Multiple Linear Regression - Estimated Regression Equation |
Popularity[t] = -1.16892826150712 -0.0807306287138021Depression[t] + 0.0453253788739521Belonging[t] + 0.0964153521063372Weighted_popularity[t] + 0.0772765190141471Parental_criticism[t] -0.0572765637003982Happiness[t] + 0.117596535487944FindingFriends[t] + 0.227711407897117KnowingPeople[t] + 0.34708334464486Liked[t] + 0.520075961070442Celebrity[t] -0.00640747869671336t + 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) | -1.16892826150712 | 2.523234 | -0.4633 | 0.643868 | 0.321934 |
Depression | -0.0807306287138021 | 0.063126 | -1.2789 | 0.202984 | 0.101492 |
Belonging | 0.0453253788739521 | 0.016962 | 2.6722 | 0.008399 | 0.0042 |
Weighted_popularity | 0.0964153521063372 | 0.05811 | 1.6592 | 0.09924 | 0.04962 |
Parental_criticism | 0.0772765190141471 | 0.064661 | 1.1951 | 0.233999 | 0.117 |
Happiness | -0.0572765637003982 | 0.085478 | -0.6701 | 0.503876 | 0.251938 |
FindingFriends | 0.117596535487944 | 0.093661 | 1.2555 | 0.211299 | 0.10565 |
KnowingPeople | 0.227711407897117 | 0.064294 | 3.5417 | 0.000535 | 0.000268 |
Liked | 0.34708334464486 | 0.093825 | 3.6993 | 0.000306 | 0.000153 |
Celebrity | 0.520075961070442 | 0.158405 | 3.2832 | 0.001286 | 0.000643 |
t | -0.00640747869671336 | 0.003735 | -1.7156 | 0.088366 | 0.044183 |
Multiple Linear Regression - Regression Statistics | |
Multiple R | 0.746865837404828 |
R-squared | 0.557808579082415 |
Adjusted R-squared | 0.527312619019133 |
F-TEST (value) | 18.2912286717622 |
F-TEST (DF numerator) | 10 |
F-TEST (DF denominator) | 145 |
p-value | 0 |
Multiple Linear Regression - Residual Statistics | |
Residual Standard Deviation | 2.01899776486645 |
Sum Squared Residuals | 591.071036307677 |
Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
1 | 15 | 13.0980845589734 | 1.90191544102664 |
2 | 12 | 9.33461110778379 | 2.66538889221621 |
3 | 15 | 13.651049054911 | 1.34895094508902 |
4 | 12 | 12.1896344205315 | -0.189634420531492 |
5 | 14 | 13.6367248402493 | 0.363275159750659 |
6 | 8 | 9.09557557624667 | -1.09557557624667 |
7 | 11 | 12.1115572596557 | -1.11155725965572 |
8 | 15 | 8.38228593856977 | 6.61771406143024 |
9 | 4 | 6.33579814388996 | -2.33579814388996 |
10 | 13 | 10.6532024118901 | 2.34679758810994 |
11 | 19 | 14.4193970585016 | 4.58060294149841 |
12 | 10 | 11.3894752132707 | -1.38947521327073 |
13 | 15 | 17.2926358827324 | -2.29263588273236 |
14 | 6 | 13.187466644766 | -7.18746664476603 |
15 | 7 | 12.1231023366937 | -5.12310233669369 |
16 | 14 | 13.4732227024492 | 0.526777297550777 |
17 | 16 | 14.3670172229621 | 1.6329827770379 |
18 | 16 | 15.8499823793242 | 0.150017620675771 |
19 | 14 | 15.2182109966908 | -1.21821099669079 |
20 | 15 | 15.2172057096217 | -0.21720570962175 |
21 | 14 | 14.5468136734371 | -0.546813673437087 |
22 | 12 | 11.2579482302368 | 0.742051769763176 |
23 | 9 | 8.98851374333351 | 0.0114862566664852 |
24 | 12 | 11.5796185686613 | 0.420381431338652 |
25 | 14 | 13.909534855217 | 0.0904651447829506 |
26 | 12 | 12.0679306250819 | -0.0679306250818924 |
