Multiple Linear Regression - Estimated Regression Equation |
Popularity[t] = + 2.39535698605526 + 0.108109507398842FindingFriends[t] + 0.211437082159555KnowingPeople[t] + 0.366476681384955Liked[t] + 0.601540871476521Celebrity[t] + 0.213410758679599Sum_friends[t] -0.255965716461004Month[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) | 2.39535698605526 | 3.624285 | 0.6609 | 0.509685 | 0.254843 |
FindingFriends | 0.108109507398842 | 0.09571 | 1.1296 | 0.260478 | 0.130239 |
KnowingPeople | 0.211437082159555 | 0.063732 | 3.3176 | 0.001141 | 0.000571 |
Liked | 0.366476681384955 | 0.096894 | 3.7822 | 0.000224 | 0.000112 |
Celebrity | 0.601540871476521 | 0.155782 | 3.8614 | 0.000168 | 8.4e-05 |
Sum_friends | 0.213410758679599 | 0.120235 | 1.7749 | 0.077949 | 0.038974 |
Month | -0.255965716461004 | 0.361236 | -0.7086 | 0.47969 | 0.239845 |
Multiple Linear Regression - Regression Statistics | |
Multiple R | 0.71491764765422 |
R-squared | 0.511107242927444 |
Adjusted R-squared | 0.491420286266804 |
F-TEST (value) | 25.9617193118173 |
F-TEST (DF numerator) | 6 |
F-TEST (DF denominator) | 149 |
p-value | 0 |
Multiple Linear Regression - Residual Statistics | |
Residual Standard Deviation | 2.09424916265587 |
Sum Squared Residuals | 653.49605373744 |
Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
1 | 13 | 11.4528492741181 | 1.54715072588193 |
2 | 12 | 11.0657882580354 | 0.934211741964616 |
3 | 15 | 13.1828777288277 | 1.81712227117231 |
4 | 12 | 11.1919083611301 | 0.808091638869943 |
5 | 10 | 10.9663115621461 | -0.966311562146098 |
6 | 12 | 9.28479275153784 | 2.71520724846216 |
7 | 15 | 16.9292219614242 | -1.92922196142420 |
8 | 9 | 10.3656052702676 | -1.36560527026762 |
9 | 12 | 12.7395788369399 | -0.739578836939947 |
10 | 11 | 7.71339869362729 | 3.28660130637271 |
11 | 11 | 13.3953574337406 | -2.39535743374061 |
12 | 11 | 12.1485744532852 | -1.14857445328522 |
13 | 15 | 12.5564543211819 | 2.44354567881813 |
14 | 7 | 11.5865595659690 | -4.58655956596901 |
15 | 11 | 11.6721110621500 | -0.67211106215004 |
16 | 11 | 10.7884794345867 | 0.211520565413267 |
17 | 10 | 12.1485744532852 | -2.14857445328522 |
18 | 14 | 14.565530758744 | -0.565530758744012 |
19 | 10 | 8.67879407146065 | 1.32120592853935 |
20 | 6 | 9.4021835689543 | -3.40218356895430 |
21 | 11 | 8.93881079792934 | 2.06118920207066 |
22 | 15 | 14.5891578666760 | 0.410842133323976 |
23 | 11 | 11.9785405576374 | -0.978540557637362 |
24 | 12 | 9.733267700309 | 2.26673229969100 |
25 | 14 | 13.1473887046288 | 0.852611295371206 |
26 | 15 | 14.7749941643835 | 0.225005835616476 |
27 | 9 | 14.5871841901560 | -5.58718419015598 |
28 | 13 | 12.9086816788211 | 0.0913183211789004 |
29 | 13 | 13.1915105403373 | -0.191510540337265 |
30 | 16 | 11.2575455853030 | 4.74245441469698 |
31 | 13 | 8.8424664821956 | 4.15753351780439 |
32 | 12 | 13.7480949965073 | -1.74809499650727 |
33 | 14 | 14.9106781327545 | -0.910678132754465 |
34 | 11 | 10.2452201156431 | 0.754779884356902 |
35 | 9 | 10.5790160289472 | -1.57901602894722 |
36 | 16 | 14.6239019181982 | 1.37609808180179 |
