Multiple Linear Regression - Estimated Regression Equation |
Popularity[t] = + 0.291123164546304 -0.0511359771771629Month[t] + 0.100278815914937FindingFriends[t] + 0.21189969527471KnowingPeople[t] + 0.384406986575043Liked[t] + 0.591650456104063Celebrity[t] + 0.312334530791982BestFriend[t] -0.0295870251376915SecondBestFriend[t] + 0.409233788979356ThirdBestFriend[t] + 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) | 0.291123164546304 | 3.563591 | 0.0817 | 0.935001 | 0.467501 |
Month | -0.0511359771771629 | 0.35484 | -0.1441 | 0.885611 | 0.442805 |
FindingFriends | 0.100278815914937 | 0.097016 | 1.0336 | 0.303007 | 0.151504 |
KnowingPeople | 0.21189969527471 | 0.063839 | 3.3193 | 0.001138 | 0.000569 |
Liked | 0.384406986575043 | 0.098679 | 3.8955 | 0.000148 | 7.4e-05 |
Celebrity | 0.591650456104063 | 0.156115 | 3.7898 | 0.000219 | 0.00011 |
BestFriend | 0.312334530791982 | 0.210576 | 1.4832 | 0.140152 | 0.070076 |
SecondBestFriend | -0.0295870251376915 | 0.201438 | -0.1469 | 0.883429 | 0.441714 |
ThirdBestFriend | 0.409233788979356 | 0.213752 | 1.9145 | 0.057496 | 0.028748 |
Multiple Linear Regression - Regression Statistics | |
Multiple R | 0.718941993490984 |
R-squared | 0.51687759000479 |
Adjusted R-squared | 0.490585213950629 |
F-TEST (value) | 19.6588390847615 |
F-TEST (DF numerator) | 8 |
F-TEST (DF denominator) | 147 |
p-value | 0 |
Multiple Linear Regression - Residual Statistics | |
Residual Standard Deviation | 2.09596780395353 |
Sum Squared Residuals | 645.782912175841 |
Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
1 | 13 | 11.156109410134 | 1.843890589866 |
2 | 12 | 10.9973203599166 | 1.00267964008339 |
3 | 15 | 13.0768983942228 | 1.92310160577722 |
4 | 12 | 11.4133960061974 | 0.586603993802553 |
5 | 10 | 10.9282941675151 | -0.928294167515105 |
6 | 12 | 9.3146120240461 | 2.6853879759539 |
7 | 15 | 16.8694298030583 | -1.86942980305829 |
8 | 9 | 10.2725550164866 | -1.27255501648659 |
9 | 12 | 12.9984786544118 | -0.998478654411791 |
10 | 11 | 7.53023514068135 | 3.46976485931865 |
11 | 11 | 13.0043488613008 | -2.00434886130083 |
12 | 11 | 12.1525974460617 | -1.15259744606174 |
13 | 15 | 12.2703841299406 | 2.72961587005939 |
14 | 7 | 11.4490660940079 | -4.44906609400788 |
15 | 11 | 11.2357071966462 | -0.235707196646161 |
16 | 11 | 10.7932536652234 | 0.206746334776617 |
17 | 10 | 11.8106758901321 | -1.81067589013207 |
18 | 14 | 14.8467791465252 | -0.846779146525168 |
19 | 10 | 8.55586344632273 | 1.44413655367727 |
20 | 6 | 9.34736154636249 | -3.34736154636249 |
21 | 11 | 8.77694508163458 | 2.22305491836542 |
22 | 15 | 14.0613805507328 | 0.938619449267243 |
23 | 11 | 11.5771781899035 | -0.577178189903485 |
24 | 12 | 9.73729076617973 | 2.26270923382027 |
25 | 14 | 13.0722686829436 | 0.927731317056361 |
26 | 15 | 14.5194231921656 | 0.480576807834442 |
27 | 9 | 14.3028672711452 | -5.30286727114516 |
28 | 13 | 12.5051707349968 | 0.494829265003239 |
29 | 13 | 13.4500725736659 | -0.450072573665892 |
30 | 16 | 11.1697236542293 | 4.83027634577075 |
31 | 13 | 8.7596233611365 | 4.2403766388635 |
