Multiple Linear Regression - Estimated Regression Equation |
Popularity[t] = + 1.65207643482502 + 0.118875597665322FindingFriends[t] + 0.240875196872858KnowingPeople[t] + 0.379030919193094Liked[t] + 0.607799529613716Celebrity[t] -0.0468917198450873B[t] + 0.165306614305527`2B`[t] + 0.499352685427422`3B`[t] -0.214487341055989Month[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) | 1.65207643482502 | 3.68147 | 0.4488 | 0.65427 | 0.327135 |
FindingFriends | 0.118875597665322 | 0.096603 | 1.2306 | 0.220453 | 0.110226 |
KnowingPeople | 0.240875196872858 | 0.06174 | 3.9015 | 0.000145 | 7.3e-05 |
Liked | 0.379030919193094 | 0.097785 | 3.8762 | 0.000159 | 8e-05 |
Celebrity | 0.607799529613716 | 0.156769 | 3.877 | 0.000159 | 7.9e-05 |
B | -0.0468917198450873 | 0.223691 | -0.2096 | 0.834249 | 0.417125 |
`2B` | 0.165306614305527 | 0.269363 | 0.6137 | 0.540366 | 0.270183 |
`3B` | 0.499352685427422 | 0.317135 | 1.5746 | 0.117504 | 0.058752 |
Month | -0.214487341055989 | 0.363362 | -0.5903 | 0.555906 | 0.277953 |
Multiple Linear Regression - Regression Statistics | |
Multiple R | 0.716996814212143 |
R-squared | 0.514084431590363 |
Adjusted R-squared | 0.487640046915008 |
F-TEST (value) | 19.4402115194413 |
F-TEST (DF numerator) | 8 |
F-TEST (DF denominator) | 147 |
p-value | 0 |
Multiple Linear Regression - Residual Statistics | |
Residual Standard Deviation | 2.10201796085084 |
Sum Squared Residuals | 649.51648763771 |
Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
1 | 15 | 13.4184571495303 | 1.58154285046974 |
2 | 12 | 11.7899855957337 | 0.210014404266271 |
3 | 9 | 11.1814371266787 | -2.1814371266787 |
4 | 10 | 11.9929929109058 | -1.99299291090584 |
5 | 13 | 13.1170535469146 | -0.117053546914642 |
6 | 16 | 15.1555247841458 | 0.844475215854184 |
7 | 14 | 12.8537742238447 | 1.14622577615535 |
8 | 16 | 13.8401439694466 | 2.15985603055342 |
9 | 10 | 10.9267726488618 | -0.926772648861791 |
10 | 8 | 10.6248810849342 | -2.62488108493419 |
11 | 12 | 12.1065952325374 | -0.106595232537396 |
12 | 15 | 14.9758225764827 | 0.0241774235173207 |
13 | 14 | 10.7636493726956 | 3.23635062730444 |
14 | 14 | 12.6641226429189 | 1.33587735708108 |
15 | 12 | 12.9213305585814 | -0.921330558581422 |
16 | 12 | 11.0518304425708 | 0.948169557429184 |
17 | 10 | 9.46125000081075 | 0.538749999189246 |
18 | 4 | 6.66536803956815 | -2.66536803956815 |
19 | 14 | 15.1411291907882 | -1.14112919078821 |
20 | 15 | 14.1433039731088 | 0.856696026891195 |
21 | 16 | 13.2591929988546 | 2.74080700114538 |
22 | 12 | 10.6254936503753 | 1.37450634962467 |
23 | 12 | 12.0274378165145 | -0.0274378165144826 |
24 | 12 | 11.2004149183701 | 0.799585081629921 |
25 | 12 | 11.4940596754490 | 0.505940324551018 |
26 | 12 | 12.2580812806832 | -0.258081280683172 |
27 | 11 | 8.41196227824612 | 2.58803772175388 |
28 | 11 | 13.0764098301540 | -2.07640983015398 |
29 | 11 | 12.1114078053663 | -1.11140780536628 |
30 | 11 | 11.7646891323986 | -0.76468913239859 |
31 | 11 | 11.4040974664287 | -0.404097466428718 |
32 | 11 | 8.62069813115668 | 2.37930186884333 |