37 | 12 | 13.2499781739601 | -1.24997817396013 |
38 | 10 | 9.69956627154015 | 0.300433728459845 |
39 | 13 | 13.04125287375 | -0.0412528737499953 |
40 | 16 | 15.8053302297393 | 0.194669770260715 |
41 | 14 | 13.1513360576689 | 0.848663942331119 |
42 | 15 | 8.17111338363724 | 6.82888661636275 |
43 | 5 | 9.82055835589392 | -4.82055835589392 |
44 | 8 | 10.4125353620942 | -2.41253536209418 |
45 | 11 | 11.4061536994077 | -0.406153699407712 |
46 | 16 | 14.0112441031315 | 1.98875589686849 |
47 | 17 | 14.5115010765752 | 2.48849892342483 |
48 | 9 | 8.31990757883191 | 0.680092421168087 |
49 | 9 | 11.5900163205952 | -2.59001632059517 |
50 | 13 | 14.6716665896228 | -1.67166658962281 |
51 | 10 | 11.2464286417128 | -1.24642864171284 |
52 | 6 | 12.2609626205605 | -6.26096262056055 |
53 | 12 | 12.0220475515976 | -0.0220475515975586 |
54 | 8 | 10.4216924287775 | -2.42169242877746 |
55 | 14 | 11.7617067010914 | 2.2382932989086 |
56 | 12 | 12.8239785618513 | -0.823978561851266 |
57 | 11 | 10.5766355538342 | 0.423364446165799 |
58 | 16 | 14.5181938683245 | 1.48180613167552 |
59 | 8 | 10.4797394641942 | -2.47973946419419 |
60 | 15 | 14.5059378278123 | 0.4940621721877 |
61 | 7 | 9.02685335855679 | -2.02685335855679 |
62 | 16 | 14.1095690277511 | 1.89043097224890 |
63 | 14 | 13.0463661132245 | 0.953633886775472 |
64 | 16 | 13.3048297613793 | 2.6951702386207 |
65 | 9 | 10.3363754497126 | -1.33637544971259 |
66 | 14 | 12.0804187110518 | 1.91958128894824 |
67 | 11 | 13.1651785828216 | -2.16517858282163 |
68 | 13 | 10.2319087780299 | 2.76809122197012 |
69 | 15 | 13.1087810998875 | 1.89121890011252 |
70 | 5 | 5.65726792090425 | -0.657267920904248 |
71 | 15 | 12.8239785618513 | 2.17602143814873 |
72 | 13 | 12.5072402284110 | 0.492759771589045 |
73 | 11 | 12.3427332380780 | -1.34273323807796 |
74 | 11 | 14.1374678631938 | -3.13746786319380 |
75 | 12 | 12.6811250029302 | -0.681125002930237 |
76 | 12 | 13.318244505527 | -1.31824450552699 |
77 | 12 | 12.2468993779048 | -0.246899377904798 |
78 | 12 | 11.8613914401360 | 0.138608559864013 |
79 | 14 | 10.7881691101624 | 3.21183088983758 |
80 | 6 | 7.8493724000558 | -1.84937240005580 |
81 | 7 | 9.63036790655335 | -2.63036790655335 |
82 | 14 | 12.3070581327891 | 1.69294186721093 |
83 | 14 | 14.1001016366435 | -0.100101636643497 |
84 | 10 | 11.07484885055 | -1.07484885055001 |
85 | 13 | 9.03277438811692 | 3.96722561188308 |
86 | 12 | 12.2121553263826 | -0.212155326382611 |
87 | 9 | 9.21415287722376 | -0.214152877223756 |
88 | 12 | 11.8499503725083 | 0.150049627491654 |
89 | 16 | 14.7213222630119 | 1.27867773698806 |
90 | 10 | 10.3719540808328 | -0.371954080832819 |
91 | 14 | 13.0389688728056 | 0.961031127194365 |
92 | 10 | 13.5202141965789 | -3.52021419657894 |
93 | 16 | 15.4440632619975 | 0.555936738002475 |
94 | 15 | 13.3134625728889 | 1.68653742711114 |
95 | 12 | 11.3963691166284 | 0.60363088337155 |
96 | 10 | 9.26191754864836 | 0.738082451351644 |
97 | 8 | 10.0250675474185 | -2.02506754741848 |
98 | 8 | 8.61739393838537 | -0.617393938385365 |