32 | 12 | 13.6311085757848 | -1.63110857578478 |
33 | 14 | 14.5708931556271 | -0.57089315562705 |
34 | 11 | 9.63304605908543 | 1.36695394091457 |
35 | 9 | 10.2429679913489 | -1.2429679913489 |
36 | 16 | 14.2058640159701 | 1.7941359840299 |
37 | 12 | 13.1612309435618 | -1.16123094356184 |
38 | 10 | 9.74717888686277 | 0.252821113137226 |
39 | 13 | 13.1693239607333 | -0.169323960733348 |
40 | 16 | 15.2492336916989 | 0.750766308301116 |
41 | 14 | 13.1250153144233 | 0.874984685576742 |
42 | 15 | 8.10866994098945 | 6.89133005901054 |
43 | 5 | 9.73044890887825 | -4.73044890887825 |
44 | 8 | 10.344783491872 | -2.34478349187198 |
45 | 11 | 11.1715972465804 | -0.171597246580374 |
46 | 16 | 14.2458162389297 | 1.75418376107027 |
47 | 17 | 14.2833334528663 | 2.71666654713366 |
48 | 9 | 8.04833749734074 | 0.951662502659259 |
49 | 9 | 11.4323057943085 | -2.43230579430853 |
50 | 13 | 14.8466231269228 | -1.84662312692283 |
51 | 10 | 10.9236847050589 | -0.92368470505885 |
52 | 6 | 12.0403434699607 | -6.04034346996074 |
53 | 12 | 11.8874045716608 | 0.112595428339184 |
54 | 8 | 10.4729821368622 | -2.47298213686223 |
55 | 14 | 11.8447631214131 | 2.15523687858689 |
56 | 12 | 12.9277332433333 | -0.927733243333258 |
57 | 11 | 11.0230223205811 | -0.0230223205810985 |
58 | 16 | 14.0935550957958 | 1.9064449042042 |
59 | 8 | 10.2043935119364 | -2.20439351193644 |
60 | 15 | 14.5606342444178 | 0.439365755582233 |
61 | 7 | 9.0661419531643 | -2.0661419531643 |
62 | 16 | 13.8705998681328 | 2.12940013186717 |
63 | 14 | 12.8415664966158 | 1.15843350338421 |
64 | 16 | 13.5746674259143 | 2.42533257408571 |
65 | 9 | 10.1872012965741 | -1.18720129657414 |
66 | 14 | 12.318017389905 | 1.68198261009502 |
67 | 11 | 13.2318077556377 | -2.23180775563771 |
68 | 13 | 10.3498777008897 | 2.65012229911031 |
69 | 15 | 12.947393053921 | 2.05260694607897 |
70 | 5 | 5.76127050334993 | -0.761270503349932 |
71 | 15 | 12.8765972661561 | 2.1234027338439 |
72 | 13 | 11.9169217836999 | 1.08307821630008 |
73 | 11 | 12.9968137479744 | -1.99681374797437 |
74 | 11 | 14.0952478000063 | -3.09524780000629 |
75 | 12 | 12.1930141708868 | -0.193014170886773 |
76 | 12 | 13.4007794696081 | -1.40077946960814 |
77 | 12 | 12.7519219616863 | -0.75192196168631 |
78 | 12 | 12.0811136174823 | -0.0811136174822851 |
79 | 14 | 11.0512754440024 | 2.94872455599759 |
80 | 6 | 7.97861965072775 | -1.97861965072775 |
81 | 7 | 9.41630568885596 | -2.41630568885596 |
82 | 14 | 12.615569258578 | 1.38443074142198 |
83 | 14 | 14.0003351977312 | -0.000335197731220436 |
84 | 10 | 10.967331825021 | -0.967331825020966 |
85 | 13 | 9.36744645971611 | 3.63255354028389 |
86 | 12 | 12.4136399800742 | -0.413639980074222 |
87 | 9 | 9.07144712585763 | -0.0714471258576259 |
88 | 12 | 12.3554364093057 | -0.355436409305705 |
89 | 16 | 15.0703028689144 | 0.929697131085605 |
90 | 10 | 10.8033161391915 | -0.80331613919145 |
91 | 14 | 12.9849893480654 | 1.01501065193457 |
92 | 10 | 13.6455152362939 | -3.64551523629387 |
93 | 16 | 14.9860419996447 | 1.01395800035532 |
