Multiple Linear Regression - Estimated Regression Equation |
Popularity[t] = + 0.184727929928006 + 0.102458915938333FindingFriends[t] + 0.241835431638645KnowingPeople[t] + 0.349828593066031Liked[t] + 0.637259261836313Celebrity[t] + 0.0988008593457305`Date `[t] -0.00641272300843145t + 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) | 0.184727929928006 | 1.456114 | 0.1269 | 0.899219 | 0.44961 |
FindingFriends | 0.102458915938333 | 0.097707 | 1.0486 | 0.296043 | 0.148022 |
KnowingPeople | 0.241835431638645 | 0.061846 | 3.9103 | 0.00014 | 7e-05 |
Liked | 0.349828593066031 | 0.09795 | 3.5715 | 0.000478 | 0.000239 |
Celebrity | 0.637259261836313 | 0.158123 | 4.0302 | 8.9e-05 | 4.4e-05 |
`Date ` | 0.0988008593457305 | 0.196706 | 0.5023 | 0.616215 | 0.308107 |
t | -0.00641272300843145 | 0.011948 | -0.5367 | 0.592247 | 0.296123 |
Multiple Linear Regression - Regression Statistics | |
Multiple R | 0.707225438473912 |
R-squared | 0.500167820824617 |
Adjusted R-squared | 0.480040350522252 |
F-TEST (value) | 24.8500091323379 |
F-TEST (DF numerator) | 6 |
F-TEST (DF denominator) | 149 |
p-value | 0 |
Multiple Linear Regression - Residual Statistics | |
Residual Standard Deviation | 2.11754990906277 |
Sum Squared Residuals | 668.118624988388 |
Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
1 | 13 | 11.4543275117720 | 1.54567248822798 |
2 | 12 | 11.168961806666 | 0.83103819333401 |
3 | 15 | 13.6117180193699 | 1.38828198063012 |
4 | 12 | 10.8943548499658 | 1.10564515003424 |
5 | 10 | 10.7288194829093 | -0.72881948290926 |
6 | 12 | 9.27712836625497 | 2.72287163374504 |
7 | 15 | 16.8349613115104 | -1.83496131151042 |
8 | 9 | 10.5190753155630 | -1.51907531556296 |
9 | 12 | 12.2876546666686 | -0.287654666668562 |
10 | 11 | 7.98266202959082 | 3.01733797040918 |
11 | 11 | 13.3158061960333 | -2.31580619603328 |
12 | 11 | 12.1177715402679 | -1.11777154026790 |
13 | 15 | 12.2309892046120 | 2.76901079538799 |
14 | 7 | 11.2771808340937 | -4.27718083409372 |
15 | 11 | 11.6859380696307 | -0.685938069630715 |
16 | 11 | 10.9514443947728 | 0.0485556052271954 |
17 | 10 | 12.0857079252257 | -2.08570792522574 |
18 | 14 | 14.3434923850977 | -0.343492385097677 |
19 | 10 | 8.77787839319097 | 1.22212160680903 |
20 | 6 | 9.54495805583856 | -3.54495805583856 |
21 | 11 | 8.68493096388894 | 2.31506903611106 |
22 | 15 | 14.4622375895413 | 0.537762410458682 |
23 | 11 | 11.6739988091688 | -0.673998809168755 |
24 | 12 | 9.54793088021921 | 2.45206911978079 |
25 | 14 | 13.4503773201246 | 0.549622679875371 |
26 | 15 | 14.8746623236532 | 0.125337676346754 |
27 | 9 | 14.6720094061378 | -5.67200940613781 |
28 | 13 | 12.4920373869371 | 0.507962613062925 |
29 | 13 | 13.2253428417033 | -0.225342841703290 |
30 | 16 | 10.8007757530054 | 5.19922424699464 |
31 | 13 | 8.49047363972408 | 4.50952636027592 |
32 | 12 | 13.5959942573866 | -1.59599425738661 |
33 | 14 | 14.4941565523869 | -0.494156552386905 |
34 | 11 | 10.114261463498 | 0.885738536501998 |
35 | 9 | 10.5435335130268 | -1.54353351302678 |
36 | 16 | 14.31767192821 | 1.68232807179001 |
