826850282 | -4.15238268502825 |
80 | 14 | 14.2927376671468 | -0.292737667146837 |
81 | 10 | 8.4972294574684 | 1.50277054253159 |
82 | 6 | 9.778959586541 | -3.778959586541 |
83 | 11 | 11.3135254367911 | -0.313525436791105 |
84 | 12 | 9.36712354727252 | 2.63287645272748 |
85 | 14 | 14.2858637651183 | -0.285863765118301 |
86 | 12 | 13.393824874013 | -1.39382487401296 |
87 | 14 | 14.3869799035657 | -0.386979903565727 |
88 | 11 | 10.1295339571697 | 0.870466042830313 |
89 | 10 | 9.31280240685697 | 0.687197593143033 |
90 | 13 | 13.4068525327782 | -0.406852532778172 |
91 | 8 | 10.3371693538776 | -2.33716935387761 |
92 | 9 | 11.8039272023981 | -2.80392720239807 |
93 | 6 | 12.0021952766312 | -6.0021952766312 |
94 | 12 | 13.1287885999813 | -1.12878859998133 |
95 | 14 | 12.1418479246633 | 1.85815207533665 |
96 | 11 | 10.4348955403776 | 0.565104459622418 |
97 | 8 | 10.567518313186 | -2.56751831318605 |
98 | 7 | 9.21588333435467 | -2.21588333435467 |
99 | 9 | 10.4441986498397 | -1.44419864983974 |
100 | 14 | 12.0891262285322 | 1.91087377146778 |
101 | 13 | 10.1836602510807 | 2.81633974891929 |
102 | 15 | 12.6166745066313 | 2.38332549336872 |
103 | 5 | 5.22559837218436 | -0.225598372184355 |
104 | 15 | 12.1546848703017 | 2.84531512969831 |
105 | 13 | 12.1776875868034 | 0.822312413196625 |
106 | 12 | 11.5236623723415 | 0.476337627658545 |
107 | 6 | 7.68133413696577 | -1.68133413696577 |
108 | 7 | 9.56300248642058 | -2.56300248642058 |
109 | 13 | 8.47050163971717 | 4.52949836028283 |
110 | 16 | 14.819878161772 | 1.180121838228 |
111 | 10 | 13.2362850097808 | -3.23628500978083 |
112 | 16 | 15.0641061926502 | 0.935893807349793 |
113 | 15 | 13.0816789573562 | 1.91832104264385 |
114 | 8 | 8.30768738998187 | -0.307687389981865 |
115 | 11 | 12.5043362098399 | -1.50433620983993 |
116 | 13 | 13.1382002746666 | -0.138200274666613 |
117 | 16 | 15.127783980841 | 0.872216019158957 |
118 | 11 | 8.59259420130102 | 2.40740579869898 |
119 | 14 | 14.3285466292558 | -0.32854662925576 |
120 | 9 | 10.1143989090423 | -1.11439890904234 |
121 | 8 | 10.1727908583271 | -2.17279085832707 |
122 | 8 | 11.0159195208167 | -3.01591952081667 |
123 | 11 | 11.76917530774 | -0.769175307740025 |
124 | 12 | 13.1879187906606 | -1.18791879066064 |
125 | 11 | 10.928099011449 | 0.0719009885509566 |
126 | 14 | 14.5188061294066 | -0.518806129406621 |
127 | 11 | 12.5720705896542 | -1.57207058965423 |
128 | 14 | 12.1874548876841 | 1.81254511231592 |
129 | 13 | 14.6398066696386 | -1.63980666963858 |
130 | 12 | 10.6435888134915 | 1.35641118650845 |
131 | 4 | 5.77603215019458 | -1.77603215019458 |
132 | 15 | 12.783910999375 | 2.21608900062504 |
133 | 10 | 11.2696200846096 | -1.26962008460959 |
134 | 13 | 13.7567513171914 | -0.756751317191428 |
135 | 15 | 14.0748769251425 | 0.925123074857494 |
136 | 12 | 13.1336737189485 | -1.13367371894854 |
137 | 13 | 13.1704274421111 | -0.170427442111091 |
138 | 8 | 7.72415846530568 | 0.275841534694315 |
139 | 10 | 10.3945396148313 | -0.394539614831348 |
140 | 15 | 13.5284138522989 | 1.47158614770114 |
141 | 16 | 14.2727781124753 | 1.72722188752472 |
142 | 16 | 14.7661164835338 | 1.23388351646619 |
143 | 14 | 12.8150343609158 | 1.18496563908422 |
144 | 14 | 12.9154330640543 | 1.08456693594569 |
