Multiple Linear Regression - Estimated Regression Equation |
Celebrity[t] = + 0.228869730297837 + 0.152948770159782Popularity[t] + 0.104099951420784KnowingPeople[t] + 0.146565226481132Liked[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) | 0.228869730297837 | 0.517949 | 0.4419 | 0.659207 | 0.329603 |
Popularity | 0.152948770159782 | 0.038134 | 4.0109 | 9.5e-05 | 4.7e-05 |
KnowingPeople | 0.104099951420784 | 0.030709 | 3.3898 | 0.000891 | 0.000446 |
Liked | 0.146565226481132 | 0.048174 | 3.0424 | 0.002766 | 0.001383 |
Multiple Linear Regression - Regression Statistics | |
Multiple R | 0.677006667554951 |
R-squared | 0.45833802791386 |
Adjusted R-squared | 0.447647331096371 |
F-TEST (value) | 42.8726055689874 |
F-TEST (DF numerator) | 3 |
F-TEST (DF denominator) | 152 |
p-value | 0 |
Multiple Linear Regression - Residual Statistics | |
Residual Standard Deviation | 1.04086140973719 |
Sum Squared Residuals | 164.675656090573 |
Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
1 | 3 | 5.57995100652068 | -2.57995100652068 |
2 | 5 | 4.8024025278362 | 0.197597472163795 |
3 | 6 | 6.11734432344208 | -0.117344323442084 |
4 | 6 | 4.55173734993429 | 1.44826265006571 |
5 | 5 | 4.41157443739595 | 0.588425562604054 |
6 | 3 | 4.55173734993429 | -1.55173734993429 |
7 | 8 | 6.82687458208748 | 1.17312541791252 |
8 | 4 | 4.36272561865695 | -0.362725618656947 |
9 | 4 | 5.57356746284204 | -1.57356746284204 |
10 | 4 | 3.85499294891033 | 0.145007051089670 |
11 | 6 | 5.62881859552383 | 0.371181404476174 |
12 | 6 | 4.81518838545764 | 1.18481161454236 |
13 | 5 | 5.80091799671956 | -0.80091799671956 |
14 | 4 | 4.3074932562393 | -0.307493256239298 |
15 | 6 | 4.54535380625564 | 1.45464619374436 |
16 | 4 | 4.87682306181808 | -0.87682306181808 |
17 | 6 | 4.66223961529786 | 1.33776038470214 |
18 | 6 | 6.27669540754465 | -0.276695407544653 |
19 | 4 | 3.80614413017133 | 0.193855869828669 |
20 | 4 | 3.69567940533603 | 0.304320594663967 |
21 | 2 | 4.54535380625564 | -2.54535380625564 |
22 | 7 | 6.17897899980252 | 0.82102100019748 |
23 | 5 | 4.93845773817852 | 0.0615422618214848 |
24 | 4 | 4.40517212345316 | -0.405172123453159 |
25 | 6 | 5.83699972810126 | 0.163000271898742 |
26 | 6 | 6.637844080546 | -0.637844080546003 |
27 | 7 | 5.36538633026461 | 1.63461366973539 |
28 | 5 | 5.72651623300182 | -0.726516233001823 |
29 | 6 | 5.72651623300182 | 0.273483766998176 |
30 | 4 | 5.56076283495647 | -1.56076283495647 |
31 | 4 | 4.22252516559033 | -0.22252516559033 |
32 | 7 | 5.42700223636091 | 1.57299776363909 |
33 | 7 | 6.02603022964274 | 0.973969770357262 |
34 | 4 | 4.64945375767642 | -0.649453757676424 |
35 | 4 | 4.36272561865695 | -0.362725618656947 |
36 | 6 | 6.54012767280387 | -0.54012767280387 |
37 | 6 | 5.30373288364004 | 0.696267116359962 |
38 | 5 | 3.91024408159211 | 1.08975591840789 |
39 | 6 | 5.57995100652069 | 0.420048993479308 |
40 | 7 | 6.686692899285 | 0.313307100714998 |
41 | 6 | 5.62879982525969 | 0.37120017474031 |
42 | 3 | 4.65581853109094 | -1.65581853109094 |
43 | 3 | 3.5851959102366 | -0.585195910236598 |