33 | 15 | 14.3416351910521 | 0.658364808947906 |
34 | 15 | 14.8354921712500 | 0.164507828749955 |
35 | 9 | 14.5825103879250 | -5.58251038792495 |
36 | 16 | 10.8128300994460 | 5.18716990055398 |
37 | 13 | 9.13085930299529 | 3.86914069700471 |
38 | 9 | 10.3514712126402 | -1.35147121264023 |
39 | 16 | 14.2155860551841 | 1.78441394481591 |
40 | 12 | 12.8892104716123 | -0.889210471612268 |
41 | 15 | 8.98739079949333 | 6.01260920050667 |
42 | 5 | 9.8035955244421 | -4.80359552444209 |
43 | 11 | 11.3883215115428 | -0.388321511542827 |
44 | 17 | 13.2247101984253 | 3.77528980157470 |
45 | 9 | 9.07818028327066 | -0.078180283270659 |
46 | 13 | 14.7134925720425 | -1.71349257204251 |
47 | 16 | 14.1423784379906 | 1.85762156200945 |
48 | 16 | 13.7409433926003 | 2.25905660739967 |
49 | 14 | 14.2538022830014 | -0.25380228300142 |
50 | 16 | 13.4724566005373 | 2.5275433994627 |
51 | 11 | 12.7420063573413 | -1.74200635734129 |
52 | 11 | 11.809892280957 | -0.809892280957004 |
53 | 11 | 13.6830321704420 | -2.68303217044197 |
54 | 12 | 12.1606604905852 | -0.160660490585163 |
55 | 12 | 13.7388048564222 | -1.73880485642224 |
56 | 12 | 12.0122072285200 | -0.0122072285200334 |
57 | 14 | 13.6575040427026 | 0.342495957297375 |
58 | 10 | 10.8391714052153 | -0.83917140521532 |
59 | 9 | 9.2939567125634 | -0.293956712563391 |
60 | 12 | 12.2127734949162 | -0.212773494916232 |
61 | 10 | 9.96228051921138 | 0.0377194807886161 |
62 | 14 | 12.9348784520841 | 1.06512154791595 |
63 | 8 | 9.87703212260633 | -1.87703212260633 |
64 | 16 | 14.4400069246892 | 1.55999307531080 |
65 | 14 | 15.6888017417311 | -1.68880174173112 |
66 | 14 | 10.6849061098300 | 3.31509389017004 |
67 | 12 | 11.1828126266884 | 0.817187373311627 |
68 | 14 | 13.3343008782171 | 0.665699121782935 |
69 | 7 | 11.0546249546423 | -4.05462495464228 |
70 | 19 | 13.8790991149206 | 5.12090088507943 |
71 | 15 | 12.8016557780134 | 2.19834422198663 |
72 | 8 | 11.2061422880038 | -3.20614228800375 |
73 | 10 | 14.2357259079165 | -4.23572590791653 |
74 | 13 | 12.8873356178642 | 0.112664382135799 |
75 | 13 | 11.3901264295417 | 1.60987357045832 |
76 | 10 | 10.5275360698955 | -0.527536069895532 |
77 | 12 | 9.20609353457326 | 2.79390646542674 |
78 | 15 | 17.4706883670544 | -2.4706883670544 |
79 | 7 | 11.2091285240368 | -4.20912852403683 |
80 | 14 | 14.3537417775043 | -0.353741777504329 |
81 | 10 | 8.55792470894237 | 1.44207529105762 |
82 | 6 | 9.81815439332957 | -3.81815439332957 |
83 | 11 | 11.3779732930419 | -0.377973293041874 |
84 | 12 | 9.43486214499388 | 2.56513785500612 |
85 | 14 | 14.3342299884452 | -0.334229988445212 |
86 | 12 | 13.4646977550006 | -1.46469775500058 |
87 | 14 | 14.4605107887174 | -0.460510788717415 |
88 | 11 | 10.1951265785125 | 0.804873421487478 |
89 | 10 | 9.38355801035 | 0.616441989650003 |
90 | 13 | 13.4751265084796 | -0.475126508479611 |
91 | 8 | 10.4176430571402 | -2.41764305714023 |
92 | 9 | 11.8862238996928 | -2.88622389969276 |
93 | 6 | 12.0063486451522 | -6.00634864515223 |
94 | 12 | 13.1214567265049 | -1.12145672650494 |
95 | 14 | 12.1503629508403 | 1.84963704915973 |
