Multiple Linear Regression - Estimated Regression Equation |
Popularity[t] = + 1.59055007677943 + 0.142714990424374`Pop*geslacht`[t] + 0.213531241972043KnowingPeople[t] + 0.25873921064204Liked[t] + 0.591645271703441Celebrity[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) | 1.59055007677943 | 1.11561 | 1.4257 | 0.156421 | 0.078211 |
`Pop*geslacht` | 0.142714990424374 | 0.033025 | 4.3215 | 3.1e-05 | 1.6e-05 |
KnowingPeople | 0.213531241972043 | 0.06396 | 3.3385 | 0.001108 | 0.000554 |
Liked | 0.25873921064204 | 0.099637 | 2.5968 | 0.010528 | 0.005264 |
Celebrity | 0.591645271703441 | 0.153945 | 3.8432 | 0.000192 | 9.6e-05 |
Multiple Linear Regression - Regression Statistics | |
Multiple R | 0.730462854365973 |
R-squared | 0.533575981608485 |
Adjusted R-squared | 0.518768869913516 |
F-TEST (value) | 36.035115598526 |
F-TEST (DF numerator) | 4 |
F-TEST (DF denominator) | 126 |
p-value | 0 |
Multiple Linear Regression - Residual Statistics | |
Residual Standard Deviation | 1.92784466060862 |
Sum Squared Residuals | 468.289714465082 |
Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
1 | 13 | 11.5738278933616 | 1.42617210663836 |
2 | 12 | 9.6206361094195 | 2.3793638905805 |
3 | 15 | 11.8426239809372 | 3.15737601906279 |
4 | 12 | 11.4525908136013 | 0.547409186398668 |
5 | 10 | 10.9573700763232 | -0.957370076323233 |
6 | 12 | 9.677654998491 | 2.32234500150900 |
7 | 15 | 14.3975179135164 | 0.602482086483648 |
8 | 9 | 9.1521061423481 | -0.152106142348093 |
9 | 12 | 12.2814973852828 | -0.281497385282823 |
10 | 11 | 7.5669715112038 | 3.4330284887962 |
11 | 11 | 12.1792705275413 | -1.17927052754131 |
12 | 11 | 10.5941358963970 | 0.405864103602983 |
13 | 15 | 12.9521324802774 | 2.04786751972265 |
14 | 7 | 10.6233815279328 | -3.62338152793279 |
15 | 11 | 11.568615033819 | -0.568615033818996 |
16 | 11 | 9.57916862629218 | 1.42083137370782 |
17 | 10 | 12.0212858006408 | -2.02128580064075 |
18 | 14 | 12.4832177068533 | 1.51678229314665 |
19 | 10 | 9.20765265741958 | 0.79234734258042 |
20 | 6 | 9.58133360095025 | -3.58133360095025 |
21 | 11 | 9.20203394700523 | 1.79796605299477 |
22 | 15 | 14.7433173823083 | 0.256682617691691 |
23 | 11 | 11.9090020659658 | -0.909002065965774 |
24 | 14 | 13.7050099408685 | 0.294990059131544 |
25 | 9 | 12.8161237679147 | -3.81612376791475 |
26 | 13 | 13.0158576474106 | -0.0158576474106384 |
27 | 16 | 11.5711698951481 | 4.42883010485194 |
28 | 13 | 9.5905896600227 | 3.4094103399773 |
29 | 12 | 12.0851141046586 | -0.085114104658626 |
30 | 14 | 12.6025925259427 | 1.39740747405729 |
31 | 11 | 10.5988557323842 | 0.401144267615845 |
32 | 9 | 10.4365410561675 | -1.43654105616746 |
33 | 16 | 14.7214495849733 | 1.27855041502667 |
34 | 12 | 12.8694021714436 | -0.869402171443577 |
35 | 10 | 8.58567926685133 | 1.41432073314867 |
36 | 13 | 13.3487637084720 | -0.34876370847204 |
37 | 16 | 15.5718340673188 | 0.428165932681193 |
38 | 14 | 13.2779474569244 | 0.722052543075628 |
39 | 15 | 9.419998275178 | 5.580001724822 |
40 | 5 | 8.17860635537057 | -3.17860635537056 |
41 | 8 | 10.3390340344131 | -2.33903403441308 |
