Multiple Linear Regression - Estimated Regression Equation |
Popularity[t] = -1.40033179694982 -0.0601894895057666Happiness[t] + 0.0719081107769415Belonging[t] -0.0399931531986961Belonging_alternative[t] -0.0760945554836357Depression[t] + 0.0941357682157754Weighted_popularity[t] + 0.0838784648670405Parental_criticism[t] + 0.118163788663958Finding_Friends[t] + 0.23002915116189Knowing_People[t] + 0.344271299678482Perceived_Liked[t] + 0.522587758027872Celebrity[t] -0.0063985411849013t + 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) | -1.40033179694982 | 2.56448 | -0.546 | 0.585877 | 0.292939 |
Happiness | -0.0601894895057666 | 0.085851 | -0.7011 | 0.484374 | 0.242187 |
Belonging | 0.0719081107769415 | 0.051482 | 1.3968 | 0.164632 | 0.082316 |
Belonging_alternative | -0.0399931531986961 | 0.073107 | -0.5471 | 0.585191 | 0.292595 |
Depression | -0.0760945554836357 | 0.063844 | -1.1919 | 0.23527 | 0.117635 |
Weighted_popularity | 0.0941357682157754 | 0.0584 | 1.6119 | 0.109169 | 0.054585 |
Parental_criticism | 0.0838784648670405 | 0.065932 | 1.2722 | 0.205353 | 0.102677 |
Finding_Friends | 0.118163788663958 | 0.093894 | 1.2585 | 0.210256 | 0.105128 |
Knowing_People | 0.23002915116189 | 0.064589 | 3.5614 | 5e-04 | 0.00025 |
Perceived_Liked | 0.344271299678482 | 0.094193 | 3.655 | 0.00036 | 0.00018 |
Celebrity | 0.522587758027872 | 0.158855 | 3.2897 | 0.001261 | 0.00063 |
t | -0.0063985411849013 | 0.003744 | -1.7091 | 0.089591 | 0.044795 |
Multiple Linear Regression - Regression Statistics | |
Multiple R | 0.747479529845818 |
R-squared | 0.558725647538526 |
Adjusted R-squared | 0.52501719005883 |
F-TEST (value) | 16.5752362852874 |
F-TEST (DF numerator) | 11 |
F-TEST (DF denominator) | 144 |
p-value | 0 |
Multiple Linear Regression - Residual Statistics | |
Residual Standard Deviation | 2.02389408044419 |
Sum Squared Residuals | 589.84520383541 |
Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
1 | 15 | 13.1041188809076 | 1.89588111909235 |
2 | 12 | 9.37957223548965 | 2.62042776451035 |
3 | 15 | 13.6692829047351 | 1.33071709526493 |
4 | 12 | 12.1780196356576 | -0.178019635657624 |
5 | 14 | 13.6340663848125 | 0.365933615187537 |
6 | 8 | 9.12171124973132 | -1.12171124973132 |
7 | 11 | 12.1232135702656 | -1.12321357026557 |
8 | 15 | 8.35269535227077 | 6.64730464772923 |
9 | 4 | 6.33029989402402 | -2.33029989402402 |
10 | 13 | 10.609066681238 | 2.39093331876201 |
11 | 19 | 14.3804043758506 | 4.61959562414936 |
12 | 10 | 11.4488108912758 | -1.44881089127583 |
13 | 15 | 17.291412674971 | -2.29141267497099 |
14 | 6 | 13.1906313519517 | -7.1906313519517 |
15 | 7 | 12.1323718286991 | -5.13237182869911 |
16 | 14 | 13.526748814351 | 0.473251185649046 |
17 | 16 | 14.3203940197277 | 1.6796059802723 |
18 | 16 | 15.7798749483539 | 0.220125051646119 |
19 | 14 | 15.1842230800641 | -1.18422308006412 |
20 | 15 | 15.2061068182984 | -0.206106818298378 |
21 | 14 | 14.6590612639979 | -0.659061263997861 |
22 | 12 | 11.365027849543 | 0.634972150456989 |
23 | 9 | 9.07843878284137 | -0.0784387828413655 |
