Multiple Linear Regression - Estimated Regression Equation |
Popularity[t] = + 0.291123164546368 -0.0511359771771675month[t] + 0.100278815914936FindingFriends[t] + 0.211899695274710KnowingPeople[t] + 0.384406986575042Liked[t] + 0.591650456104061Celebrity[t] + 0.312334530791981bestfriend[t] -0.0295870251376916secondbestfriend[t] + 0.409233788979355thirdbestfriend[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) | 0.291123164546368 | 3.563591 | 0.0817 | 0.935001 | 0.467501 |
month | -0.0511359771771675 | 0.35484 | -0.1441 | 0.885611 | 0.442805 |
FindingFriends | 0.100278815914936 | 0.097016 | 1.0336 | 0.303007 | 0.151504 |
KnowingPeople | 0.211899695274710 | 0.063839 | 3.3193 | 0.001138 | 0.000569 |
Liked | 0.384406986575042 | 0.098679 | 3.8955 | 0.000148 | 7.4e-05 |
Celebrity | 0.591650456104061 | 0.156115 | 3.7898 | 0.000219 | 0.00011 |
bestfriend | 0.312334530791981 | 0.210576 | 1.4832 | 0.140152 | 0.070076 |
secondbestfriend | -0.0295870251376916 | 0.201438 | -0.1469 | 0.883429 | 0.441714 |
thirdbestfriend | 0.409233788979355 | 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 | 11.1561094101339 | 1.84389058986607 |
2 | 12 | 10.9973203599166 | 1.00267964008338 |
3 | 15 | 13.0768983942228 | 1.92310160577722 |
4 | 12 | 11.4133960061974 | 0.586603993802554 |
5 | 10 | 10.9282941675151 | -0.928294167515113 |
6 | 12 | 9.31461202404611 | 2.68538797595389 |
7 | 15 | 16.8694298030583 | -1.86942980305829 |
8 | 9 | 10.2725550164866 | -1.27255501648660 |
9 | 12 | 12.9984786544118 | -0.998478654411798 |
10 | 11 | 7.53023514068136 | 3.46976485931864 |
11 | 11 | 13.0043488613008 | -2.00434886130083 |
12 | 11 | 12.1525974460617 | -1.15259744606174 |
13 | 15 | 12.2703841299406 | 2.72961587005938 |
14 | 7 | 11.4490660940079 | -4.44906609400788 |
15 | 11 | 11.2357071966462 | -0.235707196646161 |
16 | 11 | 10.7932536652234 | 0.206746334776610 |
17 | 10 | 11.8106758901321 | -1.81067589013207 |
18 | 14 | 14.8467791465252 | -0.84677914652517 |
19 | 10 | 8.55586344632273 | 1.44413655367727 |
20 | 6 | 9.34736154636249 | -3.34736154636249 |
21 | 11 | 8.77694508163459 | 2.22305491836541 |
22 | 15 | 14.0613805507328 | 0.93861944926724 |
23 | 11 | 11.5771781899035 | -0.577178189903492 |
24 | 12 | 9.73729076617974 | 2.26270923382026 |
25 | 14 | 13.0722686829436 | 0.927731317056356 |
26 | 15 | 14.5194231921656 | 0.480576807834437 |
27 | 9 | 14.3028672711452 | -5.30286727114516 |
28 | 13 | 12.5051707349968 | 0.494829265003233 |
29 | 13 | 13.4500725736659 | -0.450072573665895 |
30 | 16 | 11.1697236542293 | 4.83027634577075 |
31 | 13 | 8.7596233611365 | 4.2403766388635 |
32 | 12 | 13.6311085757848 | -1.63110857578479 |
33 | 14 | 14.5708931556271 | -0.570893155627051 |
34 | 11 | 9.63304605908544 | 1.36695394091456 |
35 | 9 | 10.2429679913489 | -1.24296799134890 |
36 | 16 | 14.2058640159701 | 1.7941359840299 |
37 | 12 | 13.1612309435618 | -1.16123094356184 |
38 | 10 | 9.74717888686278 | 0.252821113137221 |
39 | 13 | 13.1693239607334 | -0.169323960733352 |
40 | 16 | 15.2492336916989 | 0.750766308301114 |
41 | 14 | 13.1250153144233 | 0.87498468557674 |
42 | 15 | 8.10866994098946 | 6.89133005901054 |
43 | 5 | 9.73044890887825 | -4.73044890887825 |
44 | 8 | 10.3447834918720 | -2.34478349187199 |
45 | 11 | 11.1715972465804 | -0.171597246580375 |
46 | 16 | 14.2458162389297 | 1.75418376107027 |
47 | 17 | 14.2833334528663 | 2.71666654713366 |
48 | 9 | 8.04833749734074 | 0.951662502659255 |
