Multiple Linear Regression - Estimated Regression Equation |
Popularity[t] = -0.17879188700372 + 0.100252682453213FindingFriends[t] + 0.212183545436264KnowingPeople[t] + 0.382293973272379Liked[t] + 0.592277125614447Celebrity[t] + 0.310366099758153bestfriend[t] -0.0288664388538009secondbestfriend[t] + 0.408723247498028thirdbestfriend[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) | -0.17879188700372 | 1.432707 | -0.1248 | 0.900857 | 0.450428 |
FindingFriends | 0.100252682453213 | 0.096695 | 1.0368 | 0.301521 | 0.150761 |
KnowingPeople | 0.212183545436264 | 0.063597 | 3.3364 | 0.001073 | 0.000537 |
Liked | 0.382293973272379 | 0.09726 | 3.9306 | 0.00013 | 6.5e-05 |
Celebrity | 0.592277125614447 | 0.155538 | 3.8079 | 0.000205 | 0.000102 |
bestfriend | 0.310366099758153 | 0.209436 | 1.4819 | 0.14049 | 0.070245 |
secondbestfriend | -0.0288664388538009 | 0.200708 | -0.1438 | 0.885836 | 0.442918 |
thirdbestfriend | 0.408723247498028 | 0.213014 | 1.9188 | 0.05694 | 0.02847 |
Multiple Linear Regression - Regression Statistics | |
Multiple R | 0.718894523522317 |
R-squared | 0.516809335950379 |
Adjusted R-squared | 0.493955723461546 |
F-TEST (value) | 22.6139012465928 |
F-TEST (DF numerator) | 7 |
F-TEST (DF denominator) | 148 |
p-value | 0 |
Multiple Linear Regression - Residual Statistics | |
Residual Standard Deviation | 2.08902237966842 |
Sum Squared Residuals | 645.874146407814 |
Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
1 | 13 | 11.1232153112844 | 1.87678468871563 |
2 | 12 | 10.9632820462963 | 1.03671795370375 |
3 | 15 | 13.0403038088083 | 1.95969619119169 |
4 | 12 | 11.3794129530986 | 0.6205870469014 |
5 | 10 | 10.9007697821017 | -0.9007697821017 |
6 | 12 | 9.2826074240986 | 2.71739257590141 |
7 | 15 | 16.829161144089 | -1.82916114408904 |
8 | 9 | 10.2429676104458 | -1.24296761044584 |
9 | 12 | 12.9574984658462 | -0.95749846584623 |
10 | 11 | 7.50557974224234 | 3.49442025775766 |
11 | 11 | 12.974177001533 | -1.97417700153297 |
12 | 11 | 12.1201819347053 | -1.12018193470527 |
13 | 15 | 12.2452572983187 | 2.7547427016813 |
14 | 7 | 11.4178073027051 | -4.41780730270514 |
15 | 11 | 11.2046484527689 | -0.204648452768911 |
16 | 11 | 10.7656918490582 | 0.234308150941755 |
17 | 10 | 11.7809493960933 | -1.78094939609331 |
18 | 14 | 14.8065625745847 | -0.806562574584652 |
19 | 10 | 8.52939279970282 | 1.47060720029718 |
20 | 6 | 9.31733710730725 | -3.31733710730725 |
21 | 11 | 8.74299978554309 | 2.25700021445691 |
22 | 15 | 14.0275399565267 | 0.972460043473327 |
23 | 11 | 11.5524226318702 | -0.552422631870179 |
24 | 12 | 9.70459952845894 | 2.29540047154106 |
25 | 14 | 13.0408439899645 | 0.959156010035451 |
26 | 15 | 14.4829738793472 | 0.517026120652803 |
27 | 9 | 14.2685899408167 | -5.26858994081674 |
28 | 13 | 12.4702997844239 | 0.529700215576085 |
29 | 13 | 13.4172767656789 | -0.417276765678926 |
30 | 16 | 11.1331557025984 | 4.86684429740159 |
31 | 13 | 8.7372436457976 | 4.26275635420241 |
32 | 12 | 13.6002890138805 | -1.60028901388053 |
33 | 14 | 14.5365158864779 | -0.536515886477914 |