24 | 12 | 11.5645865588673 | 0.435413441132652 |
25 | 14 | 13.9043636743032 | 0.0956363256968042 |
26 | 12 | 12.0395860686947 | -0.0395860686946692 |
27 | 14 | 13.7449173963345 | 0.255082603665456 |
28 | 10 | 11.3237347453513 | -1.32373474535134 |
29 | 14 | 12.9587063725915 | 1.0412936274085 |
30 | 16 | 16.0209419101327 | -0.0209419101327276 |
31 | 10 | 8.830744427978 | 1.16925557202199 |
32 | 8 | 10.7103914354383 | -2.71039143543825 |
33 | 12 | 11.7448545892799 | 0.255145410720072 |
34 | 11 | 10.8912398290721 | 0.10876017092795 |
35 | 8 | 10.3166168319753 | -2.31661683197532 |
36 | 13 | 12.123788724638 | 0.876211275361968 |
37 | 11 | 10.0155668966914 | 0.984433103308588 |
38 | 12 | 9.78578488571004 | 2.21421511428996 |
39 | 16 | 15.2696303658561 | 0.730369634143929 |
40 | 16 | 12.9784721070762 | 3.02152789292375 |
41 | 13 | 13.8822688592405 | -0.882268859240485 |
42 | 14 | 15.2715261726568 | -1.27152617265676 |
43 | 5 | 5.55350869007311 | -0.553508690073111 |
44 | 14 | 13.3175077245915 | 0.682492275408456 |
45 | 13 | 9.03216589577066 | 3.96783410422934 |
46 | 16 | 15.4830206203974 | 0.516979379602637 |
47 | 14 | 14.6731379723986 | -0.673137972398647 |
48 | 15 | 14.2082259830187 | 0.791774016981327 |
49 | 15 | 13.3012294874653 | 1.69877051253468 |
50 | 11 | 12.1583384993798 | -1.15833849937976 |
51 | 15 | 13.6027018993587 | 1.39729810064131 |
52 | 16 | 12.6145287868068 | 3.38547121319317 |
53 | 13 | 13.3125508280339 | -0.312550828033872 |
54 | 11 | 13.6932708599582 | -2.69327085995817 |
55 | 12 | 13.8771452843589 | -1.87714528435891 |
56 | 12 | 11.5368928032068 | 0.46310719679322 |
57 | 10 | 13.3738483993187 | -3.37384839931873 |
58 | 8 | 9.03838872227876 | -1.03838872227876 |
59 | 9 | 9.60405812870065 | -0.60405812870065 |
60 | 12 | 12.0926494029421 | -0.0926494029421055 |
61 | 14 | 13.9481472148274 | 0.0518527851726419 |
62 | 12 | 13.0528342079952 | -1.05283420799521 |
63 | 11 | 11.0075014050402 | -0.00750140504019281 |
64 | 14 | 13.9094005521978 | 0.090599447802221 |
65 | 7 | 11.5459981683963 | -4.54599816839629 |
66 | 16 | 14.0447539727401 | 1.95524602725989 |
67 | 16 | 15.5371528714492 | 0.462847128550831 |
68 | 11 | 12.264760180326 | -1.26476018032602 |
69 | 16 | 15.3546121445055 | 0.645387855494543 |
70 | 13 | 14.4183599616621 | -1.41835996166212 |
71 | 11 | 10.8207328878061 | 0.17926711219394 |
72 | 13 | 12.8031760504 | 0.19682394960001 |
73 | 14 | 14.3362199694722 | -0.336219969472217 |
74 | 15 | 13.4861689395864 | 1.51383106041363 |
75 | 10 | 9.35965940722293 | 0.640340592777074 |
76 | 15 | 14.7244744198531 | 0.27552558014689 |
77 | 11 | 12.9958102339005 | -1.99581023390055 |
78 | 11 | 11.4024329141157 | -0.402432914115737 |
79 | 6 | 8.49918198128773 | -2.49918198128773 |
80 | 11 | 9.63233741840194 | 1.36766258159806 |
81 | 12 | 11.5566437019636 | 0.443356298036378 |
82 | 13 | 13.2091406540391 | -0.209140654039052 |
83 | 12 | 12.3210617317895 | -0.321061731789544 |
84 | 8 | 10.6490833407533 | -2.64908334075329 |
85 | 9 | 10.7349212539284 | -1.73492125392839 |
86 | 10 | 11.6467410654182 | -1.6467410654182 |