27 | 14 | 13.6645199495633 | 0.335480050436709 |
28 | 10 | 11.2303635028932 | -1.23036350289317 |
29 | 14 | 12.9603759144025 | 1.0396240855975 |
30 | 16 | 16.038856051892 | -0.0388560518920175 |
31 | 10 | 8.92206925973075 | 1.07793074026925 |
32 | 8 | 10.7539999726585 | -2.75399997265848 |
33 | 12 | 11.6968106073738 | 0.30318939262623 |
34 | 11 | 11.0749796177072 | -0.0749796177071755 |
35 | 8 | 10.3105726476984 | -2.31057264769841 |
36 | 13 | 12.2135908173589 | 0.786409182641092 |
37 | 11 | 10.0103046716484 | 0.989695328351577 |
38 | 12 | 9.8322784133195 | 2.1677215866805 |
39 | 16 | 15.2178558295842 | 0.782144170415826 |
40 | 16 | 13.0153748398144 | 2.98462516018556 |
41 | 13 | 13.9167692548379 | -0.916769254837923 |
42 | 14 | 15.3107122591626 | -1.31071225916263 |
43 | 5 | 5.59431254652437 | -0.594312546524371 |
44 | 14 | 13.2795892107624 | 0.720410789237553 |
45 | 13 | 8.95837440464955 | 4.04162559535045 |
46 | 16 | 15.4360007531475 | 0.563999246852536 |
47 | 14 | 14.6266103305611 | -0.626610330561148 |
48 | 15 | 14.1537475704718 | 0.846252429528169 |
49 | 15 | 13.3351955629063 | 1.66480443709368 |
50 | 11 | 12.2372811627391 | -1.23728116273909 |
51 | 15 | 13.6847020933967 | 1.31529790660325 |
52 | 16 | 12.6660247146445 | 3.33397528535547 |
53 | 13 | 13.3258405899626 | -0.325840589962623 |
54 | 11 | 13.7029888671069 | -2.70298886710691 |
55 | 12 | 13.9250133183881 | -1.92501331838815 |
56 | 12 | 11.609823336916 | 0.390176663083983 |
57 | 10 | 13.451342229255 | -3.45134222925503 |
58 | 8 | 9.04261103534925 | -1.04261103534925 |
59 | 9 | 9.69310574143097 | -0.693105741430971 |
60 | 12 | 12.045387994039 | -0.0453879940389717 |
61 | 14 | 13.910637057228 | 0.0893629427720447 |
62 | 12 | 13.0083713397218 | -1.00837133972183 |
63 | 11 | 10.9769221353135 | 0.0230778646865255 |
64 | 14 | 13.4987255248902 | 0.501274475109799 |
65 | 7 | 11.6308647176515 | -4.63086471765147 |
66 | 16 | 13.9993857476801 | 2.00061425231988 |
67 | 16 | 15.4900557409302 | 0.509944259069827 |
68 | 11 | 12.2982409395182 | -1.29824093951819 |
69 | 16 | 15.287028491923 | 0.712971508076961 |
70 | 13 | 14.4142657678109 | -1.4142657678109 |
71 | 11 | 10.9115304130367 | 0.0884695869632988 |
72 | 13 | 12.7985460057734 | 0.201453994226599 |
73 | 14 | 14.2807110397621 | -0.280711039762121 |
74 | 15 | 13.4844566786343 | 1.51554332136573 |
75 | 10 | 9.29277056064779 | 0.707229439352215 |
76 | 15 | 14.6465623986928 | 0.353437601307165 |
77 | 11 | 12.9527797832399 | -1.95277978323991 |
78 | 11 | 11.4043554773293 | -0.40435547732932 |
79 | 6 | 8.45757353417261 | -2.45757353417261 |
80 | 11 | 9.64537491771139 | 1.35462508228861 |
81 | 12 | 11.6342852343025 | 0.365714765697493 |
82 | 13 | 13.2443154760362 | -0.244315476036221 |
83 | 12 | 12.6581126741542 | -0.658112674154231 |
84 | 8 | 10.8160962310738 | -2.81609623107383 |
85 | 9 | 10.7024135722567 | -1.70241357225673 |
86 | 10 | 11.6212793989087 | -1.62127939890874 |
87 | 16 | 13.2429145535025 | 2.75708544649748 |
88 | 15 | 12.7826600997677 | 2.21733990023233 |
89 | 14 | 13.5253803529906 | 0.474619647009403 |