96 | 11 | 10.4471549144993 | 0.552845085500686 |
97 | 8 | 10.5771103800184 | -2.57711038001842 |
98 | 7 | 9.23248139039013 | -2.23248139039013 |
99 | 9 | 10.4396691769144 | -1.43966917691436 |
100 | 14 | 12.1030105277903 | 1.8969894722097 |
101 | 13 | 10.2072052527447 | 2.79279474725529 |
102 | 15 | 12.6392868827887 | 2.36071311721134 |
103 | 5 | 5.24571583426397 | -0.24571583426397 |
104 | 15 | 12.1781184071527 | 2.82188159284725 |
105 | 13 | 12.1967939674805 | 0.803206032519526 |
106 | 12 | 11.5559849625137 | 0.44401503748634 |
107 | 6 | 7.71700882799252 | -1.71700882799252 |
108 | 7 | 9.59940572313099 | -2.59940572313099 |
109 | 13 | 8.50985579977156 | 4.49014420022844 |
110 | 16 | 14.8533622740703 | 1.14663772592974 |
111 | 10 | 13.2784731235095 | -3.27847312350953 |
112 | 16 | 15.1068047606002 | 0.893195239399764 |
113 | 15 | 13.1241612780766 | 1.87583872192341 |
114 | 8 | 8.35241995279641 | -0.352419952796407 |
115 | 11 | 12.5549219977727 | -1.55492199777271 |
116 | 13 | 13.1528090173870 | -0.15280901738695 |
117 | 16 | 15.1819126399627 | 0.818087360037315 |
118 | 11 | 8.65113552363401 | 2.34886447636599 |
119 | 14 | 14.3882287066421 | -0.388228706642128 |
120 | 9 | 10.1679098794865 | -1.16790987948651 |
121 | 8 | 10.2345424271914 | -2.23454242719139 |
122 | 8 | 11.0763318517117 | -3.07633185171171 |
123 | 11 | 11.8381084404744 | -0.838108440474365 |
124 | 12 | 13.2533344154868 | -1.25333441548681 |
125 | 11 | 11.0064688221712 | -0.00646882217116818 |
126 | 14 | 14.5613607063352 | -0.561360706335221 |
127 | 11 | 12.643526830619 | -1.64352683061901 |
128 | 14 | 12.2562064269351 | 1.74379357306490 |
129 | 13 | 14.689172338863 | -1.68917233886299 |
130 | 12 | 10.7243918942580 | 1.27560810574196 |
131 | 4 | 5.85078078205209 | -1.85078078205209 |
132 | 15 | 12.8504119482933 | 2.14958805170674 |
133 | 10 | 11.3564045967762 | -1.35640459677622 |
134 | 13 | 13.8175481192878 | -0.817548119287846 |
135 | 15 | 14.1354380672970 | 0.86456193270296 |
136 | 12 | 13.1967164681036 | -1.19671646810364 |
137 | 13 | 13.2591929988546 | -0.259192998854616 |
138 | 8 | 7.81009460326036 | 0.189905396739644 |
139 | 10 | 10.4965022689081 | -0.496502268908092 |
140 | 15 | 13.622067794935 | 1.37793220506499 |
141 | 16 | 14.3720725835294 | 1.62792741647057 |
142 | 16 | 14.8659295637274 | 1.13407043627262 |
143 | 14 | 12.9187223289714 | 1.08127767102865 |
144 | 14 | 13.0000231426910 | 0.999976857309033 |
145 | 12 | 10.6042612720037 | 1.39573872799628 |
146 | 15 | 13.2556748339584 | 1.74432516604163 |
147 | 13 | 13.0081459995235 | -0.00814599952346191 |
148 | 16 | 13.1403174011893 | 2.85968259881071 |
149 | 14 | 13.5000681957275 | 0.499931804272526 |
150 | 8 | 9.96228051921138 | -1.96228051921138 |
151 | 16 | 13.665374810033 | 2.334625189967 |
152 | 16 | 15.8506214763561 | 0.149378523643902 |
153 | 12 | 13.1210372765344 | -1.12103727653438 |
154 | 11 | 12.2076628194322 | -1.20766281943218 |
155 | 16 | 15.8506214763561 | 0.149378523643902 |
156 | 9 | 9.96228051921138 | -0.962280519211384 |
Goldfeld-Quandt test for Heteroskedasticity | |||