49 | 9 | 11.4323057943085 | -2.43230579430853 |
50 | 13 | 14.8466231269228 | -1.84662312692284 |
51 | 10 | 10.9236847050589 | -0.92368470505885 |
52 | 6 | 12.0403434699607 | -6.04034346996074 |
53 | 12 | 11.8874045716608 | 0.112595428339179 |
54 | 8 | 10.4729821368622 | -2.47298213686223 |
55 | 14 | 11.8447631214131 | 2.15523687858688 |
56 | 12 | 12.9277332433333 | -0.927733243333263 |
57 | 11 | 11.0230223205811 | -0.0230223205810992 |
58 | 16 | 14.0935550957958 | 1.90644490420420 |
59 | 8 | 10.2043935119364 | -2.20439351193644 |
60 | 15 | 14.5606342444178 | 0.439365755582235 |
61 | 7 | 9.0661419531643 | -2.06614195316430 |
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 | 12.3180173899050 | 1.68198261009502 |
67 | 11 | 13.2318077556377 | -2.23180775563770 |
68 | 13 | 10.3498777008897 | 2.65012229911031 |
69 | 15 | 12.9473930539210 | 2.05260694607897 |
70 | 5 | 5.76127050334993 | -0.761270503349934 |
71 | 15 | 12.8765972661561 | 2.12340273384390 |
72 | 13 | 11.9169217836999 | 1.08307821630008 |
73 | 11 | 12.9968137479744 | -1.99681374797437 |
74 | 11 | 14.0952478000063 | -3.09524780000629 |
75 | 12 | 12.1930141708868 | -0.193014170886771 |
76 | 12 | 13.4007794696081 | -1.40077946960814 |
77 | 12 | 12.7519219616863 | -0.751921961686308 |
78 | 12 | 12.0811136174823 | -0.0811136174822852 |
79 | 14 | 11.0512754440024 | 2.94872455599760 |
80 | 6 | 7.97861965072775 | -1.97861965072775 |
81 | 7 | 9.41630568885595 | -2.41630568885595 |
82 | 14 | 12.6155692585780 | 1.38443074142198 |
83 | 14 | 14.0003351977312 | -0.00033519773121668 |
84 | 10 | 10.9673318250210 | -0.967331825020967 |
85 | 13 | 9.36744645971611 | 3.63255354028389 |
86 | 12 | 12.4136399800742 | -0.41363998007422 |
87 | 9 | 9.07144712585763 | -0.0714471258576263 |
88 | 12 | 12.3554364093057 | -0.355436409305704 |
89 | 16 | 15.0703028689144 | 0.929697131085609 |
90 | 10 | 10.8033161391914 | -0.803316139191449 |
91 | 14 | 12.9849893480654 | 1.01501065193458 |
92 | 10 | 13.6455152362939 | -3.64551523629387 |
93 | 16 | 14.9860419996447 | 1.01395800035533 |
94 | 15 | 13.3152222748656 | 1.68477772513440 |
95 | 12 | 11.4768444299153 | 0.523155570084742 |
96 | 10 | 9.27338542269331 | 0.726614577306685 |
97 | 8 | 10.2857412363574 | -2.28574123635735 |
98 | 8 | 8.46845460630873 | -0.468454606308727 |
99 | 11 | 12.5556942387404 | -1.55569423874035 |
100 | 13 | 12.9920015026263 | 0.0079984973736558 |
101 | 16 | 15.8784052490512 | 0.121594750948834 |
102 | 16 | 15.1704776878416 | 0.82952231215836 |
103 | 14 | 15.6644239192084 | -1.66442391920835 |
104 | 11 | 8.993938985927 | 2.00606101407300 |
105 | 4 | 7.37908943075277 | -3.37908943075277 |
106 | 14 | 14.6811824228954 | -0.681182422895399 |
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 | -0.0136006127768117 |
114 | 14 | 13.0242257324375 | 0.975774267562534 |
115 | 15 | 14.4130525414258 | 0.586947458574178 |
116 | 16 | 13.3761086868062 | 2.62389131319384 |
117 | 16 | 12.8813054662748 | 3.11869453372517 |
118 | 11 | 12.6614687734309 | -1.66146877343094 |
119 | 14 | 13.3840908499781 | 0.615909150021876 |
120 | 14 | 11.0297814360362 | 2.97021856396378 |
121 | 12 | 11.5817794715759 | 0.418220528424115 |
122 | 14 | 13.0720629785932 | 0.92793702140677 |
123 | 8 | 10.8410413471034 | -2.84104134710344 |
124 | 13 | 14.2946990610775 | -1.29469906107747 |
125 | 16 | 14.5363418010922 | 1.46365819890779 |
