Multiple Linear Regression - Estimated Regression Equation |
Popularity[t] = -0.983357375578936 + 0.089381370655549month[t] + 0.104378264723488FindingFriends[t] + 0.211622867223575KnowingPeople[t] + 0.385193850989471Liked[t] + 0.59441013592851Celebrity[t] + 0.307649945898061bestfriend[t] -0.0324002150208811secondbestfriend[t] + 0.411552931191424thirdbestfriend[t] -0.00181007322403911t + 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) | -0.983357375578936 | 6.011657 | -0.1636 | 0.870292 | 0.435146 |
month | 0.089381370655549 | 0.640842 | 0.1395 | 0.889267 | 0.444634 |
FindingFriends | 0.104378264723488 | 0.098559 | 1.059 | 0.291327 | 0.145664 |
KnowingPeople | 0.211622867223575 | 0.06405 | 3.304 | 0.001199 | 6e-04 |
Liked | 0.385193850989471 | 0.099038 | 3.8894 | 0.000152 | 7.6e-05 |
Celebrity | 0.59441013592851 | 0.156961 | 3.787 | 0.000222 | 0.000111 |
bestfriend | 0.307649945898061 | 0.211991 | 1.4512 | 0.148859 | 0.074429 |
secondbestfriend | -0.0324002150208811 | 0.20236 | -0.1601 | 0.873014 | 0.436507 |
thirdbestfriend | 0.411552931191424 | 0.214612 | 1.9177 | 0.057107 | 0.028553 |
t | -0.00181007322403911 | 0.006864 | -0.2637 | 0.792389 | 0.396194 |
Multiple Linear Regression - Regression Statistics | |
Multiple R | 0.719101919830674 |
R-squared | 0.517107571104161 |
Adjusted R-squared | 0.487340229596883 |
F-TEST (value) | 17.3716410307495 |
F-TEST (DF numerator) | 9 |
F-TEST (DF denominator) | 146 |
p-value | 0 |
Multiple Linear Regression - Residual Statistics | |
Residual Standard Deviation | 2.1026328891003 |
Sum Squared Residuals | 645.475499683636 |
Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
1 | 13 | 11.2049026711582 | 1.79509732884181 |
2 | 12 | 11.0501976167471 | 0.949802383252893 |
3 | 15 | 13.1284642259693 | 1.87153577403075 |
4 | 12 | 11.4502389709335 | 0.549761029066482 |
5 | 10 | 10.9719246015601 | -0.971924601560126 |
6 | 12 | 9.36122331907425 | 2.63877668092575 |
7 | 15 | 16.9268608320424 | -1.92686083204242 |
8 | 9 | 10.3094079411661 | -1.30940794116614 |
9 | 12 | 13.0209978602754 | -1.02099786027543 |
10 | 11 | 7.54336622238226 | 3.45663377761774 |
11 | 11 | 13.0149485846245 | -2.01494858462452 |
12 | 11 | 12.1838317170145 | -1.18383171701454 |
13 | 15 | 12.2991592688119 | 2.70084073118813 |
14 | 7 | 11.4832734656525 | -4.48327346565247 |
15 | 11 | 11.2781603020676 | -0.278160302067566 |
16 | 11 | 10.8220760751143 | 0.177923924885657 |
17 | 10 | 11.8347311899754 | -1.8347311899754 |
18 | 14 | 14.8674128169904 | -0.867412816990424 |
19 | 10 | 8.56823970010499 | 1.43176029989501 |
20 | 6 | 9.34255000441309 | -3.34255000441309 |
21 | 11 | 8.77932092658328 | 2.22067907341672 |
22 | 15 | 14.0737626346785 | 0.926237365321516 |
23 | 11 | 11.5803388330651 | -0.580338833065069 |
24 | 12 | 9.74160524658528 | 2.25839475341472 |
25 | 14 | 13.0843361390877 | 0.915663860912261 |
26 | 15 | 14.5245748735349 | 0.475425126465107 |
27 | 9 | 14.3087353508027 | -5.30873535080274 |
28 | 13 | 12.4834032242154 | 0.516596775784642 |
