Multiple Linear Regression - Estimated Regression Equation |
Popularity[t] = -5.63418426484257 + 9.18492464973122Gender[t] + 0.00230324704365767trend[t] -0.00927199770983318trend_G[t] -0.021567227584686Depression[t] -0.121606500243508Depression_G[t] + 0.0485298120141413Belonging[t] + 0.00509921018629681Belonging_G[t] + 0.0331300242551256WeightedPopularity[t] + 0.0446957854911477WeightedPopularity_G[t] + 0.17194203693447ParentalCriticism[t] -0.217763937453644ParentalCriticism_G[t] -0.00789804780864531Happiness[t] -0.189089829189876Happiness_G[t] + 0.259336367937663FindingFriends[t] -0.26414704323834FindingFriends_G[t] + 0.264170480731017KnowingPeople[t] -0.0601889711386115KnowingPeople_G[t] + 0.290831322282455Liked[t] + 0.0569803763954685Liked_G[t] + 0.527764692648576Celebrity[t] + 0.102234815794934Celebrity_G[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) | -5.63418426484257 | 4.276467 | -1.3175 | 0.189924 | 0.094962 |
Gender | 9.18492464973122 | 5.486919 | 1.674 | 0.09647 | 0.048235 |
trend | 0.00230324704365767 | 0.006202 | 0.3713 | 0.710969 | 0.355485 |
trend_G | -0.00927199770983318 | 0.008071 | -1.1488 | 0.252673 | 0.126337 |
Depression | -0.021567227584686 | 0.118609 | -0.1818 | 0.855987 | 0.427994 |
Depression_G | -0.121606500243508 | 0.145592 | -0.8353 | 0.405061 | 0.20253 |
Belonging | 0.0485298120141413 | 0.028317 | 1.7138 | 0.08888 | 0.04444 |
Belonging_G | 0.00509921018629681 | 0.036379 | 0.1402 | 0.888738 | 0.444369 |
WeightedPopularity | 0.0331300242551256 | 0.11409 | 0.2904 | 0.771971 | 0.385986 |
WeightedPopularity_G | 0.0446957854911477 | 0.135552 | 0.3297 | 0.742118 | 0.371059 |
ParentalCriticism | 0.17194203693447 | 0.113319 | 1.5173 | 0.131541 | 0.065771 |
ParentalCriticism_G | -0.217763937453644 | 0.140323 | -1.5519 | 0.12305 | 0.061525 |
Happiness | -0.00789804780864531 | 0.158552 | -0.0498 | 0.960345 | 0.480173 |
Happiness_G | -0.189089829189876 | 0.195098 | -0.9692 | 0.334189 | 0.167095 |
FindingFriends | 0.259336367937663 | 0.140909 | 1.8404 | 0.067914 | 0.033957 |
FindingFriends_G | -0.26414704323834 | 0.194901 | -1.3553 | 0.177606 | 0.088803 |
KnowingPeople | 0.264170480731017 | 0.116816 | 2.2614 | 0.025344 | 0.012672 |
KnowingPeople_G | -0.0601889711386115 | 0.141009 | -0.4268 | 0.670177 | 0.335089 |
Liked | 0.290831322282455 | 0.154827 | 1.8784 | 0.062495 | 0.031247 |
Liked_G | 0.0569803763954685 | 0.201886 | 0.2822 | 0.778194 | 0.389097 |
Celebrity | 0.527764692648576 | 0.31583 | 1.671 | 0.097047 | 0.048524 |
Celebrity_G | 0.102234815794934 | 0.369213 | 0.2769 | 0.782284 | 0.391142 |
Multiple Linear Regression - Regression Statistics | |
Multiple R | 0.766689208812685 |
R-squared | 0.587812342909821 |
Adjusted R-squared | 0.523215769783749 |
F-TEST (value) | 9.09974499363288 |
F-TEST (DF numerator) | 21 |
F-TEST (DF denominator) | 134 |
p-value | 0 |
Multiple Linear Regression - Residual Statistics | |
Residual Standard Deviation | 2.02772835975805 |
Sum Squared Residuals | 550.965428329586 |
Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
1 | 15 | 13.2759958400576 | 1.72400415994239 |
2 | 12 | 8.1340262284636 | 3.8659737715364 |
3 | 15 | 13.415997946991 | 1.58400205300899 |
4 | 12 | 11.0565539575285 | 0.943446042471506 |
5 | 14 | 12.8750176494125 | 1.12498235058745 |
6 | 8 | 8.3344185878878 | -0.334418587887804 |
7 | 11 | 12.4427990475475 | -1.44279904754751 |
8 | 15 | 9.15170867670218 | 5.84829132329782 |
9 | 4 | 5.7672863660809 | -1.7672863660809 |
10 | 13 | 9.92704830316118 | 3.07295169683882 |
11 | 19 | 13.9013636803331 | 5.09863631966693 |
12 | 10 | 11.3475549667814 | -1.34755496678145 |
13 | 15 | 17.2263741718015 | -2.2263741718015 |
14 | 6 | 11.7394270903916 | -5.73942709039158 |
15 | 7 | 11.0683475853148 | -4.06834758531479 |
16 | 14 | 12.5222386573094 | 1.47776134269056 |
17 | 16 | 13.6491050031605 | 2.3508949968395 |
18 | 16 | 14.5404845628261 | 1.45951543717389 |
19 | 14 | 14.3706390177842 | -0.370639017784193 |
20 | 15 | 14.1605842388127 | 0.839415761187271 |
21 | 14 | 14.5657795741536 | -0.565779574153627 |
22 | 12 | 10.7038659339722 | 1.29613406602777 |
23 | 9 | 8.96805777665953 | 0.0319422233404681 |
24 | 12 | 11.59930871609 | 0.400691283909992 |
25 | 14 | 13.5832088796326 | 0.416791120367408 |
26 | 12 | 12.049207024473 | -0.0492070244729714 |
27 | 14 | 13.1246490680173 | 0.875350931982731 |
28 | 10 | 10.4817468741181 | -0.48174687411809 |
29 | 14 | 13.2102921691126 | 0.789707830887418 |
30 | 16 | 16.1850785065891 | -0.18507850658912 |
31 | 10 | 8.52482748134601 | 1.47517251865399 |
32 | 8 | 11.076946131789 | -3.07694613178895 |
33 | 12 | 12.2324256249959 | -0.232425624995913 |
34 | 11 | 11.4025364911055 | -0.402536491105469 |
35 | 8 | 9.33880514733481 | -1.33880514733481 |
36 | 13 | 10.7789820683385 | 2.22101793166152 |
37 | 11 | 9.67317626387485 | 1.32682373612515 |
38 | 12 | 9.30671732337785 | 2.69328267662215 |
39 | 16 | 14.1851503750603 | 1.81484962493974 |
40 | 16 | 13.2974320695092 | 2.70256793049075 |
41 | 13 | 13.7320598473499 | -0.732059847349922 |
42 | 14 | 15.205770743808 | -1.20577074380801 |
43 | 5 | 5.1726734230187 | -0.172673423018699 |
44 | 14 | 12.6800573240357 | 1.31994267596432 |
45 | 13 | 9.69267869584 | 3.30732130416 |
46 | 16 | 16.1251462063081 | -0.125146206308122 |
47 | 14 | 13.7328513465489 | 0.267148653451068 |
48 | 15 | 13.415359182715 | 1.58464081728496 |
49 | 15 | 14.0470216464013 | 0.952978353598735 |
50 | 11 | 12.412906753837 | -1.41290675383696 |
51 | 15 | 13.6941435870677 | 1.30585641293226 |
52 | 16 | 12.9725535785433 | 3.02744642145668 |
53 | 13 | 13.8991898151183 | -0.899189815118311 |
54 | 11 | 12.9853242743521 | -1.9853242743521 |
55 | 12 | 13.0993986337065 | -1.09939863370649 |
56 | 12 | 12.0530060783113 | -0.0530060783113362 |
57 | 10 | 13.3566978555583 | -3.35669785555826 |
58 | 8 | 8.18084659772967 | -0.180846597729668 |
59 | 9 | 8.97167009489499 | 0.028329905105006 |
60 | 12 | 12.5500878077745 | -0.550087807774467 |
61 | 14 | 13.4967369872789 | 0.503263012721092 |
