Multiple Linear Regression - Estimated Regression Equation |
Popularity[t] = + 0.305904887836174 + 0.094633084474476FindingFriends[t] + 0.243797535254599KnowingPeople[t] + 0.34915593440117Liked[t] + 0.627017042711136Celebrity[t] -0.00119728221808973Date[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) | 0.305904887836174 | 1.435088 | 0.2132 | 0.831491 | 0.415745 |
FindingFriends | 0.094633084474476 | 0.096383 | 0.9818 | 0.327759 | 0.163879 |
KnowingPeople | 0.243797535254599 | 0.061591 | 3.9583 | 0.000116 | 5.8e-05 |
Liked | 0.34915593440117 | 0.097709 | 3.5734 | 0.000474 | 0.000237 |
Celebrity | 0.627017042711136 | 0.156594 | 4.0041 | 9.8e-05 | 4.9e-05 |
Date | -0.00119728221808973 | 0.062964 | -0.019 | 0.984854 | 0.492427 |
Multiple Linear Regression - Regression Statistics | |
Multiple R | 0.706541857390106 |
R-squared | 0.499201396244261 |
Adjusted R-squared | 0.482508109452403 |
F-TEST (value) | 29.9043203695357 |
F-TEST (DF numerator) | 5 |
F-TEST (DF denominator) | 150 |
p-value | 0 |
Multiple Linear Regression - Residual Statistics | |
Residual Standard Deviation | 2.11251892472136 |
Sum Squared Residuals | 669.410431095885 |
Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
1 | 13 | 11.3681814726992 | 1.63181852730078 |
2 | 12 | 11.0647972621195 | 0.935202737880534 |
3 | 15 | 13.5252060801035 | 1.47479391989646 |
4 | 12 | 10.8149615817514 | 1.1850384182486 |
5 | 10 | 10.6648142948774 | -0.664814294877374 |
6 | 12 | 9.21780970704143 | 2.78219029295857 |
7 | 15 | 16.73664142877 | -1.73664142876999 |
8 | 9 | 10.4708609563698 | -1.47086095636979 |
9 | 12 | 12.2497213653371 | -0.249721365337096 |
10 | 11 | 7.9857629044476 | 3.01423709555239 |
11 | 11 | 13.3289189299472 | -2.32891892994723 |
12 | 11 | 12.0740509761932 | -1.07405097619323 |
13 | 15 | 12.2222325908794 | 2.77776740912056 |
14 | 7 | 11.2530805949745 | -4.25308059497451 |
15 | 11 | 11.6372829385250 | -0.637282938524961 |
16 | 11 | 10.958456026879 | 0.0415439731210098 |
17 | 10 | 12.0740509761932 | -2.07405097619323 |
18 | 14 | 14.3512317703418 | -0.351231770341828 |
19 | 10 | 8.7015285798565 | 1.29847142014350 |
20 | 6 | 9.50890318127013 | -3.50890318127013 |
21 | 11 | 8.65485206308995 | 2.34514793691005 |
22 | 15 | 14.3840980611791 | 0.615901938820894 |
23 | 11 | 11.6280818390056 | -0.628081839005588 |
24 | 12 | 9.49447353313331 | 2.50552646686669 |
25 | 14 | 13.3971997693947 | 0.602800230605293 |
26 | 15 | 14.8376295586329 | 0.162370441367064 |
27 | 9 | 14.6278955964337 | -5.62789559643371 |
28 | 13 | 12.4970087879322 | 0.502991212067762 |
29 | 13 | 13.2186589151178 | -0.218658915117850 |
30 | 16 | 10.7857388715914 | 5.21426112840858 |
31 | 13 | 8.50153709623545 | 4.49846290376455 |
32 | 12 | 13.5911531079023 | -1.59115310790229 |
33 | 14 | 14.4787311456536 | -0.478731145653582 |
34 | 11 | 10.0568533170743 | 0.943146682925747 |
35 | 9 | 10.4684663919336 | -1.46846639193361 |
36 | 16 | 14.2434788067591 | 1.75652119324092 |
37 | 12 | 12.8753266797060 | -0.875326679705963 |
38 | 10 | 9.19261353770623 | 0.807386462293765 |