99 | 11 | 12.5923711263859 | -1.59237112638585 |
100 | 13 | 12.4724961768888 | 0.527503823111233 |
101 | 16 | 15.5473908367582 | 0.452609163241762 |
102 | 16 | 14.8661494984530 | 1.13385050154698 |
103 | 14 | 15.3628995742094 | -1.36289957420936 |
104 | 11 | 8.9696212960246 | 2.03037870397541 |
105 | 4 | 7.05721329823365 | -3.05721329823365 |
106 | 14 | 14.6716803892360 | -0.67168038923596 |
107 | 9 | 10.4516545476615 | -1.45165454766152 |
108 | 14 | 15.1461701038511 | -1.14617010385110 |
109 | 8 | 10.1798726295277 | -2.17987262952772 |
110 | 8 | 10.6121245780331 | -2.61212457803312 |
111 | 11 | 11.8058285367999 | -0.805828536799874 |
112 | 12 | 13.0605258300489 | -1.06052583004894 |
113 | 11 | 10.9865155722118 | 0.0134844277882477 |
114 | 14 | 13.2015021866186 | 0.798497813381411 |
115 | 15 | 14.3849041746797 | 0.615095825320293 |
116 | 16 | 13.3651745973535 | 2.63482540264646 |
117 | 16 | 12.8330518287136 | 3.16694817128641 |
118 | 11 | 12.7242042158854 | -1.72420421588537 |
119 | 14 | 14.1115427042711 | -0.111542704271138 |
120 | 14 | 10.7928545686319 | 3.20714543136811 |
121 | 12 | 11.4808515160953 | 0.51914848390472 |
122 | 14 | 12.4535545274262 | 1.54644547257378 |
123 | 8 | 10.7987755981920 | -2.79877559819202 |
124 | 13 | 14.0062414529904 | -1.00624145299038 |
125 | 16 | 13.8981319455915 | 2.10186805440846 |
126 | 12 | 10.5400142999606 | 1.45998570003937 |
127 | 16 | 15.4093192104753 | 0.590680789524662 |
128 | 12 | 12.6780122294882 | -0.678012229488191 |
129 | 11 | 11.3801461163627 | -0.380146116362679 |
130 | 4 | 5.8412685850392 | -1.84126858503920 |
131 | 16 | 16.0495514865141 | -0.0495514865141337 |
132 | 15 | 12.5758237516495 | 2.42417624835052 |
133 | 10 | 11.3077117142527 | -1.30771171425273 |
134 | 13 | 13.9537913230963 | -0.953791323096314 |
135 | 15 | 13.0484362639132 | 1.95156373608677 |
136 | 12 | 10.4197187522574 | 1.58028124774258 |
137 | 14 | 13.5766116795131 | 0.423388320486901 |
138 | 7 | 10.2974495280342 | -3.29744952803416 |
139 | 19 | 13.8377871096173 | 5.1622128903827 |
140 | 12 | 12.8689349771578 | -0.86893497715778 |
141 | 12 | 11.7916688199755 | 0.20833118002454 |
142 | 13 | 13.2598733460728 | -0.259873346072788 |
143 | 15 | 12.3629234485305 | 2.63707655146954 |
144 | 8 | 8.703243084643 | -0.703243084643001 |
145 | 12 | 10.8445665930966 | 1.15543340690343 |
146 | 10 | 10.6737245918115 | -0.673724591811528 |
147 | 8 | 11.1762992229593 | -3.17629922295934 |
148 | 10 | 14.5889371491730 | -4.58893714917302 |
149 | 15 | 13.7880487616727 | 1.21195123832735 |
150 | 16 | 13.9797360887325 | 2.02026391126752 |
151 | 13 | 13.177364623126 | -0.177364623126001 |
152 | 16 | 15.0192154211584 | 0.980784578841628 |
153 | 9 | 9.73172180479402 | -0.731721804794023 |
154 | 14 | 12.9872568483409 | 1.01274315165905 |
155 | 14 | 13.0590427519428 | 0.940957248057168 |
156 | 12 | 10.1112891062892 | 1.88871089371080 |
Goldfeld-Quandt test for Heteroskedasticity | |||
p-values | Alternative Hypothesis | ||
breakpoint index | greater | 2-sided | less |