37 | 12 | 12.9627055313080 | -0.962705531308016 |
38 | 10 | 9.22409654509813 | 0.775903454901866 |
39 | 13 | 13.1151057097753 | -0.115105709775341 |
40 | 16 | 15.2791088910786 | 0.720891108921397 |
41 | 14 | 12.9629037480582 | 1.03709625194183 |
42 | 15 | 8.10299585248457 | 6.89700414751543 |
43 | 5 | 9.7866715130881 | -4.78667151308811 |
44 | 8 | 10.4913532514399 | -2.49135325143995 |
45 | 11 | 11.2757881888268 | -0.275788188826849 |
46 | 16 | 13.8154690719800 | 2.18453092801998 |
47 | 17 | 13.0182086885763 | 3.98179131142375 |
48 | 9 | 8.50888192434085 | 0.491118075659152 |
49 | 9 | 11.9300483545774 | -2.93004835457742 |
50 | 13 | 14.6801813150963 | -1.68018131509631 |
51 | 10 | 10.9640930648647 | -0.964093064864687 |
52 | 6 | 12.4678015836414 | -6.46780158364138 |
53 | 12 | 12.4554858308938 | -0.455485830893791 |
54 | 8 | 10.4946435264284 | -2.49464352642843 |
55 | 14 | 12.4371261393879 | 1.56287386061212 |
56 | 12 | 12.4676310161414 | -0.467631016141424 |
57 | 11 | 10.7855417430767 | 0.214458256923307 |
58 | 16 | 14.4203036425596 | 1.57969635744041 |
59 | 8 | 10.2689305211847 | -2.26893052118467 |
60 | 15 | 15.2952505273873 | -0.295250527387342 |
61 | 7 | 9.46266661046707 | -2.46266661046707 |
62 | 16 | 14.0023723122088 | 1.9976276877912 |
63 | 14 | 13.7144319501692 | 0.285568049830753 |
64 | 16 | 13.7532456800423 | 2.24675431995765 |
65 | 9 | 9.92048663101368 | -0.92048663101368 |
66 | 14 | 12.2641272703568 | 1.73587272964320 |
67 | 11 | 13.0288160793959 | -2.02881607939594 |
68 | 13 | 10.4504606414420 | 2.54953935855797 |
69 | 15 | 12.9809492225135 | 2.01905077748645 |
70 | 5 | 5.65526965476048 | -0.655269654760477 |
71 | 15 | 12.4702410303607 | 2.52975896963932 |
72 | 13 | 12.3244517916519 | 0.675548208348061 |
73 | 11 | 12.0817378824939 | -1.08173788249391 |
74 | 11 | 13.9752819157442 | -2.97528191574416 |
75 | 12 | 12.4957196209476 | -0.495719620947646 |
76 | 12 | 13.4197310247318 | -1.41973102473182 |
77 | 12 | 12.2868539311207 | -0.286853931120729 |
78 | 12 | 11.8761397898480 | 0.123860210151982 |
79 | 14 | 10.7829549036294 | 3.21704509637059 |
80 | 6 | 7.96886701447297 | -1.96886701447297 |
81 | 7 | 9.82863683984184 | -2.82863683984184 |
82 | 14 | 11.9330017347079 | 2.06699826529209 |
83 | 14 | 13.8381979636553 | 0.161802036344736 |
84 | 10 | 11.2090818273308 | -1.20908182733077 |
85 | 13 | 8.6820558226945 | 4.31794417730549 |
86 | 12 | 12.3827278226039 | -0.382727822603868 |
87 | 9 | 9.32868069070523 | -0.328680690705233 |
88 | 12 | 12.0243408260259 | -0.0243408260258715 |
89 | 16 | 15.0650478471956 | 0.934952152804355 |
90 | 10 | 10.2509351394506 | -0.250935139450645 |
91 | 14 | 13.1601907440176 | 0.839809255982394 |
92 | 10 | 13.5294557228591 | -3.52945572285908 |
93 | 16 | 15.3380960656073 | 0.661903934392739 |
94 | 15 | 13.4400204696878 | 1.55997953031224 |
95 | 12 | 11.3398016495221 | 0.660198350477909 |
96 | 10 | 9.72325369263371 | 0.276746307366287 |
97 | 8 | 10.2113803731837 | -2.21138037318372 |
98 | 8 | 8.5839638760142 | -0.583963876014194 |
99 | 11 | 12.7817660837874 | -1.78176608378739 |