39 | 13 | 13.0575718674475 | -0.0575718674475427 |
40 | 16 | 15.2196517838714 | 0.780348216128617 |
41 | 14 | 12.9084074166674 | 1.09159258333258 |
42 | 15 | 8.09476488427146 | 6.90523511572854 |
43 | 5 | 9.74311193128328 | -4.74311193128328 |
44 | 8 | 10.4791917066057 | -2.47919170660571 |
45 | 11 | 11.2456307215188 | -0.245630721518783 |
46 | 16 | 13.7899473093052 | 2.21005269069475 |
47 | 17 | 13.0235082943922 | 3.97649170560783 |
48 | 9 | 8.48591016588054 | 0.514089834119459 |
49 | 9 | 11.9429597542272 | -2.94295975422721 |
50 | 13 | 14.6872678256347 | -1.68726782563472 |
51 | 10 | 10.9580271346306 | -0.958027134630632 |
52 | 6 | 12.4125940827328 | -6.41259408273276 |
53 | 12 | 12.3855514908848 | -0.385551490884766 |
54 | 8 | 10.4341883727541 | -2.43418837275407 |
55 | 14 | 12.3748261762127 | 1.62517382378733 |
56 | 12 | 12.4293575425183 | -0.429357542518318 |
57 | 11 | 10.7763233259479 | 0.223676674052136 |
58 | 16 | 14.4021712899932 | 1.59782871000679 |
59 | 8 | 10.2714281421689 | -2.27142814216886 |
60 | 15 | 15.2525180747087 | -0.252518074708661 |
61 | 7 | 9.45801539564176 | -2.45801539564176 |
62 | 16 | 13.9877586746143 | 2.01224132538570 |
63 | 14 | 13.7369401581523 | 0.263059841847675 |
64 | 16 | 13.7546864540318 | 2.24531354596821 |
65 | 9 | 9.9405551571314 | -0.940555157131408 |
66 | 14 | 12.2801930917382 | 1.71980690826181 |
67 | 11 | 13.0456492705574 | -2.04564927055736 |
68 | 13 | 10.4682519458094 | 2.53174805419057 |
69 | 15 | 12.9060128522312 | 2.09398714776876 |
70 | 5 | 5.59978555783491 | -0.59978555783491 |
71 | 15 | 12.4281602603002 | 2.57183973969977 |
72 | 13 | 12.2789958095201 | 0.721004190479895 |
73 | 11 | 12.0459235889376 | -1.04592358893760 |
74 | 11 | 13.9786356182437 | -2.97863561824366 |
75 | 12 | 12.4729491480277 | -0.47294914802769 |
76 | 12 | 13.3936079227404 | -1.39360792274044 |
77 | 12 | 12.268270494848 | -0.26827049484801 |
78 | 12 | 11.9004634716222 | 0.0995365283777986 |
79 | 14 | 10.7821470249371 | 3.21785297506285 |
80 | 6 | 7.99305006580217 | -1.99305006580217 |
81 | 7 | 9.84003762088021 | -2.84003762088021 |
82 | 14 | 11.9890584109832 | 2.01094158901678 |
83 | 14 | 13.8588475709603 | 0.141152429039728 |
84 | 10 | 11.2529786356608 | -1.25297863566079 |
85 | 13 | 8.72542550765988 | 4.27457449234012 |
86 | 12 | 12.4076924670499 | -0.407692467049949 |
87 | 9 | 9.2896929206399 | -0.289692920639904 |
88 | 12 | 12.0153499032228 | -0.0153499032227770 |
89 | 16 | 15.0063259750179 | 0.993674024982118 |
90 | 10 | 10.2318023246968 | -0.231802324696840 |
91 | 14 | 13.1262576829784 | 0.873742317021613 |
92 | 10 | 13.5084943543410 | -3.50849435434101 |
93 | 16 | 15.3106930216916 | 0.68930697830841 |
94 | 15 | 13.446942006828 | 1.55305799317201 |
95 | 12 | 11.3464144379172 | 0.653585562082827 |
96 | 10 | 9.73348193951555 | 0.266518060484451 |
97 | 8 | 10.2374723303494 | -2.23747233034939 |
98 | 8 | 8.60814451162312 | -0.608144511623122 |
99 | 11 | 12.8413755934610 | -1.84137559346105 |
100 | 13 | 12.4172204995040 | 0.582779500496046 |
101 | 16 | 15.4598574724717 | 0.540142527528288 |
102 | 16 | 14.7177395520358 | 1.28226044796418 |