10 | 0.127891435208484 | 0.255782870416968 | 0.872108564791516 |
11 | 0.148786160625616 | 0.297572321251233 | 0.851213839374384 |
12 | 0.0780975221103143 | 0.156195044220629 | 0.921902477889686 |
13 | 0.565769576087115 | 0.86846084782577 | 0.434230423912885 |
14 | 0.834551472369617 | 0.330897055260766 | 0.165448527630383 |
15 | 0.765397977192753 | 0.469204045614493 | 0.234602022807247 |
16 | 0.682640577516971 | 0.634718844966057 | 0.317359422483029 |
17 | 0.627862766508355 | 0.744274466983291 | 0.372137233491645 |
18 | 0.541147043920611 | 0.917705912158779 | 0.458852956079389 |
19 | 0.459312550753235 | 0.91862510150647 | 0.540687449246765 |
20 | 0.74280399893436 | 0.514392002131281 | 0.257196001065641 |
21 | 0.684296996404343 | 0.631406007191314 | 0.315703003595657 |
22 | 0.652496879700231 | 0.695006240599538 | 0.347503120299769 |
23 | 0.584636569680495 | 0.83072686063901 | 0.415363430319505 |
24 | 0.564201395716613 | 0.871597208566775 | 0.435798604283387 |
25 | 0.523000649204438 | 0.953998701591124 | 0.476999350795562 |
26 | 0.459701943012236 | 0.919403886024472 | 0.540298056987764 |
27 | 0.71719242453584 | 0.565615150928319 | 0.282807575464160 |
28 | 0.663069401328821 | 0.673861197342357 | 0.336930598671179 |
29 | 0.604044439687815 | 0.79191112062437 | 0.395955560312185 |
30 | 0.735450615906114 | 0.529098768187771 | 0.264549384093886 |
31 | 0.823372015790588 | 0.353255968418824 | 0.176627984209412 |
32 | 0.788885237884124 | 0.422229524231752 | 0.211114762115876 |
33 | 0.745928830600179 | 0.508142338799642 | 0.254071169399821 |
34 | 0.704230684387494 | 0.591538631225012 | 0.295769315612506 |
35 | 0.694758234870179 | 0.610483530259642 | 0.305241765129821 |
36 | 0.693676570662987 | 0.612646858674026 | 0.306323429337013 |
37 | 0.66490032201647 | 0.670199355967061 | 0.335099677983531 |
38 | 0.614375406028553 | 0.771249187942894 | 0.385624593971447 |
39 | 0.567455347111986 | 0.865089305776028 | 0.432544652888014 |
40 | 0.52658727219048 | 0.94682545561904 | 0.47341272780952 |
41 | 0.491865861723546 | 0.983731723447092 | 0.508134138276454 |
42 | 0.813225177999172 | 0.373549644001657 | 0.186774822000828 |
43 | 0.950230645269395 | 0.0995387094612093 | 0.0497693547306046 |
44 | 0.955255314656835 | 0.0894893706863304 | 0.0447446853431652 |
45 | 0.942146721738118 | 0.115706556523764 | 0.057853278261882 |
46 | 0.948658196373985 | 0.102683607252030 | 0.0513418036260152 |
47 | 0.95268483685115 | 0.0946303262976987 | 0.0473151631488494 |
48 | 0.946734666625133 | 0.106530666749734 | 0.0532653333748668 |
49 | 0.93907560281203 | 0.12184879437594 | 0.06092439718797 |
50 | 0.923835711546406 | 0.152328576907188 | 0.076164288453594 |
51 | 0.917045576373746 | 0.165908847252507 | 0.0829544236262537 |
52 | 0.960944094385291 | 0.078111811229418 | 0.039055905614709 |
53 | 0.97507692614946 | 0.0498461477010793 | 0.0249230738505397 |
54 | 0.971837159425216 | 0.0563256811495677 | 0.0281628405747839 |
55 | 0.988982381555178 | 0.0220352368896448 | 0.0110176184448224 |
56 | 0.985210960943165 | 0.02957807811367 | 0.014789039056835 |
