Multiple Linear Regression - Estimated Regression Equation |
Future[t] = + 2.88086949626936 + 0.192484920465587Popular[t] + 0.00370138668767256`Friends(s)`[t] + 0.0391435615499212`Friends(f)`[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) | 2.88086949626936 | 0.249779 | 11.5337 | 0 | 0 |
Popular | 0.192484920465587 | 0.092765 | 2.075 | 0.039708 | 0.019854 |
`Friends(s)` | 0.00370138668767256 | 0.09127 | 0.0406 | 0.967706 | 0.483853 |
`Friends(f)` | 0.0391435615499212 | 0.094358 | 0.4148 | 0.678856 | 0.339428 |
Multiple Linear Regression - Regression Statistics | |
Multiple R | 0.242865244796705 |
R-squared | 0.0589835271301634 |
Adjusted R-squared | 0.0400368867368109 |
F-TEST (value) | 3.11313910569909 |
F-TEST (DF numerator) | 3 |
F-TEST (DF denominator) | 149 |
p-value | 0.0281363255655216 |
Multiple Linear Regression - Residual Statistics | |
Residual Standard Deviation | 0.683086713038985 |
Sum Squared Residuals | 69.5245111720302 |
Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
1 | 4 | 3.58685910237899 | 0.41314089762101 |
2 | 4 | 3.58685910237891 | 0.413140897621087 |
3 | 3 | 3.78304540953217 | -0.783045409532169 |
4 | 4 | 3.58685910237891 | 0.41314089762109 |
5 | 3 | 3.54401415414132 | -0.544014154141317 |
6 | 4 | 3.54771554082899 | 0.452284459171011 |
7 | 4 | 3.6297040506165 | 0.370295949383496 |
8 | 4 | 3.35152923367573 | 0.64847076632427 |
9 | 4 | 3.58685910237891 | 0.413140897621090 |
10 | 2 | 3.55141692751666 | -1.55141692751666 |
11 | 2 | 3.62600266392883 | -1.62600266392883 |
12 | 4 | 3.58685910237891 | 0.413140897621090 |
13 | 4 | 3.59056048906658 | 0.409439510933417 |
14 | 4 | 3.35152923367573 | 0.64847076632427 |
15 | 4 | 3.58315771569124 | 0.416842284308762 |
16 | 3 | 3.54771554082899 | -0.547715540828989 |
17 | 4 | 3.39067279522565 | 0.609327204774349 |
18 | 4 | 3.59056048906658 | 0.409439510933417 |
19 | 3 | 3.35152923367573 | -0.351529233675730 |
20 | 2 | 3.19448648807239 | -1.19448648807239 |
21 | 2 | 3.3552306203634 | -1.35523062036340 |
22 | 4 | 3.59056048906658 | 0.409439510933417 |
23 | 3 | 3.58315771569124 | -0.583157715691238 |
24 | 4 | 3.54771554082899 | 0.452284459171011 |
25 | 4 | 3.58685910237891 | 0.413140897621090 |
26 | 3 | 3.59056048906658 | -0.590560489066583 |
27 | 3 | 3.43351774346324 | -0.433517743463244 |
28 | 2 | 3.58685910237891 | -1.58685910237891 |
29 | 3 | 3.59056048906658 | -0.590560489066583 |
30 | 4 | 3.74390184798225 | 0.256098152017751 |
31 | 3 | 3.55141692751666 | -0.551416927516662 |
32 | 3 | 3.62600266392883 | -0.626002663928832 |
33 | 4 | 3.6297040506165 | 0.370295949383496 |
34 | 4 | 3.39067279522565 | 0.609327204774349 |
35 | 3 | 3.6297040506165 | -0.629704050616504 |
36 | 4 | 3.58685910237891 | 0.413140897621090 |
37 | 2 | 3.54401415414132 | -1.54401415414132 |
38 | 3 | 3.59056048906658 | -0.590560489066583 |
39 | 4 | 3.82218897108209 | 0.177811028917909 |
40 | 4 | 3.59056048906658 | 0.409439510933417 |
41 | 3 | 3.59056048906658 | -0.590560489066583 |