44 | 4 | 4.25224212355751 | -0.252242123557513 |
45 | 6 | 4.50288853119529 | 1.49711146880471 |
46 | 7 | 6.08126259206039 | 0.918737407939613 |
47 | 5 | 6.44241126506174 | -1.44241126506174 |
48 | 4 | 3.40253018210963 | 0.597469817890367 |
49 | 5 | 4.7599560230400 | 0.240043976960005 |
50 | 6 | 6.22784658880565 | -0.227846588805655 |
51 | 6 | 4.18420513325429 | 1.81579486674571 |
52 | 6 | 4.32027911386074 | 1.67972088613926 |
53 | 5 | 5.36536756000047 | -0.365367560000474 |
54 | 4 | 4.19060744719708 | -0.190607447197077 |
55 | 5 | 5.62879982525969 | -0.62879982525969 |
56 | 5 | 5.42700223636091 | -0.427002236360909 |
57 | 4 | 4.91928833687843 | -0.919288336878428 |
58 | 6 | 6.686692899285 | -0.686692899285002 |
59 | 2 | 4.69193780300091 | -2.69193780300091 |
60 | 8 | 6.2830789512233 | 1.71692104877670 |
61 | 3 | 3.89109345055616 | -0.891093450556163 |
62 | 6 | 6.39356244632274 | -0.393562446322738 |
63 | 6 | 6.10683430730326 | -0.106834307303261 |
64 | 6 | 6.3319277699623 | -0.331927769962302 |
65 | 5 | 3.98879108803416 | 1.01120891196584 |
66 | 5 | 5.62879982525969 | -0.62879982525969 |
67 | 6 | 5.23158819114078 | 0.768411808859221 |
68 | 5 | 4.70468612009407 | 0.295313879905927 |
69 | 6 | 5.78174859541947 | 0.218251404580527 |
70 | 2 | 2.14283951918554 | -0.142839519185540 |
71 | 5 | 5.88584854684026 | -0.885848546840256 |
72 | 5 | 5.47585105509991 | -0.475851055099908 |
73 | 5 | 5.10831883841991 | -0.108318838419907 |
74 | 6 | 5.86031437212565 | 0.139685627874346 |
75 | 6 | 5.21880233351934 | 0.781197666480658 |
76 | 6 | 5.53110218778169 | 0.468897812218307 |
77 | 5 | 5.28043700987978 | -0.280437009879777 |
78 | 5 | 5.32290228494013 | -0.322902284940125 |
79 | 4 | 5.2548652946369 | -1.25486529463690 |
80 | 2 | 3.38337955107368 | -1.38337955107368 |
81 | 4 | 3.78699349913538 | 0.213006500864621 |
82 | 6 | 5.48223459877856 | 0.517765401221442 |
83 | 6 | 6.06849550470309 | -0.0684955047030857 |
84 | 5 | 4.66223961529786 | 0.337760384702139 |
85 | 3 | 4.49648621725251 | -1.49648621725251 |
86 | 6 | 5.07223710703821 | 0.92776289296179 |
87 | 4 | 3.90386053791346 | 0.096139462086536 |
88 | 5 | 5.40783283506082 | -0.407832835060822 |
89 | 8 | 6.3319277699623 | 1.66807223003770 |
90 | 4 | 4.45403971245629 | -0.454039712456294 |
91 | 6 | 5.75619565044073 | 0.243804349559266 |
92 | 6 | 5.31013519758282 | 0.689864802417176 |
93 | 7 | 6.686692899285 | 0.313307100714998 |
94 | 6 | 6.09404844968182 | -0.094048449681824 |
95 | 5 | 4.96813715561743 | 0.0318628443825739 |
96 | 4 | 4.20337453455438 | -0.203374534554378 |
97 | 6 | 3.77420764151394 | 2.22579235848606 |
98 | 3 | 3.6468118163329 | -0.646811816332898 |
99 | 5 | 5.56718391916339 | -0.567183919163391 |
100 | 6 | 5.26765115225834 | 0.73234884774166 |
101 | 7 | 6.79079285070579 | 0.209207149294215 |
102 | 7 | 6.43602772138309 | 0.563972278616914 |
103 | 6 | 6.77802576334848 | -0.778025763348484 |
104 | 3 | 4.33715390341407 | -1.33715390341407 |
105 | 2 | 2.72271688143142 | -0.722716881431417 |