100 | 13 | 12.3972848053206 | 0.60271519467939 |
101 | 16 | 15.4261707972401 | 0.573829202759878 |
102 | 16 | 14.6887175338267 | 1.31128246617330 |
103 | 14 | 15.783120023334 | -1.78312002333401 |
104 | 11 | 8.8039257060694 | 2.19607429393059 |
105 | 4 | 6.86893251038793 | -2.86893251038793 |
106 | 14 | 14.5434362544404 | -0.543436254440425 |
107 | 9 | 10.3345009862217 | -1.33450098622172 |
108 | 14 | 15.2838424010198 | -1.28384240101982 |
109 | 8 | 10.4296687016322 | -2.42966870163224 |
110 | 8 | 10.8611316540725 | -2.86113165407251 |
111 | 11 | 12.1750326425653 | -1.17503264256529 |
112 | 12 | 13.6138983132027 | -1.61389831320273 |
113 | 11 | 11.4453785390021 | -0.44537853900215 |
114 | 14 | 13.5896355919577 | 0.410364408042348 |
115 | 15 | 14.3284752922129 | 0.671524707787082 |
116 | 16 | 13.3663580685751 | 2.63364193142493 |
117 | 16 | 13.4624042615050 | 2.53759573849503 |
118 | 11 | 12.7046361347967 | -1.70463613479673 |
119 | 14 | 13.6914142471268 | 0.308585752873245 |
120 | 14 | 10.8828606034594 | 3.11713939654063 |
121 | 12 | 11.3287353894553 | 0.6712646105447 |
122 | 14 | 12.4746361458334 | 1.5253638541666 |
123 | 8 | 10.1381161395181 | -2.13811613951814 |
124 | 13 | 13.7618095480229 | -0.76180954802293 |
125 | 16 | 13.6529379090762 | 2.34706209092383 |
126 | 12 | 10.8327470394836 | 1.16725296051639 |
127 | 16 | 15.3724527412253 | 0.627547258774656 |
128 | 12 | 13.2838711469848 | -1.28387114698484 |
129 | 11 | 11.3710149332596 | -0.371014933259570 |
130 | 4 | 6.26171529119994 | -2.26171529119994 |
131 | 16 | 15.3468018491916 | 0.653198150808382 |
132 | 15 | 12.4302550440968 | 2.56974495590315 |
133 | 10 | 11.3339267659976 | -1.33392676599763 |
134 | 13 | 13.0801691844501 | -0.080169184450065 |
135 | 15 | 13.1051398157146 | 1.89486018428544 |
136 | 12 | 10.5070382494129 | 1.49296175058711 |
137 | 14 | 13.4735263170367 | 0.526473682963344 |
138 | 7 | 10.573267534394 | -3.573267534394 |
139 | 19 | 14.0117892393699 | 4.98821076063011 |
140 | 12 | 12.5715353979438 | -0.571535397943801 |
141 | 12 | 12.1641645992487 | -0.164164599248650 |
142 | 13 | 13.4008870456399 | -0.400887045639917 |
143 | 15 | 12.8196129850909 | 2.18038701490908 |
144 | 8 | 8.14265477299094 | -0.142654772990937 |
145 | 12 | 10.7899600333214 | 1.21003996667861 |
146 | 10 | 10.7095121600920 | -0.709512160092038 |
147 | 8 | 11.2805515789296 | -3.28055157892957 |
148 | 10 | 14.261451480109 | -4.261451480109 |
149 | 15 | 13.7372099319199 | 1.26279006808015 |
150 | 16 | 14.5890623743796 | 1.41093762562044 |
151 | 13 | 13.2420751468102 | -0.242075146810153 |
152 | 16 | 15.1131134138541 | 0.886886586145918 |
153 | 9 | 10.6373404646853 | -1.63734046468531 |
154 | 14 | 13.5779794235252 | 0.422020576474805 |
155 | 14 | 13.1082107005343 | 0.891789299465703 |
156 | 12 | 10.5269118213967 | 1.47308817860326 |
Goldfeld-Quandt test for Heteroskedasticity | |||
p-values | Alternative Hypothesis | ||
breakpoint index | greater | 2-sided | less |
10 | 0.0738539342406383 | 0.147707868481277 | 0.926146065759362 |
11 | 0.111412168598257 | 0.222824337196515 | 0.888587831401742 |