94 | 15 | 13.3152222748656 | 1.6847777251344 |
95 | 12 | 11.4768444299153 | 0.523155570084741 |
96 | 10 | 9.27338542269332 | 0.726614577306685 |
97 | 8 | 10.2857412363574 | -2.28574123635736 |
98 | 8 | 8.46845460630873 | -0.468454606308727 |
99 | 11 | 12.5556942387403 | -1.55569423874035 |
100 | 13 | 12.9920015026263 | 0.00799849737365134 |
101 | 16 | 15.8784052490512 | 0.121594750948831 |
102 | 16 | 15.1704776878416 | 0.829522312158356 |
103 | 14 | 15.6644239192084 | -1.66442391920836 |
104 | 11 | 8.993938985927 | 2.006061014073 |
105 | 4 | 7.37908943075277 | -3.37908943075277 |
106 | 14 | 14.6811824228954 | -0.681182422895407 |
107 | 9 | 10.5776716883672 | -1.57767168836724 |
108 | 14 | 15.2526155390514 | -1.25261553905141 |
109 | 8 | 10.0286106598962 | -2.02861065989624 |
110 | 8 | 10.4919319595558 | -2.49193195955582 |
111 | 11 | 11.9776325185835 | -0.977632518583453 |
112 | 12 | 13.2116678982108 | -1.21166789821079 |
113 | 11 | 11.0136006127768 | -0.0136006127768161 |
114 | 14 | 13.0242257324375 | 0.975774267562531 |
115 | 15 | 14.4130525414258 | 0.586947458574173 |
116 | 16 | 13.3761086868062 | 2.62389131319384 |
117 | 16 | 12.8813054662748 | 3.11869453372517 |
118 | 11 | 12.6614687734309 | -1.66146877343094 |
119 | 14 | 13.3840908499781 | 0.615909150021873 |
120 | 14 | 11.0297814360362 | 2.97021856396378 |
121 | 12 | 11.5817794715759 | 0.418220528424114 |
122 | 14 | 13.0720629785932 | 0.92793702140677 |
123 | 8 | 10.8410413471034 | -2.84104134710344 |
124 | 13 | 14.2946990610775 | -1.29469906107748 |
125 | 16 | 14.5363418010922 | 1.46365819890779 |
126 | 12 | 10.5944574479731 | 1.40554255202691 |
127 | 16 | 15.8673232021964 | 0.132676797803643 |
128 | 12 | 12.7087981749745 | -0.708798174974494 |
129 | 11 | 11.3236884710665 | -0.323688471066468 |
130 | 4 | 5.75762186245885 | -1.75762186245885 |
131 | 16 | 16.120483682713 | -0.120483682712955 |
132 | 15 | 13.1036223819861 | 1.89637761801388 |
133 | 10 | 11.1658333304308 | -1.16583333043084 |
134 | 13 | 14.3080532885827 | -1.30805328858272 |
135 | 15 | 12.6102317207247 | 2.38976827927527 |
136 | 12 | 10.2245120659804 | 1.77548793401958 |
137 | 14 | 12.9041652702215 | 1.09583472977847 |
138 | 7 | 10.4379749603298 | -3.43797496032983 |
139 | 19 | 13.7603596537789 | 5.23964034622113 |
140 | 12 | 13.0934132037665 | -1.09341320376652 |
141 | 12 | 11.9494526729181 | 0.0505473270818768 |
142 | 13 | 13.2609522301165 | -0.260952230116492 |
143 | 15 | 12.4668185272168 | 2.53318147278321 |
144 | 8 | 8.98814186294263 | -0.988141862942632 |
145 | 12 | 11.1875671061642 | 0.812432893835842 |
146 | 10 | 10.4485933177299 | -0.448593317729932 |
147 | 8 | 11.3305913693145 | -3.33059136931449 |
148 | 10 | 14.343943607178 | -4.34394360717797 |
149 | 15 | 14.2387288914726 | 0.761271108527371 |
150 | 16 | 14.0252139745086 | 1.97478602549142 |
151 | 13 | 13.2564520239731 | -0.256452023973137 |
152 | 16 | 15.04875162725 | 0.951248372750044 |
153 | 9 | 9.76941328862813 | -0.769413288628131 |
154 | 14 | 13.3629237502419 | 0.637076249758086 |