p-values | Alternative Hypothesis | ||
breakpoint index | greater | 2-sided | less |
12 | 0.32896021364012 | 0.65792042728024 | 0.67103978635988 |
13 | 0.430347063820874 | 0.860694127641747 | 0.569652936179126 |
14 | 0.302321610407188 | 0.604643220814376 | 0.697678389592812 |
15 | 0.195967867432362 | 0.391935734864723 | 0.804032132567639 |
16 | 0.149433425278951 | 0.298866850557902 | 0.85056657472105 |
17 | 0.109264500794582 | 0.218529001589163 | 0.890735499205418 |
18 | 0.169135972250133 | 0.338271944500266 | 0.830864027749867 |
19 | 0.281094884295363 | 0.562189768590725 | 0.718905115704637 |
20 | 0.207068979868893 | 0.414137959737786 | 0.792931020131107 |
21 | 0.233217654939827 | 0.466435309879655 | 0.766782345060173 |
22 | 0.174368990010263 | 0.348737980020526 | 0.825631009989737 |
23 | 0.135448191942885 | 0.270896383885769 | 0.864551808057116 |
24 | 0.0951741577198061 | 0.190348315439612 | 0.904825842280194 |
25 | 0.070632875932601 | 0.141265751865202 | 0.929367124067399 |
26 | 0.0566383230383321 | 0.113276646076664 | 0.943361676961668 |
27 | 0.0806000683312881 | 0.161200136662576 | 0.919399931668712 |
28 | 0.148411350154335 | 0.296822700308669 | 0.851588649845665 |
29 | 0.117035344138738 | 0.234070688277476 | 0.882964655861262 |
30 | 0.0903384878449066 | 0.180676975689813 | 0.909661512155093 |
31 | 0.066056317437478 | 0.132112634874956 | 0.933943682562522 |
32 | 0.0583022771088072 | 0.116604554217614 | 0.941697722891193 |
33 | 0.0415894157954200 | 0.0831788315908399 | 0.95841058420458 |
34 | 0.0295278087999596 | 0.0590556175999193 | 0.97047219120004 |
35 | 0.205711811957273 | 0.411423623914546 | 0.794288188042727 |
36 | 0.407803223801948 | 0.815606447603896 | 0.592196776198052 |
37 | 0.548008602111476 | 0.903982795777048 | 0.451991397888524 |
38 | 0.494078825352244 | 0.988157650704487 | 0.505921174647756 |
39 | 0.47252039425318 | 0.94504078850636 | 0.52747960574682 |
40 | 0.437572339596923 | 0.875144679193845 | 0.562427660403077 |
41 | 0.682081959413621 | 0.635836081172758 | 0.317918040586379 |
42 | 0.843228926728527 | 0.313542146542946 | 0.156771073271473 |
43 | 0.80874998642989 | 0.38250002714022 | 0.19125001357011 |
44 | 0.849050993212815 | 0.301898013574370 | 0.150949006787185 |
45 | 0.823411046966297 | 0.353177906067407 | 0.176588953033703 |
46 | 0.818539203025999 | 0.362921593948003 | 0.181460796974001 |
47 | 0.794605124387706 | 0.410789751224589 | 0.205394875612294 |
48 | 0.81453496938487 | 0.370930061230259 | 0.185465030615130 |
49 | 0.777892552544747 | 0.444214894910506 | 0.222107447455253 |
50 | 0.79435208897037 | 0.411295822059262 | 0.205647911029631 |
51 | 0.771099400130383 | 0.457801199739234 | 0.228900599869617 |
52 | 0.746586679473186 | 0.506826641053629 | 0.253413320526814 |
53 | 0.847374306281003 | 0.305251387437994 | 0.152625693718997 |
54 | 0.815438837314818 | 0.369122325370363 | 0.184561162685182 |
55 | 0.809423953393434 | 0.381152093213132 | 0.190576046606566 |
56 | 0.777545799468447 | 0.444908401063107 | 0.222454200531553 |
57 | 0.738464329730409 | 0.523071340539183 | 0.261535670269591 |