145 | 12 | 10.5149301647128 | 1.48506983528721 |
146 | 15 | 13.1038147889474 | 1.89618521105256 |
147 | 13 | 12.8368377178223 | 0.163162282177732 |
148 | 16 | 13.0302388201548 | 2.96976117984522 |
149 | 14 | 13.3894213009251 | 0.61057869907493 |
150 | 8 | 9.84763560704182 | -1.84763560704182 |
151 | 16 | 13.5598070242855 | 2.44019297571448 |
152 | 16 | 15.7469438831333 | 0.25305611686666 |
153 | 12 | 13.0038791776363 | -1.00387917763625 |
154 | 11 | 12.1176937259202 | -1.11769372592018 |
155 | 16 | 15.7413013223975 | 0.258698677602547 |
156 | 9 | 9.83635048557004 | -0.836350485570044 |
Goldfeld-Quandt test for Heteroskedasticity | |||
p-values | Alternative Hypothesis | ||
breakpoint index | greater | 2-sided | less |
13 | 0.565235017893787 | 0.869529964212426 | 0.434764982106213 |
14 | 0.395844308804126 | 0.791688617608252 | 0.604155691195874 |
15 | 0.269509968134723 | 0.539019936269446 | 0.730490031865277 |
16 | 0.186636967441124 | 0.373273934882248 | 0.813363032558876 |
17 | 0.120239139388344 | 0.240478278776689 | 0.879760860611656 |
18 | 0.217017024159084 | 0.434034048318167 | 0.782982975840916 |
19 | 0.364243292701171 | 0.728486585402341 | 0.63575670729883 |
20 | 0.275005018713094 | 0.550010037426187 | 0.724994981286906 |
21 | 0.283088104208521 | 0.566176208417041 | 0.71691189579148 |
22 | 0.2108870105713 | 0.421774021142601 | 0.7891129894287 |
23 | 0.176694478721541 | 0.353388957443081 | 0.82330552127846 |
24 | 0.125654982914781 | 0.251309965829561 | 0.874345017085219 |
25 | 0.086641782883841 | 0.173283565767682 | 0.913358217116159 |
26 | 0.0765812365536045 | 0.153162473107209 | 0.923418763446396 |
27 | 0.0671015388700469 | 0.134203077740094 | 0.932898461129953 |
28 | 0.172415686860242 | 0.344831373720483 | 0.827584313139758 |
29 | 0.144493922184317 | 0.288987844368633 | 0.855506077815683 |
30 | 0.1148369847796 | 0.2296739695592 | 0.8851630152204 |
31 | 0.084780953573215 | 0.16956190714643 | 0.915219046426785 |
32 | 0.0728711260172474 | 0.145742252034495 | 0.927128873982753 |
33 | 0.0518076382115338 | 0.103615276423068 | 0.948192361788466 |
34 | 0.0379218229756794 | 0.0758436459513588 | 0.96207817702432 |
35 | 0.225157413559947 | 0.450314827119894 | 0.774842586440053 |
36 | 0.446130916308309 | 0.892261832616617 | 0.553869083691691 |
37 | 0.577861687757512 | 0.844276624484977 | 0.422138312242488 |
38 | 0.524759880017355 | 0.95048023996529 | 0.475240119982645 |
39 | 0.495880210901419 | 0.991760421802838 | 0.504119789098581 |
40 | 0.467811263222468 | 0.935622526444936 | 0.532188736777532 |
41 | 0.699023071202614 | 0.601953857594771 | 0.300976928797386 |
42 | 0.85881548724376 | 0.28236902551248 | 0.14118451275624 |
43 | 0.827155014403286 | 0.345689971193428 | 0.172844985596714 |
44 | 0.863579993966095 | 0.272840012067809 | 0.136420006033905 |
45 | 0.837186335844402 | 0.325627328311195 | 0.162813664155598 |
46 | 0.836228403939024 | 0.327543192121953 | 0.163771596060976 |
47 | 0.814300414805883 | 0.371399170388233 | 0.185699585194117 |
48 | 0.824409901755058 | 0.351180196489883 | 0.175590098244942 |
49 | 0.789352148479073 | 0.421295703041854 | 0.210647851520927 |
50 | 0.795803066118476 | 0.408393867763049 | 0.204196933881524 |
51 | 0.772248233313521 | 0.455503533372958 | 0.227751766686479 |