106 | 8 | 5.75619565044073 | 2.24380434955927 |
107 | 3 | 4.65585607161921 | -1.65585607161921 |
108 | 8 | 6.13013018106352 | 1.86986981893648 |
109 | 3 | 4.54537257651978 | -1.54537257651978 |
110 | 4 | 4.58783785158012 | -0.587837851580125 |
111 | 5 | 5.21241878984069 | -0.212418789840691 |
112 | 7 | 5.53110218778169 | 1.46889781221831 |
113 | 6 | 4.54535380625564 | 1.45464619374436 |
114 | 6 | 5.92193027822195 | 0.0780697217780461 |
115 | 7 | 6.11734432344208 | 0.882655676557916 |
116 | 6 | 6.18536254348117 | -0.185362543481170 |
117 | 6 | 6.18536254348117 | -0.185362543481170 |
118 | 6 | 5.08914943711982 | 0.91085056288018 |
119 | 6 | 5.98356495458239 | 0.0164350454176105 |
120 | 4 | 5.37813464735777 | -1.37813464735777 |
121 | 4 | 5.21880233351934 | -1.21880233351934 |
122 | 5 | 5.79453445304091 | -0.79453445304091 |
123 | 4 | 4.14814217213673 | -0.148142172136729 |
124 | 6 | 5.83061618442261 | 0.169383815577393 |
125 | 6 | 6.28946249490195 | -0.289462494901954 |
126 | 5 | 4.74076785147577 | 0.259232148524229 |
127 | 8 | 6.47849299644343 | 1.52150700355657 |
128 | 6 | 5.53110218778169 | 0.468897812218307 |
129 | 5 | 5.00421888699912 | -0.00421888699912362 |
130 | 4 | 2.05152542538619 | 1.94847457461381 |
131 | 8 | 6.47849299644343 | 1.52150700355657 |
132 | 6 | 5.67764864399869 | 0.322351356001311 |
133 | 4 | 4.93620066696004 | -0.936200666960037 |
134 | 6 | 5.5607816052206 | 0.439218394779396 |
135 | 6 | 5.9283138219006 | 0.0716861780993956 |
136 | 4 | 4.90650247925699 | -0.90650247925699 |
137 | 6 | 5.98356495458239 | 0.0164350454176105 |
138 | 3 | 4.41159320766008 | -1.41159320766008 |
139 | 6 | 6.89487403186243 | -0.894874031862433 |
140 | 5 | 5.57356746284204 | -0.573567462842041 |
141 | 4 | 5.63520213920248 | -1.63520213920248 |
142 | 6 | 5.72651623300182 | 0.273483766998176 |
143 | 4 | 6.32554422628365 | -2.32554422628365 |
144 | 4 | 3.37285076467072 | 0.627149235329278 |
145 | 4 | 5.01060243067777 | -1.01060243067777 |
146 | 6 | 4.08010518183351 | 1.91989481816649 |
147 | 5 | 4.33717267367821 | 0.662827326321791 |
148 | 6 | 5.51833510042439 | 0.481664899575608 |
149 | 6 | 6.24061367616296 | -0.240613676162956 |
150 | 8 | 6.12372786712073 | 1.87627213287926 |
151 | 7 | 5.37175110367912 | 1.62824889632088 |
152 | 7 | 6.58259294786422 | 0.417407052135782 |
153 | 4 | 4.30109094229651 | -0.301090942296511 |
154 | 6 | 5.81783032680117 | 0.18216967319883 |
155 | 6 | 5.58633455019934 | 0.413665449800658 |
156 | 2 | 5.26126760857969 | -3.26126760857969 |
Goldfeld-Quandt test for Heteroskedasticity | |||
p-values | Alternative Hypothesis | ||
breakpoint index | greater | 2-sided | less |
7 | 0.822113740480269 | 0.355772519039462 | 0.177886259519731 |
8 | 0.787696930494068 | 0.424606139011864 | 0.212303069505932 |
9 | 0.79697303978785 | 0.4060539204243 | 0.20302696021215 |
10 | 0.844814093246948 | 0.310371813506104 | 0.155185906753052 |
11 | 0.821251656578976 | 0.357496686842048 | 0.178748343421024 |
12 | 0.852567641812129 | 0.294864716375742 | 0.147432358187871 |