90 | 12 | 13.5699261701497 | -1.56992617014973 |
91 | 12 | 10.2345994239918 | 1.76540057600822 |
92 | 10 | 8.70936337421506 | 1.29063662578494 |
93 | 12 | 11.4454672608604 | 0.554532739139586 |
94 | 8 | 9.29247098996122 | -1.29247098996122 |
95 | 16 | 14.0357440822437 | 1.96425591775626 |
96 | 11 | 7.72297792212706 | 3.27702207787294 |
97 | 12 | 11.4421523820269 | 0.557847617973136 |
98 | 9 | 10.3074555378289 | -1.30745553782888 |
99 | 14 | 11.4472873308141 | 2.55271266918589 |
100 | 15 | 14.3144549553595 | 0.685545044640456 |
101 | 8 | 10.5692779610823 | -2.56927796108232 |
102 | 12 | 12.373175300765 | -0.373175300764953 |
103 | 10 | 10.4270650991506 | -0.42706509915059 |
104 | 16 | 14.7883128061137 | 1.21168719388628 |
105 | 17 | 14.2054764572608 | 2.79452354273925 |
106 | 8 | 10.0343820261573 | -2.03438202615729 |
107 | 9 | 10.7078936298132 | -1.70789362981318 |
108 | 8 | 11.3302451431894 | -3.33024514318938 |
109 | 11 | 12.3481588429061 | -1.34815884290607 |
110 | 16 | 15.3080417520942 | 0.69195824790584 |
111 | 13 | 13.4300882747453 | -0.430088274745342 |
112 | 5 | 7.92422944710671 | -2.92422944710671 |
113 | 15 | 12.763995451971 | 2.23600454802897 |
114 | 15 | 13.8647885275956 | 1.13521147240442 |
115 | 12 | 11.4004404714328 | 0.599559528567214 |
116 | 12 | 11.4507509945712 | 0.549249005428757 |
117 | 16 | 15.7306935649448 | 0.269306435055161 |
118 | 12 | 12.4165342860829 | -0.416534286082865 |
119 | 10 | 11.7091963037699 | -1.70919630376992 |
120 | 12 | 10.6646637160973 | 1.33533628390266 |
121 | 4 | 6.22150795113951 | -2.22150795113951 |
122 | 11 | 12.9228174382834 | -1.92281743828336 |
123 | 16 | 14.6557390563799 | 1.34426094362011 |
124 | 7 | 8.76472456379762 | -1.76472456379762 |
125 | 9 | 10.71615589177 | -1.71615589177001 |
126 | 14 | 10.7909293947773 | 3.2090706052227 |
127 | 11 | 9.67850783494508 | 1.32149216505492 |
128 | 10 | 10.8792289215278 | -0.879228921527816 |
129 | 6 | 8.48388602635172 | -2.48388602635172 |
130 | 14 | 12.802020537476 | 1.19797946252395 |
131 | 11 | 10.8668887147792 | 0.133111285220822 |
132 | 11 | 9.15272311030956 | 1.84727688969044 |
133 | 9 | 13.8708137524157 | -4.8708137524157 |
134 | 16 | 11.3572487923575 | 4.64275120764247 |
135 | 7 | 7.81813032982012 | -0.818130329820121 |
136 | 8 | 8.78068323292848 | -0.78068323292848 |
137 | 10 | 9.86739005992512 | 0.132609940074876 |
138 | 14 | 11.9469551594703 | 2.05304484052966 |
139 | 9 | 9.60739523239862 | -0.60739523239862 |
140 | 13 | 12.2984550955551 | 0.701544904444911 |
141 | 13 | 9.52203060730148 | 3.47796939269852 |
142 | 12 | 11.7700311004715 | 0.229968899528461 |
143 | 11 | 12.56425405171 | -1.56425405170999 |
144 | 10 | 14.9395072859872 | -4.93950728598721 |
145 | 12 | 11.9287747754756 | 0.0712252245243581 |
146 | 14 | 13.2838800909699 | 0.71611990903015 |
147 | 11 | 13.3075729058824 | -2.30757290588238 |
148 | 13 | 10.9874302433392 | 2.01256975666079 |
149 | 14 | 13.5223999685667 | 0.477600031433273 |
150 | 13 | 12.5557308965328 | 0.444269103467224 |
151 | 16 | 15.9668113575049 | 0.0331886424950528 |