87 | 16 | 13.1158790701389 | 2.88412092986112 |
88 | 15 | 12.7652299159938 | 2.23477008400617 |
89 | 14 | 13.5696071875676 | 0.430392812432437 |
90 | 12 | 13.6433703651392 | -1.64337036513921 |
91 | 12 | 10.2682747618807 | 1.73172523811934 |
92 | 10 | 8.82033206271318 | 1.17966793728682 |
93 | 12 | 11.4263746133836 | 0.573625386616375 |
94 | 8 | 9.3413456607946 | -1.3413456607946 |
95 | 16 | 14.0520765069226 | 1.94792349307736 |
96 | 11 | 7.75087376463123 | 3.24912623536877 |
97 | 12 | 11.492274480577 | 0.507725519422964 |
98 | 9 | 10.2998349775947 | -1.29983497759473 |
99 | 14 | 11.3107199255873 | 2.6892800744127 |
100 | 15 | 14.4417914627296 | 0.558208537270422 |
101 | 8 | 10.7050914338505 | -2.70509143385053 |
102 | 12 | 12.2985131903579 | -0.298513190357941 |
103 | 10 | 10.4127573387016 | -0.41275733870163 |
104 | 16 | 14.7838902026429 | 1.21610979735713 |
105 | 17 | 14.2719966698276 | 2.72800333017243 |
106 | 8 | 10.0794170593795 | -2.07941705937949 |
107 | 9 | 10.5838716669163 | -1.58387166691634 |
108 | 8 | 11.3755467072374 | -3.37554670723741 |
109 | 11 | 12.3744237176035 | -1.37442371760347 |
110 | 16 | 15.2759600290629 | 0.724039970937074 |
111 | 13 | 13.4306727557511 | -0.430672755751127 |
112 | 5 | 7.71119025790908 | -2.71119025790908 |
113 | 15 | 12.7846787100066 | 2.21532128999338 |
114 | 15 | 13.940839216779 | 1.05916078322098 |
115 | 12 | 11.3972919071503 | 0.602708092849717 |
116 | 12 | 11.3956027799066 | 0.604397220093366 |
117 | 16 | 15.7234388724739 | 0.276561127526108 |
118 | 12 | 12.4369449584 | -0.436944958399992 |
119 | 10 | 11.6255542363726 | -1.62555423637263 |
120 | 12 | 10.5660991565575 | 1.43390084344252 |
121 | 4 | 6.22293211352812 | -2.22293211352812 |
122 | 11 | 12.9176944639492 | -1.91769446394925 |
123 | 16 | 14.678810116074 | 1.32118988392603 |
124 | 7 | 8.79712611731686 | -1.79712611731686 |
125 | 9 | 10.7125218131455 | -1.71252181314546 |
126 | 14 | 10.8281029013785 | 3.17189709862155 |
127 | 11 | 9.64537312488018 | 1.35462687511982 |
128 | 10 | 10.7811590578546 | -0.781159057854594 |
129 | 6 | 8.4773317134976 | -2.4773317134976 |
130 | 14 | 12.8023524491645 | 1.19764755083546 |
131 | 11 | 10.8201744273176 | 0.179825572682426 |
132 | 11 | 9.11860432423373 | 1.88139567576627 |
133 | 9 | 13.8648278690724 | -4.86482786907244 |
134 | 16 | 11.372357927454 | 4.62764207254599 |
135 | 7 | 8.44596341492408 | -1.44596341492408 |
136 | 8 | 8.78090798916262 | -0.780907989162621 |
137 | 10 | 9.90724711312378 | 0.0927528868762198 |
138 | 14 | 11.9107259183342 | 2.0892740816658 |
139 | 9 | 9.55187003377597 | -0.551870033775968 |
140 | 13 | 12.2440385058042 | 0.755961494195769 |
141 | 13 | 9.58402687019161 | 3.41597312980839 |
142 | 12 | 11.6521364140392 | 0.347863585960846 |
143 | 11 | 12.5351681163983 | -1.53516811639826 |
144 | 10 | 14.902001440007 | -4.90200144000699 |
145 | 12 | 11.9172044351705 | 0.0827955648294778 |
146 | 14 | 13.2419318675388 | 0.758068132461206 |
147 | 11 | 13.3186321462926 | -2.3186321462926 |
148 | 13 | 10.9918777612752 | 2.00812223872484 |
149 | 14 | 13.5428872367615 | 0.45711276323845 |