12 | 0.0734578741372411 | 0.146915748274482 | 0.926542125862759 |
13 | 0.54882734548451 | 0.90234530903098 | 0.45117265451549 |
14 | 0.718699208630822 | 0.562601582738355 | 0.281300791369178 |
15 | 0.652090412310227 | 0.695819175379545 | 0.347909587689773 |
16 | 0.576112492137822 | 0.847775015724356 | 0.423887507862178 |
17 | 0.48920416864993 | 0.97840833729986 | 0.51079583135007 |
18 | 0.451879492529462 | 0.903758985058924 | 0.548120507470538 |
19 | 0.366000416506306 | 0.732000833012613 | 0.633999583493694 |
20 | 0.510038740501302 | 0.979922518997395 | 0.489961259498698 |
21 | 0.516426674721423 | 0.967146650557155 | 0.483573325278577 |
22 | 0.545846586045827 | 0.908306827908346 | 0.454153413954173 |
23 | 0.472361536131051 | 0.944723072262103 | 0.527638463868949 |
24 | 0.477945431608222 | 0.955890863216444 | 0.522054568391778 |
25 | 0.434731365974649 | 0.869462731949298 | 0.565268634025351 |
26 | 0.374386151119236 | 0.748772302238472 | 0.625613848880764 |
27 | 0.62007359797052 | 0.759852804058961 | 0.379926402029481 |
28 | 0.574954642758156 | 0.850090714483688 | 0.425045357241844 |
29 | 0.51976053627608 | 0.96047892744784 | 0.48023946372392 |
30 | 0.71176397013349 | 0.576472059733021 | 0.288236029866510 |
31 | 0.812570598711138 | 0.374858802577725 | 0.187429401288862 |
32 | 0.776825716797297 | 0.446348566405406 | 0.223174283202703 |
33 | 0.730783095040027 | 0.538433809919946 | 0.269216904959973 |
34 | 0.697861985984421 | 0.604276028031158 | 0.302138014015579 |
35 | 0.695750871668919 | 0.608498256662162 | 0.304249128331081 |
36 | 0.708445328680888 | 0.583109342638225 | 0.291554671319112 |
37 | 0.675394706082227 | 0.649210587835545 | 0.324605293917773 |
38 | 0.626334916756152 | 0.747330166487696 | 0.373665083243848 |
39 | 0.57289741138009 | 0.85420517723982 | 0.42710258861991 |
40 | 0.54355096482102 | 0.91289807035796 | 0.45644903517898 |
41 | 0.50209155902974 | 0.995816881940519 | 0.497908440970259 |
42 | 0.757528815664884 | 0.484942368670232 | 0.242471184335116 |
43 | 0.956307047538371 | 0.0873859049232579 | 0.0436929524616289 |
44 | 0.966683420979718 | 0.0666331580405634 | 0.0333165790202817 |
45 | 0.956290274161252 | 0.0874194516774964 | 0.0437097258387482 |
46 | 0.961225446856714 | 0.0775491062865716 | 0.0387745531432858 |
47 | 0.980650982255261 | 0.0386980354894772 | 0.0193490177447386 |
48 | 0.974216525457869 | 0.0515669490842624 | 0.0257834745421312 |
49 | 0.982136641646371 | 0.0357267167072569 | 0.0178633583536285 |
50 | 0.979210150922893 | 0.0415796981542144 | 0.0207898490771072 |
51 | 0.97446674575257 | 0.0510665084948609 | 0.0255332542474305 |
52 | 0.997597461351614 | 0.00480507729677206 | 0.00240253864838603 |
53 | 0.996534554484524 | 0.00693089103095237 | 0.00346544551547619 |
54 | 0.997121346101836 | 0.00575730779632819 | 0.00287865389816409 |
55 | 0.99710451393585 | 0.00579097212829866 | 0.00289548606414933 |
56 | 0.995913070323251 | 0.00817385935349709 | 0.00408692967674855 |
57 | 0.994229234073585 | 0.0115415318528297 | 0.00577076592641486 |
58 | 0.993564980729086 | 0.0128700385418285 | 0.00643501927091427 |