152 | 13 | 12.0786978209033 | 0.921302179096672 |
153 | 12 | 11.256323242947 | 0.743676757053048 |
154 | 9 | 9.15504321665876 | -0.155043216658764 |
155 | 14 | 11.2037893392544 | 2.7962106607456 |
156 | 15 | 14.5756124214192 | 0.424387578580834 |
Goldfeld-Quandt test for Heteroskedasticity | |||
p-values | Alternative Hypothesis | ||
breakpoint index | greater | 2-sided | less |
14 | 0.999749261256894 | 0.000501477486212082 | 0.000250738743106041 |
15 | 0.99989713684738 | 0.00020572630524052 | 0.00010286315262026 |
16 | 0.999895147707139 | 0.000209704585722791 | 0.000104852292861396 |
17 | 0.999831570022249 | 0.000336859955502813 | 0.000168429977751407 |
18 | 0.999879645502272 | 0.000240708995456489 | 0.000120354497728244 |
19 | 0.999737854529744 | 0.000524290940512481 | 0.00026214547025624 |
20 | 0.999565437028515 | 0.00086912594296917 | 0.000434562971484585 |
21 | 0.99913746035658 | 0.00172507928683947 | 0.000862539643419733 |
22 | 0.99945292409578 | 0.0010941518084406 | 0.000547075904220301 |
23 | 0.999208320382809 | 0.00158335923438185 | 0.000791679617190925 |
24 | 0.998583016213701 | 0.00283396757259791 | 0.00141698378629896 |
25 | 0.997645021888355 | 0.0047099562232894 | 0.0023549781116447 |
26 | 0.996094335257995 | 0.00781132948401086 | 0.00390566474200543 |
27 | 0.99532081257678 | 0.0093583748464394 | 0.0046791874232197 |
28 | 0.992611219526769 | 0.0147775609464626 | 0.00738878047323132 |
29 | 0.995435437406731 | 0.00912912518653741 | 0.0045645625932687 |
30 | 0.994247663756647 | 0.0115046724867066 | 0.0057523362433533 |
31 | 0.991496442152955 | 0.0170071156940903 | 0.00850355784704514 |
32 | 0.995431158992026 | 0.00913768201594855 | 0.00456884100797427 |
33 | 0.993208901775156 | 0.0135821964496872 | 0.00679109822484358 |
34 | 0.989941891798939 | 0.0201162164021219 | 0.0100581082010609 |
35 | 0.988535632976139 | 0.0229287340477226 | 0.0114643670238613 |
36 | 0.983902334680705 | 0.0321953306385892 | 0.0160976653192946 |
37 | 0.980597121472098 | 0.0388057570558038 | 0.0194028785279019 |
38 | 0.982481820415247 | 0.0350363591695061 | 0.017518179584753 |
39 | 0.981212062109044 | 0.0375758757819113 | 0.0187879378909557 |
40 | 0.986739698724478 | 0.0265206025510432 | 0.0132603012755216 |
41 | 0.982369664659814 | 0.0352606706803719 | 0.0176303353401859 |
42 | 0.97620518482119 | 0.04758963035762 | 0.02379481517881 |
43 | 0.967815068479323 | 0.0643698630413536 | 0.0321849315206768 |
44 | 0.960266750527368 | 0.079466498945264 | 0.039733249472632 |
45 | 0.98920352982355 | 0.0215929403529001 | 0.01079647017645 |
46 | 0.985482740769604 | 0.029034518460793 | 0.0145172592303965 |
47 | 0.980581356335585 | 0.0388372873288309 | 0.0194186436644155 |
48 | 0.975122975524426 | 0.0497540489511477 | 0.0248770244755738 |
49 | 0.972052944540958 | 0.0558941109180839 | 0.0279470554590419 |
50 | 0.967509099819537 | 0.0649818003609251 | 0.0324909001804625 |
51 | 0.963585532875297 | 0.072828934249406 | 0.036414467124703 |
52 | 0.977541989832513 | 0.0449160203349737 | 0.0224580101674869 |
53 | 0.970240788467859 | 0.0595184230642828 | 0.0297592115321414 |