42 | 11 | 11.523407065149 | -0.523407065148999 |
43 | 16 | 14.4137619201186 | 1.5862380798814 |
44 | 17 | 13.8002488510802 | 3.19975114891982 |
45 | 9 | 8.59266721438112 | 0.407332785618876 |
46 | 9 | 11.7591959911270 | -2.75919599112702 |
47 | 13 | 14.5520438243422 | -1.55204382434224 |
48 | 12 | 12.4460801730422 | -0.44608017304218 |
49 | 8 | 10.1707107611110 | -2.17071076111103 |
50 | 14 | 10.6882923192797 | 3.3117076807203 |
51 | 12 | 12.6144034463442 | -0.614403446344225 |
52 | 11 | 11.1942414896303 | -0.194241489630285 |
53 | 16 | 14.9801887956154 | 1.01981120438463 |
54 | 8 | 9.93196112293232 | -1.93196112293232 |
55 | 15 | 15.5484938959838 | -0.548493895983793 |
56 | 7 | 9.17761128834118 | -2.17761128834118 |
57 | 16 | 12.1792705275413 | 3.82072947245869 |
58 | 14 | 14.3003956981146 | -0.300395698114586 |
59 | 9 | 10.2192693286527 | -1.21926932865272 |
60 | 14 | 12.6863021852209 | 1.31369781477907 |
61 | 11 | 13.0181257589533 | -2.01812575895330 |
62 | 15 | 11.2799375909831 | 3.72006240901686 |
63 | 15 | 13.0425484176173 | 1.95745158238265 |
64 | 13 | 12.5435871947966 | 0.456412805203444 |
65 | 11 | 12.0898339406458 | -1.08983394064576 |
66 | 11 | 12.5284256755233 | -1.52842567552334 |
67 | 12 | 12.7789862341036 | -0.778986234103582 |
68 | 12 | 13.4195799600197 | -1.41957996001971 |
69 | 12 | 12.3556642357022 | -0.355664235702185 |
70 | 12 | 12.4008722043722 | -0.400872204372183 |
71 | 14 | 11.2857399142993 | 2.71426008570068 |
72 | 6 | 7.75744933162724 | -1.75744933162724 |
73 | 7 | 9.55572531807258 | -2.55572531807258 |
74 | 14 | 14.0541650888505 | -0.0541650888504911 |
75 | 10 | 11.4296405289373 | -1.42964052893731 |
76 | 13 | 7.53801262945444 | 5.46198737054556 |
77 | 12 | 12.5202470234615 | -0.520247023461542 |
78 | 9 | 9.53720811960929 | -0.537208119609288 |
79 | 12 | 10.7787082566197 | 1.22129174338031 |
80 | 16 | 15.4776776444361 | 0.522322355563876 |
81 | 10 | 10.4109327732898 | -0.410932773289784 |
82 | 10 | 13.2245659165110 | -3.22456591651096 |
83 | 16 | 13.2883942205288 | 2.71160577947117 |
84 | 15 | 14.0612561732649 | 0.938743826735128 |
85 | 10 | 8.51151241643197 | 1.48848758356803 |
86 | 8 | 10.4998763366297 | -2.49987633662975 |
87 | 8 | 8.58931661550943 | -0.589316615509431 |
88 | 11 | 12.9891668772039 | -1.98916687720393 |
89 | 13 | 12.7081699825559 | 0.291830017444087 |
90 | 16 | 15.7853653092908 | 0.214634690709151 |
91 | 14 | 15.4257684780227 | -1.42576847802274 |
92 | 9 | 10.3623742057481 | -1.36237420574809 |
93 | 8 | 10.2648671839937 | -2.26486718399372 |
94 | 8 | 10.9017204243672 | -2.90172042436716 |
95 | 11 | 12.3033651826178 | -1.30336518261781 |
96 | 12 | 14.0112252317232 | -2.01122523172315 |
97 | 14 | 13.7954258782085 | 0.204574121791549 |
98 | 15 | 14.5749941090063 | 0.425005890993736 |
99 | 16 | 14.0356478903872 | 1.9643521096128 |
100 | 16 | 14.0356478903872 | 1.9643521096128 |
101 | 11 | 12.5583639077172 | -1.55836390771716 |
102 | 14 | 13.9637491515105 | 0.0362508484895038 |
103 | 14 | 11.6223864609034 | 2.37761353909659 |
104 | 12 | 11.5956956906967 | 0.404304309303302 |
105 | 13 | 13.8210341610861 | -0.821034161086123 |