155 | 14 | 13.4257622916148 | 0.574237708385211 |
156 | 12 | 10.0614732457738 | 1.9385267542262 |
Goldfeld-Quandt test for Heteroskedasticity | |||
p-values | Alternative Hypothesis | ||
breakpoint index | greater | 2-sided | less |
12 | 0.267851334500297 | 0.535702669000594 | 0.732148665499703 |
13 | 0.731529606659303 | 0.536940786681393 | 0.268470393340697 |
14 | 0.914217608110061 | 0.171564783779878 | 0.0857823918899391 |
15 | 0.866476907794969 | 0.267046184410061 | 0.133523092205031 |
16 | 0.80932561050175 | 0.381348778996499 | 0.19067438949825 |
17 | 0.739676230751042 | 0.520647538497916 | 0.260323769248958 |
18 | 0.653738513018349 | 0.692522973963302 | 0.346261486981651 |
19 | 0.57356768347048 | 0.85286463305904 | 0.42643231652952 |
20 | 0.798092253147343 | 0.403815493705315 | 0.201907746852657 |
21 | 0.741599450169642 | 0.516801099660716 | 0.258400549830358 |
22 | 0.739847510564675 | 0.52030497887065 | 0.260152489435325 |
23 | 0.673825735686907 | 0.652348528626186 | 0.326174264313093 |
24 | 0.668104488912188 | 0.663791022175625 | 0.331895511087812 |
25 | 0.632002133001176 | 0.735995733997649 | 0.367997866998824 |
26 | 0.571128837906888 | 0.857742324186224 | 0.428871162093112 |
27 | 0.782043545414309 | 0.435912909171382 | 0.217956454585691 |
28 | 0.741339637825131 | 0.517320724349739 | 0.258660362174869 |
29 | 0.683231163606275 | 0.63353767278745 | 0.316768836393725 |
30 | 0.789418428423549 | 0.421163143152902 | 0.210581571576451 |
31 | 0.847108877642808 | 0.305782244714384 | 0.152891122357192 |
32 | 0.812860853051502 | 0.374278293896996 | 0.187139146948498 |
33 | 0.768612768065328 | 0.462774463869344 | 0.231387231934672 |
34 | 0.731835603705885 | 0.53632879258823 | 0.268164396294115 |
35 | 0.706367759331849 | 0.587264481336302 | 0.293632240668151 |
36 | 0.735487244046577 | 0.529025511906846 | 0.264512755953423 |
37 | 0.712434629932255 | 0.575130740135489 | 0.287565370067745 |
38 | 0.666628997855147 | 0.666742004289706 | 0.333371002144853 |
39 | 0.617651363890346 | 0.764697272219308 | 0.382348636109654 |
40 | 0.575214959701756 | 0.849570080596487 | 0.424785040298244 |
41 | 0.527993850036624 | 0.944012299926752 | 0.472006149963376 |
42 | 0.861221780511165 | 0.27755643897767 | 0.138778219488835 |
43 | 0.966583310438297 | 0.0668333791234066 | 0.0334166895617033 |
44 | 0.968195765983341 | 0.0636084680333188 | 0.0318042340166594 |
45 | 0.959256047933049 | 0.0814879041339026 | 0.0407439520669513 |
46 | 0.964720518292833 | 0.0705589634143338 | 0.0352794817071669 |
47 | 0.971786803183193 | 0.0564263936336143 | 0.0282131968168071 |
48 | 0.968360992512938 | 0.0632780149741234 | 0.0316390074870617 |
49 | 0.964612424908323 | 0.070775150183353 | 0.0353875750916765 |
50 | 0.955528699561904 | 0.0889426008761917 | 0.0444713004380958 |
51 | 0.949332844304233 | 0.101334311391534 | 0.050667155695767 |
52 | 0.990090983361845 | 0.0198180332763104 | 0.0099090166381552 |
53 | 0.986436003532825 | 0.0271279929343494 | 0.0135639964671747 |
54 | 0.991022306072572 | 0.017955387854856 | 0.00897769392742801 |