52 | 0.759289056428259 | 0.481421887143482 | 0.240710943571741 |
53 | 0.865944463348877 | 0.268111073302246 | 0.134055536651123 |
54 | 0.836170975523148 | 0.327658048953705 | 0.163829024476852 |
55 | 0.827198761776506 | 0.345602476446989 | 0.172801238223494 |
56 | 0.796107818027485 | 0.40778436394503 | 0.203892181972515 |
57 | 0.759485827938305 | 0.48102834412339 | 0.240514172061695 |
58 | 0.719117428808091 | 0.561765142383818 | 0.280882571191909 |
59 | 0.685380388094897 | 0.629239223810207 | 0.314619611905104 |
60 | 0.664386453757087 | 0.671227092485826 | 0.335613546242913 |
61 | 0.618521528683074 | 0.762956942633853 | 0.381478471316927 |
62 | 0.585334957621423 | 0.829330084757155 | 0.414665042378577 |
63 | 0.558549411223518 | 0.882901177552965 | 0.441450588776482 |
64 | 0.559571123606091 | 0.880857752787819 | 0.440428876393909 |
65 | 0.547553139729246 | 0.904893720541509 | 0.452446860270754 |
66 | 0.632981773528819 | 0.734036452942363 | 0.367018226471181 |
67 | 0.595982954574339 | 0.808034090851322 | 0.404017045425661 |
68 | 0.561406758864247 | 0.877186482271506 | 0.438593241135753 |
69 | 0.697139419948196 | 0.605721160103609 | 0.302860580051804 |
70 | 0.881308796297054 | 0.237382407405892 | 0.118691203702946 |
71 | 0.892818244579679 | 0.214363510840642 | 0.107181755420321 |
72 | 0.907673365353169 | 0.184653269293662 | 0.092326634646831 |
73 | 0.94842616692006 | 0.103147666159878 | 0.0515738330799391 |
74 | 0.936156595506957 | 0.127686808986086 | 0.0638434044930429 |
75 | 0.929024153402011 | 0.141951693195977 | 0.0709758465979886 |
76 | 0.911499692139989 | 0.177000615720022 | 0.0885003078600112 |
77 | 0.932844757086761 | 0.134310485826477 | 0.0671552429132387 |
78 | 0.934912594926411 | 0.130174810147178 | 0.0650874050735888 |
79 | 0.97112368128819 | 0.0577526374236188 | 0.0288763187118094 |
80 | 0.96214294606661 | 0.075714107866781 | 0.0378570539333905 |
81 | 0.959431357363503 | 0.0811372852729943 | 0.0405686426364971 |
82 | 0.977480615906263 | 0.0450387681874732 | 0.0225193840937366 |
83 | 0.97121752101839 | 0.0575649579632204 | 0.0287824789816102 |
84 | 0.977142269322926 | 0.0457154613541484 | 0.0228577306770742 |
85 | 0.969794988119506 | 0.0604100237609889 | 0.0302050118804944 |
86 | 0.963184775566767 | 0.0736304488664664 | 0.0368152244332332 |
87 | 0.953074449887289 | 0.093851100225422 | 0.046925550112711 |
88 | 0.945970004105975 | 0.10805999178805 | 0.0540299958940252 |
89 | 0.950468259915745 | 0.0990634801685105 | 0.0495317400842552 |
90 | 0.937362904954242 | 0.125274190091516 | 0.0626370950457579 |
91 | 0.934860491214444 | 0.130279017571111 | 0.0651395087855555 |
92 | 0.954056048692624 | 0.0918879026147511 | 0.0459439513073756 |
93 | 0.996063614766598 | 0.00787277046680392 | 0.00393638523340196 |
94 | 0.994402529207958 | 0.0111949415840841 | 0.00559747079204203 |
95 | 0.993580566514058 | 0.0128388669718848 | 0.00641943348594242 |
96 | 0.991405820205139 | 0.0171883595897227 | 0.00859417979486136 |
97 | 0.991430563688612 | 0.0171388726227768 | 0.00856943631138841 |
98 | 0.992487052784944 | 0.0150258944301114 | 0.00751294721505569 |
99 | 0.989469729272089 | 0.021060541455822 | 0.010530270727911 |
100 | 0.988305806983068 | 0.0233883860338637 | 0.0116941930169318 |