34 | 11 | 9.6018952134032 | 1.3981047865968 |
35 | 9 | 10.214101171592 | -1.21410117159204 |
36 | 16 | 14.1699960215429 | 1.83000397845709 |
37 | 12 | 13.1243710179722 | -1.12437101797221 |
38 | 10 | 9.72142279708293 | 0.27857720291707 |
39 | 13 | 13.1371310095731 | -0.137131009573099 |
40 | 16 | 15.2140578293158 | 0.785942170684194 |
41 | 14 | 13.0946908554761 | 0.905309144523878 |
42 | 15 | 8.07683116485417 | 6.92316883514583 |
43 | 5 | 9.69719186915463 | -4.69719186915462 |
44 | 8 | 10.3128253558287 | -2.31282535582874 |
45 | 11 | 11.1425032250712 | -0.142503225071184 |
46 | 16 | 14.2098846627818 | 1.79011533721819 |
47 | 17 | 14.2500353897462 | 2.74996461025383 |
48 | 9 | 8.02555991104887 | 0.974440088951125 |
49 | 9 | 11.4013974458299 | -2.40139744582994 |
50 | 13 | 14.808632702716 | -1.80863270271598 |
51 | 10 | 10.8901420967481 | -0.89014209674811 |
52 | 6 | 12.0161222660924 | -6.01612226609242 |
53 | 12 | 11.8550776627017 | 0.144922337298265 |
54 | 8 | 10.4404956295679 | -2.44049562956788 |
55 | 14 | 11.8140863561726 | 2.18591364382737 |
56 | 12 | 12.8958442537491 | -0.895844253749078 |
57 | 11 | 11.0437674770327 | -0.0437674770327478 |
58 | 16 | 14.1109092390368 | 1.88909076096322 |
59 | 8 | 10.2174201467094 | -2.21742014670938 |
60 | 15 | 14.5793674055268 | 0.420632594473168 |
61 | 7 | 9.08606772203683 | -2.08606772203683 |
62 | 16 | 13.8879547307237 | 2.11204526927626 |
63 | 14 | 12.8672936124656 | 1.13270638753437 |
64 | 16 | 13.5913528563597 | 2.4086471436403 |
65 | 9 | 10.2068533045821 | -1.20685330458214 |
66 | 14 | 12.3345658732357 | 1.66543412676427 |
67 | 11 | 13.2504157773547 | -2.25041577735468 |
68 | 13 | 10.3688045275876 | 2.63119547241239 |
69 | 15 | 12.9674672688824 | 2.03253273111755 |
70 | 5 | 5.79023616619341 | -0.790236166193413 |
71 | 15 | 12.8958442537491 | 2.10415574625092 |
72 | 13 | 11.9376004569162 | 1.06239954308383 |
73 | 11 | 13.0096865681784 | -2.00968656817842 |
74 | 11 | 14.1073106126889 | -3.10731061268895 |
75 | 12 | 12.2155458199278 | -0.215545819927803 |
76 | 12 | 13.4207007986088 | -1.42070079860878 |
77 | 12 | 12.7717885230907 | -0.771788523090728 |
78 | 12 | 12.1014030000488 | -0.101403000048823 |
79 | 14 | 11.0636649937123 | 2.93633500628766 |
80 | 6 | 7.99749563203563 | -1.99749563203563 |
81 | 7 | 9.43729486336121 | -2.43729486336121 |
82 | 14 | 12.6332558392609 | 1.3667441607391 |
83 | 14 | 14.0140965062464 | -0.0140965062463691 |
84 | 10 | 10.9881669055724 | -0.98816690557244 |
85 | 13 | 9.3806153850025 | 3.6193846149975 |
86 | 12 | 12.4326181625947 | -0.432618162594745 |
87 | 9 | 9.09500387955766 | -0.095003879557659 |
88 | 12 | 12.3702376121216 | -0.37023761212164 |
89 | 16 | 15.0862732073467 | 0.91372679265325 |
90 | 10 | 10.8197311576487 | -0.819731157648661 |
91 | 14 | 12.9976890612934 | 1.00231093870665 |
92 | 10 | 13.6606689718278 | -3.66066897182779 |
93 | 16 | 15.0039444120109 | 0.996055587989134 |
94 | 15 | 13.3340218313987 | 1.66597816860126 |
95 | 12 | 11.4971428355237 | 0.502857164476318 |