29 | 13 | 13.4529879522718 | -0.452987952271803 |
30 | 16 | 11.1694519977055 | 4.83054800229448 |
31 | 13 | 8.75162527439104 | 4.24837472560896 |
32 | 12 | 13.624849081948 | -1.62484908194797 |
33 | 14 | 14.569783025129 | -0.569783025128966 |
34 | 11 | 9.60790170281557 | 1.39209829718443 |
35 | 9 | 10.2281357490962 | -1.22813574909621 |
36 | 16 | 14.1849071539586 | 1.81509284604136 |
37 | 12 | 13.1540413424309 | -1.15404134243088 |
38 | 10 | 9.71307390046834 | 0.286926099531656 |
39 | 13 | 13.1545469131956 | -0.154546913195554 |
40 | 16 | 15.2287736182529 | 0.771226381747057 |
41 | 14 | 13.1151849345199 | 0.88481506548013 |
42 | 15 | 8.07058331810839 | 6.92941668189161 |
43 | 5 | 9.71510528588547 | -4.71510528588547 |
44 | 8 | 10.3134380241431 | -2.31343802414315 |
45 | 11 | 11.1487052586015 | -0.148705258601458 |
46 | 16 | 14.2175074662197 | 1.78249253378025 |
47 | 17 | 14.2475308431785 | 2.75246915682148 |
48 | 9 | 8.02879397139069 | 0.971206028609306 |
49 | 9 | 11.39958743349 | -2.39958743349002 |
50 | 13 | 14.8178416598702 | -1.81784165987017 |
51 | 10 | 10.8886453480061 | -0.888645348006095 |
52 | 6 | 11.9910442211409 | -5.99104422114088 |
53 | 12 | 11.8495190412859 | 0.150480958714061 |
54 | 8 | 10.433166443441 | -2.43316644344104 |
55 | 14 | 11.8091063908163 | 2.19089360918367 |
56 | 12 | 12.876118033608 | -0.87611803360804 |
57 | 11 | 11.1092335643711 | -0.109233564371146 |
58 | 16 | 14.1747570596022 | 1.82524294039776 |
59 | 8 | 10.2776291475077 | -2.27762914750774 |
60 | 15 | 14.6575447101163 | 0.342455289883668 |
61 | 7 | 9.1511205984398 | -2.1511205984398 |
62 | 16 | 13.9464110345232 | 2.05358896547681 |
63 | 14 | 12.9130473900452 | 1.08695260995478 |
64 | 16 | 13.661414209331 | 2.338585790669 |
65 | 9 | 10.2507224958308 | -1.25072249583077 |
66 | 14 | 12.3894985830801 | 1.61050141691991 |
67 | 11 | 13.2954002601194 | -2.29540026011942 |
68 | 13 | 10.423297436403 | 2.57670256359697 |
69 | 15 | 13.0175810545881 | 1.98241894541192 |
70 | 5 | 5.82162779891744 | -0.821627798917437 |
71 | 15 | 12.938348305903 | 2.061651694097 |
72 | 13 | 11.9737875527751 | 1.02621244722485 |
73 | 11 | 13.0575037847135 | -2.0575037847135 |
74 | 11 | 14.1346593713084 | -3.13465937130842 |
75 | 12 | 12.2462910576544 | -0.246291057654353 |
76 | 12 | 13.4605564914878 | -1.46055649148784 |
77 | 12 | 12.815850975058 | -0.815850975058034 |
78 | 12 | 12.1256704010635 | -0.125670401063511 |
79 | 14 | 11.0986370101107 | 2.90136298988933 |
80 | 6 | 8.02152943171599 | -2.02152943171599 |
81 | 7 | 9.46530618764307 | -2.46530618764307 |
82 | 14 | 12.6302867701622 | 1.36971322983782 |
83 | 14 | 14.0434433176965 | -0.0434433176964576 |
84 | 10 | 10.9996709892448 | -0.999670989244845 |
85 | 13 | 9.39576007708632 | 3.60423992291368 |
86 | 12 | 12.4552688010383 | -0.455268801038256 |
87 | 9 | 9.09895259471804 | -0.0989525947180396 |
88 | 12 | 12.3827335866523 | -0.382733586652306 |
89 | 16 | 15.1126325964851 | 0.887367403514892 |
90 | 10 | 10.8271360363588 | -0.827136036358805 |
91 | 14 | 13.0149414140629 | 0.985058585937122 |