13 | 0.882458443833406 | 0.235083112333187 | 0.117541556166594 |
14 | 0.840396504171915 | 0.319206991656169 | 0.159603495828085 |
15 | 0.824241714157715 | 0.351516571684570 | 0.175758285842285 |
16 | 0.770684269407245 | 0.458631461185510 | 0.229315730592755 |
17 | 0.795431699225557 | 0.409136601548886 | 0.204568300774443 |
18 | 0.736844628872018 | 0.526310742255963 | 0.263155371127982 |
19 | 0.672178436173532 | 0.655643127652936 | 0.327821563826468 |
20 | 0.606695197265579 | 0.786609605468843 | 0.393304802734421 |
21 | 0.91570175256244 | 0.168596494875120 | 0.0842982474375602 |
22 | 0.911421069114624 | 0.177157861770751 | 0.0885789308853757 |
23 | 0.888156056426452 | 0.223687887147095 | 0.111843943573548 |
24 | 0.856257378571309 | 0.287485242857383 | 0.143742621428691 |
25 | 0.822278304955757 | 0.355443390088487 | 0.177721695044243 |
26 | 0.787012199161394 | 0.425975601677213 | 0.212987800838606 |
27 | 0.810851813266109 | 0.378296373467782 | 0.189148186733891 |
28 | 0.782174521631378 | 0.435650956737245 | 0.217825478368622 |
29 | 0.739420723964448 | 0.521158552071103 | 0.260579276035552 |
30 | 0.751686823128482 | 0.496626353743035 | 0.248313176871518 |
31 | 0.715607228114119 | 0.568785543771762 | 0.284392771885881 |
32 | 0.773495270674063 | 0.453009458651874 | 0.226504729325937 |
33 | 0.769889329141931 | 0.460221341716138 | 0.230110670858069 |
34 | 0.743356357538004 | 0.513287284923992 | 0.256643642461996 |
35 | 0.705747108372162 | 0.588505783255676 | 0.294252891627838 |
36 | 0.66117461792696 | 0.67765076414608 | 0.33882538207304 |
37 | 0.625757140712544 | 0.748485718574912 | 0.374242859287456 |
38 | 0.640219856960394 | 0.719560286079212 | 0.359780143039606 |
39 | 0.598682896765033 | 0.802634206469934 | 0.401317103234967 |
40 | 0.554785719086181 | 0.890428561827638 | 0.445214280913819 |
41 | 0.513201008123132 | 0.973597983753735 | 0.486798991876868 |
42 | 0.544172283948294 | 0.911655432103411 | 0.455827716051706 |
43 | 0.54531649683982 | 0.90936700632036 | 0.45468350316018 |
44 | 0.501442532107138 | 0.997114935785724 | 0.498557467892862 |
45 | 0.563519265920159 | 0.872961468159682 | 0.436480734079841 |
46 | 0.563329613715386 | 0.873340772569229 | 0.436670386284614 |
47 | 0.592084011495037 | 0.815831977009927 | 0.407915988504963 |
48 | 0.561446884041635 | 0.877106231916729 | 0.438553115958365 |
49 | 0.513517703529427 | 0.972964592941145 | 0.486482296470573 |
50 | 0.46826797033178 | 0.93653594066356 | 0.53173202966822 |
51 | 0.549035378429732 | 0.901929243140535 | 0.450964621570268 |
52 | 0.604472084246955 | 0.79105583150609 | 0.395527915753045 |
53 | 0.564648415340149 | 0.870703169319702 | 0.435351584659851 |
54 | 0.528604645734526 | 0.942790708530948 | 0.471395354265474 |
55 | 0.494142839591674 | 0.988285679183348 | 0.505857160408326 |
56 | 0.453997219876139 | 0.907994439752279 | 0.546002780123861 |
57 | 0.446058487682776 | 0.892116975365551 | 0.553941512317224 |
58 | 0.413117393351279 | 0.826234786702559 | 0.586882606648721 |
59 | 0.709056435894335 | 0.581887128211331 | 0.290943564105665 |
