Multiple Linear Regression - Estimated Regression Equation |
New[t] = + 2.94270390531953 + 0.185263472328658Popularity[t] + 0.0505286866563771Friends[t] -0.087130072775124Known[t] + 0.0597825118886497Names[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) | 2.94270390531953 | 0.243624 | 12.0789 | 0 | 0 |
Popularity | 0.185263472328658 | 0.095506 | 1.9398 | 0.054265 | 0.027133 |
Friends | 0.0505286866563771 | 0.089776 | 0.5628 | 0.574386 | 0.287193 |
Known | -0.087130072775124 | 0.075564 | -1.1531 | 0.250708 | 0.125354 |
Names | 0.0597825118886497 | 0.071594 | 0.835 | 0.405027 | 0.202514 |
Multiple Linear Regression - Regression Statistics | |
Multiple R | 0.247547090880362 |
R-squared | 0.06127956220333 |
Adjusted R-squared | 0.0364127956391799 |
F-TEST (value) | 2.46431565781758 |
F-TEST (DF numerator) | 4 |
F-TEST (DF denominator) | 151 |
p-value | 0.0475045513703866 |
Multiple Linear Regression - Residual Statistics | |
Residual Standard Deviation | 0.70860242857057 |
Sum Squared Residuals | 75.8197276681926 |
Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
1 | 4 | 3.48090762684009 | 0.519092373159909 |
2 | 4 | 3.59538526050169 | 0.404614739498314 |
3 | 3 | 3.65691727393647 | -0.656917273936472 |
4 | 4 | 3.44847267583791 | 0.551527324162088 |
5 | 3 | 3.51750901295883 | -0.517509012958834 |
6 | 4 | 3.68251533327681 | 0.317484666723191 |
7 | 4 | 3.59121882538511 | 0.408781174614886 |
8 | 4 | 3.27246302874153 | 0.727536971258473 |
9 | 4 | 3.54069013872874 | 0.459309861271263 |
10 | 2 | 3.67326150804454 | -1.67326150804454 |
11 | 2 | 3.54069013872874 | -1.54069013872874 |
12 | 4 | 3.56803769961521 | 0.431962300384789 |
13 | 4 | 3.59121882538511 | 0.408781174614886 |
14 | 4 | 3.1853329559664 | 0.814667044033597 |
15 | 4 | 3.63198664662043 | 0.368013353379568 |
16 | 3 | 3.42112511495144 | -0.421125114951438 |
17 | 4 | 3.4193756134053 | 0.5806243865947 |
18 | 4 | 3.53143631349646 | 0.468563686503536 |
19 | 3 | 3.35959310151665 | -0.359593101516651 |
20 | 2 | 3.03667086975649 | -1.03667086975649 |
21 | 2 | 3.26320920350925 | -1.26320920350925 |
22 | 4 | 3.67834889816024 | 0.321651101839762 |
23 | 3 | 3.57729152484748 | -0.577291524847484 |
24 | 4 | 3.59538526050169 | 0.404614739498315 |
25 | 4 | 3.54069013872874 | 0.459309861271263 |
26 | 3 | 3.59121882538511 | -0.591218825385114 |
27 | 3 | 3.35542666640008 | -0.355426666400079 |
28 | 2 | 3.48090762684009 | -1.48090762684009 |
29 | 3 | 3.53143631349646 | -0.531436313496464 |
30 | 4 | 3.83117741948672 | 0.168822580513280 |
31 | 3 | 3.64591394715806 | -0.645913947158063 |
32 | 3 | 3.42112511495144 | -0.421125114951438 |
33 | 4 | 3.67834889816024 | 0.321651101839762 |
34 | 2 | 3.53560274861304 | -1.53560274861304 |
35 | 4 | 3.47915812529395 | 0.52084187470605 |
36 | 3 | 3.59121882538511 | -0.591218825385114 |
37 | 4 | 3.44847267583791 | 0.551527324162088 |
38 | 2 | 3.54485657384531 | -1.54485657384531 |
39 | 3 | 3.53143631349646 | -0.531436313496464 |
40 | 4 | 3.77648229771377 | 0.223517702286228 |
41 | 4 | 3.61856638627159 | 0.381433613728412 |
42 | 3 | 3.67326150804454 | -0.673261508044537 |
43 | 5 | 3.23411214107664 | 1.76588785892336 |
44 | 3 | 3.35959310151665 | -0.359593101516651 |
45 | 3 | 3.53560274861304 | -0.535602748613036 |
46 | 4 | 3.71669978582512 | 0.283300214174878 |
47 | 4 | 3.91414105714527 | 0.0858589428547271 |
48 | 5 | 3.299810589628 | 1.700189410372 |