92 | 10 | 13.6743590227115 | -3.67435902271152 |
93 | 16 | 15.0189494268598 | 0.981050573140156 |
94 | 15 | 13.3269385259384 | 1.67306147406163 |
95 | 12 | 11.4956913796953 | 0.504308620304673 |
96 | 10 | 9.29698432053747 | 0.703015679462534 |
97 | 8 | 10.2975523598291 | -2.29755235982908 |
98 | 8 | 8.4817653155485 | -0.4817653155485 |
99 | 11 | 12.5542135160764 | -1.55421351607642 |
100 | 13 | 13.0145764114289 | -0.0145764114289043 |
101 | 16 | 15.8957167506989 | 0.104283249301134 |
102 | 16 | 15.1898453567617 | 0.810154643238305 |
103 | 14 | 15.6944063024031 | -1.69440630240308 |
104 | 11 | 8.99400888584843 | 2.00599111415157 |
105 | 4 | 7.37063441742284 | -3.37063441742284 |
106 | 14 | 14.6930170629043 | -0.693017062904347 |
107 | 9 | 10.5659658154158 | -1.56596581541582 |
108 | 14 | 15.2574638574311 | -1.25746385743106 |
109 | 8 | 10.0167137756442 | -2.01671377564415 |
110 | 8 | 10.4697500279441 | -2.46975002794406 |
111 | 11 | 11.9652097964192 | -0.965209796419187 |
112 | 12 | 13.1931382162864 | -1.19313821628645 |
113 | 11 | 11.0137981823412 | -0.0137981823411882 |
114 | 14 | 13.0197127994167 | 0.980287200583342 |
115 | 15 | 14.4011837376831 | 0.598816262316853 |
116 | 16 | 13.3534432962753 | 2.64655670372468 |
117 | 16 | 12.8731118109995 | 3.12688818900047 |
118 | 11 | 12.6472019672902 | -1.64720196729016 |
119 | 14 | 13.3630666028829 | 0.63693339711708 |
120 | 14 | 10.9961495101169 | 3.00385048988307 |
121 | 12 | 11.5554143228783 | 0.444585677121668 |
122 | 14 | 13.0527898702698 | 0.947210129730189 |
123 | 8 | 10.8065061752171 | -2.80650617521712 |
124 | 13 | 14.2747980236383 | -1.27479802363834 |
125 | 16 | 14.5086598466098 | 1.49134015339024 |
126 | 12 | 10.5694280782661 | 1.43057192173393 |
127 | 16 | 15.8410718755826 | 0.158928124417358 |
128 | 12 | 12.6796300217692 | -0.679630021769198 |
129 | 11 | 11.2682259994715 | -0.268225999471477 |
130 | 4 | 5.69832608065274 | -1.69832608065274 |
131 | 16 | 16.0766810985428 | -0.0766810985427846 |
132 | 15 | 13.0638986707597 | 1.93610132924026 |
133 | 10 | 11.1235806511745 | -1.12358065117449 |
134 | 13 | 14.278455374957 | -1.27845537495703 |
135 | 15 | 12.5641071957015 | 2.43589280429852 |
136 | 12 | 10.1741917457575 | 1.82580825424246 |
137 | 14 | 12.8469543039562 | 1.15304569604381 |
138 | 7 | 10.3775092422047 | -3.37750924220472 |
139 | 19 | 13.7053566491609 | 5.29464335083911 |
140 | 12 | 13.0227660694378 | -1.02276606943781 |
141 | 12 | 11.8821733463978 | 0.117826653602182 |
142 | 13 | 13.2070126965691 | -0.20701269656909 |
143 | 15 | 12.4076173372964 | 2.59238266270357 |
144 | 8 | 8.9046262949945 | -0.904626294994498 |
145 | 12 | 11.1211270460751 | 0.878872953924875 |
146 | 10 | 10.3911752139798 | -0.39117521397978 |
147 | 8 | 11.2623122209065 | -3.26231222090646 |
148 | 10 | 14.2774505151922 | -4.27745051519218 |
149 | 15 | 14.1609097605415 | 0.839090239458519 |
150 | 16 | 13.9641477830056 | 2.03585221699442 |
151 | 13 | 13.1799642692192 | -0.179964269219201 |
152 | 16 | 14.9690796300644 | 1.03092036993558 |