62 | 12 | 13.6961549656755 | -1.69615496567551 |
63 | 11 | 10.1780448676603 | 0.821955132339716 |
64 | 14 | 13.4291014435579 | 0.570898556442102 |
65 | 7 | 11.2839993319433 | -4.2839993319433 |
66 | 16 | 13.5312833042277 | 2.46871669577234 |
67 | 16 | 15.4072553142332 | 0.592744685766771 |
68 | 11 | 13.1124261135569 | -2.11242611355686 |
69 | 16 | 17.2106617492342 | -1.21066174923418 |
70 | 13 | 14.0959265231572 | -1.09592652315721 |
71 | 11 | 10.9958716157884 | 0.00412838421159362 |
72 | 13 | 13.3293650328085 | -0.329365032808534 |
73 | 14 | 14.2992369840814 | -0.299236984081361 |
74 | 15 | 12.5759205978244 | 2.42407940217559 |
75 | 10 | 7.97117145303042 | 2.02882854696958 |
76 | 15 | 15.6495348865898 | -0.64953488658979 |
77 | 11 | 12.4122609001172 | -1.41226090011715 |
78 | 11 | 12.1728912222776 | -1.17289122227761 |
79 | 6 | 8.81330165247662 | -2.81330165247662 |
80 | 11 | 10.1499109271726 | 0.850089072827393 |
81 | 12 | 11.3374457983146 | 0.662554201685405 |
82 | 13 | 13.1995960719836 | -0.199596071983587 |
83 | 12 | 13.2376046495221 | -1.2376046495221 |
84 | 8 | 10.7600459564978 | -2.76004595649785 |
85 | 9 | 10.8836766200139 | -1.88367662001395 |
86 | 10 | 11.3673566473549 | -1.3673566473549 |
87 | 16 | 12.7966434442645 | 3.20335655573546 |
88 | 15 | 13.0525762116854 | 1.94742378831456 |
89 | 14 | 13.6293846977137 | 0.370615302286297 |
90 | 12 | 13.6743621358241 | -1.67436213582408 |
91 | 12 | 11.0025560419154 | 0.997443958084582 |
92 | 10 | 9.5801280956123 | 0.419871904387699 |
93 | 12 | 11.3305362188998 | 0.669463781100173 |
94 | 8 | 9.40430226823121 | -1.40430226823121 |
95 | 16 | 14.5196025800184 | 1.4803974199816 |
96 | 11 | 8.83318131290252 | 2.16681868709748 |
97 | 12 | 11.6095760287716 | 0.390423971228418 |
98 | 9 | 10.9813752972926 | -1.98137529729258 |
99 | 14 | 11.6099170067986 | 2.39008299320144 |
100 | 15 | 13.8321025568294 | 1.16789744317058 |
101 | 8 | 10.2714766374347 | -2.27147663743473 |
102 | 12 | 12.8573957465154 | -0.857395746515445 |
103 | 10 | 9.85633895813615 | 0.143661041863849 |
104 | 16 | 15.2465038614127 | 0.753496138587303 |
105 | 17 | 15.3404928139371 | 1.65950718606293 |
106 | 8 | 9.60384738462476 | -1.60384738462476 |
107 | 9 | 11.879064375873 | -2.87906437587303 |
108 | 8 | 11.9421186017172 | -3.94211860171718 |
109 | 11 | 12.0563998316784 | -1.0563998316784 |
110 | 16 | 15.6109004739734 | 0.389099526026618 |
111 | 13 | 13.5241728208553 | -0.524172820855276 |
112 | 5 | 7.81356877600441 | -2.81356877600441 |
113 | 15 | 13.4354451005812 | 1.56455489941884 |
114 | 15 | 14.4733561770563 | 0.526643822943703 |
115 | 12 | 11.2036938887711 | 0.796306111228928 |
116 | 12 | 11.5664672015403 | 0.433532798459679 |
117 | 16 | 16.827024206619 | -0.827024206618975 |
118 | 12 | 12.9670128268691 | -0.967012826869131 |
119 | 10 | 11.8629947303403 | -1.8629947303403 |
120 | 12 | 10.6871445727976 | 1.31285542720237 |
121 | 4 | 5.91082913335389 | -1.91082913335389 |
122 | 11 | 12.2307507294481 | -1.23075072944806 |