42 | 5 | 3.15904431321014 | 1.84095568678986 |
43 | 3 | 3.35152923367573 | -0.351529233675730 |
44 | 3 | 3.58685910237891 | -0.58685910237891 |
45 | 4 | 3.82218897108209 | 0.177811028917909 |
46 | 4 | 3.82589035776976 | 0.174109642230236 |
47 | 5 | 3.35152923367573 | 1.64847076632427 |
48 | 3 | 3.20188926144774 | -0.201889261447736 |
49 | 4 | 3.58685910237891 | 0.413140897621090 |
50 | 4 | 3.58315771569124 | 0.416842284308762 |
51 | 2 | 3.15904431321014 | -1.15904431321014 |
52 | 4 | 3.62600266392883 | 0.373997336071168 |
53 | 4 | 3.39067279522565 | 0.609327204774349 |
54 | 4 | 3.6297040506165 | 0.370295949383496 |
55 | 3 | 3.58685910237891 | -0.58685910237891 |
56 | 3 | 3.39437418191332 | -0.394374181913323 |
57 | 3 | 3.82218897108209 | -0.822188971082091 |
58 | 2 | 3.11619936497255 | -1.11619936497255 |
59 | 4 | 3.6297040506165 | 0.370295949383496 |
60 | 4 | 3.35152923367573 | 0.64847076632427 |
61 | 4 | 3.78304540953217 | 0.21695459046783 |
62 | 3 | 3.59056048906658 | -0.590560489066583 |
63 | 4 | 3.78304540953217 | 0.21695459046783 |
64 | 3 | 3.58315771569124 | -0.583157715691238 |
65 | 4 | 3.6297040506165 | 0.370295949383496 |
66 | 4 | 3.54401415414132 | 0.455985845858683 |
67 | 4 | 3.55141692751666 | 0.448583072483338 |
68 | 4 | 3.6297040506165 | 0.370295949383496 |
69 | 4 | 3.11619936497255 | 0.883800635027451 |
70 | 4 | 3.6297040506165 | 0.370295949383496 |
71 | 4 | 3.6297040506165 | 0.370295949383496 |
72 | 4 | 3.58685910237891 | 0.413140897621090 |
73 | 2 | 3.3552306203634 | -1.35523062036340 |
74 | 3 | 3.58685910237891 | -0.58685910237891 |
75 | 4 | 3.58685910237891 | 0.413140897621090 |
76 | 4 | 3.58685910237891 | 0.413140897621090 |
77 | 3 | 3.39437418191332 | -0.394374181913323 |
78 | 4 | 3.6297040506165 | 0.370295949383496 |
79 | 4 | 3.34782784698806 | 0.652172153011943 |
80 | 4 | 3.39437418191332 | 0.605625818086677 |
81 | 3 | 3.59056048906658 | -0.590560489066583 |
82 | 3 | 3.58685910237891 | -0.58685910237891 |
83 | 3 | 3.3552306203634 | -0.355230620363402 |
84 | 3 | 3.35893200705107 | -0.358932007051075 |
85 | 4 | 3.58685910237891 | 0.413140897621090 |
86 | 4 | 3.35152923367573 | 0.64847076632427 |
87 | 2 | 3.58685910237891 | -1.58685910237891 |
88 | 4 | 3.78304540953217 | 0.21695459046783 |
89 | 3 | 3.39437418191332 | -0.394374181913323 |
90 | 4 | 3.59056048906658 | 0.409439510933417 |
91 | 3 | 3.43351774346324 | -0.433517743463244 |
92 | 4 | 3.82218897108209 | 0.177811028917909 |
93 | 3 | 3.6297040506165 | -0.629704050616504 |
94 | 3 | 3.58685910237891 | -0.58685910237891 |
95 | 4 | 3.54401415414132 | 0.455985845858683 |
96 | 3 | 3.57945632900357 | -0.579456329003566 |
97 | 4 | 3.35152923367573 | 0.64847076632427 |
98 | 2 | 3.58315771569124 | -1.58315771569124 |
99 | 4 | 3.7793440228445 | 0.220655977155502 |
100 | 4 | 3.82218897108209 | 0.177811028917909 |
101 | 4 | 3.78304540953217 | 0.21695459046783 |
102 | 4 | 3.58685910237891 | 0.413140897621090 |
103 | 4 | 3.54771554082899 | 0.452284459171011 |