60 | 0.781154933955987 | 0.437690132088025 | 0.218845066044013 |
61 | 0.772871381578442 | 0.454257236843115 | 0.227128618421558 |
62 | 0.740114431196294 | 0.519771137607413 | 0.259885568803706 |
63 | 0.700923785893619 | 0.598152428212762 | 0.299076214106381 |
64 | 0.662551146681184 | 0.674897706637633 | 0.337448853318816 |
65 | 0.658407961394759 | 0.683184077210482 | 0.341592038605241 |
66 | 0.629279568371307 | 0.741440863257386 | 0.370720431628693 |
67 | 0.609065293452736 | 0.781869413094528 | 0.390934706547264 |
68 | 0.569083876851203 | 0.861832246297595 | 0.430916123148797 |
69 | 0.52597822130006 | 0.94804355739988 | 0.47402177869994 |
70 | 0.482123168526574 | 0.964246337053147 | 0.517876831473426 |
71 | 0.468412553619972 | 0.936825107239943 | 0.531587446380028 |
72 | 0.431276219665297 | 0.862552439330593 | 0.568723780334703 |
73 | 0.386174103278898 | 0.772348206557796 | 0.613825896721102 |
74 | 0.345128442634427 | 0.690256885268853 | 0.654871557365573 |
75 | 0.326765897078424 | 0.653531794156849 | 0.673234102921576 |
76 | 0.295034433643658 | 0.590068867287315 | 0.704965566356343 |
77 | 0.258551834656222 | 0.517103669312443 | 0.741448165343778 |
78 | 0.225235833196572 | 0.450471666393144 | 0.774764166803428 |
79 | 0.246927187719025 | 0.49385437543805 | 0.753072812280975 |
80 | 0.277457692546865 | 0.554915385093729 | 0.722542307453135 |
81 | 0.241644396802827 | 0.483288793605654 | 0.758355603197173 |
82 | 0.214689325396757 | 0.429378650793515 | 0.785310674603243 |
83 | 0.182388348847110 | 0.364776697694219 | 0.81761165115289 |
84 | 0.156314335308282 | 0.312628670616564 | 0.843685664691718 |
85 | 0.213725850268548 | 0.427451700537097 | 0.786274149731451 |
86 | 0.205826371042955 | 0.411652742085910 | 0.794173628957045 |
87 | 0.174236331587895 | 0.348472663175789 | 0.825763668412105 |
88 | 0.149335201370396 | 0.298670402740791 | 0.850664798629604 |
89 | 0.194498985637980 | 0.388997971275960 | 0.80550101436202 |
90 | 0.170412246800622 | 0.340824493601244 | 0.829587753199378 |
91 | 0.145064060649000 | 0.290128121298001 | 0.854935939351 |
92 | 0.138757343805996 | 0.277514687611991 | 0.861242656194004 |
93 | 0.116965448891013 | 0.233930897782027 | 0.883034551108987 |
94 | 0.0954593424042026 | 0.190918684808405 | 0.904540657595797 |
95 | 0.0770413120590242 | 0.154082624118048 | 0.922958687940976 |
96 | 0.063124939855477 | 0.126249879710954 | 0.936875060144523 |
97 | 0.124019797280039 | 0.248039594560078 | 0.875980202719961 |
98 | 0.111749643701836 | 0.223499287403672 | 0.888250356298164 |
99 | 0.0948176264591275 | 0.189635252918255 | 0.905182373540872 |
100 | 0.0828697305135704 | 0.165739461027141 | 0.91713026948643 |
101 | 0.067184110867224 | 0.134368221734448 | 0.932815889132776 |
102 | 0.0563275569936639 | 0.112655113987328 | 0.943672443006336 |
103 | 0.0476962360209802 | 0.0953924720419604 | 0.95230376397902 |
104 | 0.0687437486867594 | 0.137487497373519 | 0.93125625131324 |
105 | 0.0626740253785119 | 0.125348050757024 | 0.937325974621488 |
106 | 0.122649136777656 | 0.245298273555312 | 0.877350863222344 |