153 | 9 | 9.68624860025679 | -0.686248600256794 |
154 | 14 | 13.2785335658949 | 0.72146643410509 |
155 | 14 | 13.3355686009417 | 0.664431399058301 |
156 | 12 | 9.96088127603093 | 2.03911872396907 |
Goldfeld-Quandt test for Heteroskedasticity | |||
p-values | Alternative Hypothesis | ||
breakpoint index | greater | 2-sided | less |
13 | 0.836001792063908 | 0.327996415872184 | 0.163998207936092 |
14 | 0.90195839407854 | 0.196083211842921 | 0.0980416059214604 |
15 | 0.879240557644519 | 0.241518884710961 | 0.120759442355481 |
16 | 0.808616793673195 | 0.38276641265361 | 0.191383206326805 |
17 | 0.726585161757706 | 0.546829676484588 | 0.273414838242294 |
18 | 0.666797038131055 | 0.66640592373789 | 0.333202961868945 |
19 | 0.607910346534052 | 0.784179306931897 | 0.392089653465948 |
20 | 0.702128356781856 | 0.595743286436287 | 0.297871643218144 |
21 | 0.69419228673152 | 0.611615426536959 | 0.30580771326848 |
22 | 0.745316120165674 | 0.509367759668653 | 0.254683879834326 |
23 | 0.683418423843553 | 0.633163152312894 | 0.316581576156447 |
24 | 0.707777132038689 | 0.584445735922623 | 0.292222867961311 |
25 | 0.684535775162728 | 0.630928449674544 | 0.315464224837272 |
26 | 0.626079763990607 | 0.747840472018787 | 0.373920236009393 |
27 | 0.806167163016805 | 0.387665673966391 | 0.193832836983195 |
28 | 0.770975653320348 | 0.458048693359304 | 0.229024346679652 |
29 | 0.717035116657026 | 0.565929766685948 | 0.282964883342974 |
30 | 0.818623909680045 | 0.362752180639911 | 0.181376090319955 |
31 | 0.860156619654829 | 0.279686760690342 | 0.139843380345171 |
32 | 0.829666210992467 | 0.340667578015066 | 0.170333789007533 |
33 | 0.787312593252715 | 0.425374813494571 | 0.212687406747285 |
34 | 0.754905410599089 | 0.490189178801822 | 0.245094589400911 |
35 | 0.736412067999249 | 0.527175864001502 | 0.263587932000751 |
36 | 0.756719463465379 | 0.486561073069242 | 0.243280536534621 |
37 | 0.740078036428823 | 0.519843927142353 | 0.259921963571177 |
38 | 0.69646218881162 | 0.607075622376759 | 0.30353781118838 |
39 | 0.646302343994341 | 0.707395312011319 | 0.353697656005659 |
40 | 0.602581686654111 | 0.794836626691778 | 0.397418313345889 |
41 | 0.552645639537826 | 0.894708720924349 | 0.447354360462174 |
42 | 0.843176300736538 | 0.313647398526925 | 0.156823699263462 |
43 | 0.970814918196872 | 0.0583701636062565 | 0.0291850818031283 |
44 | 0.971754476204528 | 0.0564910475909441 | 0.028245523795472 |
45 | 0.96311606905583 | 0.0737678618883392 | 0.0368839309441696 |
46 | 0.968695846103815 | 0.0626083077923702 | 0.0313041538961851 |
47 | 0.975019136896098 | 0.0499617262078041 | 0.024980863103902 |
48 | 0.971592200610985 | 0.0568155987780294 | 0.0284077993890147 |
49 | 0.968059130521681 | 0.0638817389566385 | 0.0319408694783192 |
50 | 0.959432758930122 | 0.0811344821397565 | 0.0405672410698783 |
51 | 0.952729142815978 | 0.0945417143680442 | 0.0472708571840221 |
52 | 0.98927272721028 | 0.0214545455794395 | 0.0107272727897198 |
53 | 0.985803425906301 | 0.0283931481873985 | 0.0141965740936992 |