103 | 14 | 15.8150515519863 | -1.81505155198634 |
104 | 11 | 8.884117990894 | 2.11588200910600 |
105 | 4 | 6.96583560972476 | -2.96583560972476 |
106 | 14 | 14.5695579373496 | -0.56955793734961 |
107 | 9 | 10.3457059202035 | -1.34570592020351 |
108 | 14 | 15.2489262280544 | -1.24892622805439 |
109 | 8 | 10.4510643193501 | -2.45106431935008 |
110 | 8 | 10.8995405077844 | -2.89954050778435 |
111 | 11 | 12.1926934752815 | -1.19269347528154 |
112 | 12 | 13.6396980631175 | -1.63969806311749 |
113 | 11 | 11.4408330762675 | -0.44083307626747 |
114 | 14 | 13.6019301565974 | 0.3980698434026 |
115 | 15 | 14.3343055984551 | 0.665694401544895 |
116 | 16 | 13.4019386729764 | 2.59806132702365 |
117 | 16 | 13.4965717574508 | 2.50342824254917 |
118 | 11 | 12.7320984147256 | -1.73209841472558 |
119 | 14 | 13.7403692927054 | 0.259630707294573 |
120 | 14 | 10.9619976482425 | 3.03800235175745 |
121 | 12 | 11.4057866671182 | 0.594213332881809 |
122 | 14 | 12.5642048319721 | 1.43579516802792 |
123 | 8 | 10.2306050424788 | -2.23060504247875 |
124 | 13 | 13.8350023771799 | -0.835002377179903 |
125 | 16 | 13.7403692927054 | 2.25963070729457 |
126 | 12 | 10.9191744327029 | 1.08082556729709 |
127 | 16 | 15.4489177116754 | 0.551082288324562 |
128 | 12 | 13.3912133583043 | -1.39121335830426 |
129 | 11 | 11.5158322358234 | -0.515832235823396 |
130 | 4 | 6.42206570808217 | -2.42206570808217 |
131 | 16 | 15.4489177116754 | 0.551082288324562 |
132 | 15 | 12.5651876680660 | 2.43481233193401 |
133 | 10 | 11.4780643293033 | -1.47806432930331 |
134 | 13 | 13.2089681705627 | -0.208968170562678 |
135 | 15 | 13.2527742221962 | 1.74722577780377 |
136 | 12 | 10.6743940613544 | 1.32560593864560 |
137 | 14 | 13.6457362082310 | 0.354263791769049 |
138 | 7 | 10.6722139430424 | -3.6722139430424 |
139 | 19 | 14.0883279448885 | 4.91167205511149 |
140 | 12 | 12.6790912635727 | -0.679091263572652 |
141 | 12 | 12.2851464414440 | -0.28514644144402 |
142 | 13 | 13.4953744752327 | -0.495374475232739 |
143 | 15 | 12.9396522586128 | 2.06034774138719 |
144 | 8 | 8.28363660463377 | -0.283636604633769 |
145 | 12 | 10.9169943143909 | 1.08300568560910 |
146 | 10 | 10.8028762727601 | -0.80287627276006 |
147 | 8 | 11.4055722209940 | -3.40557222099401 |
148 | 10 | 14.3722271983119 | -4.37222719831194 |
149 | 15 | 13.8883364612675 | 1.11166353873254 |
150 | 16 | 14.6097721423289 | 1.39022785767111 |
151 | 13 | 13.1886128641229 | -0.188612864122853 |
152 | 16 | 15.0621063575646 | 0.937893642435368 |
153 | 9 | 10.2222240669521 | -1.22222406695212 |
154 | 14 | 13.1604854768672 | 0.839514523132779 |
155 | 14 | 12.6952458286474 | 1.30475417135261 |
156 | 12 | 10.1540969208414 | 1.84590307915861 |
Goldfeld-Quandt test for Heteroskedasticity | |||
p-values | Alternative Hypothesis | ||
breakpoint index | greater | 2-sided | less |
9 | 0.109732326342069 | 0.219464652684137 | 0.890267673657931 |
10 | 0.0478334606174779 | 0.0956669212349558 | 0.952166539382522 |
11 | 0.0725632970548877 | 0.145126594109775 | 0.927436702945112 |
12 | 0.0379086060481914 | 0.0758172120963829 | 0.962091393951809 |