107 | 0.153270962705769 | 0.306541925411537 | 0.846729037294231 |
108 | 0.249083424821404 | 0.498166849642807 | 0.750916575178596 |
109 | 0.279940155955615 | 0.559880311911229 | 0.720059844044385 |
110 | 0.247537899973966 | 0.495075799947932 | 0.752462100026034 |
111 | 0.209429374842192 | 0.418858749684384 | 0.790570625157808 |
112 | 0.275192620452029 | 0.550385240904058 | 0.724807379547971 |
113 | 0.281740536534206 | 0.563481073068411 | 0.718259463465794 |
114 | 0.239939352732113 | 0.479878705464225 | 0.760060647267887 |
115 | 0.2264488195163 | 0.4528976390326 | 0.7735511804837 |
116 | 0.189528979982280 | 0.379057959964559 | 0.81047102001772 |
117 | 0.156442047082485 | 0.31288409416497 | 0.843557952917515 |
118 | 0.145820325024606 | 0.291640650049211 | 0.854179674975394 |
119 | 0.118534927883435 | 0.237069855766869 | 0.881465072116565 |
120 | 0.156100701323439 | 0.312201402646878 | 0.84389929867656 |
121 | 0.166042000171109 | 0.332084000342217 | 0.833957999828891 |
122 | 0.149392213048437 | 0.298784426096874 | 0.850607786951563 |
123 | 0.119155444745006 | 0.238310889490012 | 0.880844555254994 |
124 | 0.096877212607462 | 0.193754425214924 | 0.903122787392538 |
125 | 0.0764806018961012 | 0.152961203792202 | 0.923519398103899 |
126 | 0.0595701576730777 | 0.119140315346155 | 0.940429842326922 |
127 | 0.0828649597581289 | 0.165729919516258 | 0.917135040241871 |
128 | 0.073152173648854 | 0.146304347297708 | 0.926847826351146 |
129 | 0.0541644306209418 | 0.108328861241884 | 0.945835569379058 |
130 | 0.062862447844704 | 0.125724895689408 | 0.937137552155296 |
131 | 0.0908389119331097 | 0.181677823866219 | 0.90916108806689 |
132 | 0.0675559359308351 | 0.135111871861670 | 0.932444064069165 |
133 | 0.0589660597917383 | 0.117932119583477 | 0.941033940208262 |
134 | 0.0443874936288299 | 0.0887749872576598 | 0.95561250637117 |
135 | 0.030729524141823 | 0.061459048283646 | 0.969270475858177 |
136 | 0.0322223584890982 | 0.0644447169781963 | 0.967777641510902 |
137 | 0.0228813842327218 | 0.0457627684654435 | 0.977118615767278 |
138 | 0.0191194151250758 | 0.0382388302501515 | 0.980880584874924 |
139 | 0.0159123182866624 | 0.0318246365733248 | 0.984087681713338 |
140 | 0.00994243289328027 | 0.0198848657865605 | 0.99005756710672 |
141 | 0.00939983230568245 | 0.0187996646113649 | 0.990600167694317 |
142 | 0.00579467851341887 | 0.0115893570268377 | 0.994205321486581 |
143 | 0.0211662838828577 | 0.0423325677657154 | 0.978833716117142 |
144 | 0.0143939258700069 | 0.0287878517400137 | 0.985606074129993 |
145 | 0.0158570271019589 | 0.0317140542039177 | 0.98414297289804 |
146 | 0.0153342027739372 | 0.0306684055478744 | 0.984665797226063 |
147 | 0.0138921838179649 | 0.0277843676359297 | 0.986107816182035 |
148 | 0.056576468602217 | 0.113152937204434 | 0.943423531397783 |
149 | 0.0265475866121463 | 0.0530951732242926 | 0.973452413387854 |
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 | 11 | 0.0769230769230769 | NOK |
10% type I error level | 16 | 0.111888111888112 | NOK |