126 | 12 | 10.5944574479731 | 1.40554255202692 |
127 | 16 | 15.8673232021964 | 0.132676797803649 |
128 | 12 | 12.7087981749745 | -0.708798174974494 |
129 | 11 | 11.3236884710665 | -0.323688471066468 |
130 | 4 | 5.75762186245885 | -1.75762186245885 |
131 | 16 | 16.1204836827130 | -0.120483682712950 |
132 | 15 | 13.1036223819861 | 1.89637761801388 |
133 | 10 | 11.1658333304308 | -1.16583333043083 |
134 | 13 | 14.3080532885827 | -1.30805328858271 |
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 | 0.0505473270818735 |
142 | 13 | 13.2609522301165 | -0.260952230116489 |
143 | 15 | 12.4668185272168 | 2.53318147278321 |
144 | 8 | 8.98814186294263 | -0.988141862942634 |
145 | 12 | 11.1875671061642 | 0.812432893835844 |
146 | 10 | 10.4485933177299 | -0.448593317729926 |
147 | 8 | 11.3305913693145 | -3.33059136931448 |
148 | 10 | 14.3439436071780 | -4.34394360717797 |
149 | 15 | 14.2387288914726 | 0.761271108527372 |
150 | 16 | 14.0252139745086 | 1.97478602549143 |
151 | 13 | 13.2564520239731 | -0.256452023973133 |
152 | 16 | 15.0487516272500 | 0.951248372750046 |
153 | 9 | 9.76941328862813 | -0.769413288628131 |
154 | 14 | 13.3629237502419 | 0.637076249758089 |
155 | 14 | 13.4257622916148 | 0.574237708385213 |
156 | 12 | 10.0614732457738 | 1.93852675422620 |
Goldfeld-Quandt test for Heteroskedasticity | |||
p-values | Alternative Hypothesis | ||
breakpoint index | greater | 2-sided | less |
12 | 0.267851334500296 | 0.535702669000592 | 0.732148665499704 |
13 | 0.731529606659303 | 0.536940786681393 | 0.268470393340697 |
14 | 0.914217608110061 | 0.171564783779878 | 0.085782391889939 |
15 | 0.86647690779497 | 0.267046184410060 | 0.133523092205030 |
16 | 0.80932561050175 | 0.381348778996500 | 0.190674389498250 |
17 | 0.739676230751042 | 0.520647538497917 | 0.260323769248958 |
18 | 0.65373851301835 | 0.692522973963301 | 0.346261486981651 |
19 | 0.573567683470478 | 0.852864633059044 | 0.426432316529522 |
20 | 0.798092253147342 | 0.403815493705316 | 0.201907746852658 |
21 | 0.741599450169642 | 0.516801099660717 | 0.258400549830358 |
22 | 0.739847510564674 | 0.520304978870652 | 0.260152489435326 |
23 | 0.673825735686908 | 0.652348528626185 | 0.326174264313092 |
24 | 0.668104488912187 | 0.663791022175626 | 0.331895511087813 |
25 | 0.632002133001176 | 0.735995733997649 | 0.367997866998824 |
26 | 0.571128837906888 | 0.857742324186224 | 0.428871162093112 |
27 | 0.78204354541431 | 0.435912909171381 | 0.217956454585690 |
28 | 0.74133963782513 | 0.517320724349741 | 0.258660362174870 |
29 | 0.683231163606276 | 0.633537672787448 | 0.316768836393724 |
30 | 0.789418428423551 | 0.421163143152897 | 0.210581571576449 |
31 | 0.847108877642807 | 0.305782244714385 | 0.152891122357193 |
32 | 0.812860853051502 | 0.374278293896997 | 0.187139146948498 |
33 | 0.768612768065328 | 0.462774463869344 | 0.231387231934672 |
34 | 0.731835603705885 | 0.53632879258823 | 0.268164396294115 |
35 | 0.70636775933185 | 0.587264481336299 | 0.293632240668150 |
36 | 0.735487244046579 | 0.529025511906842 | 0.264512755953421 |
37 | 0.712434629932257 | 0.575130740135487 | 0.287565370067743 |
38 | 0.666628997855148 | 0.666742004289705 | 0.333371002144852 |
39 | 0.617651363890346 | 0.764697272219307 | 0.382348636109653 |
40 | 0.575214959701759 | 0.849570080596483 | 0.424785040298241 |
41 | 0.527993850036620 | 0.94401229992676 | 0.47200614996338 |
42 | 0.861221780511167 | 0.277556438977666 | 0.138778219488833 |