59 | 0.99514767680476 | 0.00970464639048043 | 0.00485232319524021 |
60 | 0.993662276710802 | 0.0126754465783970 | 0.00633772328919849 |
61 | 0.994486780541911 | 0.0110264389161778 | 0.00551321945808889 |
62 | 0.995041687770348 | 0.00991662445930408 | 0.00495831222965204 |
63 | 0.993354910372801 | 0.0132901792543976 | 0.00664508962719878 |
64 | 0.993715406157568 | 0.0125691876848637 | 0.00628459384243185 |
65 | 0.992074101296807 | 0.0158517974063868 | 0.00792589870319338 |
66 | 0.991233013479951 | 0.0175339730400972 | 0.0087669865200486 |
67 | 0.991193655492438 | 0.0176126890151239 | 0.00880634450756193 |
68 | 0.99240860329775 | 0.0151827934045008 | 0.0075913967022504 |
69 | 0.992622989007231 | 0.0147540219855378 | 0.00737701099276888 |
70 | 0.990035459478192 | 0.0199290810436164 | 0.0099645405218082 |
71 | 0.991512344594023 | 0.0169753108119530 | 0.00848765540597649 |
72 | 0.988744712009448 | 0.0225105759811049 | 0.0112552879905525 |
73 | 0.985875535529372 | 0.0282489289412562 | 0.0141244644706281 |
74 | 0.98968395411071 | 0.0206320917785783 | 0.0103160458892892 |
75 | 0.986064984710967 | 0.0278700305780664 | 0.0139350152890332 |
76 | 0.983814010657478 | 0.0323719786850447 | 0.0161859893425223 |
77 | 0.978757230581325 | 0.0424855388373509 | 0.0212427694186755 |
78 | 0.97189841343023 | 0.0562031731395393 | 0.0281015865697696 |
79 | 0.981928839719815 | 0.036142320560369 | 0.0180711602801845 |
80 | 0.981171189093485 | 0.0376576218130295 | 0.0188288109065148 |
81 | 0.984465618766586 | 0.0310687624668274 | 0.0155343812334137 |
82 | 0.985531580579376 | 0.0289368388412482 | 0.0144684194206241 |
83 | 0.980548112818612 | 0.0389037743627762 | 0.0194518871813881 |
84 | 0.976025194854872 | 0.0479496102902564 | 0.0239748051451282 |
85 | 0.993614742822052 | 0.0127705143558967 | 0.00638525717794835 |
86 | 0.991186158493816 | 0.0176276830123688 | 0.00881384150618442 |
87 | 0.987937413476295 | 0.0241251730474104 | 0.0120625865237052 |
88 | 0.984168771851926 | 0.0316624562961476 | 0.0158312281480738 |
89 | 0.980266995450385 | 0.0394660090992293 | 0.0197330045496146 |
90 | 0.973933446018776 | 0.0521331079624473 | 0.0260665539812236 |
91 | 0.96894737673181 | 0.0621052465363801 | 0.0310526232681900 |
92 | 0.981483206720742 | 0.0370335865585168 | 0.0185167932792584 |
93 | 0.976077099013598 | 0.0478458019728037 | 0.0239229009864018 |
94 | 0.972824609097762 | 0.0543507818044761 | 0.0271753909022380 |
95 | 0.965979035563559 | 0.068041928872882 | 0.034020964436441 |
96 | 0.957543997112153 | 0.0849120057756946 | 0.0424560028878473 |
97 | 0.953597370111768 | 0.0928052597764631 | 0.0464026298882316 |
98 | 0.941028716771498 | 0.117942566457003 | 0.0589712832285017 |
99 | 0.935332034240117 | 0.129335931519765 | 0.0646679657598827 |
100 | 0.921498373330872 | 0.157003253338257 | 0.0785016266691284 |
101 | 0.902660289705945 | 0.194679420588110 | 0.0973397102940552 |
102 | 0.888687169237796 | 0.222625661524408 | 0.111312830762204 |
103 | 0.891890462252401 | 0.216219075495198 | 0.108109537747599 |
104 | 0.928929204993892 | 0.142141590012215 | 0.0710707950061076 |