106 | 12 | 9.45231283611744 | 2.54768716388256 |
107 | 16 | 15.7364168550782 | 0.263583144921837 |
108 | 12 | 13.4195799600197 | -1.41957996001971 |
109 | 11 | 11.8763026986737 | -0.876302698673722 |
110 | 4 | 6.8441354196911 | -2.84413541969110 |
111 | 16 | 15.7364168550782 | 0.263583144921837 |
112 | 10 | 11.2323583738859 | -1.23235837388590 |
113 | 13 | 13.22564840384 | -0.225648403839993 |
114 | 14 | 13.9637491515105 | 0.0362508484895038 |
115 | 7 | 10.2452674982014 | -3.24526749820139 |
116 | 12 | 12.8731426569863 | -0.873142656986265 |
117 | 12 | 10.7372407734924 | 1.26275922650761 |
118 | 13 | 13.6075029191141 | -0.60750291911408 |
119 | 15 | 13.2271207778400 | 1.77287922215998 |
120 | 12 | 11.1686332067526 | 0.831366793247386 |
121 | 10 | 10.7853063174785 | -0.785306317478495 |
122 | 8 | 11.0210952434565 | -3.02109524345652 |
123 | 10 | 13.6516284004550 | -3.65162840045504 |
124 | 15 | 14.3199953839069 | 0.680004616093088 |
125 | 16 | 15.0506151604920 | 0.949384839507961 |
126 | 13 | 13.5133464962314 | -0.513346496231397 |
127 | 16 | 15.3583028253468 | 0.641697174653236 |
128 | 9 | 10.2682177828654 | -1.26821778286541 |
129 | 14 | 13.5818946362364 | 0.418105363763591 |
130 | 14 | 13.2327394882544 | 0.767260511745626 |
131 | 12 | 10.4576131159598 | 1.54238688404019 |
Goldfeld-Quandt test for Heteroskedasticity | |||
p-values | Alternative Hypothesis | ||
breakpoint index | greater | 2-sided | less |
8 | 0.0459535442652245 | 0.0919070885304489 | 0.954046455734776 |
9 | 0.0458934872623727 | 0.0917869745247454 | 0.954106512737627 |
10 | 0.127743279436854 | 0.255486558873708 | 0.872256720563146 |
11 | 0.0687360517383393 | 0.137472103476679 | 0.93126394826166 |
12 | 0.0340428092771499 | 0.0680856185542998 | 0.96595719072285 |
13 | 0.331229728172681 | 0.662459456345361 | 0.66877027182732 |
14 | 0.725215881031035 | 0.54956823793793 | 0.274784118968965 |
15 | 0.703415953314134 | 0.593168093371733 | 0.296584046685866 |
16 | 0.636024679228908 | 0.727950641542183 | 0.363975320771092 |
17 | 0.627106076784115 | 0.74578784643177 | 0.372893923215885 |
18 | 0.561819294117399 | 0.876361411765202 | 0.438180705882601 |
19 | 0.482596931401864 | 0.965193862803727 | 0.517403068598136 |
20 | 0.748410310242935 | 0.50317937951413 | 0.251589689757065 |
21 | 0.693045360980263 | 0.613909278039475 | 0.306954639019737 |
22 | 0.633492602047735 | 0.73301479590453 | 0.366507397952265 |
23 | 0.565308378547561 | 0.869383242904878 | 0.434691621452439 |
24 | 0.505715120159673 | 0.988569759680653 | 0.494284879840327 |
25 | 0.689466457586018 | 0.621067084827963 | 0.310533542413982 |
26 | 0.626677633836962 | 0.746644732326075 | 0.373322366163038 |
27 | 0.733642483197155 | 0.53271503360569 | 0.266357516802845 |
28 | 0.819122265256642 | 0.361755469486716 | 0.180877734743358 |
29 | 0.779173084311012 | 0.441653831377975 | 0.220826915688988 |
30 | 0.758901513966229 | 0.482196972067543 | 0.241098486033771 |
31 | 0.723460733484106 | 0.553078533031788 | 0.276539266515894 |
32 | 0.71363670229454 | 0.572726595410919 | 0.286363297705459 |