54 | 0.989154915195705 | 0.0216901696085896 | 0.0108450848042948 |
55 | 0.992767891002053 | 0.0144642179958943 | 0.00723210899794715 |
56 | 0.990211719081638 | 0.0195765618367242 | 0.00978828091836212 |
57 | 0.986513154464591 | 0.0269736910708179 | 0.013486845535409 |
58 | 0.985847831176756 | 0.028304337646489 | 0.0141521688232445 |
59 | 0.989059578811089 | 0.021880842377823 | 0.0109404211889115 |
60 | 0.987859033576145 | 0.0242819328477105 | 0.0121409664238553 |
61 | 0.987798331713595 | 0.0244033365728105 | 0.0122016682864052 |
62 | 0.989447218573091 | 0.0211055628538186 | 0.0105527814269093 |
63 | 0.987885575354576 | 0.0242288492908483 | 0.0121144246454241 |
64 | 0.988287441365562 | 0.0234251172688757 | 0.0117125586344378 |
65 | 0.98765989832796 | 0.0246802033440793 | 0.0123401016720396 |
66 | 0.985670308211707 | 0.0286593835765869 | 0.0143296917882935 |
67 | 0.987314716348945 | 0.0253705673021094 | 0.0126852836510547 |
68 | 0.988869906293761 | 0.0222601874124775 | 0.0111300937062388 |
69 | 0.988298091441909 | 0.023403817116181 | 0.0117019085580905 |
70 | 0.985082355025686 | 0.029835289948629 | 0.0149176449743145 |
71 | 0.985556940612976 | 0.028886118774047 | 0.0144430593870235 |
72 | 0.982164316846268 | 0.0356713663074636 | 0.0178356831537318 |
73 | 0.982498792377714 | 0.035002415244572 | 0.017501207622286 |
74 | 0.987403010396265 | 0.0251939792074704 | 0.0125969896037352 |
75 | 0.983349535585278 | 0.0333009288294439 | 0.016650464414722 |
76 | 0.980156242237186 | 0.0396875155256276 | 0.0198437577628138 |
77 | 0.974293116574389 | 0.0514137668512229 | 0.0257068834256115 |
78 | 0.96666173246263 | 0.0666765350747409 | 0.0333382675373705 |
79 | 0.975640128211654 | 0.0487197435766924 | 0.0243598717883462 |
80 | 0.9739942985895 | 0.0520114028209996 | 0.0260057014104998 |
81 | 0.974966944190363 | 0.0500661116192739 | 0.0250330558096369 |
82 | 0.972983482915995 | 0.0540330341680101 | 0.0270165170840051 |
83 | 0.964448945316954 | 0.0711021093660914 | 0.0355510546830457 |
84 | 0.955210581156972 | 0.0895788376860568 | 0.0447894188430284 |
85 | 0.981998073761221 | 0.036003852477558 | 0.018001926238779 |
86 | 0.976014075078278 | 0.0479718498434434 | 0.0239859249217217 |
87 | 0.968722511477615 | 0.0625549770447704 | 0.0312774885223852 |
88 | 0.959748950399902 | 0.080502099200195 | 0.0402510496000975 |
89 | 0.95100817915353 | 0.0979836416929399 | 0.04899182084647 |
90 | 0.938475804561582 | 0.123048390876835 | 0.0615241954384177 |
91 | 0.930631177696469 | 0.138737644607062 | 0.0693688223035308 |
92 | 0.954772078472272 | 0.090455843055456 | 0.045227921527728 |
93 | 0.94515126031908 | 0.10969747936184 | 0.0548487396809201 |
94 | 0.943430756043238 | 0.113138487913525 | 0.0565692439567624 |
95 | 0.932003167323059 | 0.135993665353882 | 0.067996832676941 |
96 | 0.919702800854298 | 0.160594398291405 | 0.0802971991457023 |
97 | 0.912761396376893 | 0.174477207246214 | 0.087238603623107 |
98 | 0.894459962283812 | 0.211080075432376 | 0.105540037716188 |
99 | 0.878928225372389 | 0.242143549255223 | 0.121071774627611 |