55 | 0.993004133562015 | 0.0139917328759696 | 0.0069958664379848 |
56 | 0.990883733796613 | 0.0182325324067733 | 0.00911626620338664 |
57 | 0.987474042420854 | 0.0250519151582928 | 0.0125259575791464 |
58 | 0.987149205674605 | 0.0257015886507898 | 0.0128507943253949 |
59 | 0.99020016521662 | 0.0195996695667594 | 0.00979983478337972 |
60 | 0.989018955123747 | 0.0219620897525049 | 0.0109810448762525 |
61 | 0.988863729907921 | 0.0222725401841581 | 0.011136270092079 |
62 | 0.990426082140181 | 0.0191478357196388 | 0.0095739178598194 |
63 | 0.988880380817605 | 0.0222392383647901 | 0.011119619182395 |
64 | 0.989295536736392 | 0.0214089265272169 | 0.0107044632636085 |
65 | 0.988765738900037 | 0.0224685221999259 | 0.0112342610999629 |
66 | 0.986713682394569 | 0.0265726352108617 | 0.0132863176054309 |
67 | 0.988428403213569 | 0.0231431935728628 | 0.0115715967864314 |
68 | 0.989826418319203 | 0.0203471633615935 | 0.0101735816807967 |
69 | 0.989206381890125 | 0.021587236219751 | 0.0107936181098755 |
70 | 0.986375738127255 | 0.027248523745491 | 0.0136242618727455 |
71 | 0.986462443949735 | 0.0270751121005294 | 0.0135375560502647 |
72 | 0.982921268377207 | 0.0341574632455864 | 0.0170787316227932 |
73 | 0.984150493637228 | 0.0316990127255433 | 0.0158495063627717 |
74 | 0.989499613487193 | 0.0210007730256148 | 0.0105003865128074 |
75 | 0.985993152923994 | 0.0280136941520127 | 0.0140068470760064 |
76 | 0.983731221588844 | 0.0325375568223119 | 0.0162687784111559 |
77 | 0.979027526019643 | 0.0419449479607139 | 0.020972473980357 |
78 | 0.972743830040853 | 0.0545123399182933 | 0.0272561699591466 |
79 | 0.978904693927037 | 0.0421906121459257 | 0.0210953060729628 |
80 | 0.978666833914724 | 0.0426663321705513 | 0.0213331660852756 |
81 | 0.980298795133093 | 0.0394024097338145 | 0.0197012048669072 |
82 | 0.978072652136558 | 0.0438546957268833 | 0.0219273478634417 |
83 | 0.970875888786057 | 0.0582482224278855 | 0.0291241112139427 |
84 | 0.963612914580624 | 0.072774170838751 | 0.0363870854193755 |
85 | 0.984468697908029 | 0.0310626041839427 | 0.0155313020919714 |
86 | 0.979530176024867 | 0.0409396479502657 | 0.0204698239751329 |
87 | 0.972941769530301 | 0.0541164609393979 | 0.027058230469699 |
88 | 0.96531881830544 | 0.0693623633891191 | 0.0346811816945595 |
89 | 0.956503549604284 | 0.0869929007914314 | 0.0434964503957157 |
90 | 0.945679005183953 | 0.108641989632094 | 0.0543209948160471 |
91 | 0.936049539038855 | 0.127900921922289 | 0.0639504609611447 |
92 | 0.963166649795986 | 0.0736667004080281 | 0.036833350204014 |
93 | 0.953976103877734 | 0.0920477922445327 | 0.0460238961222664 |
94 | 0.948960354309091 | 0.102079291381818 | 0.0510396456909092 |
95 | 0.936390937631744 | 0.127218124736513 | 0.0636090623682565 |
96 | 0.921425005003787 | 0.157149989992426 | 0.0785749949962131 |
97 | 0.917424809309991 | 0.165150381380019 | 0.0825751906900093 |
98 | 0.89759480693174 | 0.20481038613652 | 0.10240519306826 |
99 | 0.88813378309076 | 0.22373243381848 | 0.11186621690924 |
100 | 0.86179285718119 | 0.276414285637621 | 0.13820714281881 |