96 | 10 | 9.2960508743789 | 0.703949125621102 |
97 | 8 | 10.3039187256395 | -2.30391872563946 |
98 | 8 | 8.49104857341337 | -0.491048573413374 |
99 | 11 | 12.5710940967919 | -1.57109409679194 |
100 | 13 | 13.0095563032155 | -0.00955630321554896 |
101 | 16 | 15.8926974999577 | 0.107302500042301 |
102 | 16 | 15.186289118266 | 0.813710881733994 |
103 | 14 | 15.6755434598453 | -1.67554345984527 |
104 | 11 | 9.01116250273822 | 1.98883749726178 |
105 | 4 | 7.39905245048233 | -3.39905245048233 |
106 | 14 | 14.6931147771868 | -0.693114777186823 |
107 | 9 | 10.594629875114 | -1.59462987511395 |
108 | 14 | 15.2695903139292 | -1.26959031392921 |
109 | 8 | 10.0456509556939 | -2.04565095569389 |
110 | 8 | 10.5072804617848 | -2.50728046178481 |
111 | 11 | 11.9938048364073 | -0.993804836407263 |
112 | 12 | 13.2321103857661 | -1.23211038576614 |
113 | 11 | 11.0330095267163 | -0.0330095267162853 |
114 | 14 | 13.0418323070248 | 0.958167692975176 |
115 | 15 | 14.4249520599917 | 0.575047940008309 |
116 | 16 | 13.3922013962518 | 2.6077986037482 |
117 | 16 | 12.9005883180425 | 3.09941168195749 |
118 | 11 | 12.673574652874 | -1.67357465287404 |
119 | 14 | 13.4060293555616 | 0.593970644438402 |
120 | 14 | 11.0475585464594 | 2.95244145354057 |
121 | 12 | 11.5995959110711 | 0.400404088928909 |
122 | 14 | 13.0940073967967 | 0.905992603203296 |
123 | 8 | 10.8603554276809 | -2.86035542768093 |
124 | 13 | 14.3119707018324 | -1.31197070183239 |
125 | 16 | 14.5509505579911 | 1.44904944200886 |
126 | 12 | 10.610842828938 | 1.38915717106205 |
127 | 16 | 15.8791859628305 | 0.120814037169506 |
128 | 12 | 12.7304778902064 | -0.730477890206395 |
129 | 11 | 11.3400659417745 | -0.340065941774508 |
130 | 4 | 5.79461524078687 | -1.79461524078687 |
131 | 16 | 16.131819184881 | -0.131819184881045 |
132 | 15 | 13.1214871661986 | 1.8785128338014 |
133 | 10 | 11.178654301887 | -1.17865430188699 |
134 | 13 | 14.3237444497438 | -1.32374444974382 |
135 | 15 | 12.6306718948986 | 2.36932810510136 |
136 | 12 | 10.2439559275061 | 1.75604407249388 |
137 | 14 | 12.9259198644642 | 1.07408013553584 |
138 | 7 | 10.4573515489763 | -3.4573515489763 |
139 | 19 | 13.7765654976555 | 5.22343450234449 |
140 | 12 | 13.1083948356822 | -1.10839483568217 |
141 | 12 | 11.9682206017187 | 0.0317793982812942 |
142 | 13 | 13.2804451266867 | -0.280445126686737 |
143 | 15 | 12.4806220133584 | 2.51937798664163 |
144 | 8 | 9.01775498964167 | -1.01775498964167 |
145 | 12 | 11.2040952590524 | 0.795904740947636 |
146 | 10 | 10.4678451340069 | -0.467845134006906 |
147 | 8 | 11.3455760195686 | -3.34557601956863 |
148 | 10 | 14.3588232059195 | -4.3588232059195 |
149 | 15 | 14.2541581734762 | 0.745841826523842 |
150 | 16 | 14.0430694516713 | 1.95693054832875 |
151 | 13 | 13.2761746054612 | -0.276174605461218 |
152 | 16 | 15.0615026963005 | 0.938497303699518 |
153 | 9 | 9.79027571063433 | -0.790275710634327 |
154 | 14 | 13.3770991827921 | 0.622900817207884 |
155 | 14 | 13.4450599447031 | 0.554940055296899 |
156 | 12 | 10.0761761577271 | 1.92382384227293 |
Goldfeld-Quandt test for Heteroskedasticity | |||