54 | 0.971280164490389 | 0.0574396710192229 | 0.0287198355096115 |
55 | 0.967915695553621 | 0.0641686088927588 | 0.0320843044463794 |
56 | 0.959308986251442 | 0.0813820274971165 | 0.0406910137485582 |
57 | 0.971841589791808 | 0.0563168204163831 | 0.0281584102081915 |
58 | 0.964518270499693 | 0.0709634590006143 | 0.0354817295003071 |
59 | 0.954098476272736 | 0.0918030474545273 | 0.0459015237272636 |
60 | 0.941539606602083 | 0.116920786795834 | 0.0584603933979171 |
61 | 0.927251226628062 | 0.145497546743876 | 0.072748773371938 |
62 | 0.912433476506909 | 0.175133046986182 | 0.087566523493091 |
63 | 0.891893796740901 | 0.216212406518197 | 0.108106203259099 |
64 | 0.876186377987996 | 0.247627244024008 | 0.123813622012004 |
65 | 0.9350949811981 | 0.1298100376038 | 0.0649050188019 |
66 | 0.941443412075438 | 0.117113175849123 | 0.0585565879245615 |
67 | 0.92840195362912 | 0.14319609274176 | 0.0715980463708799 |
68 | 0.916398728296698 | 0.167202543406604 | 0.0836012717033019 |
69 | 0.900010507892478 | 0.199978984215044 | 0.0999894921075221 |
70 | 0.887382152220274 | 0.225235695559452 | 0.112617847779726 |
71 | 0.864926657720126 | 0.270146684559748 | 0.135073342279874 |
72 | 0.839251605670032 | 0.321496788659935 | 0.160748394329968 |
73 | 0.823824626039971 | 0.352350747920057 | 0.176175373960029 |
74 | 0.817228864291542 | 0.365542271416915 | 0.182771135708458 |
75 | 0.793604852935953 | 0.412790294128094 | 0.206395147064047 |
76 | 0.760977110085849 | 0.478045779828301 | 0.239022889914151 |
77 | 0.751013752577392 | 0.497972494845216 | 0.248986247422608 |
78 | 0.710736279267143 | 0.578527441465715 | 0.289263720732857 |
79 | 0.715234139465913 | 0.569531721068174 | 0.284765860534087 |
80 | 0.701133365086989 | 0.597733269826023 | 0.298866634913011 |
81 | 0.664457148929157 | 0.671085702141685 | 0.335542851070843 |
82 | 0.621793567250475 | 0.756412865499049 | 0.378206432749525 |
83 | 0.574654462548001 | 0.850691074903997 | 0.425345537451999 |
84 | 0.596875340109213 | 0.806249319781573 | 0.403124659890787 |
85 | 0.578059906190994 | 0.843880187618013 | 0.421940093809006 |
86 | 0.554541979181378 | 0.890916041637243 | 0.445458020818622 |
87 | 0.597158260300979 | 0.805683479398042 | 0.402841739699021 |
88 | 0.625231013567802 | 0.749537972864396 | 0.374768986432198 |
89 | 0.591222178954448 | 0.817555642091104 | 0.408777821045552 |
90 | 0.571895448856189 | 0.856209102287622 | 0.428104551143811 |
91 | 0.564112156439351 | 0.871775687121298 | 0.435887843560649 |
92 | 0.537258931070455 | 0.92548213785909 | 0.462741068929545 |
93 | 0.493864503218887 | 0.987729006437774 | 0.506135496781113 |
94 | 0.475131578945245 | 0.95026315789049 | 0.524868421054755 |
95 | 0.490170899331651 | 0.980341798663302 | 0.509829100668349 |
96 | 0.6343305385041 | 0.7313389229918 | 0.3656694614959 |
97 | 0.59080546835735 | 0.8183890632853 | 0.40919453164265 |
98 | 0.555719365408635 | 0.888561269182731 | 0.444280634591365 |
99 | 0.613568629414604 | 0.772862741170792 | 0.386431370585396 |
100 | 0.584549558090764 | 0.830900883818472 | 0.415450441909236 |
