Multiple Linear Regression - Estimated Regression Equation |
Popularity[t] = + 1.04499634277411 + 0.119499232591394FindingFriends[t] + 0.241564101757528KnowingPeople[t] + 0.378018708974302Liked[t] + 0.607491789609728Celebrity[t] -0.0489828130821504B[t] + 0.174147430517712`2B`[t] + 0.508543630098061`3B`[t] -0.136999283939156Month[t] -0.00188085357862904t + 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) | 1.04499634277411 | 3.928053 | 0.266 | 0.790588 | 0.395294 |
FindingFriends | 0.119499232591394 | 0.096875 | 1.2335 | 0.219357 | 0.109678 |
KnowingPeople | 0.241564101757528 | 0.061926 | 3.9008 | 0.000146 | 7.3e-05 |
Liked | 0.378018708974302 | 0.098076 | 3.8543 | 0.000173 | 8.7e-05 |
Celebrity | 0.607491789609728 | 0.157196 | 3.8645 | 0.000167 | 8.3e-05 |
B | -0.0489828130821504 | 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 | -0.136999283939156 | 0.40264 | -0.3403 | 0.734156 | 0.367078 |
t | -0.00188085357862904 | 0.00416 | -0.4522 | 0.651825 | 0.325912 |
Multiple Linear Regression - Regression Statistics | |
Multiple R | 0.717470503794906 |
R-squared | 0.514763923815717 |
Adjusted R-squared | 0.484852110900247 |
F-TEST (value) | 17.2093856454115 |
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 | 0.10188999122863 |
3 | 9 | 11.2935847722229 | -2.29358477222292 |
4 | 10 | 12.0768505287867 | -2.07685052878672 |
5 | 13 | 13.1972017006551 | -0.197201700655100 |
6 | 16 | 15.2319939102505 | 0.768006089749506 |
7 | 14 | 12.9323548805402 | 1.06764511945981 |
8 | 16 | 13.9216499103898 | 2.07835008961024 |
9 | 10 | 10.9960803593227 | -0.996080359322713 |
10 | 8 | 10.7774869517918 | -2.77748695179182 |
11 | 12 | 12.2534224487608 | -0.253422448760775 |
12 | 15 | 15.1206012967996 | -0.120601296799614 |
13 | 14 | 10.9134325266142 | 3.08656747338582 |
14 | 14 | 12.8294273946596 | 1.17057260534035 |
15 | 12 | 13.0880808678829 | -1.08808086788290 |
16 | 12 | 11.1902899797029 | 0.809710020297105 |
17 | 10 | 9.59770555485905 | 0.402294445140954 |
18 | 4 | 6.79756754087376 | -2.79756754087376 |
19 | 14 | 15.2815827522669 | -1.28158275226692 |
20 | 15 | 14.2708883148540 | 0.729111685146033 |
21 | 16 | 13.3886064572321 | 2.61139354276794 |
22 | 12 | 10.7600502371897 | 1.23994976281026 |
23 | 12 | 12.1554714328047 | -0.155471432804704 |
24 | 12 | 11.3322488313704 | 0.667751168629636 |
25 | 12 | 11.5427480347434 | 0.457251965256587 |
26 | 12 | 12.3012178940586 | -0.301217894058613 |
27 | 11 | 8.46962533788692 | 2.53037466211308 |
28 | 11 | 13.1100905284140 | -2.11009052841396 |
29 | 11 | 12.1549938067566 | -1.15499380675656 |
30 | 11 | 11.8038737203049 | -0.803873720304908 |
31 | 11 | 11.4519360188544 | -0.451936018854355 |
32 | 11 | 8.6474840743162 | 2.35251592568380 |
33 | 15 | 14.3690467642203 | 0.630953235779697 |
34 | 15 | 14.8623851352788 | 0.137614864721169 |
35 | 9 | 14.6068491588206 | -5.60684915882057 |