13 | 0.440216848849322 | 0.880433697698644 | 0.559783151150678 |
14 | 0.760291219104802 | 0.479417561790395 | 0.239708780895198 |
15 | 0.679090383786212 | 0.641819232427576 | 0.320909616213788 |
16 | 0.58962820657995 | 0.820743586840099 | 0.410371793420050 |
17 | 0.529743023336689 | 0.94051395332662 | 0.47025697666331 |
18 | 0.442218125560302 | 0.884436251120604 | 0.557781874439698 |
19 | 0.360695671345517 | 0.721391342691033 | 0.639304328654483 |
20 | 0.547648792862149 | 0.904702414275702 | 0.452351207137851 |
21 | 0.508989005839123 | 0.982021988321755 | 0.491010994160877 |
22 | 0.551326979645805 | 0.89734604070839 | 0.448673020354195 |
23 | 0.484808020958034 | 0.969616041916068 | 0.515191979041966 |
24 | 0.472439346095565 | 0.94487869219113 | 0.527560653904435 |
25 | 0.428515489407216 | 0.857030978814433 | 0.571484510592784 |
26 | 0.365029840767791 | 0.730059681535582 | 0.634970159232209 |
27 | 0.633228084209867 | 0.733543831580266 | 0.366771915790133 |
28 | 0.576387895918473 | 0.847224208163054 | 0.423612104081527 |
29 | 0.515143066332431 | 0.969713867335138 | 0.484856933667569 |
30 | 0.67575325628607 | 0.648493487427862 | 0.324246743713931 |
31 | 0.785614438622079 | 0.428771122755842 | 0.214385561377921 |
32 | 0.747004056509213 | 0.505991886981574 | 0.252995943490787 |
33 | 0.699155669188381 | 0.601688661623239 | 0.300844330811619 |
34 | 0.66800657021906 | 0.66398685956188 | 0.33199342978094 |
35 | 0.674127760395117 | 0.651744479209767 | 0.325872239604883 |
36 | 0.681879440344056 | 0.636241119311889 | 0.318120559655944 |
37 | 0.648895360446243 | 0.702209279107515 | 0.351104639553757 |
38 | 0.59964638768087 | 0.80070722463826 | 0.40035361231913 |
39 | 0.545677464766908 | 0.908645070466185 | 0.454322535233092 |
40 | 0.516899303518623 | 0.966201392962754 | 0.483100696481377 |
41 | 0.47695980062112 | 0.95391960124224 | 0.52304019937888 |
42 | 0.756466814005642 | 0.487066371988716 | 0.243533185994358 |
43 | 0.951208463021776 | 0.0975830739564483 | 0.0487915369782241 |
44 | 0.96239092051831 | 0.0752181589633814 | 0.0376090794816907 |
45 | 0.951166801615597 | 0.0976663967688057 | 0.0488331983844028 |
46 | 0.956997103691428 | 0.0860057926171443 | 0.0430028963085722 |
47 | 0.97938888625303 | 0.0412222274939395 | 0.0206111137469698 |
48 | 0.97275725223996 | 0.0544854955200808 | 0.0272427477600404 |
49 | 0.980406011357663 | 0.039187977284674 | 0.019593988642337 |
50 | 0.977271607676881 | 0.0454567846462377 | 0.0227283923231189 |
51 | 0.972524692924262 | 0.0549506141514769 | 0.0274753070757384 |
52 | 0.997283162359902 | 0.00543367528019548 | 0.00271683764009774 |
53 | 0.996084008803852 | 0.00783198239229663 | 0.00391599119614831 |
54 | 0.996682988511785 | 0.00663402297642927 | 0.00331701148821464 |
55 | 0.996706869426715 | 0.00658626114657042 | 0.00329313057328521 |
56 | 0.995342840543343 | 0.00931431891331428 | 0.00465715945665714 |
57 | 0.993506829882361 | 0.0129863402352772 | 0.00649317011763862 |
58 | 0.992949994914736 | 0.0141000101705283 | 0.00705000508526415 |
59 | 0.994502483801805 | 0.0109950323963897 | 0.00549751619819487 |