49 | 3 | 3.34442333962167 | -0.344423339621670 |
50 | 4 | 3.54069013872874 | 0.459309861271263 |
51 | 4 | 3.57220413473178 | 0.427795865268217 |
52 | 2 | 3.03250443463992 | -1.03250443463992 |
53 | 4 | 3.71495028427899 | 0.285049715721015 |
54 | 4 | 3.27246302874153 | 0.727536971258473 |
55 | 4 | 3.59121882538511 | 0.408781174614886 |
56 | 3 | 3.48090762684009 | -0.480907626840087 |
57 | 3 | 3.32299171539790 | -0.322991715397904 |
58 | 3 | 3.77648229771377 | -0.776482297713772 |
59 | 2 | 3.12380094253162 | -1.12380094253162 |
60 | 4 | 3.67834889816024 | 0.321651101839762 |
61 | 4 | 3.35959310151665 | 0.640406898483349 |
62 | 4 | 3.77648229771377 | 0.223517702286228 |
63 | 3 | 3.56387126449864 | -0.56387126449864 |
64 | 4 | 3.86361237048890 | 0.136387629511104 |
65 | 3 | 3.57220413473178 | -0.572204134731783 |
66 | 4 | 3.61856638627159 | 0.381433613728412 |
67 | 4 | 3.49016145207236 | 0.50983854792764 |
68 | 4 | 3.58613143526941 | 0.413868564730587 |
69 | 4 | 3.61856638627159 | 0.381433613728412 |
70 | 4 | 3.15114850341809 | 0.84885149658191 |
71 | 4 | 3.67834889816024 | 0.321651101839762 |
72 | 4 | 3.76547897093536 | 0.234521029064638 |
73 | 4 | 3.50825518772656 | 0.491744812273438 |
74 | 2 | 3.35542666640008 | -1.35542666640008 |
75 | 3 | 3.56803769961521 | -0.568037699615211 |
76 | 4 | 3.54069013872874 | 0.459309861271263 |
77 | 4 | 3.54069013872874 | 0.459309861271263 |
78 | 3 | 3.4425567391752 | -0.442556739175203 |
79 | 4 | 3.58613143526941 | 0.413868564730587 |
80 | 4 | 3.3961944876354 | 0.603805512364602 |
81 | 4 | 3.35033927628438 | 0.649660723715622 |
82 | 3 | 3.61856638627159 | -0.618566386271588 |
83 | 3 | 3.48090762684009 | -0.480907626840087 |
84 | 3 | 3.5570343728368 | -0.557034372836801 |
85 | 3 | 3.48799803571588 | -0.487998035715879 |
86 | 4 | 3.56803769961521 | 0.431962300384789 |
87 | 4 | 3.35959310151665 | 0.640406898483349 |
88 | 2 | 3.65516777239034 | -1.65516777239034 |
89 | 4 | 3.86361237048890 | 0.136387629511104 |
90 | 3 | 3.41012178817303 | -0.410121788173028 |
91 | 4 | 3.64591394715806 | 0.354086052841937 |
92 | 3 | 3.38277422728655 | -0.382774227286554 |
93 | 4 | 3.77648229771377 | 0.223517702286228 |
94 | 3 | 3.59121882538511 | -0.591218825385114 |
95 | 3 | 3.71495028427899 | -0.714950284278985 |
96 | 4 | 3.54485657384531 | 0.455143426154692 |
97 | 3 | 3.52167544807541 | -0.521675448075406 |
98 | 4 | 3.35959310151665 | 0.640406898483349 |
99 | 2 | 3.57729152484748 | -1.57729152484748 |
100 | 4 | 3.75330117194387 | 0.246698828056131 |
101 | 4 | 3.77648229771377 | 0.223517702286228 |
102 | 4 | 3.77648229771377 | 0.223517702286228 |
103 | 4 | 3.48090762684009 | 0.519092373159913 |
104 | 4 | 3.59538526050169 | 0.404614739498315 |
105 | 3 | 3.15114850341809 | -0.151148503418090 |
106 | 4 | 3.69351866005522 | 0.306481339944781 |
107 | 3 | 3.22485831584437 | -0.22485831584437 |
108 | 4 | 3.67834889816024 | 0.321651101839762 |
109 | 3 | 3.27246302874153 | -0.272463028741527 |
110 | 2 | 3.299810589628 | -1.29981058962800 |
111 | 3 | 3.50825518772656 | -0.508255187726562 |
112 | 2 | 3.71495028427899 | -1.71495028427899 |
113 | 4 | 3.41012178817303 | 0.589878211826972 |
114 | 4 | 3.61856638627159 | 0.381433613728412 |
115 | 4 | 3.70569645904671 | 0.294303540953288 |
116 | 1 | 3.80382985860025 | -2.80382985860025 |
117 | 4 | 3.77648229771377 | 0.223517702286228 |