104 | 3 | 3.11619936497255 | -0.116199364972549 |
105 | 4 | 3.7793440228445 | 0.220655977155502 |
106 | 3 | 3.20188926144774 | -0.201889261447736 |
107 | 4 | 3.6297040506165 | 0.370295949383496 |
108 | 3 | 3.35152923367573 | -0.351529233675730 |
109 | 3 | 3.58685910237891 | -0.58685910237891 |
110 | 2 | 3.62600266392883 | -1.62600266392883 |
111 | 4 | 3.39437418191332 | 0.605625818086677 |
112 | 4 | 3.6297040506165 | 0.370295949383496 |
113 | 4 | 3.6297040506165 | 0.370295949383496 |
114 | 1 | 3.78304540953217 | -2.78304540953217 |
115 | 4 | 3.78304540953217 | 0.21695459046783 |
116 | 4 | 3.58315771569124 | 0.416842284308762 |
117 | 4 | 3.58685910237891 | 0.413140897621090 |
118 | 3 | 3.59056048906658 | -0.590560489066583 |
119 | 4 | 3.58685910237891 | 0.413140897621090 |
120 | 4 | 3.59056048906658 | 0.409439510933417 |
121 | 3 | 3.19818787476006 | -0.198187874760064 |
122 | 4 | 3.43721913015092 | 0.562780869849083 |
123 | 4 | 3.78304540953217 | 0.21695459046783 |
124 | 4 | 3.54771554082899 | 0.452284459171011 |
125 | 4 | 3.82218897108209 | 0.177811028917909 |
126 | 4 | 3.58685910237891 | 0.413140897621090 |
127 | 3 | 3.39437418191332 | -0.394374181913323 |
128 | 3 | 3.11619936497255 | -0.116199364972549 |
129 | 4 | 3.82218897108209 | 0.177811028917909 |
130 | 4 | 3.59056048906658 | 0.409439510933417 |
131 | 4 | 3.54401415414132 | 0.455985845858683 |
132 | 4 | 3.54771554082899 | 0.452284459171011 |
133 | 4 | 3.82218897108209 | 0.177811028917909 |
134 | 4 | 3.58685910237891 | 0.413140897621090 |
135 | 4 | 3.6297040506165 | 0.370295949383496 |
136 | 4 | 3.15904431321014 | 0.840955686789858 |
137 | 4 | 3.82589035776976 | 0.174109642230236 |
138 | 3 | 3.43351774346324 | -0.433517743463244 |
139 | 3 | 3.39807556860100 | -0.398075568600996 |
140 | 4 | 3.58685910237891 | 0.413140897621090 |
141 | 4 | 3.59056048906658 | 0.409439510933417 |
142 | 2 | 3.35152923367573 | -1.35152923367573 |
143 | 4 | 3.58685910237891 | 0.413140897621090 |
144 | 4 | 3.58685910237891 | 0.413140897621090 |
145 | 4 | 3.39067279522565 | 0.609327204774349 |
146 | 4 | 3.6297040506165 | 0.370295949383496 |
147 | 4 | 3.78304540953217 | 0.21695459046783 |
148 | 4 | 3.7793440228445 | 0.220655977155502 |
149 | 4 | 3.82218897108209 | 0.177811028917909 |
150 | 4 | 3.35152923367573 | 0.64847076632427 |
151 | 4 | 3.59056048906658 | 0.409439510933417 |
152 | 4 | 3.6297040506165 | 0.370295949383496 |
153 | 4 | 3.54771554082899 | 0.452284459171011 |
Goldfeld-Quandt test for Heteroskedasticity | |||
p-values | Alternative Hypothesis | ||
breakpoint index | greater | 2-sided | less |
7 | 0.110388916039681 | 0.220777832079362 | 0.889611083960319 |
8 | 0.098014475772235 | 0.19602895154447 | 0.901985524227765 |
9 | 0.0513418193193445 | 0.102683638638689 | 0.948658180680656 |
10 | 0.246111816534223 | 0.492223633068446 | 0.753888183465777 |
11 | 0.931009033597079 | 0.137981932805842 | 0.0689909664029208 |
12 | 0.906836471803777 | 0.186327056392446 | 0.0931635281962229 |