60 | 0.992773569170312 | 0.0144528616593765 | 0.00722643082968827 |
61 | 0.993514173201735 | 0.0129716535965305 | 0.00648582679826523 |
62 | 0.99432346964115 | 0.0113530607177012 | 0.00567653035885061 |
63 | 0.992452697737018 | 0.0150946045259632 | 0.0075473022629816 |
64 | 0.993170112478232 | 0.0136597750435366 | 0.0068298875217683 |
65 | 0.99132118824474 | 0.0173576235105211 | 0.00867881175526056 |
66 | 0.990725501566732 | 0.0185489968665366 | 0.00927449843326828 |
67 | 0.99033430604444 | 0.0193313879111183 | 0.00966569395555914 |
68 | 0.992138135789397 | 0.0157237284212055 | 0.00786186421060273 |
69 | 0.992450282163557 | 0.0150994356728853 | 0.00754971783644266 |
70 | 0.989832111473835 | 0.0203357770523309 | 0.0101678885261655 |
71 | 0.991554868697349 | 0.0168902626053025 | 0.00844513130265125 |
72 | 0.988873365472085 | 0.02225326905583 | 0.011126634527915 |
73 | 0.986018843274534 | 0.0279623134509329 | 0.0139811567254665 |
74 | 0.98977068868429 | 0.0204586226314218 | 0.0102293113157109 |
75 | 0.9861640044799 | 0.0276719910402 | 0.0138359955201 |
76 | 0.983576708689035 | 0.0328465826219308 | 0.0164232913109654 |
77 | 0.978257061542919 | 0.0434858769141629 | 0.0217429384570814 |
78 | 0.971388475531427 | 0.0572230489371462 | 0.0286115244685731 |
79 | 0.982499485833596 | 0.0350010283328089 | 0.0175005141664045 |
80 | 0.98155601880475 | 0.0368879623905008 | 0.0184439811952504 |
81 | 0.984382562756068 | 0.0312348744878645 | 0.0156174372439322 |
82 | 0.985625207805358 | 0.0287495843892847 | 0.0143747921946423 |
83 | 0.980746255353035 | 0.0385074892939293 | 0.0192537446469647 |
84 | 0.976074547456143 | 0.047850905087715 | 0.0239254525438575 |
85 | 0.994130243519745 | 0.0117395129605102 | 0.00586975648025509 |
86 | 0.991856810864198 | 0.0162863782716042 | 0.0081431891358021 |
87 | 0.9889140053842 | 0.0221719892315976 | 0.0110859946157988 |
88 | 0.985491406105674 | 0.0290171877886515 | 0.0145085938943257 |
89 | 0.98187731264427 | 0.0362453747114609 | 0.0181226873557305 |
90 | 0.976056160626933 | 0.0478876787461345 | 0.0239438393730673 |
91 | 0.97138847642604 | 0.0572230471479186 | 0.0286115235739593 |
92 | 0.983093098792092 | 0.0338138024158166 | 0.0169069012079083 |
93 | 0.978149555768749 | 0.043700888462503 | 0.0218504442312515 |
94 | 0.975447144052553 | 0.0491057118948942 | 0.0245528559474471 |
95 | 0.969263366009464 | 0.0614732679810728 | 0.0307366339905364 |
96 | 0.961362010690354 | 0.0772759786192916 | 0.0386379893096458 |
97 | 0.957766317042826 | 0.0844673659143478 | 0.0422336829571739 |
98 | 0.945951249835362 | 0.108097500329275 | 0.0540487501646376 |
99 | 0.940975331168636 | 0.118049337662727 | 0.0590246688313636 |
100 | 0.927576095201148 | 0.144847809597704 | 0.0724239047988522 |
101 | 0.910046230250982 | 0.179907539498037 | 0.0899537697490184 |
102 | 0.89586644876648 | 0.208267102467041 | 0.104133551233521 |
103 | 0.901750648992908 | 0.196498702014184 | 0.0982493510070922 |
104 | 0.93592171543225 | 0.128156569135500 | 0.0640782845677502 |
105 | 0.933126584117226 | 0.133746831765548 | 0.066873415882774 |