36 | 16 | 10.8330247477272 | 5.16697525227284 |
37 | 13 | 9.18087166625341 | 3.81912833374659 |
38 | 9 | 10.3709164058374 | -1.37091640583742 |
39 | 16 | 14.2333980566539 | 1.76660194334614 |
40 | 12 | 12.9016318251215 | -0.901631825121455 |
41 | 15 | 9.01596982045074 | 5.98403017954927 |
42 | 5 | 9.81670811647123 | -4.81670811647123 |
43 | 11 | 11.4096349362273 | -0.409634936227334 |
44 | 17 | 13.2472484232903 | 3.75275157670972 |
45 | 9 | 9.10604536654858 | -0.106045366548582 |
46 | 13 | 14.7177500231691 | -1.71775002316915 |
47 | 16 | 14.2203721878772 | 1.77962781212282 |
48 | 16 | 13.8209516141241 | 2.17904838587587 |
49 | 14 | 14.3483495841271 | -0.348349584127119 |
50 | 16 | 13.5435983667526 | 2.45640163324742 |
51 | 11 | 12.8177075336821 | -1.81770753368211 |
52 | 11 | 11.8786166688209 | -0.878616668820854 |
53 | 11 | 13.7454798740905 | -2.74547987409047 |
54 | 12 | 12.2263929114652 | -0.226392911465155 |
55 | 12 | 13.8219110758755 | -1.82191107587552 |
56 | 12 | 12.0787466070131 | -0.078746607013105 |
57 | 14 | 13.7158698120011 | 0.284130187998903 |
58 | 10 | 10.8938292706448 | -0.89382927064478 |
59 | 9 | 9.36948662402635 | -0.369486624026353 |
60 | 12 | 12.2721352488986 | -0.272135248898607 |
61 | 10 | 10.0150315755398 | -0.015031575539804 |
62 | 14 | 12.9817732388354 | 1.01822676116463 |
63 | 8 | 9.91845471742309 | -1.91845471742309 |
64 | 16 | 14.4858215406104 | 1.51417845938958 |
65 | 14 | 15.7326316930428 | -1.73263169304281 |
66 | 14 | 10.7303196129192 | 3.26968038708076 |
67 | 12 | 11.2259567009063 | 0.774043299093691 |
68 | 14 | 13.3732883951205 | 0.626711604879522 |
69 | 7 | 11.1119568444562 | -4.11195684445617 |
70 | 19 | 13.9160274426111 | 5.08397255738893 |
71 | 15 | 12.8356176170298 | 2.16438238297025 |
72 | 8 | 11.2358065245671 | -3.23580652456708 |
73 | 10 | 14.2688825796494 | -4.26888257964936 |
74 | 13 | 12.9157668620937 | 0.0842331379063027 |
75 | 13 | 11.3430448027132 | 1.65695519728685 |
76 | 10 | 10.4753560056011 | -0.475356005601083 |
77 | 12 | 9.15081644168751 | 2.84918355831249 |
78 | 15 | 17.4307739990282 | -2.43077399902825 |
79 | 7 | 11.1523826850283 | -4.15238268502825 |
80 | 14 | 14.2927376671468 | -0.292737667146839 |
81 | 10 | 8.49722945746842 | 1.50277054253158 |
82 | 6 | 9.778959586541 | -3.77895958654100 |
83 | 11 | 11.3135254367911 | -0.31352543679111 |
84 | 12 | 9.36712354727253 | 2.63287645272747 |
85 | 14 | 14.2858637651183 | -0.285863765118304 |
86 | 12 | 13.3938248740130 | -1.39382487401296 |
87 | 14 | 14.3869799035657 | -0.386979903565729 |
88 | 11 | 10.1295339571697 | 0.870466042830311 |
89 | 10 | 9.31280240685697 | 0.687197593143026 |
90 | 13 | 13.4068525327782 | -0.406852532778176 |
91 | 8 | 10.3371693538776 | -2.33716935387761 |
92 | 9 | 11.8039272023981 | -2.80392720239807 |
93 | 6 | 12.0021952766312 | -6.00219527663121 |
94 | 12 | 13.1287885999813 | -1.12878859998133 |