123 | 16 | 14.0638766720116 | 1.93612332798838 |
124 | 7 | 8.50716619499291 | -1.50716619499291 |
125 | 9 | 11.0016637639058 | -2.00166376390576 |
126 | 14 | 11.3381986807959 | 2.66180131920409 |
127 | 11 | 10.5105014070531 | 0.489498592946897 |
128 | 10 | 11.9828216254215 | -1.98282162542155 |
129 | 6 | 8.27209422333465 | -2.27209422333465 |
130 | 14 | 13.574096906046 | 0.425903093953981 |
131 | 11 | 12.1653679336672 | -1.16536793366721 |
132 | 11 | 9.6373737169921 | 1.36262628300789 |
133 | 9 | 13.5657248941332 | -4.56572489413315 |
134 | 16 | 11.8922489062465 | 4.10775109375348 |
135 | 7 | 8.01417690154054 | -1.01417690154054 |
136 | 8 | 8.59924945771092 | -0.599249457710921 |
137 | 10 | 9.83099090880023 | 0.16900909119977 |
138 | 14 | 11.9790827970625 | 2.02091720293752 |
139 | 9 | 9.76422983745289 | -0.76422983745289 |
140 | 13 | 12.8639434625053 | 0.136056537494721 |
141 | 13 | 9.21960194043838 | 3.78039805956162 |
142 | 12 | 11.9784152890646 | 0.0215847109353778 |
143 | 11 | 11.8441408302318 | -0.844140830231831 |
144 | 10 | 15.1108902374318 | -5.11089023743181 |
145 | 12 | 12.5312725440459 | -0.531272544045935 |
146 | 14 | 14.2637820424306 | -0.263782042430586 |
147 | 11 | 12.0116907117981 | -1.01169071179814 |
148 | 13 | 11.4432533425889 | 1.5567466574111 |
149 | 14 | 13.2163053584443 | 0.783694641555702 |
150 | 13 | 13.1129526357795 | -0.112952635779527 |
151 | 16 | 16.2346039333436 | -0.234603933343586 |
152 | 13 | 12.8940100751332 | 0.105989924866784 |
153 | 12 | 12.1657475669748 | -0.165747566974779 |
154 | 9 | 9.73805271087334 | -0.738052710873337 |
155 | 14 | 12.4076385222726 | 1.59236147772737 |
156 | 15 | 14.4702010359803 | 0.529798964019667 |
Goldfeld-Quandt test for Heteroskedasticity | |||
p-values | Alternative Hypothesis | ||
breakpoint index | greater | 2-sided | less |
25 | 0.621337454391344 | 0.757325091217311 | 0.378662545608656 |
26 | 0.827047461718165 | 0.34590507656367 | 0.172952538281835 |
27 | 0.797667878844858 | 0.404664242310284 | 0.202332121155142 |
28 | 0.742520744291712 | 0.514958511416577 | 0.257479255708288 |
29 | 0.647400198029026 | 0.705199603941948 | 0.352599801970974 |
30 | 0.554926153458507 | 0.890147693082986 | 0.445073846541493 |
31 | 0.508638917356965 | 0.98272216528607 | 0.491361082643035 |
32 | 0.832170860414729 | 0.335658279170542 | 0.167829139585271 |
33 | 0.781641664074386 | 0.436716671851228 | 0.218358335925614 |
34 | 0.725375472198511 | 0.549249055602978 | 0.274624527801489 |
35 | 0.83212943629685 | 0.335741127406301 | 0.16787056370315 |
36 | 0.841104865548423 | 0.317790268903155 | 0.158895134451577 |
37 | 0.821260678384557 | 0.357478643230886 | 0.178739321615443 |
38 | 0.799270560870701 | 0.401458878258598 | 0.200729439129299 |
39 | 0.754618538769744 | 0.490762922460513 | 0.245381461230256 |
40 | 0.745705448079767 | 0.508589103840465 | 0.254294551920233 |
41 | 0.696413088795298 | 0.607173822409404 | 0.303586911204702 |
42 | 0.673698671734663 | 0.652602656530675 | 0.326301328265337 |