106 | 0.915366425464635 | 0.169267149070730 | 0.0846335745353651 |
107 | 0.896991737865532 | 0.206016524268935 | 0.103008262134468 |
108 | 0.891440600454891 | 0.217118799090218 | 0.108559399545109 |
109 | 0.887263373489942 | 0.225473253020116 | 0.112736626510058 |
110 | 0.90504062255482 | 0.189918754890359 | 0.0949593774451794 |
111 | 0.893555306290796 | 0.212889387418408 | 0.106444693709204 |
112 | 0.921601018936764 | 0.156797962126472 | 0.0783989810632361 |
113 | 0.899993722750785 | 0.200012554498430 | 0.100006277249215 |
114 | 0.87465357556155 | 0.2506928488769 | 0.12534642443845 |
115 | 0.845373780576912 | 0.309252438846176 | 0.154626219423088 |
116 | 0.847493292799829 | 0.305013414400342 | 0.152506707200171 |
117 | 0.857816436644454 | 0.284367126711093 | 0.142183563355546 |
118 | 0.846274096123627 | 0.307451807752747 | 0.153725903876373 |
119 | 0.80970547163423 | 0.380589056731539 | 0.190294528365770 |
120 | 0.866610074544322 | 0.266779850911356 | 0.133389925455678 |
121 | 0.841727180934622 | 0.316545638130755 | 0.158272819065378 |
122 | 0.820500446297295 | 0.35899910740541 | 0.179499553702705 |
123 | 0.807159276986429 | 0.385681446027142 | 0.192840723013571 |
124 | 0.766077986582995 | 0.467844026834011 | 0.233922013417005 |
125 | 0.770079067549306 | 0.459841864901387 | 0.229920932450694 |
126 | 0.756640301322839 | 0.486719397354322 | 0.243359698677161 |
127 | 0.704220769419521 | 0.591558461160958 | 0.295779230580479 |
128 | 0.672219235858587 | 0.655561528282827 | 0.327780764141413 |
129 | 0.678450557814505 | 0.64309888437099 | 0.321549442185495 |
130 | 0.67083467524328 | 0.658330649513439 | 0.329165324756719 |
131 | 0.611218910135329 | 0.777562179729341 | 0.388781089864671 |
132 | 0.596622454026247 | 0.806755091947505 | 0.403377545973753 |
133 | 0.569621223431652 | 0.860757553136696 | 0.430378776568348 |
134 | 0.494839198306356 | 0.989678396612712 | 0.505160801693644 |
135 | 0.466044420676628 | 0.932088841353255 | 0.533955579323372 |
136 | 0.462599010992722 | 0.925198021985445 | 0.537400989007278 |
137 | 0.386926968913845 | 0.77385393782769 | 0.613073031086155 |
138 | 0.447548600580040 | 0.895097201160081 | 0.55245139941996 |
139 | 0.802035821194748 | 0.395928357610503 | 0.197964178805251 |
140 | 0.827418680766961 | 0.345162638466078 | 0.172581319233039 |
141 | 0.790552960739502 | 0.418894078520995 | 0.209447039260498 |
142 | 0.711298383720851 | 0.577403232558297 | 0.288701616279149 |
143 | 0.657294189701565 | 0.68541162059687 | 0.342705810298435 |
144 | 0.545068287359323 | 0.909863425281354 | 0.454931712640677 |
145 | 0.536845720468542 | 0.926308559062917 | 0.463154279531458 |
146 | 0.669325694184239 | 0.661348611631522 | 0.330674305815761 |
147 | 0.571604863782527 | 0.856790272434947 | 0.428395136217473 |
Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
Description | # significant tests | % significant tests | OK/NOK |
1% type I error level | 5 | 0.0359712230215827 | NOK |
5% type I error level | 44 | 0.316546762589928 | NOK |
10% type I error level | 57 | 0.410071942446043 | NOK |