13 | 0.886912496027557 | 0.226175007944886 | 0.113087503972443 |
14 | 0.840833047370037 | 0.318333905259926 | 0.159166952629963 |
15 | 0.792754445558527 | 0.414491108882945 | 0.207245554441473 |
16 | 0.749736463995895 | 0.50052707200821 | 0.250263536004105 |
17 | 0.689227894008329 | 0.621544211983343 | 0.310772105991671 |
18 | 0.653179685995844 | 0.693640628008312 | 0.346820314004156 |
19 | 0.672323660387114 | 0.655352679225771 | 0.327676339612886 |
20 | 0.878456223010478 | 0.243087553979044 | 0.121543776989522 |
21 | 0.9224941862606 | 0.1550116274788 | 0.0775058137394 |
22 | 0.910438872600753 | 0.179122254798493 | 0.0895611273992466 |
23 | 0.902998442970606 | 0.194003114058788 | 0.0970015570293938 |
24 | 0.887536998072963 | 0.224926003854074 | 0.112463001927037 |
25 | 0.86519032667836 | 0.269619346643282 | 0.134809673321641 |
26 | 0.847176014162638 | 0.305647971674724 | 0.152823985837362 |
27 | 0.812441208504949 | 0.375117582990102 | 0.187558791495051 |
28 | 0.922281070355826 | 0.155437859288349 | 0.0777189296441745 |
29 | 0.907597139904716 | 0.184805720190569 | 0.0924028600952843 |
30 | 0.883178604610836 | 0.233642790778327 | 0.116821395389164 |
31 | 0.863027532547663 | 0.273944934904674 | 0.136972467452337 |
32 | 0.846448413598789 | 0.307103172802422 | 0.153551586401211 |
33 | 0.834491437222236 | 0.331017125555529 | 0.165508562777764 |
34 | 0.836971570282701 | 0.326056859434598 | 0.163028429717299 |
35 | 0.81713611210189 | 0.36572777579622 | 0.18286388789811 |
36 | 0.79601826510874 | 0.407963469782520 | 0.203981734891260 |
37 | 0.906375480967185 | 0.187249038065630 | 0.0936245190328148 |
38 | 0.893749797857353 | 0.212500404285294 | 0.106250202142647 |
39 | 0.869795975834849 | 0.260408048330303 | 0.130204024165151 |
40 | 0.856263173200115 | 0.287473653599769 | 0.143736826799885 |
41 | 0.840993653924495 | 0.31801269215101 | 0.159006346075505 |
42 | 0.959770499373173 | 0.080459001253654 | 0.040229500626827 |
43 | 0.950815812026748 | 0.0983683759465035 | 0.0491841879732517 |
44 | 0.9439794159149 | 0.112041168170198 | 0.056020584085099 |
45 | 0.933426217517977 | 0.133147564964046 | 0.0665737824820232 |
46 | 0.918988995683136 | 0.162022008633729 | 0.0810110043168643 |
47 | 0.974134319801456 | 0.0517313603970874 | 0.0258656801985437 |
48 | 0.967778100796158 | 0.0644437984076833 | 0.0322218992038417 |
49 | 0.962338194016632 | 0.0753236119667358 | 0.0376618059833679 |
50 | 0.956110809375445 | 0.0877783812491106 | 0.0438891906245553 |
51 | 0.973507949183963 | 0.0529841016320741 | 0.0264920508160371 |
52 | 0.968053622354583 | 0.0638927552908329 | 0.0319463776454165 |
53 | 0.96586261859607 | 0.0682747628078584 | 0.0341373814039292 |
54 | 0.959217502808256 | 0.0815649943834877 | 0.0407824971917439 |
55 | 0.955341969457423 | 0.0893160610851545 | 0.0446580305425772 |
56 | 0.94663033474287 | 0.106739330514260 | 0.0533696652571301 |
57 | 0.949763342848868 | 0.100473314302264 | 0.0502366571511322 |
58 | 0.966364919234824 | 0.067270161530351 | 0.0336350807651755 |