43 | 0.966583310438297 | 0.0668333791234058 | 0.0334166895617029 |
44 | 0.96819576598334 | 0.0636084680333181 | 0.0318042340166591 |
45 | 0.95925604793305 | 0.0814879041339019 | 0.0407439520669509 |
46 | 0.964720518292831 | 0.0705589634143375 | 0.0352794817071687 |
47 | 0.971786803183192 | 0.0564263936336163 | 0.0282131968168081 |
48 | 0.96836099251294 | 0.0632780149741217 | 0.0316390074870608 |
49 | 0.964612424908324 | 0.070775150183352 | 0.035387575091676 |
50 | 0.955528699561904 | 0.0889426008761924 | 0.0444713004380962 |
51 | 0.949332844304232 | 0.101334311391536 | 0.0506671556957681 |
52 | 0.990090983361845 | 0.0198180332763105 | 0.00990901663815524 |
53 | 0.986436003532825 | 0.0271279929343491 | 0.0135639964671746 |
54 | 0.991022306072572 | 0.0179553878548560 | 0.00897769392742801 |
55 | 0.993004133562015 | 0.0139917328759697 | 0.00699586643798484 |
56 | 0.990883733796613 | 0.0182325324067731 | 0.00911626620338653 |
57 | 0.987474042420853 | 0.0250519151582930 | 0.0125259575791465 |
58 | 0.987149205674605 | 0.0257015886507902 | 0.0128507943253951 |
59 | 0.99020016521662 | 0.0195996695667594 | 0.0097998347833797 |
60 | 0.989018955123747 | 0.0219620897525050 | 0.0109810448762525 |
61 | 0.98886372990792 | 0.0222725401841581 | 0.0111362700920791 |
62 | 0.99042608214018 | 0.0191478357196388 | 0.00957391785981939 |
63 | 0.988880380817605 | 0.0222392383647899 | 0.0111196191823949 |
64 | 0.989295536736391 | 0.0214089265272172 | 0.0107044632636086 |
65 | 0.988765738900037 | 0.0224685221999260 | 0.0112342610999630 |
66 | 0.98671368239457 | 0.0265726352108617 | 0.0132863176054308 |
67 | 0.988428403213568 | 0.0231431935728632 | 0.0115715967864316 |
68 | 0.989826418319203 | 0.0203471633615937 | 0.0101735816807968 |
69 | 0.989206381890125 | 0.0215872362197506 | 0.0107936181098753 |
70 | 0.986375738127255 | 0.0272485237454905 | 0.0136242618727453 |
71 | 0.986462443949735 | 0.0270751121005291 | 0.0135375560502646 |
72 | 0.982921268377207 | 0.0341574632455866 | 0.0170787316227933 |
73 | 0.984150493637228 | 0.0316990127255433 | 0.0158495063627716 |
74 | 0.989499613487193 | 0.0210007730256145 | 0.0105003865128073 |
75 | 0.985993152923994 | 0.0280136941520126 | 0.0140068470760063 |
76 | 0.983731221588844 | 0.0325375568223122 | 0.0162687784111561 |
77 | 0.979027526019643 | 0.0419449479607137 | 0.0209724739803568 |
78 | 0.972743830040854 | 0.054512339918293 | 0.0272561699591465 |
79 | 0.978904693927037 | 0.0421906121459253 | 0.0210953060729627 |
80 | 0.978666833914724 | 0.0426663321705513 | 0.0213331660852757 |
81 | 0.980298795133093 | 0.0394024097338148 | 0.0197012048669074 |
82 | 0.978072652136558 | 0.0438546957268834 | 0.0219273478634417 |
83 | 0.970875888786057 | 0.0582482224278853 | 0.0291241112139427 |
84 | 0.963612914580625 | 0.0727741708387508 | 0.0363870854193754 |
85 | 0.984468697908029 | 0.0310626041839428 | 0.0155313020919714 |
86 | 0.979530176024867 | 0.0409396479502659 | 0.0204698239751329 |
87 | 0.97294176953030 | 0.0541164609393982 | 0.0270582304696991 |
88 | 0.965318818305441 | 0.0693623633891184 | 0.0346811816945592 |
89 | 0.956503549604284 | 0.0869929007914318 | 0.0434964503957159 |
90 | 0.945679005183953 | 0.108641989632094 | 0.0543209948160468 |
91 | 0.936049539038855 | 0.127900921922290 | 0.0639504609611449 |
92 | 0.963166649795986 | 0.0736667004080280 | 0.0368333502040140 |
93 | 0.953976103877733 | 0.0920477922445334 | 0.0460238961222667 |