57 | 0.981010684421946 | 0.0379786311561071 | 0.0189893155780536 |
58 | 0.980633391742666 | 0.0387332165146681 | 0.0193666082573340 |
59 | 0.985253208163603 | 0.0294935836727950 | 0.0147467918363975 |
60 | 0.985555438472469 | 0.0288891230550616 | 0.0144445615275308 |
61 | 0.984538482096426 | 0.0309230358071472 | 0.0154615179035736 |
62 | 0.986442420533483 | 0.0271151589330342 | 0.0135575794665171 |
63 | 0.98509894013097 | 0.0298021197380623 | 0.0149010598690312 |
64 | 0.988687193031725 | 0.0226256139365493 | 0.0113128069682746 |
65 | 0.986794778167644 | 0.0264104436647128 | 0.0132052218323564 |
66 | 0.986499967988942 | 0.0270000640221167 | 0.0135000320110583 |
67 | 0.986634075104435 | 0.0267318497911292 | 0.0133659248955646 |
68 | 0.989704745532994 | 0.0205905089340127 | 0.0102952544670063 |
69 | 0.989202194390346 | 0.0215956112193081 | 0.0107978056096541 |
70 | 0.985867530935757 | 0.0282649381284853 | 0.0141324690642427 |
71 | 0.98628220282973 | 0.0274355943405408 | 0.0137177971702704 |
72 | 0.981769266103638 | 0.0364614677927242 | 0.0182307338963621 |
73 | 0.9785160596516 | 0.0429678806967993 | 0.0214839403483997 |
74 | 0.985161944024766 | 0.0296761119504678 | 0.0148380559752339 |
75 | 0.98052919607703 | 0.0389416078459408 | 0.0194708039229704 |
76 | 0.977311033104489 | 0.0453779337910227 | 0.0226889668955113 |
77 | 0.970457932201994 | 0.059084135596012 | 0.029542067798006 |
78 | 0.961502157950696 | 0.076995684098608 | 0.038497842049304 |
79 | 0.975122841854285 | 0.0497543162914295 | 0.0248771581457147 |
80 | 0.973372974593985 | 0.0532540508120308 | 0.0266270254060154 |
81 | 0.976560291652205 | 0.0468794166955905 | 0.0234397083477953 |
82 | 0.97604724143845 | 0.0479055171231011 | 0.0239527585615505 |
83 | 0.968388046065408 | 0.0632239078691843 | 0.0316119539345921 |
84 | 0.961192097383956 | 0.0776158052320889 | 0.0388079026160445 |
85 | 0.9871212122698 | 0.0257575754604011 | 0.0128787877302006 |
86 | 0.982915998782178 | 0.0341680024356442 | 0.0170840012178221 |
87 | 0.977252992712076 | 0.0454940145758482 | 0.0227470072879241 |
88 | 0.970550090305963 | 0.0588998193880742 | 0.0294499096940371 |
89 | 0.964825571767684 | 0.070348856464632 | 0.035174428232316 |
90 | 0.954833385232667 | 0.0903332295346658 | 0.0451666147673329 |
91 | 0.946382285350417 | 0.107235429299166 | 0.053617714649583 |
92 | 0.968459416169427 | 0.0630811676611466 | 0.0315405838305733 |
93 | 0.959598822973557 | 0.0808023540528861 | 0.0404011770264430 |
94 | 0.954719984594765 | 0.0905600308104694 | 0.0452800154052347 |
95 | 0.943535878580419 | 0.112928242839163 | 0.0564641214195815 |
96 | 0.930370551534034 | 0.139258896931932 | 0.0696294484659659 |
97 | 0.923459803751226 | 0.153080392497548 | 0.0765401962487741 |
98 | 0.904881903310375 | 0.190236193379250 | 0.0951180966896251 |
99 | 0.898100579583368 | 0.203798840833264 | 0.101899420416632 |
100 | 0.87619510532684 | 0.24760978934632 | 0.12380489467316 |
101 | 0.850179425098482 | 0.299641149803037 | 0.149820574901518 |
102 | 0.82590686861214 | 0.348186262775719 | 0.174093131387860 |