59 | 0.959655877541495 | 0.0806882449170104 | 0.0403441224585052 |
60 | 0.958934517784108 | 0.082130964431783 | 0.0410654822158915 |
61 | 0.949137888492642 | 0.101724223014716 | 0.0508621115073578 |
62 | 0.945397212033407 | 0.109205575933185 | 0.0546027879665926 |
63 | 0.933040598608021 | 0.133918802783957 | 0.0669594013919787 |
64 | 0.927916207527487 | 0.144167584945026 | 0.0720837924725129 |
65 | 0.915762750300083 | 0.168474499399833 | 0.0842372496999166 |
66 | 0.905596957892397 | 0.188806084215205 | 0.0944030421076025 |
67 | 0.894354476723948 | 0.211291046552104 | 0.105645523276052 |
68 | 0.878343005933935 | 0.24331398813213 | 0.121656994066065 |
69 | 0.892304735787625 | 0.215390528424750 | 0.107695264212375 |
70 | 0.876106432813287 | 0.247787134373425 | 0.123893567186713 |
71 | 0.85813193943182 | 0.28373612113636 | 0.14186806056818 |
72 | 0.840543251199303 | 0.318913497601395 | 0.159456748800697 |
73 | 0.911199093141311 | 0.177601813717378 | 0.088800906858689 |
74 | 0.90605778191832 | 0.187884436163362 | 0.0939422180816808 |
75 | 0.892709331813645 | 0.214581336372709 | 0.107290668186355 |
76 | 0.878000321012024 | 0.243999357975953 | 0.121999678987976 |
77 | 0.861372015535337 | 0.277255968929326 | 0.138627984464663 |
78 | 0.842254795045594 | 0.315490409908813 | 0.157745204954406 |
79 | 0.840462121968125 | 0.31907575606375 | 0.159537878031875 |
80 | 0.834127186809114 | 0.331745626381771 | 0.165872813190885 |
81 | 0.829967564997277 | 0.340064870005446 | 0.170032435002723 |
82 | 0.822049315014229 | 0.355901369971543 | 0.177950684985771 |
83 | 0.803205328143534 | 0.393589343712932 | 0.196794671856466 |
84 | 0.795653041496969 | 0.408693917006062 | 0.204346958503031 |
85 | 0.773365155447075 | 0.453269689105851 | 0.226634844552925 |
86 | 0.767564423377878 | 0.464871153244245 | 0.232435576622122 |
87 | 0.898847102835146 | 0.202305794329708 | 0.101152897164854 |
88 | 0.878038017846164 | 0.243923964307673 | 0.121961982153836 |
89 | 0.862985848444913 | 0.274028303110175 | 0.137014151555087 |
90 | 0.842205922280838 | 0.315588155438323 | 0.157794077719162 |
91 | 0.821391895273629 | 0.357216209452742 | 0.178608104726371 |
92 | 0.790426349468003 | 0.419147301063994 | 0.209573650531997 |
93 | 0.788314043530607 | 0.423371912938785 | 0.211685956469393 |
94 | 0.781963563536867 | 0.436072872926267 | 0.218036436463133 |
95 | 0.760769772299285 | 0.47846045540143 | 0.239230227700715 |
96 | 0.739187581303034 | 0.521624837393933 | 0.260812418696966 |
97 | 0.73195561947174 | 0.536088761056521 | 0.268044380528260 |
98 | 0.87699158448667 | 0.246016831026661 | 0.123008415513331 |
99 | 0.851723666755197 | 0.296552666489607 | 0.148276333244803 |
100 | 0.82219151304311 | 0.355616973913779 | 0.177808486956890 |
101 | 0.789557842144584 | 0.420884315710832 | 0.210442157855416 |
102 | 0.762371652524418 | 0.475256694951164 | 0.237628347475582 |
103 | 0.734835522655482 | 0.530328954689037 | 0.265164477344518 |
104 | 0.694503155413431 | 0.610993689173137 | 0.305496844586569 |