150 | 13 | 12.5641894932098 | 0.435810506790193 |
151 | 16 | 16.0433459968012 | -0.0433459968011492 |
152 | 13 | 12.1290136015778 | 0.870986398422214 |
153 | 12 | 11.1692656051966 | 0.830734394803353 |
154 | 9 | 9.09291427494277 | -0.0929142749427665 |
155 | 14 | 11.2577678270325 | 2.74223217296745 |
156 | 15 | 14.5279979189494 | 0.472002081050605 |
Goldfeld-Quandt test for Heteroskedasticity | |||
p-values | Alternative Hypothesis | ||
breakpoint index | greater | 2-sided | less |
15 | 0.933649257395567 | 0.132701485208867 | 0.0663507426044334 |
16 | 0.999930621874146 | 0.000138756251707922 | 6.9378125853961e-05 |
17 | 0.99982533042272 | 0.000349339154560418 | 0.000174669577280209 |
18 | 0.999578824249336 | 0.000842351501327172 | 0.000421175750663586 |
19 | 0.99944246296334 | 0.00111507407331862 | 0.000557537036659308 |
20 | 0.998941708262373 | 0.00211658347525391 | 0.00105829173762695 |
21 | 0.999034755321167 | 0.00193048935766503 | 0.000965244678832513 |
22 | 0.999567250471365 | 0.00086549905727098 | 0.00043274952863549 |
23 | 0.999157827831607 | 0.00168434433678614 | 0.00084217216839307 |
24 | 0.998445326001666 | 0.00310934799666861 | 0.0015546739983343 |
25 | 0.997235517460621 | 0.00552896507875733 | 0.00276448253937867 |
26 | 0.995267882314468 | 0.00946423537106506 | 0.00473211768553253 |
27 | 0.995942688768337 | 0.00811462246332688 | 0.00405731123166344 |
28 | 0.993516932421401 | 0.0129661351571972 | 0.00648306757859861 |
29 | 0.996582457718479 | 0.00683508456304209 | 0.00341754228152104 |
30 | 0.995217176268008 | 0.00956564746398338 | 0.00478282373199169 |
31 | 0.992921336992382 | 0.0141573260152366 | 0.0070786630076183 |
32 | 0.996284334548904 | 0.00743133090219153 | 0.00371566545109576 |
33 | 0.994330861757432 | 0.0113382764851356 | 0.00566913824256781 |
34 | 0.992277437072564 | 0.0154451258548713 | 0.00772256292743563 |
35 | 0.991279356100053 | 0.0174412877998933 | 0.00872064389994665 |
36 | 0.987757815396007 | 0.0244843692079856 | 0.0122421846039928 |
37 | 0.984893642637731 | 0.0302127147245371 | 0.0151063573622685 |
38 | 0.986023059249697 | 0.0279538815006069 | 0.0139769407503034 |
39 | 0.985261760143423 | 0.0294764797131533 | 0.0147382398565766 |
40 | 0.989836355867045 | 0.0203272882659101 | 0.010163644132955 |
41 | 0.98602298353575 | 0.0279540329285007 | 0.0139770164642504 |
42 | 0.98077854240216 | 0.0384429151956804 | 0.0192214575978402 |
43 | 0.973489036583066 | 0.0530219268338684 | 0.0265109634169342 |
44 | 0.96769041426965 | 0.0646191714607014 | 0.0323095857303507 |
45 | 0.991292554964444 | 0.0174148900711114 | 0.00870744503555572 |
46 | 0.988013678177197 | 0.0239726436456057 | 0.0119863218228028 |
47 | 0.983986894232742 | 0.0320262115345168 | 0.0160131057672584 |
48 | 0.979021719539053 | 0.0419565609218938 | 0.0209782804609469 |
49 | 0.976520832207837 | 0.0469583355843259 | 0.023479167792163 |
50 | 0.972010259031865 | 0.0559794819362692 | 0.0279897409681346 |
51 | 0.969431950633464 | 0.0611360987330717 | 0.0305680493665358 |
52 | 0.982138988658216 | 0.0357220226835679 | 0.0178610113417839 |