95 | 14 | 12.1418479246633 | 1.85815207533665 |
96 | 11 | 10.4348955403776 | 0.565104459622418 |
97 | 8 | 10.5675183131860 | -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 | -0.225598372184357 |
104 | 15 | 12.1546848703017 | 2.84531512969832 |
105 | 13 | 12.1776875868034 | 0.822312413196627 |
106 | 12 | 11.5236623723415 | 0.476337627658545 |
107 | 6 | 7.68133413696577 | -1.68133413696577 |
108 | 7 | 9.56300248642058 | -2.56300248642058 |
109 | 13 | 8.47050163971716 | 4.52949836028284 |
110 | 16 | 14.819878161772 | 1.180121838228 |
111 | 10 | 13.2362850097808 | -3.23628500978083 |
112 | 16 | 15.0641061926502 | 0.935893807349795 |
113 | 15 | 13.0816789573562 | 1.91832104264385 |
114 | 8 | 8.30768738998187 | -0.307687389981865 |
115 | 11 | 12.5043362098399 | -1.50433620983993 |
116 | 13 | 13.1382002746666 | -0.138200274666611 |
117 | 16 | 15.1277839808410 | 0.872216019158957 |
118 | 11 | 8.59259420130102 | 2.40740579869898 |
119 | 14 | 14.3285466292558 | -0.328546629255758 |
120 | 9 | 10.1143989090423 | -1.11439890904234 |
121 | 8 | 10.1727908583271 | -2.17279085832707 |
122 | 8 | 11.0159195208167 | -3.01591952081667 |
123 | 11 | 11.7691753077400 | -0.769175307740024 |
124 | 12 | 13.1879187906606 | -1.18791879066065 |
125 | 11 | 10.9280990114490 | 0.0719009885509587 |
126 | 14 | 14.5188061294066 | -0.518806129406618 |
127 | 11 | 12.5720705896542 | -1.57207058965423 |
128 | 14 | 12.1874548876841 | 1.81254511231592 |
129 | 13 | 14.6398066696386 | -1.63980666963858 |
130 | 12 | 10.6435888134915 | 1.35641118650846 |
131 | 4 | 5.77603215019459 | -1.77603215019459 |
132 | 15 | 12.7839109993750 | 2.21608900062505 |
133 | 10 | 11.2696200846096 | -1.26962008460959 |
134 | 13 | 13.7567513171914 | -0.756751317191425 |
135 | 15 | 14.0748769251425 | 0.925123074857496 |
136 | 12 | 13.1336737189485 | -1.13367371894854 |
137 | 13 | 13.1704274421111 | -0.170427442111091 |
138 | 8 | 7.72415846530569 | 0.275841534694312 |
139 | 10 | 10.3945396148313 | -0.394539614831347 |
140 | 15 | 13.5284138522989 | 1.47158614770114 |
141 | 16 | 14.2727781124753 | 1.72722188752472 |
142 | 16 | 14.7661164835338 | 1.23388351646619 |
143 | 14 | 12.8150343609158 | 1.18496563908423 |
144 | 14 | 12.9154330640543 | 1.08456693594569 |
145 | 12 | 10.5149301647128 | 1.48506983528721 |
146 | 15 | 13.1038147889474 | 1.89618521105255 |
147 | 13 | 12.8368377178223 | 0.163162282177728 |
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 | 0.253056116866661 |
153 | 12 | 13.0038791776363 | -1.00387917763625 |
154 | 11 | 12.1176937259202 | -1.11769372592018 |
155 | 16 | 15.7413013223975 | 0.258698677602548 |
156 | 9 | 9.83635048557004 | -0.836350485570045 |
Goldfeld-Quandt test for Heteroskedasticity | |||
p-values | Alternative Hypothesis | ||
breakpoint index | greater | 2-sided | less |
13 | 0.565235017893787 | 0.869529964212425 | 0.434764982106213 |