94 | 0.94896035430909 | 0.102079291381819 | 0.0510396456909093 |
95 | 0.936390937631744 | 0.127218124736513 | 0.0636090623682564 |
96 | 0.921425005003787 | 0.157149989992426 | 0.0785749949962131 |
97 | 0.91742480930999 | 0.165150381380018 | 0.0825751906900092 |
98 | 0.89759480693174 | 0.204810386136522 | 0.102405193068261 |
99 | 0.88813378309076 | 0.223732433818481 | 0.111866216909240 |
100 | 0.86179285718119 | 0.276414285637621 | 0.138207142818810 |
101 | 0.83262567189655 | 0.334748656206899 | 0.167374328103450 |
102 | 0.801849136971911 | 0.396301726056177 | 0.198150863028089 |
103 | 0.83025034619864 | 0.339499307602719 | 0.169749653801360 |
104 | 0.872528287551913 | 0.254943424896174 | 0.127471712448087 |
105 | 0.879408339913797 | 0.241183320172405 | 0.120591660086203 |
106 | 0.852491560219525 | 0.295016879560949 | 0.147508439780475 |
107 | 0.828686556519089 | 0.342626886961823 | 0.171313443480911 |
108 | 0.822586054606012 | 0.354827890787976 | 0.177413945393988 |
109 | 0.812576971778244 | 0.374846056443512 | 0.187423028221756 |
110 | 0.834747212330976 | 0.330505575338048 | 0.165252787669024 |
111 | 0.820540928486847 | 0.358918143026306 | 0.179459071513153 |
112 | 0.867531975525258 | 0.264936048949483 | 0.132468024474742 |
113 | 0.834454896623193 | 0.331090206753614 | 0.165545103376807 |
114 | 0.801076197783575 | 0.397847604432849 | 0.198923802216425 |
115 | 0.760017224608492 | 0.479965550783015 | 0.239982775391508 |
116 | 0.772319613638931 | 0.455360772722138 | 0.227680386361069 |
117 | 0.78208395998174 | 0.435832080036518 | 0.217916040018259 |
118 | 0.762200018641286 | 0.475599962717428 | 0.237799981358714 |
119 | 0.716557374778685 | 0.566885250442629 | 0.283442625221315 |
120 | 0.802196243653025 | 0.395607512693950 | 0.197803756346975 |
121 | 0.768066552121913 | 0.463866895756174 | 0.231933447878087 |
122 | 0.718107649450573 | 0.563784701098853 | 0.281892350549427 |
123 | 0.716778496832857 | 0.566443006334287 | 0.283221503167144 |
124 | 0.68193671505839 | 0.636126569883221 | 0.318063284941610 |
125 | 0.655177156610557 | 0.689645686778885 | 0.344822843389443 |
126 | 0.636624975522513 | 0.726750048954974 | 0.363375024477487 |
127 | 0.570312300490665 | 0.85937539901867 | 0.429687699509335 |
128 | 0.552937924830732 | 0.894124150338536 | 0.447062075169268 |
129 | 0.541560975749484 | 0.916878048501031 | 0.458439024250516 |
130 | 0.527317168301533 | 0.945365663396933 | 0.472682831698467 |
131 | 0.458210747592227 | 0.916421495184453 | 0.541789252407773 |
132 | 0.427590417090005 | 0.85518083418001 | 0.572409582909995 |
133 | 0.391322998815491 | 0.782645997630982 | 0.608677001184509 |
134 | 0.346312414681866 | 0.692624829363733 | 0.653687585318134 |
135 | 0.298773924810124 | 0.597547849620248 | 0.701226075189876 |
136 | 0.274118017018751 | 0.548236034037502 | 0.725881982981249 |
137 | 0.241330563724718 | 0.482661127449436 | 0.758669436275282 |
138 | 0.264217980801055 | 0.52843596160211 | 0.735782019198945 |
139 | 0.643546302035173 | 0.712907395929653 | 0.356453697964826 |
140 | 0.633255871622839 | 0.733488256754322 | 0.366744128377161 |
141 | 0.526023833069466 | 0.947952333861067 | 0.473976166930534 |
142 | 0.51212567630266 | 0.97574864739468 | 0.48787432369734 |
143 | 0.378082678354520 | 0.756165356709039 | 0.62191732164548 |
144 | 0.257890618619672 | 0.515781237239344 | 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 |