105 | 0.925456916449307 | 0.149086167101387 | 0.0745430835506933 |
106 | 0.90562530027135 | 0.188749399457301 | 0.0943746997286505 |
107 | 0.885230909702821 | 0.229538180594358 | 0.114769090297179 |
108 | 0.879548215760315 | 0.240903568479370 | 0.120451784239685 |
109 | 0.876971448272647 | 0.246057103454706 | 0.123028551727353 |
110 | 0.896714705031345 | 0.206570589937311 | 0.103285294968655 |
111 | 0.888818831945975 | 0.222362336108050 | 0.111181168054025 |
112 | 0.926529602725404 | 0.146940794549192 | 0.0734703972745962 |
113 | 0.904866008509663 | 0.190267982980674 | 0.095133991490337 |
114 | 0.882761840721651 | 0.234476318556697 | 0.117238159278349 |
115 | 0.856578652191078 | 0.286842695617844 | 0.143421347808922 |
116 | 0.847360482630238 | 0.305279034739525 | 0.152639517369762 |
117 | 0.845160067878448 | 0.309679864243104 | 0.154839932121552 |
118 | 0.846213905052698 | 0.307572189894603 | 0.153786094947302 |
119 | 0.814040652836466 | 0.371918694327068 | 0.185959347163534 |
120 | 0.851321019990752 | 0.297357960018496 | 0.148678980009248 |
121 | 0.818990515920393 | 0.362018968159214 | 0.181009484079607 |
122 | 0.79045236724802 | 0.419095265503961 | 0.209547632751980 |
123 | 0.782510780887198 | 0.434978438225603 | 0.217489219112802 |
124 | 0.746706356137427 | 0.506587287725146 | 0.253293643862573 |
125 | 0.734130909366523 | 0.531738181266955 | 0.265869090633477 |
126 | 0.715398152194316 | 0.569203695611367 | 0.284601847805683 |
127 | 0.657211416468591 | 0.685577167062817 | 0.342788583531409 |
128 | 0.629278984908165 | 0.74144203018367 | 0.370721015091835 |
129 | 0.636265128901008 | 0.727469742197983 | 0.363734871098992 |
130 | 0.640084554700865 | 0.719830890598271 | 0.359915445299135 |
131 | 0.594546146744681 | 0.810907706510639 | 0.405453853255319 |
132 | 0.553103349561024 | 0.893793300877953 | 0.446896650438976 |
133 | 0.543699901622874 | 0.912600196754253 | 0.456300098377126 |
134 | 0.471346782798363 | 0.942693565596725 | 0.528653217201637 |
135 | 0.414315595537165 | 0.82863119107433 | 0.585684404462835 |
136 | 0.393702835618114 | 0.787405671236229 | 0.606297164381886 |
137 | 0.320790451030566 | 0.641580902061132 | 0.679209548969434 |
138 | 0.411615168913242 | 0.823230337826484 | 0.588384831086758 |
139 | 0.771364571464273 | 0.457270857071455 | 0.228635428535727 |
140 | 0.76377510119909 | 0.472449797601821 | 0.236224898800910 |
141 | 0.709611408881837 | 0.580777182236326 | 0.290388591118163 |
142 | 0.623349240400771 | 0.753301519198457 | 0.376650759599229 |
143 | 0.559951555234119 | 0.880096889531761 | 0.440048444765881 |
144 | 0.434662285853637 | 0.869324571707275 | 0.565337714146363 |
145 | 0.699580655627783 | 0.600838688744433 | 0.300419344372217 |
146 | 0.849248587677245 | 0.30150282464551 | 0.150751412322755 |
Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
Description | # significant tests | % significant tests | OK/NOK |
1% type I error level | 7 | 0.0510948905109489 | NOK |
5% type I error level | 42 | 0.306569343065693 | NOK |
10% type I error level | 55 | 0.401459854014599 | NOK |