p-values | Alternative Hypothesis | ||
breakpoint index | greater | 2-sided | less |
11 | 0.261461129222117 | 0.522922258444234 | 0.738538870777883 |
12 | 0.13888298902184 | 0.27776597804368 | 0.86111701097816 |
13 | 0.613315968719905 | 0.77336806256019 | 0.386684031280095 |
14 | 0.864709048614367 | 0.270581902771267 | 0.135290951385633 |
15 | 0.805918223082224 | 0.388163553835552 | 0.194081776917776 |
16 | 0.740120266376842 | 0.519759467246316 | 0.259879733623158 |
17 | 0.663676658246522 | 0.672646683506957 | 0.336323341753478 |
18 | 0.573374334761589 | 0.853251330476823 | 0.426625665238411 |
19 | 0.494043379044287 | 0.988086758088574 | 0.505956620955713 |
20 | 0.744042586032448 | 0.511914827935103 | 0.255957413967552 |
21 | 0.683772221791443 | 0.632455556417114 | 0.316227778208557 |
22 | 0.685156950631647 | 0.629686098736705 | 0.314843049368353 |
23 | 0.615886058067833 | 0.768227883864334 | 0.384113941932167 |
24 | 0.612940630765622 | 0.774118738468757 | 0.387059369234378 |
25 | 0.577285707503833 | 0.845428584992335 | 0.422714292496167 |
26 | 0.516435180888059 | 0.967129638223883 | 0.483564819111942 |
27 | 0.742561049638454 | 0.514877900723091 | 0.257438950361546 |
28 | 0.69979835144288 | 0.60040329711424 | 0.30020164855712 |
29 | 0.638879944191044 | 0.722240111617912 | 0.361120055808956 |
30 | 0.756608118744544 | 0.486783762510912 | 0.243391881255456 |
31 | 0.820768691404323 | 0.358462617191355 | 0.179231308595677 |
32 | 0.78460751272131 | 0.43078497455738 | 0.21539248727869 |
33 | 0.737828268253584 | 0.524343463492832 | 0.262171731746416 |
34 | 0.698741073649531 | 0.602517852700938 | 0.301258926350469 |
35 | 0.673536449192064 | 0.652927101615872 | 0.326463550807936 |
36 | 0.704543700821158 | 0.590912598357684 | 0.295456299178842 |
37 | 0.682052180767615 | 0.63589563846477 | 0.317947819232385 |
38 | 0.634364540725974 | 0.731270918548052 | 0.365635459274026 |
39 | 0.584939035906339 | 0.830121928187323 | 0.415060964093661 |
40 | 0.541809562294046 | 0.916380875411907 | 0.458190437705954 |
41 | 0.493389910925422 | 0.986779821850844 | 0.506610089074578 |
42 | 0.820151022344117 | 0.359697955311766 | 0.179848977655883 |
43 | 0.957503192576703 | 0.0849936148465945 | 0.0424968074232972 |
44 | 0.961509395146503 | 0.0769812097069945 | 0.0384906048534972 |
45 | 0.950626429353704 | 0.0987471412925916 | 0.0493735706462958 |
46 | 0.954359048717966 | 0.0912819025640688 | 0.0456409512820344 |
47 | 0.955288137241416 | 0.089423725517168 | 0.044711862758584 |
48 | 0.946072145045743 | 0.107855709908513 | 0.0539278549542566 |
49 | 0.946745920298258 | 0.106508159403484 | 0.0532540797017418 |
50 | 0.941048545847936 | 0.117902908304128 | 0.0589514541520638 |
51 | 0.933030902170691 | 0.133938195658619 | 0.0669690978293093 |
52 | 0.989153719690974 | 0.0216925606180521 | 0.010846280309026 |
53 | 0.985245002705137 | 0.0295099945897256 | 0.0147549972948628 |
54 | 0.990190054539324 | 0.0196198909213529 | 0.00980994546067645 |
55 | 0.992416640799626 | 0.0151667184007484 | 0.00758335920037418 |