33 | 0.682595885040932 | 0.634808229918137 | 0.317404114959068 |
34 | 0.665153975939829 | 0.669692048120343 | 0.334846024060171 |
35 | 0.632933977355756 | 0.734132045288487 | 0.367066022644244 |
36 | 0.576598099156099 | 0.846803801687801 | 0.423401900843901 |
37 | 0.522946690076296 | 0.954106619847408 | 0.477053309923704 |
38 | 0.471956956803423 | 0.943913913606846 | 0.528043043196577 |
39 | 0.743705932498876 | 0.512588135002248 | 0.256294067501124 |
40 | 0.866073951154957 | 0.267852097690085 | 0.133926048845043 |
41 | 0.892369713201682 | 0.215260573596637 | 0.107630286798318 |
42 | 0.875753115657858 | 0.248493768684284 | 0.124246884342142 |
43 | 0.862275543299379 | 0.275448913401242 | 0.137724456700621 |
44 | 0.903020888638969 | 0.193958222722062 | 0.0969791113610309 |
45 | 0.883724175809352 | 0.232551648381296 | 0.116275824190648 |
46 | 0.91672563829966 | 0.166548723400682 | 0.0832743617003408 |
47 | 0.91414766687941 | 0.171704666241181 | 0.0858523331205903 |
48 | 0.895629555389476 | 0.208740889221047 | 0.104370444610524 |
49 | 0.912347037988906 | 0.175305924022188 | 0.087652962011094 |
50 | 0.944768410162782 | 0.110463179674437 | 0.0552315898372184 |
51 | 0.930535845910982 | 0.138928308178036 | 0.0694641540890178 |
52 | 0.91229959654224 | 0.175400806915521 | 0.0877004034577605 |
53 | 0.894927276097236 | 0.210145447805527 | 0.105072723902764 |
54 | 0.899111553705157 | 0.201776892589685 | 0.100888446294843 |
55 | 0.878178870292653 | 0.243642259414694 | 0.121821129707347 |
56 | 0.886132234661855 | 0.227735530676290 | 0.113867765338145 |
57 | 0.940079136179172 | 0.119841727641656 | 0.0599208638208278 |
58 | 0.923325716391099 | 0.153348567217803 | 0.0766742836089014 |
59 | 0.91333203628078 | 0.173335927438442 | 0.0866679637192208 |
60 | 0.902691404550759 | 0.194617190898482 | 0.097308595449241 |
61 | 0.90438213415077 | 0.191235731698458 | 0.0956178658492292 |
62 | 0.950308584189414 | 0.0993828316211712 | 0.0496914158105856 |
63 | 0.951676014162154 | 0.0966479716756924 | 0.0483239858378462 |
64 | 0.938841683723074 | 0.122316632553853 | 0.0611583162769263 |
65 | 0.927760544946709 | 0.144478910106583 | 0.0722394550532913 |
66 | 0.924410875353537 | 0.151178249292927 | 0.0755891246464633 |
67 | 0.907824088309188 | 0.184351823381624 | 0.092175911690812 |
68 | 0.896726715822461 | 0.206546568355078 | 0.103273284177539 |
69 | 0.872267629156807 | 0.255464741686386 | 0.127732370843193 |
70 | 0.844251909699032 | 0.311496180601937 | 0.155748090300968 |
71 | 0.883653168038558 | 0.232693663922885 | 0.116346831961443 |
72 | 0.874302223008163 | 0.251395553983675 | 0.125697776991837 |
73 | 0.889313407362803 | 0.221373185274394 | 0.110686592637197 |
74 | 0.862763000616085 | 0.274473998767829 | 0.137236999383915 |
75 | 0.846812732549008 | 0.306374534901983 | 0.153187267450992 |
76 | 0.983427349815912 | 0.0331453003681768 | 0.0165726501840884 |
77 | 0.977380160119567 | 0.0452396797608656 | 0.0226198398804328 |
78 | 0.97000652633356 | 0.0599869473328809 | 0.0299934736664404 |
79 | 0.965884658263239 | 0.0682306834735221 | 0.0341153417367611 |
80 | 0.954994068015835 | 0.0900118639683305 | 0.0450059319841652 |