53 | 0.976067376203782 | 0.047865247592435 | 0.0239326237962175 |
54 | 0.976737935371232 | 0.0465241292575351 | 0.0232620646287676 |
55 | 0.973376010621936 | 0.0532479787561288 | 0.0266239893780644 |
56 | 0.966385646299197 | 0.0672287074016061 | 0.0336143537008031 |
57 | 0.975072812968049 | 0.0498543740639027 | 0.0249271870319514 |
58 | 0.968604685384795 | 0.0627906292304105 | 0.0313953146152052 |
59 | 0.958784031714413 | 0.0824319365711745 | 0.0412159682855873 |
60 | 0.946744710982143 | 0.106510578035714 | 0.0532552890178571 |
61 | 0.93284309119605 | 0.1343138176079 | 0.06715690880395 |
62 | 0.919899115767244 | 0.160201768465511 | 0.0801008842327557 |
63 | 0.900251949790252 | 0.199496100419496 | 0.099748050209748 |
64 | 0.884622774641363 | 0.230754450717275 | 0.115377225358637 |
65 | 0.936158227263074 | 0.127683545473852 | 0.0638417727369259 |
66 | 0.941302434161088 | 0.117395131677823 | 0.0586975658389116 |
67 | 0.928161402578554 | 0.143677194842892 | 0.0718385974214462 |
68 | 0.915566004464005 | 0.16886799107199 | 0.0844339955359948 |
69 | 0.898446226792583 | 0.203107546414835 | 0.101553773207417 |
70 | 0.885460236405788 | 0.229079527188424 | 0.114539763594212 |
71 | 0.862778079944178 | 0.274443840111644 | 0.137221920055822 |
72 | 0.83686833746627 | 0.326263325067459 | 0.163131662533729 |
73 | 0.820712211572718 | 0.358575576854564 | 0.179287788427282 |
74 | 0.815138334240323 | 0.369723331519353 | 0.184861665759677 |
75 | 0.790247551034458 | 0.419504897931083 | 0.209752448965542 |
76 | 0.756152108081877 | 0.487695783836246 | 0.243847891918123 |
77 | 0.746658574939359 | 0.506682850121282 | 0.253341425060641 |
78 | 0.705733685052797 | 0.588532629894406 | 0.294266314947203 |
79 | 0.711337750520456 | 0.577324498959089 | 0.288662249479544 |
80 | 0.697204070710098 | 0.605591858579804 | 0.302795929289902 |
81 | 0.661898688272875 | 0.676202623454249 | 0.338101311727125 |
82 | 0.619964852095303 | 0.760070295809393 | 0.380035147904697 |
83 | 0.57265445659414 | 0.85469108681172 | 0.42734554340586 |
84 | 0.581423658877747 | 0.837152682244506 | 0.418576341122253 |
85 | 0.563090203733515 | 0.87381959253297 | 0.436909796266485 |
86 | 0.539508849729025 | 0.92098230054195 | 0.460491150270975 |
87 | 0.591790927840139 | 0.816418144319722 | 0.408209072159861 |
88 | 0.620743725162608 | 0.758512549674783 | 0.379256274837392 |
89 | 0.585861475621068 | 0.828277048757864 | 0.414138524378932 |
90 | 0.56991682606862 | 0.86016634786276 | 0.43008317393138 |
91 | 0.558209635856615 | 0.88358072828677 | 0.441790364143385 |
92 | 0.526465841611337 | 0.947068316777325 | 0.473534158388663 |
93 | 0.48294747544257 | 0.96589495088514 | 0.51705252455743 |
94 | 0.465465526368108 | 0.930931052736215 | 0.534534473631893 |
95 | 0.479307314937569 | 0.958614629875137 | 0.520692685062431 |
96 | 0.619056654163524 | 0.761886691672953 | 0.380943345836476 |
97 | 0.573905600368762 | 0.852188799262477 | 0.426094399631238 |
98 | 0.537911331018491 | 0.924177337963019 | 0.462088668981509 |
99 | 0.604984796249612 | 0.790030407500777 | 0.395015203750388 |