43 | 0.610349045795791 | 0.779301908408417 | 0.389650954204209 |
44 | 0.570089910606687 | 0.859820178786626 | 0.429910089393313 |
45 | 0.830346957169521 | 0.339306085660959 | 0.169653042830479 |
46 | 0.797689969307922 | 0.404620061384156 | 0.202310030692078 |
47 | 0.807493979052688 | 0.385012041894624 | 0.192506020947312 |
48 | 0.773531205495104 | 0.452937589009792 | 0.226468794504896 |
49 | 0.730708948869392 | 0.538582102261217 | 0.269291051130608 |
50 | 0.705379938297298 | 0.589240123405404 | 0.294620061702702 |
51 | 0.794507986516016 | 0.410984026967969 | 0.205492013483984 |
52 | 0.81787103100739 | 0.36425793798522 | 0.18212896899261 |
53 | 0.78695373603275 | 0.426092527934499 | 0.21304626396725 |
54 | 0.884215065115059 | 0.231569869769882 | 0.115784934884941 |
55 | 0.869061013595133 | 0.261877972809735 | 0.130938986404867 |
56 | 0.860885179453613 | 0.278229641092774 | 0.139114820546387 |
57 | 0.916918848848088 | 0.166162302303824 | 0.0830811511519119 |
58 | 0.898241814567868 | 0.203516370864264 | 0.101758185432132 |
59 | 0.871652374617998 | 0.256695250764003 | 0.128347625382002 |
60 | 0.845954125744072 | 0.308091748511857 | 0.154045874255928 |
61 | 0.812220934628496 | 0.375558130743007 | 0.187779065371504 |
62 | 0.836162252488911 | 0.327675495022178 | 0.163837747511089 |
63 | 0.818627063444473 | 0.362745873111053 | 0.181372936555527 |
64 | 0.839047940057857 | 0.321904119884285 | 0.160952059942143 |
65 | 0.943080771878779 | 0.113838456242443 | 0.0569192281212213 |
66 | 0.945460482001139 | 0.109079035997723 | 0.0545395179988613 |
67 | 0.929384223908222 | 0.141231552183555 | 0.0706157760917776 |
68 | 0.9237468355778 | 0.1525063288444 | 0.0762531644221998 |
69 | 0.908255011692881 | 0.183489976614238 | 0.0917449883071189 |
70 | 0.892317184415188 | 0.215365631169623 | 0.107682815584812 |
71 | 0.871411924439387 | 0.257176151121226 | 0.128588075560613 |
72 | 0.842613193049866 | 0.314773613900269 | 0.157386806950134 |
73 | 0.823106193144137 | 0.353787613711727 | 0.176893806855863 |
74 | 0.841103540635682 | 0.317792918728636 | 0.158896459364318 |
75 | 0.827216837591567 | 0.345566324816865 | 0.172783162408432 |
76 | 0.79940638597624 | 0.40118722804752 | 0.20059361402376 |
77 | 0.869005486878494 | 0.261989026243012 | 0.130994513121506 |
78 | 0.846858135294178 | 0.306283729411644 | 0.153141864705822 |
79 | 0.871876384715482 | 0.256247230569036 | 0.128123615284518 |
80 | 0.849753934618661 | 0.300492130762679 | 0.150246065381339 |
81 | 0.819846335953316 | 0.360307328093368 | 0.180153664046684 |
82 | 0.784739727151115 | 0.43052054569777 | 0.215260272848885 |
83 | 0.75367010026557 | 0.492659799468861 | 0.24632989973443 |
84 | 0.769511857911348 | 0.460976284177303 | 0.230488142088652 |
85 | 0.76615350986136 | 0.46769298027728 | 0.23384649013864 |
86 | 0.74690718949688 | 0.50618562100624 | 0.25309281050312 |
87 | 0.773458735604901 | 0.453082528790198 | 0.226541264395099 |
88 | 0.766959573576645 | 0.466080852846709 | 0.233040426423355 |