118 | 4 | 3.54485657384531 | 0.455143426154692 |
119 | 4 | 3.54069013872874 | 0.459309861271263 |
120 | 3 | 3.67834889816024 | -0.678348898160238 |
121 | 4 | 3.56803769961521 | 0.431962300384789 |
122 | 4 | 3.59121882538511 | 0.408781174614886 |
123 | 3 | 3.23411214107664 | -0.234112141076643 |
124 | 4 | 3.49308542583158 | 0.50691457416842 |
125 | 4 | 3.71669978582512 | 0.283300214174878 |
126 | 4 | 3.68251533327681 | 0.317484666723191 |
127 | 4 | 3.71669978582512 | 0.283300214174878 |
128 | 4 | 3.54069013872874 | 0.459309861271263 |
129 | 3 | 3.41012178817303 | -0.410121788173028 |
130 | 3 | 3.15114850341809 | -0.151148503418090 |
131 | 4 | 3.65691727393647 | 0.343082726063528 |
132 | 4 | 3.76547897093536 | 0.234521029064638 |
133 | 4 | 3.54485657384531 | 0.455143426154692 |
134 | 4 | 3.50825518772656 | 0.491744812273438 |
135 | 4 | 3.80382985860025 | 0.196170141399754 |
136 | 4 | 3.59538526050169 | 0.404614739498315 |
137 | 4 | 3.67834889816024 | 0.321651101839762 |
138 | 4 | 3.14698206830152 | 0.853017931698481 |
139 | 4 | 3.82701098437015 | 0.172989015629851 |
140 | 3 | 3.38277422728655 | -0.382774227286554 |
141 | 3 | 3.40595535305646 | -0.405955353056456 |
142 | 4 | 3.62782021150386 | 0.372179788496139 |
143 | 4 | 3.53143631349646 | 0.468563686503536 |
144 | 2 | 3.27246302874153 | -1.27246302874153 |
145 | 4 | 3.59538526050169 | 0.404614739498315 |
146 | 4 | 3.62273282138816 | 0.37726717861184 |
147 | 4 | 3.35959310151665 | 0.640406898483349 |
148 | 5 | 3.29564415451143 | 1.70435584548857 |
149 | 4 | 3.59121882538511 | 0.408781174614886 |
150 | 4 | 3.80382985860025 | 0.196170141399754 |
151 | 4 | 3.75330117194387 | 0.246698828056131 |
152 | 4 | 3.86361237048890 | 0.136387629511104 |
153 | 4 | 3.35959310151665 | 0.640406898483349 |
154 | 4 | 3.67834889816024 | 0.321651101839762 |
155 | 4 | 3.53143631349646 | 0.468563686503536 |
156 | 4 | 3.59538526050169 | 0.404614739498315 |
Goldfeld-Quandt test for Heteroskedasticity | |||
p-values | Alternative Hypothesis | ||
breakpoint index | greater | 2-sided | less |
8 | 0.110067422146674 | 0.220134844293348 | 0.889932577853326 |
9 | 0.0799012366956454 | 0.159802473391291 | 0.920098763304355 |
10 | 0.684370004919834 | 0.631259990160332 | 0.315629995080166 |
11 | 0.935289312908133 | 0.129421374183735 | 0.0647106870918674 |
12 | 0.913175504140266 | 0.173648991719468 | 0.086824495859734 |
13 | 0.882162888976307 | 0.235674222047385 | 0.117837111023693 |
14 | 0.837637756129237 | 0.324724487741525 | 0.162362243870763 |
15 | 0.803360627136587 | 0.393278745726826 | 0.196639372863413 |
16 | 0.767925390614061 | 0.464149218771878 | 0.232074609385939 |
17 | 0.702773391702411 | 0.594453216595178 | 0.297226608297589 |
18 | 0.661794877382845 | 0.67641024523431 | 0.338205122617155 |
19 | 0.678714836888012 | 0.642570326223976 | 0.321285163111988 |
20 | 0.84059718836044 | 0.31880562327912 | 0.15940281163956 |
21 | 0.86387047912727 | 0.272259041745459 | 0.136129520872729 |
22 | 0.825496240064596 | 0.349007519870809 | 0.174503759935404 |
23 | 0.84036310833691 | 0.319273783326179 | 0.159636891663090 |
24 | 0.81601715385109 | 0.367965692297819 | 0.183982846148910 |
25 | 0.776658422820779 | 0.446683154358443 | 0.223341577179221 |
26 | 0.764424990440522 | 0.471150019118957 | 0.235575009559478 |
27 | 0.721313454534552 | 0.557373090930896 | 0.278686545465448 |
28 | 0.84774841970003 | 0.30450316059994 | 0.15225158029997 |