100 | 0.570591213403751 | 0.858817573192498 | 0.429408786596249 |
101 | 0.590821822007805 | 0.818356355984391 | 0.409178177992195 |
102 | 0.544423758730519 | 0.911152482538961 | 0.455576241269481 |
103 | 0.49421230885123 | 0.98842461770246 | 0.50578769114877 |
104 | 0.500220397650356 | 0.999559204699288 | 0.499779602349644 |
105 | 0.551934366440813 | 0.896131267118373 | 0.448065633559187 |
106 | 0.554892150976265 | 0.89021569804747 | 0.445107849023735 |
107 | 0.511942038192078 | 0.976115923615845 | 0.488057961807922 |
108 | 0.60972456271276 | 0.78055087457448 | 0.39027543728724 |
109 | 0.593066740902704 | 0.813866518194592 | 0.406933259097296 |
110 | 0.550577261245747 | 0.898845477508506 | 0.449422738754253 |
111 | 0.494826599668514 | 0.989653199337027 | 0.505173400331486 |
112 | 0.616809343277845 | 0.76638131344431 | 0.383190656722155 |
113 | 0.626154390803579 | 0.747691218392841 | 0.373845609196421 |
114 | 0.615235488097311 | 0.769529023805379 | 0.384764511902689 |
115 | 0.559987629609117 | 0.880024740781765 | 0.440012370390883 |
116 | 0.521138877655043 | 0.957722244689913 | 0.478861122344957 |
117 | 0.477016181848517 | 0.954032363697034 | 0.522983818151483 |
118 | 0.463883416582803 | 0.927766833165606 | 0.536116583417197 |
119 | 0.494739372148821 | 0.989478744297641 | 0.505260627851179 |
120 | 0.44153085835672 | 0.88306171671344 | 0.55846914164328 |
121 | 0.413482952204302 | 0.826965904408604 | 0.586517047795698 |
122 | 0.368587832917052 | 0.737175665834104 | 0.631412167082948 |
123 | 0.426064031980694 | 0.852128063961388 | 0.573935968019306 |
124 | 0.387390103702172 | 0.774780207404344 | 0.612609896297828 |
125 | 0.415133168427088 | 0.830266336854177 | 0.584866831572912 |
126 | 0.444862550468139 | 0.889725100936277 | 0.555137449531861 |
127 | 0.432032123037266 | 0.864064246074531 | 0.567967876962734 |
128 | 0.361613594633677 | 0.723227189267354 | 0.638386405366323 |
129 | 0.598066118848159 | 0.803867762303682 | 0.401933881151841 |
130 | 0.738468831650332 | 0.523062336699335 | 0.261531168349668 |
131 | 0.741820011049845 | 0.51635997790031 | 0.258179988950155 |
132 | 0.789267218156796 | 0.421465563686408 | 0.210732781843204 |
133 | 0.762622726087926 | 0.474754547824149 | 0.237377273912074 |
134 | 0.808958022446945 | 0.38208395510611 | 0.191041977553055 |
135 | 0.732637529174615 | 0.53472494165077 | 0.267362470825385 |
136 | 0.668174881262815 | 0.663650237474369 | 0.331825118737185 |
137 | 0.758245179336004 | 0.483509641327992 | 0.241754820663996 |
138 | 0.704237223954689 | 0.591525552090622 | 0.295762776045311 |
139 | 0.646950914700122 | 0.706098170599756 | 0.353049085299878 |
140 | 0.503093950827841 | 0.993812098344318 | 0.496906049172159 |
141 | 0.402127666541331 | 0.804255333082663 | 0.597872333458669 |
Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
Description | # significant tests | % significant tests | OK/NOK |
1% type I error level | 15 | 0.118110236220472 | NOK |
5% type I error level | 36 | 0.283464566929134 | NOK |
10% type I error level | 44 | 0.346456692913386 | NOK |