58 | 0.69856581999184 | 0.60286836001632 | 0.30143418000816 |
59 | 0.664060228264741 | 0.671879543470517 | 0.335939771735259 |
60 | 0.642113948128808 | 0.715772103742384 | 0.357886051871192 |
61 | 0.594604357709274 | 0.810791284581452 | 0.405395642290726 |
62 | 0.555084592250538 | 0.889830815498924 | 0.444915407749462 |
63 | 0.536286805315793 | 0.927426389368414 | 0.463713194684207 |
64 | 0.528090856300788 | 0.943818287398424 | 0.471909143699212 |
65 | 0.524981559245403 | 0.950036881509193 | 0.475018440754597 |
66 | 0.594108493790074 | 0.811783012419852 | 0.405891506209926 |
67 | 0.550788429153248 | 0.898423141693505 | 0.449211570846752 |
68 | 0.510385001915492 | 0.979229996169015 | 0.489614998084508 |
69 | 0.674201597134799 | 0.651596805730402 | 0.325798402865201 |
70 | 0.844384055870127 | 0.311231888259747 | 0.155615944129873 |
71 | 0.841037382599993 | 0.317925234800013 | 0.158962617400007 |
72 | 0.874450071761273 | 0.251099856477454 | 0.125549928238727 |
73 | 0.940192628146165 | 0.119614743707671 | 0.0598073718538355 |
74 | 0.925185907388453 | 0.149628185223095 | 0.0748140926115474 |
75 | 0.915979657293713 | 0.168040685412574 | 0.0840203427062869 |
76 | 0.896546830902256 | 0.206906338195488 | 0.103453169097744 |
77 | 0.918832782285214 | 0.162334435429573 | 0.0811672177147863 |
78 | 0.926118960946253 | 0.147762078107494 | 0.0738810390537472 |
79 | 0.968659621247293 | 0.0626807575054139 | 0.0313403787527070 |
80 | 0.959570537975871 | 0.0808589240482575 | 0.0404294620241288 |
81 | 0.955232835588176 | 0.0895343288236487 | 0.0447671644118243 |
82 | 0.978449661780366 | 0.043100676439268 | 0.021550338219634 |
83 | 0.9725384090455 | 0.0549231819089985 | 0.0274615909544992 |
84 | 0.976718021143186 | 0.0465639577136289 | 0.0232819788568144 |
85 | 0.969324486320533 | 0.0613510273589334 | 0.0306755136794667 |
86 | 0.964221758791657 | 0.0715564824166859 | 0.0357782412083429 |
87 | 0.9550371394109 | 0.0899257211782006 | 0.0449628605891003 |
88 | 0.946482330833396 | 0.107035338333208 | 0.0535176691666038 |
89 | 0.947742014810473 | 0.104515970379054 | 0.0522579851895269 |
90 | 0.933510371327346 | 0.132979257345308 | 0.066489628672654 |
91 | 0.936269089910977 | 0.127461820178046 | 0.0637309100890231 |
92 | 0.962301191080293 | 0.075397617839413 | 0.0376988089197065 |
93 | 0.997433857667213 | 0.00513228466557359 | 0.00256614233278679 |
94 | 0.996467905180277 | 0.00706418963944601 | 0.00353209481972301 |
95 | 0.995680767898137 | 0.0086384642037259 | 0.00431923210186295 |
96 | 0.994145524272307 | 0.0117089514553851 | 0.00585447572769257 |
97 | 0.994577171886353 | 0.0108456562272931 | 0.00542282811364655 |
98 | 0.995305492615521 | 0.0093890147689575 | 0.00469450738447875 |
99 | 0.993570554407893 | 0.0128588911842143 | 0.00642944559210713 |
100 | 0.992294011811768 | 0.0154119763764638 | 0.0077059881882319 |
101 | 0.99487214946781 | 0.0102557010643788 | 0.00512785053218939 |
102 | 0.994855587553962 | 0.0102888248920769 | 0.00514441244603844 |
103 | 0.9928063673531 | 0.0143872652937992 | 0.00719363264689962 |