56 | 0.990310672631011 | 0.0193786547379774 | 0.00968932736898872 |
57 | 0.987202682552208 | 0.0255946348955836 | 0.0127973174477918 |
58 | 0.986679971496181 | 0.0266400570076375 | 0.0133200285038188 |
59 | 0.990472872210774 | 0.0190542555784517 | 0.00952712778922585 |
60 | 0.988569772169275 | 0.0228604556614509 | 0.0114302278307254 |
61 | 0.988998880057266 | 0.0220022398854682 | 0.0110011199427341 |
62 | 0.99016365069662 | 0.0196726986067603 | 0.00983634930338016 |
63 | 0.988980276454835 | 0.0220394470903309 | 0.0110197235451655 |
64 | 0.990236495293778 | 0.0195270094124442 | 0.00976350470622212 |
65 | 0.988800098337982 | 0.0223998033240362 | 0.0111999016620181 |
66 | 0.987368312001295 | 0.025263375997409 | 0.0126316879987045 |
67 | 0.988633085175611 | 0.0227338296487779 | 0.011366914824389 |
68 | 0.99060364039371 | 0.0187927192125801 | 0.00939635960629004 |
69 | 0.99066992991873 | 0.0186601401625411 | 0.00933007008127055 |
70 | 0.987728182581703 | 0.0245436348365936 | 0.0122718174182968 |
71 | 0.988379041652139 | 0.0232419166957227 | 0.0116209583478613 |
72 | 0.98566468443591 | 0.0286706311281782 | 0.0143353155640891 |
73 | 0.985591140776001 | 0.0288177184479975 | 0.0144088592239987 |
74 | 0.990015022867939 | 0.019969954264123 | 0.00998497713206149 |
75 | 0.986601826772714 | 0.0267963464545719 | 0.0133981732272859 |
76 | 0.984343274103383 | 0.0313134517932351 | 0.0156567258966175 |
77 | 0.9797632039356 | 0.0404735921288005 | 0.0202367960644003 |
78 | 0.9736679342668 | 0.0526641314664009 | 0.0263320657332004 |
79 | 0.980061998484135 | 0.039876003031729 | 0.0199380015158645 |
80 | 0.979643363499448 | 0.0407132730011045 | 0.0203566365005523 |
81 | 0.98126414528746 | 0.0374717094250785 | 0.0187358547125393 |
82 | 0.97918775414938 | 0.041624491701239 | 0.0208122458506195 |
83 | 0.97234998802768 | 0.0553000239446415 | 0.0276500119723208 |
84 | 0.965491770195112 | 0.0690164596097759 | 0.034508229804888 |
85 | 0.985548477816903 | 0.0289030443661936 | 0.0144515221830968 |
86 | 0.980943974632421 | 0.0381120507351575 | 0.0190560253675788 |
87 | 0.97478094419514 | 0.0504381116097199 | 0.02521905580486 |
88 | 0.967650775406632 | 0.0646984491867356 | 0.0323492245933678 |
89 | 0.959427414529498 | 0.0811451709410032 | 0.0405725854705016 |
90 | 0.949263356319127 | 0.101473287361745 | 0.0507366436808727 |
91 | 0.940297991627452 | 0.119404016745097 | 0.0597020083725485 |
92 | 0.966256364634164 | 0.0674872707316718 | 0.0337436353658359 |
93 | 0.95770964114874 | 0.0845807177025204 | 0.0422903588512602 |
94 | 0.95316076757293 | 0.0936784648541402 | 0.0468392324270701 |
95 | 0.941540002333498 | 0.116919995333003 | 0.0584599976665017 |
96 | 0.927696148657647 | 0.144607702684706 | 0.0723038513423532 |
97 | 0.924170536424758 | 0.151658927150484 | 0.075829463575242 |
98 | 0.90578151832675 | 0.1884369633465 | 0.0942184816732498 |
99 | 0.897308907354435 | 0.205382185291131 | 0.102691092645565 |
100 | 0.872699781340802 | 0.254600437318395 | 0.127300218659198 |
101 | 0.84525211771284 | 0.30949576457432 | 0.15474788228716 |