101 | 0.992325520224263 | 0.015348959551474 | 0.007674479775737 |
102 | 0.992727005229716 | 0.0145459895405682 | 0.00727299477028412 |
103 | 0.989896971569295 | 0.0202060568614096 | 0.0101030284307048 |
104 | 0.992825164871735 | 0.0143496702565307 | 0.00717483512826536 |
105 | 0.989949408274573 | 0.0201011834508546 | 0.0100505917254273 |
106 | 0.987266617746458 | 0.025466764507084 | 0.012733382253542 |
107 | 0.985281666146469 | 0.0294366677070626 | 0.0147183338535313 |
108 | 0.989717739714185 | 0.0205645205716297 | 0.0102822602858148 |
109 | 0.998983993828767 | 0.00203201234246677 | 0.00101600617123339 |
110 | 0.998671567811605 | 0.00265686437678938 | 0.00132843218839469 |
111 | 0.999577555351422 | 0.000844889297155985 | 0.000422444648577992 |
112 | 0.999304829128739 | 0.00139034174252294 | 0.000695170871261469 |
113 | 0.999293458297452 | 0.00141308340509546 | 0.000706541702547731 |
114 | 0.998843361918988 | 0.002313276162024 | 0.001156638081012 |
115 | 0.998266299464972 | 0.00346740107005555 | 0.00173370053502778 |
116 | 0.99713469342585 | 0.00573061314829885 | 0.00286530657414942 |
117 | 0.99557115566991 | 0.008857688660181 | 0.0044288443300905 |
118 | 0.99928575384014 | 0.00142849231972 | 0.000714246159860001 |
119 | 0.99875689838233 | 0.0024862032353388 | 0.0012431016176694 |
120 | 0.997906634033036 | 0.00418673193392748 | 0.00209336596696374 |
121 | 0.99737515821669 | 0.00524968356661813 | 0.00262484178330906 |
122 | 0.996628323039009 | 0.0067433539219828 | 0.0033716769609914 |
123 | 0.994724900840254 | 0.0105501983194923 | 0.00527509915974613 |
124 | 0.994622704684837 | 0.0107545906303261 | 0.00537729531516303 |
125 | 0.991111858656729 | 0.0177762826865429 | 0.00888814134327143 |
126 | 0.98706737337536 | 0.0258652532492802 | 0.0129326266246401 |
127 | 0.983650942186366 | 0.0326981156272681 | 0.0163490578136341 |
128 | 0.97589199526384 | 0.0482160094723218 | 0.0241080047361609 |
129 | 0.987690671533919 | 0.0246186569321617 | 0.0123093284660809 |
130 | 0.989789219226607 | 0.0204215615467852 | 0.0102107807733926 |
131 | 0.984899765858125 | 0.0302004682837503 | 0.0151002341418751 |
132 | 0.98199610693167 | 0.0360077861366613 | 0.0180038930683307 |
133 | 0.97488405455083 | 0.0502318908983413 | 0.0251159454491706 |
134 | 0.96221397071084 | 0.0755720585783198 | 0.0377860292891599 |
135 | 0.937878628501461 | 0.124242742997077 | 0.0621213714985387 |
136 | 0.953839477303385 | 0.0923210453932305 | 0.0461605226966152 |
137 | 0.972144179918852 | 0.0557116401622961 | 0.0278558200811481 |
138 | 0.947584174198594 | 0.104831651602811 | 0.0524158258014057 |
139 | 0.90425799252785 | 0.1914840149443 | 0.0957420074721502 |
140 | 0.853858044619189 | 0.292283910761623 | 0.146141955380811 |
141 | 0.773120447739717 | 0.453759104520565 | 0.226879552260283 |
142 | 0.709951349663682 | 0.580097300672637 | 0.290048650336318 |
143 | 0.554429649931078 | 0.891140700137844 | 0.445570350068922 |
Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
Description | # significant tests | % significant tests | OK/NOK |
1% type I error level | 15 | 0.114503816793893 | NOK |
5% type I error level | 42 | 0.320610687022901 | NOK |
10% type I error level | 56 | 0.427480916030534 | NOK |