89 | 0.726101559091764 | 0.547796881816472 | 0.273898440908236 |
90 | 0.706909058245815 | 0.58618188350837 | 0.293090941754185 |
91 | 0.684533550671585 | 0.63093289865683 | 0.315466449328415 |
92 | 0.639940825824654 | 0.720118348350693 | 0.360059174175346 |
93 | 0.591743600582609 | 0.816512798834782 | 0.408256399417391 |
94 | 0.584382982570665 | 0.831234034858669 | 0.415617017429334 |
95 | 0.55750918874401 | 0.884981622511979 | 0.442490811255989 |
96 | 0.672784707345896 | 0.654430585308209 | 0.327215292654104 |
97 | 0.625864134645425 | 0.74827173070915 | 0.374135865354575 |
98 | 0.608424126433919 | 0.783151747132161 | 0.391575873566081 |
99 | 0.716619046722265 | 0.566761906555471 | 0.283380953277735 |
100 | 0.736482806890351 | 0.527034386219298 | 0.263517193109649 |
101 | 0.733769322724534 | 0.532461354550932 | 0.266230677275466 |
102 | 0.690288259847892 | 0.619423480304217 | 0.309711740152108 |
103 | 0.638451109249461 | 0.723097781501078 | 0.361548890750539 |
104 | 0.596472243529768 | 0.807055512940464 | 0.403527756470232 |
105 | 0.563928325969456 | 0.872143348061089 | 0.436071674030544 |
106 | 0.593739749573955 | 0.812520500852089 | 0.406260250426045 |
107 | 0.570716595764032 | 0.858566808471936 | 0.429283404235968 |
108 | 0.786474108093764 | 0.427051783812472 | 0.213525891906236 |
109 | 0.756637037477389 | 0.486725925045222 | 0.243362962522611 |
110 | 0.703575548219202 | 0.592848903561596 | 0.296424451780798 |
111 | 0.660368660405694 | 0.679262679188612 | 0.339631339594306 |
112 | 0.706389799624807 | 0.587220400750385 | 0.293610200375193 |
113 | 0.680338310267257 | 0.639323379465486 | 0.319661689732743 |
114 | 0.64459360366585 | 0.7108127926683 | 0.35540639633415 |
115 | 0.580063126810204 | 0.839873746379592 | 0.419936873189796 |
116 | 0.682473457843085 | 0.635053084313831 | 0.317526542156915 |
117 | 0.616527593096631 | 0.766944813806737 | 0.383472406903369 |
118 | 0.548320174459155 | 0.903359651081691 | 0.451679825540845 |
119 | 0.622410769375705 | 0.755178461248589 | 0.377589230624294 |
120 | 0.588521622253658 | 0.822956755492684 | 0.411478377746342 |
121 | 0.556139528375785 | 0.887720943248431 | 0.443860471624215 |
122 | 0.515493951500583 | 0.969012096998833 | 0.484506048499417 |
123 | 0.456098063626399 | 0.912196127252798 | 0.543901936373601 |
124 | 0.38696564334681 | 0.77393128669362 | 0.61303435665319 |
125 | 0.369536066781091 | 0.739072133562181 | 0.630463933218909 |
126 | 0.976454533573283 | 0.0470909328534332 | 0.0235454664267166 |
127 | 0.953694697539898 | 0.0926106049202033 | 0.0463053024601016 |
128 | 0.97389407453841 | 0.0522118509231794 | 0.0261059254615897 |
129 | 0.948549997363588 | 0.102900005272824 | 0.0514500026364122 |
130 | 0.983706389617159 | 0.0325872207656815 | 0.0162936103828408 |
131 | 0.99198072629093 | 0.01603854741814 | 0.00801927370907001 |
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 | 3 | 0.0280373831775701 | OK |
10% type I error level | 5 | 0.0467289719626168 | OK |