81 | 0.941666342815078 | 0.116667314369844 | 0.0583336571849218 |
82 | 0.966903079995017 | 0.066193840009966 | 0.033096920004983 |
83 | 0.979870845620403 | 0.0402583087591942 | 0.0201291543795971 |
84 | 0.974122992169726 | 0.0517540156605475 | 0.0258770078302737 |
85 | 0.985014699450067 | 0.0299706010998655 | 0.0149853005499328 |
86 | 0.985312456011374 | 0.0293750879772512 | 0.0146875439886256 |
87 | 0.979593070825157 | 0.0408138583496864 | 0.0204069291748432 |
88 | 0.979112410674135 | 0.0417751786517300 | 0.0208875893258650 |
89 | 0.971436831981545 | 0.0571263360369105 | 0.0285631680184552 |
90 | 0.96046347218321 | 0.079073055633579 | 0.0395365278167895 |
91 | 0.958667902926637 | 0.082664194146726 | 0.041332097073363 |
92 | 0.948653105976234 | 0.102693788047532 | 0.051346894023766 |
93 | 0.950571190063015 | 0.0988576198739706 | 0.0494288099369853 |
94 | 0.966451136756683 | 0.0670977264866346 | 0.0335488632433173 |
95 | 0.95955056404197 | 0.0808988719160616 | 0.0404494359580308 |
96 | 0.957595199932488 | 0.0848096001350238 | 0.0424048000675119 |
97 | 0.941276850653867 | 0.117446298692265 | 0.0587231493461326 |
98 | 0.920715162561674 | 0.158569674876652 | 0.0792848374383261 |
99 | 0.920575467797918 | 0.158849064404164 | 0.0794245322020822 |
100 | 0.92338832097843 | 0.153223358043139 | 0.0766116790215694 |
101 | 0.916069960016446 | 0.167860079967107 | 0.0839300399835536 |
102 | 0.886930192018945 | 0.226139615962110 | 0.113069807981055 |
103 | 0.924936904248193 | 0.150126191503613 | 0.0750630957518066 |
104 | 0.903005028543354 | 0.193989942913293 | 0.0969949714566465 |
105 | 0.872814983619751 | 0.254370032760499 | 0.127185016380249 |
106 | 0.969530545057275 | 0.0609389098854491 | 0.0304694549427246 |
107 | 0.953925454418663 | 0.0921490911626747 | 0.0460745455813373 |
108 | 0.94384248015414 | 0.112315039691718 | 0.056157519845859 |
109 | 0.918668739067279 | 0.162662521865443 | 0.0813312609327213 |
110 | 0.89565344564259 | 0.208693108714819 | 0.104346554357410 |
111 | 0.85334338077946 | 0.293313238441079 | 0.146656619220539 |
112 | 0.807078991223225 | 0.38584201755355 | 0.192921008776775 |
113 | 0.741802146474079 | 0.516395707051842 | 0.258197853525921 |
114 | 0.665033836770552 | 0.669932326458895 | 0.334966163229448 |
115 | 0.810405913713478 | 0.379188172573044 | 0.189594086286522 |
116 | 0.772947603287559 | 0.454104793424882 | 0.227052396712441 |
117 | 1 | 1.03952623803669e-141 | 5.19763119018347e-142 |
118 | 1 | 1.28888100164261e-122 | 6.44440500821304e-123 |
119 | 1 | 1.51917273998704e-108 | 7.5958636999352e-109 |
120 | 1 | 2.97616944314037e-92 | 1.48808472157019e-92 |
121 | 1 | 3.9516372614307e-78 | 1.97581863071535e-78 |
122 | 1 | 4.50595214666178e-62 | 2.25297607333089e-62 |
123 | 1 | 5.42176106127711e-48 | 2.71088053063855e-48 |
Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
Description | # significant tests | % significant tests | OK/NOK |
1% type I error level | 7 | 0.0603448275862069 | NOK |
5% type I error level | 14 | 0.120689655172414 | NOK |
10% type I error level | 33 | 0.284482758620690 | NOK |