101 | 0.598361243831265 | 0.803277512337469 | 0.401638756168735 |
102 | 0.551468978123976 | 0.897062043752047 | 0.448531021876024 |
103 | 0.501431790816359 | 0.997136418367282 | 0.498568209183641 |
104 | 0.50909542766829 | 0.98180914466342 | 0.49090457233171 |
105 | 0.566618183517896 | 0.866763632964208 | 0.433381816482104 |
106 | 0.566941290670047 | 0.866117418659907 | 0.433058709329953 |
107 | 0.526553304467624 | 0.946893391064751 | 0.473446695532376 |
108 | 0.611330904665018 | 0.777338190669965 | 0.388669095334982 |
109 | 0.59241920652089 | 0.81516158695822 | 0.40758079347911 |
110 | 0.549306197284816 | 0.901387605430368 | 0.450693802715184 |
111 | 0.493986853568009 | 0.987973707136018 | 0.506013146431991 |
112 | 0.645166851973817 | 0.709666296052366 | 0.354833148026183 |
113 | 0.659509930975526 | 0.680980138048948 | 0.340490069024474 |
114 | 0.651828986166506 | 0.696342027666988 | 0.348171013833494 |
115 | 0.59898648599867 | 0.802027028002659 | 0.40101351400133 |
116 | 0.561466366592206 | 0.877067266815589 | 0.438533633407794 |
117 | 0.518482211969976 | 0.963035576060047 | 0.481517788030024 |
118 | 0.505786421165175 | 0.98842715766965 | 0.494213578834825 |
119 | 0.526586649171405 | 0.946826701657189 | 0.473413350828595 |
120 | 0.471928099689009 | 0.943856199378018 | 0.528071900310991 |
121 | 0.44665603984859 | 0.89331207969718 | 0.55334396015141 |
122 | 0.406297163200945 | 0.812594326401891 | 0.593702836799055 |
123 | 0.451333397496003 | 0.902666794992006 | 0.548666602503997 |
124 | 0.410943106769868 | 0.821886213539736 | 0.589056893230132 |
125 | 0.444516545447413 | 0.889033090894827 | 0.555483454552587 |
126 | 0.464048662979817 | 0.928097325959634 | 0.535951337020183 |
127 | 0.452229736055376 | 0.904459472110752 | 0.547770263944624 |
128 | 0.382619801158781 | 0.765239602317562 | 0.617380198841219 |
129 | 0.606933859317905 | 0.786132281364191 | 0.393066140682095 |
130 | 0.716758395021369 | 0.566483209957261 | 0.283241604978631 |
131 | 0.771268256887777 | 0.457463486224446 | 0.228731743112223 |
132 | 0.829064516229621 | 0.341870967540758 | 0.170935483770379 |
133 | 0.806886769917046 | 0.386226460165908 | 0.193113230082954 |
134 | 0.862086889347524 | 0.275826221304951 | 0.137913110652476 |
135 | 0.802924978724534 | 0.394150042550932 | 0.197075021275466 |
136 | 0.747757640293216 | 0.504484719413568 | 0.252242359706784 |
137 | 0.807384602337044 | 0.385230795325911 | 0.192615397662956 |
138 | 0.74855138807117 | 0.502897223857661 | 0.25144861192883 |
139 | 0.64412932912165 | 0.7117413417567 | 0.35587067087835 |
140 | 0.513651020773495 | 0.972697958453009 | 0.486348979226505 |
141 | 0.481893920794528 | 0.963787841589055 | 0.518106079205472 |
142 | 0.336423223892389 | 0.672846447784778 | 0.663576776107611 |
Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
Description | # significant tests | % significant tests | OK/NOK |
1% type I error level | 16 | 0.124031007751938 | NOK |
5% type I error level | 34 | 0.263565891472868 | NOK |
10% type I error level | 46 | 0.356589147286822 | NOK |