105 | 0.65121308988724 | 0.69757382022552 | 0.34878691011276 |
106 | 0.613788060376704 | 0.772423879246593 | 0.386211939623296 |
107 | 0.573964903659489 | 0.852070192681022 | 0.426035096340511 |
108 | 0.54433737904034 | 0.91132524191932 | 0.45566262095966 |
109 | 0.539955710480163 | 0.920088579039674 | 0.460044289519837 |
110 | 0.810780324009516 | 0.378439351980968 | 0.189219675990484 |
111 | 0.792905350186545 | 0.414189299626910 | 0.207094649813455 |
112 | 0.758245183654504 | 0.483509632690991 | 0.241754816345496 |
113 | 0.720428431130574 | 0.559143137738853 | 0.279571568869426 |
114 | 0.999923417219478 | 0.000153165561045106 | 7.6582780522553e-05 |
115 | 0.999865122106047 | 0.000269755787906066 | 0.000134877893953033 |
116 | 0.999770770540183 | 0.00045845891963336 | 0.00022922945981668 |
117 | 0.999624099932415 | 0.000751800135170536 | 0.000375900067585268 |
118 | 0.9998232051608 | 0.000353589678399459 | 0.000176794839199730 |
119 | 0.99970328291529 | 0.000593434169418824 | 0.000296717084709412 |
120 | 0.999496413092402 | 0.00100717381519591 | 0.000503586907597957 |
121 | 0.99918559715839 | 0.00162880568321830 | 0.000814402841609149 |
122 | 0.999098630762545 | 0.00180273847491066 | 0.000901369237455328 |
123 | 0.998496640154991 | 0.00300671969001782 | 0.00150335984500891 |
124 | 0.997533015369552 | 0.0049339692608957 | 0.00246698463044785 |
125 | 0.995925631610736 | 0.00814873677852861 | 0.00407436838926431 |
126 | 0.993600657063679 | 0.0127986858726430 | 0.00639934293632149 |
127 | 0.99293431644219 | 0.0141313671156199 | 0.00706568355780997 |
128 | 0.990020992073513 | 0.0199580158529735 | 0.00997900792648677 |
129 | 0.984016236843606 | 0.0319675263127877 | 0.0159837631563938 |
130 | 0.975808866385532 | 0.0483822672289354 | 0.0241911336144677 |
131 | 0.963413594148303 | 0.0731728117033946 | 0.0365864058516973 |
132 | 0.946471770535698 | 0.107056458928604 | 0.0535282294643020 |
133 | 0.921577937726937 | 0.156844124546126 | 0.0784220622730629 |
134 | 0.889938628108107 | 0.220122743783786 | 0.110061371891893 |
135 | 0.849882875734764 | 0.300234248530472 | 0.150117124265236 |
136 | 0.896896485093708 | 0.206207029812583 | 0.103103514906292 |
137 | 0.85567522695528 | 0.288649546089439 | 0.144324773044720 |
138 | 0.84464219833461 | 0.310715603330782 | 0.155357801665391 |
139 | 0.827414513576426 | 0.345170972847147 | 0.172585486423574 |
140 | 0.759603289725247 | 0.480793420549506 | 0.240396710274753 |
141 | 0.671385924966954 | 0.657228150066093 | 0.328614075033046 |
142 | 1 | 2.55644938728601e-103 | 1.27822469364301e-103 |
143 | 1 | 0 | 0 |
144 | 1 | 0 | 0 |
145 | 1 | 1.58668748111154e-59 | 7.93343740555772e-60 |
146 | 1 | 0 | 0 |
Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
Description | # significant tests | % significant tests | OK/NOK |
1% type I error level | 17 | 0.121428571428571 | NOK |
5% type I error level | 22 | 0.157142857142857 | NOK |
10% type I error level | 37 | 0.264285714285714 | NOK |