104 | 0.994556519435815 | 0.0108869611283695 | 0.00544348056418477 |
105 | 0.992151452338304 | 0.0156970953233918 | 0.00784854766169588 |
106 | 0.989637340506016 | 0.020725318987967 | 0.0103626594939835 |
107 | 0.988632968773223 | 0.0227340624535534 | 0.0113670312267767 |
108 | 0.992715225382654 | 0.0145695492346921 | 0.00728477461734604 |
109 | 0.999196910702276 | 0.00160617859544776 | 0.000803089297723881 |
110 | 0.998826078834382 | 0.00234784233123571 | 0.00117392116561786 |
111 | 0.999724541436235 | 0.000550917127529005 | 0.000275458563764503 |
112 | 0.999533943441265 | 0.00093211311747012 | 0.00046605655873506 |
113 | 0.99946413090732 | 0.00107173818536121 | 0.000535869092680606 |
114 | 0.999165667361723 | 0.00166866527655385 | 0.000834332638276923 |
115 | 0.998809387899737 | 0.00238122420052484 | 0.00119061210026242 |
116 | 0.998028804684133 | 0.00394239063173328 | 0.00197119531586664 |
117 | 0.996835042450736 | 0.0063299150985287 | 0.00316495754926435 |
118 | 0.999350714821428 | 0.00129857035714462 | 0.00064928517857231 |
119 | 0.99901788069341 | 0.00196423861317857 | 0.000982119306589283 |
120 | 0.998403071815296 | 0.00319385636940862 | 0.00159692818470431 |
121 | 0.99825395489838 | 0.00349209020324089 | 0.00174604510162044 |
122 | 0.997821309805526 | 0.00435738038894845 | 0.00217869019447422 |
123 | 0.996661658080476 | 0.00667668383904817 | 0.00333834191952409 |
124 | 0.996806288918021 | 0.00638742216395701 | 0.00319371108197851 |
125 | 0.994628296769586 | 0.0107434064608278 | 0.00537170323041389 |
126 | 0.991860195116645 | 0.0162796097667096 | 0.00813980488335478 |
127 | 0.989173802820303 | 0.0216523943593941 | 0.0108261971796970 |
128 | 0.984374360963883 | 0.0312512780722343 | 0.0156256390361172 |
129 | 0.991419207719256 | 0.0171615845614878 | 0.00858079228074389 |
130 | 0.99410042779256 | 0.0117991444148791 | 0.00589957220743954 |
131 | 0.990859393583142 | 0.0182812128337157 | 0.00914060641685786 |
132 | 0.989622377635367 | 0.0207552447292669 | 0.0103776223646334 |
133 | 0.984449545963209 | 0.0311009080735826 | 0.0155504540367913 |
134 | 0.973963684751102 | 0.0520726304977959 | 0.0260363152488980 |
135 | 0.95584814707239 | 0.0883037058552193 | 0.0441518529276097 |
136 | 0.948544467579975 | 0.102911064840049 | 0.0514555324200246 |
137 | 0.930998434602684 | 0.138003130794632 | 0.0690015653973161 |
138 | 0.901226268093157 | 0.197547463813686 | 0.0987737319068429 |
139 | 0.874539518908223 | 0.250920962183553 | 0.125460481091777 |
140 | 0.805238170246671 | 0.389523659506657 | 0.194761829753329 |
141 | 0.831736741158426 | 0.336526517683147 | 0.168263258841574 |
142 | 0.733328209284037 | 0.533343581431926 | 0.266671790715963 |
143 | 0.6146867160109 | 0.770626567978201 | 0.385313283989100 |
144 | 0.685372843446449 | 0.629254313107101 | 0.314627156553551 |
Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
Description | # significant tests | % significant tests | OK/NOK |
1% type I error level | 20 | 0.150375939849624 | NOK |
5% type I error level | 43 | 0.323308270676692 | NOK |
10% type I error level | 55 | 0.413533834586466 | NOK |