100 | 0.853022706717131 | 0.293954586565738 | 0.146977293282869 |
101 | 0.822265889314234 | 0.355468221371532 | 0.177734110685766 |
102 | 0.79571302322072 | 0.408573953558561 | 0.20428697677928 |
103 | 0.808179866772119 | 0.383640266455761 | 0.191820133227881 |
104 | 0.864435874821127 | 0.271128250357745 | 0.135564125178873 |
105 | 0.861859391898908 | 0.276281216202184 | 0.138140608101092 |
106 | 0.829887256031703 | 0.340225487936594 | 0.170112743968297 |
107 | 0.797467852063354 | 0.405064295873292 | 0.202532147936646 |
108 | 0.783656372757128 | 0.432687254485745 | 0.216343627242872 |
109 | 0.764854625535922 | 0.470290748928157 | 0.235145374464078 |
110 | 0.784143309068944 | 0.431713381862112 | 0.215856690931056 |
111 | 0.769045385873406 | 0.461909228253187 | 0.230954614126594 |
112 | 0.834324256100617 | 0.331351487798766 | 0.165675743899383 |
113 | 0.797250203792304 | 0.405499592415392 | 0.202749796207696 |
114 | 0.766332162739474 | 0.467335674521052 | 0.233667837260526 |
115 | 0.722976130244068 | 0.554047739511864 | 0.277023869755932 |
116 | 0.732170131757852 | 0.535659736484297 | 0.267829868242148 |
117 | 0.744374822732679 | 0.511250354534642 | 0.255625177267321 |
118 | 0.725622971067391 | 0.548754057865217 | 0.274377028932609 |
119 | 0.675379918339688 | 0.649240163320624 | 0.324620081660312 |
120 | 0.771318547410679 | 0.457362905178642 | 0.228681452589321 |
121 | 0.740958354445508 | 0.518083291108985 | 0.259041645554492 |
122 | 0.688252418566368 | 0.623495162867264 | 0.311747581433632 |
123 | 0.674328362110953 | 0.651343275778095 | 0.325671637889047 |
124 | 0.631483536872456 | 0.737032926255087 | 0.368516463127544 |
125 | 0.612176877947888 | 0.775646244104224 | 0.387823122052112 |
126 | 0.612552819280794 | 0.774894361438413 | 0.387447180719206 |
127 | 0.54603567075918 | 0.90792865848164 | 0.45396432924082 |
128 | 0.504878729170788 | 0.990242541658424 | 0.495121270829212 |
129 | 0.482994137738117 | 0.965988275476233 | 0.517005862261883 |
130 | 0.465009250028874 | 0.930018500057748 | 0.534990749971126 |
131 | 0.392923101575465 | 0.785846203150931 | 0.607076898424534 |
132 | 0.371462252534148 | 0.742924505068295 | 0.628537747465852 |
133 | 0.325667334331613 | 0.651334668663227 | 0.674332665668387 |
134 | 0.281323824371726 | 0.562647648743452 | 0.718676175628274 |
135 | 0.237546151569607 | 0.475092303139213 | 0.762453848430394 |
136 | 0.219069151340993 | 0.438138302681985 | 0.780930848659007 |
137 | 0.18430668893371 | 0.368613377867421 | 0.81569331106629 |
138 | 0.197580908202361 | 0.395161816404722 | 0.802419091797639 |
139 | 0.616069745068915 | 0.767860509862171 | 0.383930254931085 |
140 | 0.526150517910437 | 0.947698964179127 | 0.473849482089563 |
141 | 0.405569862606173 | 0.811139725212346 | 0.594430137393827 |
142 | 0.400851681624012 | 0.801703363248024 | 0.599148318375988 |
143 | 0.278089005617193 | 0.556178011234386 | 0.721910994382807 |
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 | 0.221374045801527 | NOK |
10% type I error level | 48 | 0.366412213740458 | NOK |