14 | 0.395844308804128 | 0.791688617608256 | 0.604155691195872 |
15 | 0.269509968134723 | 0.539019936269445 | 0.730490031865277 |
16 | 0.186636967441124 | 0.373273934882248 | 0.813363032558876 |
17 | 0.120239139388344 | 0.240478278776689 | 0.879760860611656 |
18 | 0.217017024159083 | 0.434034048318165 | 0.782982975840917 |
19 | 0.364243292701171 | 0.728486585402342 | 0.635756707298829 |
20 | 0.275005018713093 | 0.550010037426185 | 0.724994981286907 |
21 | 0.283088104208519 | 0.566176208417038 | 0.716911895791481 |
22 | 0.210887010571301 | 0.421774021142601 | 0.7891129894287 |
23 | 0.176694478721541 | 0.353388957443083 | 0.823305521278459 |
24 | 0.125654982914780 | 0.251309965829560 | 0.87434501708522 |
25 | 0.0866417828838418 | 0.173283565767684 | 0.913358217116158 |
26 | 0.0765812365536047 | 0.153162473107209 | 0.923418763446395 |
27 | 0.067101538870047 | 0.134203077740094 | 0.932898461129953 |
28 | 0.172415686860241 | 0.344831373720482 | 0.827584313139759 |
29 | 0.144493922184316 | 0.288987844368633 | 0.855506077815684 |
30 | 0.1148369847796 | 0.2296739695592 | 0.8851630152204 |
31 | 0.0847809535732146 | 0.169561907146429 | 0.915219046426785 |
32 | 0.0728711260172475 | 0.145742252034495 | 0.927128873982753 |
33 | 0.0518076382115338 | 0.103615276423068 | 0.948192361788466 |
34 | 0.0379218229756792 | 0.0758436459513583 | 0.962078177024321 |
35 | 0.225157413559948 | 0.450314827119896 | 0.774842586440052 |
36 | 0.44613091630831 | 0.89226183261662 | 0.55386908369169 |
37 | 0.577861687757512 | 0.844276624484975 | 0.422138312242488 |
38 | 0.524759880017355 | 0.95048023996529 | 0.475240119982645 |
39 | 0.495880210901419 | 0.991760421802838 | 0.504119789098581 |
40 | 0.46781126322247 | 0.93562252644494 | 0.53218873677753 |
41 | 0.699023071202616 | 0.601953857594768 | 0.300976928797384 |
42 | 0.85881548724376 | 0.28236902551248 | 0.14118451275624 |
43 | 0.827155014403285 | 0.34568997119343 | 0.172844985596715 |
44 | 0.863579993966096 | 0.272840012067808 | 0.136420006033904 |
45 | 0.837186335844403 | 0.325627328311194 | 0.162813664155597 |
46 | 0.836228403939023 | 0.327543192121954 | 0.163771596060977 |
47 | 0.81430041480588 | 0.371399170388238 | 0.185699585194119 |
48 | 0.824409901755058 | 0.351180196489884 | 0.175590098244942 |
49 | 0.789352148479074 | 0.421295703041851 | 0.210647851520926 |
50 | 0.795803066118476 | 0.408393867763047 | 0.204196933881524 |
51 | 0.77224823331352 | 0.455503533372959 | 0.227751766686479 |
52 | 0.75928905642826 | 0.48142188714348 | 0.24071094357174 |
53 | 0.865944463348877 | 0.268111073302247 | 0.134055536651123 |
54 | 0.836170975523148 | 0.327658048953705 | 0.163829024476852 |
55 | 0.827198761776506 | 0.345602476446989 | 0.172801238223494 |
56 | 0.796107818027485 | 0.407784363945029 | 0.203892181972515 |
57 | 0.759485827938305 | 0.481028344123391 | 0.240514172061695 |