103 | 0.838554170863019 | 0.322891658273963 | 0.161445829136981 |
104 | 0.882816730637804 | 0.234366538724391 | 0.117183269362196 |
105 | 0.882992594097098 | 0.234014811805804 | 0.117007405902902 |
106 | 0.857655586636667 | 0.284688826726666 | 0.142344413363333 |
107 | 0.833677975400939 | 0.332644049198122 | 0.166322024599061 |
108 | 0.82756098697927 | 0.344878026041461 | 0.172439013020730 |
109 | 0.823048918768799 | 0.353902162462402 | 0.176951081231201 |
110 | 0.84870981002075 | 0.302580379958498 | 0.151290189979249 |
111 | 0.834726792630815 | 0.33054641473837 | 0.165273207369185 |
112 | 0.879707548657549 | 0.240584902684902 | 0.120292451342451 |
113 | 0.849731550748274 | 0.300536898503451 | 0.150268449251726 |
114 | 0.818803497057266 | 0.362393005885468 | 0.181196502942734 |
115 | 0.780187265662848 | 0.439625468674304 | 0.219812734337152 |
116 | 0.78055290142237 | 0.438894197155258 | 0.219447098577629 |
117 | 0.796134345179927 | 0.407731309640146 | 0.203865654820073 |
118 | 0.783285729316027 | 0.433428541367946 | 0.216714270683973 |
119 | 0.737280914472618 | 0.525438171054764 | 0.262719085527382 |
120 | 0.80488337677909 | 0.39023324644182 | 0.19511662322091 |
121 | 0.771422196067994 | 0.457155607864013 | 0.228577803932006 |
122 | 0.741815375785039 | 0.516369248429921 | 0.258184624214961 |
123 | 0.737583153508597 | 0.524833692982805 | 0.262416846491403 |
124 | 0.691400887372585 | 0.61719822525483 | 0.308599112627415 |
125 | 0.687011648050497 | 0.625976703899007 | 0.312988351949503 |
126 | 0.668733614861058 | 0.662532770277885 | 0.331266385138942 |
127 | 0.609345952397273 | 0.781308095205454 | 0.390654047602727 |
128 | 0.575283686154436 | 0.849432627691128 | 0.424716313845564 |
129 | 0.590936279322617 | 0.818127441354767 | 0.409063720677383 |
130 | 0.581619857332299 | 0.836760285335402 | 0.418380142667701 |
131 | 0.512533893330391 | 0.974932213339218 | 0.487466106669609 |
132 | 0.498465836191323 | 0.996931672382646 | 0.501534163808677 |
133 | 0.463611742282113 | 0.927223484564226 | 0.536388257717887 |
134 | 0.394957592629450 | 0.789915185258899 | 0.605042407370550 |
135 | 0.368037545036676 | 0.736075090073353 | 0.631962454963324 |
136 | 0.360543483951051 | 0.721086967902103 | 0.639456516048948 |
137 | 0.290790798057117 | 0.581581596114235 | 0.709209201942883 |
138 | 0.363706140509017 | 0.727412281018034 | 0.636293859490983 |
139 | 0.718987445670285 | 0.56202510865943 | 0.281012554329715 |
140 | 0.739664531501608 | 0.520670936996784 | 0.260335468498392 |
141 | 0.684094092137304 | 0.631811815725393 | 0.315905907862697 |
142 | 0.584421476124033 | 0.831157047751933 | 0.415578523875967 |
143 | 0.530379105427788 | 0.939241789144423 | 0.469620894572212 |
144 | 0.405352823036498 | 0.810705646072997 | 0.594647176963502 |
145 | 0.371890674606971 | 0.743781349213942 | 0.628109325393029 |
146 | 0.507389047636315 | 0.985221904727371 | 0.492610952363685 |
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 | 29 | 0.211678832116788 | NOK |
10% type I error level | 45 | 0.328467153284672 | NOK |