101 | 0.832625671896551 | 0.334748656206898 | 0.167374328103449 |
102 | 0.801849136971912 | 0.396301726056176 | 0.198150863028088 |
103 | 0.830250346198641 | 0.339499307602718 | 0.169749653801359 |
104 | 0.872528287551913 | 0.254943424896173 | 0.127471712448087 |
105 | 0.879408339913798 | 0.241183320172404 | 0.120591660086202 |
106 | 0.852491560219525 | 0.295016879560949 | 0.147508439780475 |
107 | 0.82868655651909 | 0.342626886961821 | 0.17131344348091 |
108 | 0.822586054606013 | 0.354827890787974 | 0.177413945393987 |
109 | 0.812576971778245 | 0.374846056443511 | 0.187423028221755 |
110 | 0.834747212330977 | 0.330505575338046 | 0.165252787669023 |
111 | 0.820540928486847 | 0.358918143026306 | 0.179459071513153 |
112 | 0.867531975525258 | 0.264936048949484 | 0.132468024474742 |
113 | 0.834454896623193 | 0.331090206753614 | 0.165545103376807 |
114 | 0.801076197783576 | 0.397847604432849 | 0.198923802216424 |
115 | 0.760017224608493 | 0.479965550783015 | 0.239982775391507 |
116 | 0.772319613638931 | 0.455360772722138 | 0.227680386361069 |
117 | 0.782083959981741 | 0.435832080036517 | 0.217916040018259 |
118 | 0.762200018641286 | 0.475599962717428 | 0.237799981358714 |
119 | 0.716557374778684 | 0.566885250442632 | 0.283442625221316 |
120 | 0.802196243653025 | 0.39560751269395 | 0.197803756346975 |
121 | 0.768066552121913 | 0.463866895756174 | 0.231933447878087 |
122 | 0.718107649450574 | 0.563784701098853 | 0.281892350549426 |
123 | 0.716778496832857 | 0.566443006334286 | 0.283221503167143 |
124 | 0.68193671505839 | 0.636126569883221 | 0.31806328494161 |
125 | 0.655177156610558 | 0.689645686778885 | 0.344822843389442 |
126 | 0.636624975522514 | 0.726750048954973 | 0.363375024477486 |
127 | 0.570312300490667 | 0.859375399018667 | 0.429687699509333 |
128 | 0.552937924830731 | 0.894124150338538 | 0.447062075169269 |
129 | 0.541560975749483 | 0.916878048501033 | 0.458439024250517 |
130 | 0.527317168301533 | 0.945365663396933 | 0.472682831698467 |
131 | 0.458210747592225 | 0.916421495184451 | 0.541789252407775 |
132 | 0.427590417090005 | 0.855180834180009 | 0.572409582909996 |
133 | 0.391322998815491 | 0.782645997630982 | 0.608677001184509 |
134 | 0.346312414681866 | 0.692624829363731 | 0.653687585318134 |
135 | 0.298773924810123 | 0.597547849620245 | 0.701226075189877 |
136 | 0.274118017018751 | 0.548236034037503 | 0.725881982981249 |
137 | 0.241330563724719 | 0.482661127449439 | 0.758669436275281 |
138 | 0.264217980801053 | 0.528435961602107 | 0.735782019198947 |
139 | 0.643546302035174 | 0.712907395929652 | 0.356453697964826 |
140 | 0.633255871622839 | 0.733488256754321 | 0.366744128377161 |
141 | 0.526023833069467 | 0.947952333861067 | 0.473976166930533 |
142 | 0.51212567630266 | 0.97574864739468 | 0.48787432369734 |
143 | 0.378082678354519 | 0.756165356709038 | 0.621917321645481 |
144 | 0.257890618619672 | 0.515781237239345 | 0.742109381380328 |
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 | 32 | 0.240601503759398 | NOK |
10% type I error level | 48 | 0.360902255639098 | NOK |