58 | 0.71911742880809 | 0.561765142383819 | 0.280882571191910 |
59 | 0.685380388094898 | 0.629239223810203 | 0.314619611905102 |
60 | 0.664386453757087 | 0.671227092485827 | 0.335613546242913 |
61 | 0.618521528683077 | 0.762956942633845 | 0.381478471316923 |
62 | 0.585334957621423 | 0.829330084757155 | 0.414665042378577 |
63 | 0.558549411223517 | 0.882901177552966 | 0.441450588776483 |
64 | 0.559571123606092 | 0.880857752787817 | 0.440428876393908 |
65 | 0.547553139729245 | 0.90489372054151 | 0.452446860270755 |
66 | 0.632981773528818 | 0.734036452942365 | 0.367018226471182 |
67 | 0.595982954574342 | 0.808034090851316 | 0.404017045425658 |
68 | 0.561406758864246 | 0.877186482271509 | 0.438593241135754 |
69 | 0.697139419948196 | 0.605721160103608 | 0.302860580051804 |
70 | 0.881308796297056 | 0.237382407405889 | 0.118691203702944 |
71 | 0.892818244579678 | 0.214363510840645 | 0.107181755420322 |
72 | 0.90767336535317 | 0.184653269293659 | 0.0923266346468293 |
73 | 0.94842616692006 | 0.103147666159878 | 0.0515738330799391 |
74 | 0.936156595506957 | 0.127686808986085 | 0.0638434044930427 |
75 | 0.929024153402011 | 0.141951693195979 | 0.0709758465979893 |
76 | 0.911499692139989 | 0.177000615720023 | 0.0885003078600114 |
77 | 0.932844757086761 | 0.134310485826478 | 0.0671552429132392 |
78 | 0.934912594926411 | 0.130174810147178 | 0.0650874050735889 |
79 | 0.97112368128819 | 0.0577526374236194 | 0.0288763187118097 |
80 | 0.96214294606661 | 0.0757141078667812 | 0.0378570539333906 |
81 | 0.959431357363502 | 0.0811372852729951 | 0.0405686426364976 |
82 | 0.977480615906263 | 0.0450387681874737 | 0.0225193840937368 |
83 | 0.97121752101839 | 0.057564957963219 | 0.0287824789816095 |
84 | 0.977142269322926 | 0.0457154613541484 | 0.0228577306770742 |
85 | 0.969794988119506 | 0.0604100237609889 | 0.0302050118804944 |
86 | 0.963184775566766 | 0.0736304488664676 | 0.0368152244332338 |
87 | 0.953074449887289 | 0.0938511002254219 | 0.0469255501127109 |
88 | 0.945970004105975 | 0.108059991788050 | 0.0540299958940251 |
89 | 0.950468259915745 | 0.0990634801685103 | 0.0495317400842551 |
90 | 0.937362904954242 | 0.125274190091517 | 0.0626370950457583 |
91 | 0.934860491214444 | 0.130279017571112 | 0.065139508785556 |
92 | 0.954056048692625 | 0.0918879026147508 | 0.0459439513073754 |
93 | 0.996063614766598 | 0.00787277046680392 | 0.00393638523340196 |
94 | 0.994402529207958 | 0.0111949415840838 | 0.00559747079204192 |
95 | 0.993580566514058 | 0.0128388669718848 | 0.00641943348594238 |
96 | 0.991405820205138 | 0.0171883595897232 | 0.0085941797948616 |
97 | 0.991430563688612 | 0.0171388726227768 | 0.00856943631138839 |
98 | 0.992487052784944 | 0.0150258944301113 | 0.00751294721505564 |
99 | 0.989469729272089 | 0.0210605414558221 | 0.0105302707279111 |
100 | 0.988305806983068 | 0.0233883860338648 | 0.0116941930169324 |
101 | 0.992325520224263 | 0.0153489595514739 | 0.00767447977573696 |