102 | 0.816108349970765 | 0.36778330005847 | 0.183891650029235 |
103 | 0.84401597281025 | 0.311968054379501 | 0.155984027189751 |
104 | 0.884448452137034 | 0.231103095725931 | 0.115551547862966 |
105 | 0.891802422686169 | 0.216395154627662 | 0.108197577313831 |
106 | 0.867174934472917 | 0.265650131054167 | 0.132825065527083 |
107 | 0.845696087573755 | 0.308607824852489 | 0.154303912426245 |
108 | 0.840845629590787 | 0.318308740818426 | 0.159154370409213 |
109 | 0.832676320552864 | 0.334647358894273 | 0.167323679447136 |
110 | 0.854595467445651 | 0.290809065108698 | 0.145404532554349 |
111 | 0.84220023346248 | 0.315599533075039 | 0.157799766537519 |
112 | 0.88616038795857 | 0.22767922408286 | 0.11383961204143 |
113 | 0.856450737082678 | 0.287098525834644 | 0.143549262917322 |
114 | 0.825650166885159 | 0.348699666229682 | 0.174349833114841 |
115 | 0.787821694841171 | 0.424356610317658 | 0.212178305158829 |
116 | 0.799328243706175 | 0.401343512587651 | 0.200671756293825 |
117 | 0.808361487041376 | 0.383277025917249 | 0.191638512958624 |
118 | 0.790836706763782 | 0.418326586472436 | 0.209163293236218 |
119 | 0.748676543938378 | 0.502646912123244 | 0.251323456061622 |
120 | 0.829517887299593 | 0.340964225400814 | 0.170482112700407 |
121 | 0.798913804738225 | 0.40217239052355 | 0.201086195261775 |
122 | 0.753178065840193 | 0.493643868319614 | 0.246821934159807 |
123 | 0.753511796991328 | 0.492976406017344 | 0.246488203008672 |
124 | 0.722134836882699 | 0.555730326234603 | 0.277865163117301 |
125 | 0.697977220986737 | 0.604045558026527 | 0.302022779013263 |
126 | 0.681689325333196 | 0.636621349333607 | 0.318310674666804 |
127 | 0.619085066737338 | 0.761829866525324 | 0.380914933262662 |
128 | 0.60409832040882 | 0.79180335918236 | 0.39590167959118 |
129 | 0.59508712788076 | 0.80982574423848 | 0.40491287211924 |
130 | 0.58391677672224 | 0.83216644655552 | 0.41608322327776 |
131 | 0.517032869680371 | 0.965934260639258 | 0.482967130319629 |
132 | 0.488146002922837 | 0.976292005845674 | 0.511853997077163 |
133 | 0.453610614218248 | 0.907221228436496 | 0.546389385781752 |
134 | 0.409441783959971 | 0.818883567919942 | 0.590558216040029 |
135 | 0.360971276955665 | 0.72194255391133 | 0.639028723044335 |
136 | 0.337252872026252 | 0.674505744052505 | 0.662747127973748 |
137 | 0.304213898931773 | 0.608427797863547 | 0.695786101068227 |
138 | 0.335276433501748 | 0.670552867003497 | 0.664723566498252 |
139 | 0.729826853073804 | 0.540346293852392 | 0.270173146926196 |
140 | 0.727597419912 | 0.544805160175999 | 0.272402580088 |
141 | 0.635969982353419 | 0.728060035293161 | 0.364030017646581 |
142 | 0.634713512865379 | 0.730572974269242 | 0.365286487134621 |
143 | 0.512819813794224 | 0.974360372411551 | 0.487180186205776 |
144 | 0.395603929558432 | 0.791207859116864 | 0.604396070441568 |
145 | 0.350774998743705 | 0.70154999748741 | 0.649225001256295 |
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 | 0.237037037037037 | NOK |
10% type I error level | 46 | 0.340740740740741 | NOK |