102 | 0.992727005229716 | 0.0145459895405683 | 0.00727299477028416 |
103 | 0.989896971569295 | 0.0202060568614103 | 0.0101030284307051 |
104 | 0.992825164871735 | 0.0143496702565307 | 0.00717483512826537 |
105 | 0.989949408274573 | 0.0201011834508546 | 0.0100505917254273 |
106 | 0.987266617746458 | 0.0254667645070842 | 0.0127333822535421 |
107 | 0.98528166614647 | 0.0294366677070614 | 0.0147183338535307 |
108 | 0.989717739714185 | 0.0205645205716299 | 0.0102822602858150 |
109 | 0.998983993828767 | 0.00203201234246683 | 0.00101600617123342 |
110 | 0.998671567811605 | 0.00265686437678947 | 0.00132843218839473 |
111 | 0.999577555351422 | 0.000844889297155976 | 0.000422444648577988 |
112 | 0.999304829128739 | 0.00139034174252301 | 0.000695170871261506 |
113 | 0.999293458297452 | 0.00141308340509546 | 0.000706541702547729 |
114 | 0.998843361918988 | 0.00231327616202400 | 0.00115663808101200 |
115 | 0.998266299464972 | 0.00346740107005558 | 0.00173370053502779 |
116 | 0.99713469342585 | 0.00573061314829891 | 0.00286530657414946 |
117 | 0.99557115566991 | 0.00885768866018059 | 0.00442884433009030 |
118 | 0.99928575384014 | 0.00142849231972000 | 0.000714246159859999 |
119 | 0.99875689838233 | 0.00248620323533879 | 0.00124310161766940 |
120 | 0.997906634033036 | 0.00418673193392749 | 0.00209336596696375 |
121 | 0.99737515821669 | 0.00524968356661817 | 0.00262484178330908 |
122 | 0.996628323039009 | 0.0067433539219827 | 0.00337167696099135 |
123 | 0.994724900840254 | 0.0105501983194925 | 0.00527509915974623 |
124 | 0.994622704684837 | 0.0107545906303261 | 0.00537729531516306 |
125 | 0.991111858656729 | 0.0177762826865428 | 0.00888814134327138 |
126 | 0.98706737337536 | 0.0258652532492800 | 0.0129326266246400 |
127 | 0.983650942186366 | 0.032698115627268 | 0.016349057813634 |
128 | 0.97589199526384 | 0.048216009472322 | 0.024108004736161 |
129 | 0.987690671533919 | 0.0246186569321619 | 0.0123093284660809 |
130 | 0.989789219226607 | 0.0204215615467852 | 0.0102107807733926 |
131 | 0.984899765858125 | 0.0302004682837506 | 0.0151002341418753 |
132 | 0.981996106931669 | 0.0360077861366615 | 0.0180038930683308 |
133 | 0.97488405455083 | 0.0502318908983413 | 0.0251159454491706 |
134 | 0.96221397071084 | 0.0755720585783199 | 0.0377860292891600 |
135 | 0.937878628501461 | 0.124242742997078 | 0.0621213714985389 |
136 | 0.953839477303385 | 0.0923210453932298 | 0.0461605226966149 |
137 | 0.972144179918852 | 0.0557116401622958 | 0.0278558200811479 |
138 | 0.947584174198594 | 0.104831651602812 | 0.0524158258014058 |
139 | 0.90425799252785 | 0.191484014944301 | 0.0957420074721503 |
140 | 0.853858044619189 | 0.292283910761622 | 0.146141955380811 |
141 | 0.773120447739717 | 0.453759104520566 | 0.226879552260283 |
142 | 0.709951349663682 | 0.580097300672636 | 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 |