29 | 0.819264733201846 | 0.361470533596308 | 0.180735266798154 |
30 | 0.77977518368333 | 0.44044963263334 | 0.22022481631667 |
31 | 0.75289226076776 | 0.494215478464479 | 0.247107739232240 |
32 | 0.711652671520499 | 0.576694656959002 | 0.288347328479501 |
33 | 0.671159389449207 | 0.657681221101586 | 0.328840610550793 |
34 | 0.780651320899657 | 0.438697358200685 | 0.219348679100343 |
35 | 0.750005136737948 | 0.499989726524104 | 0.249994863262052 |
36 | 0.730749162328106 | 0.538501675343787 | 0.269250837671894 |
37 | 0.750675191613602 | 0.498649616772796 | 0.249324808386398 |
38 | 0.868356717548298 | 0.263286564903403 | 0.131643282451702 |
39 | 0.849434822180131 | 0.301130355639738 | 0.150565177819869 |
40 | 0.818862352729707 | 0.362275294540587 | 0.181137647270293 |
41 | 0.798180702166528 | 0.403638595666943 | 0.201819297833472 |
42 | 0.779198459812053 | 0.441603080375894 | 0.220801540187947 |
43 | 0.91212842370368 | 0.175743152592639 | 0.0878715762963194 |
44 | 0.895024351429624 | 0.209951297140752 | 0.104975648570376 |
45 | 0.881833816986995 | 0.236332366026010 | 0.118166183013005 |
46 | 0.869031934977104 | 0.261936130045792 | 0.130968065022896 |
47 | 0.840087587111252 | 0.319824825777495 | 0.159912412888748 |
48 | 0.949290537678596 | 0.101418924642808 | 0.0507094623214039 |
49 | 0.945640388059008 | 0.108719223881984 | 0.054359611940992 |
50 | 0.936608548754392 | 0.126782902491215 | 0.0633914512456076 |
51 | 0.927353377746986 | 0.145293244506028 | 0.0726466222530141 |
52 | 0.9442453815366 | 0.111509236926801 | 0.0557546184634006 |
53 | 0.932620055216403 | 0.134759889567193 | 0.0673799447835967 |
54 | 0.933211620169676 | 0.133576759660648 | 0.0667883798303242 |
55 | 0.922768564858327 | 0.154462870283347 | 0.0772314351416733 |
56 | 0.912989432590656 | 0.174021134818687 | 0.0870105674093437 |
57 | 0.897815891795913 | 0.204368216408173 | 0.102184108204087 |
58 | 0.900565446531648 | 0.198869106936703 | 0.0994345534683515 |
59 | 0.93044118471139 | 0.139117630577220 | 0.0695588152886102 |
60 | 0.917209473064178 | 0.165581053871643 | 0.0827905269358216 |
61 | 0.913391746431267 | 0.173216507137467 | 0.0866082535687335 |
62 | 0.89515833902465 | 0.209683321950699 | 0.104841660975349 |
63 | 0.88751938598287 | 0.224961228034260 | 0.112480614017130 |
64 | 0.864488612539806 | 0.271022774920388 | 0.135511387460194 |
65 | 0.855345526138497 | 0.289308947723007 | 0.144654473861503 |
66 | 0.836187840595447 | 0.327624318809106 | 0.163812159404553 |
67 | 0.819883943125419 | 0.360232113749163 | 0.180116056874581 |
68 | 0.803473128780772 | 0.393053742438456 | 0.196526871219228 |
69 | 0.779181865556877 | 0.441636268886245 | 0.220818134443123 |
70 | 0.791568597491059 | 0.416862805017882 | 0.208431402508941 |
71 | 0.76421188423909 | 0.47157623152182 | 0.23578811576091 |
72 | 0.736722799500135 | 0.52655440099973 | 0.263277200499865 |
73 | 0.716112718592203 | 0.567774562815594 | 0.283887281407797 |
74 | 0.816556549675882 | 0.366886900648237 | 0.183443450324118 |
75 | 0.806986834357273 | 0.386026331285454 | 0.193013165642727 |
76 | 0.786254188618423 | 0.427491622763155 | 0.213745811381577 |
77 | 0.764180788385532 | 0.471638423228936 | 0.235819211614468 |
78 | 0.74093794178934 | 0.518124116421321 | 0.259062058210660 |
79 | 0.71524588099307 | 0.56950823801386 | 0.28475411900693 |
80 | 0.71346848436288 | 0.573063031274241 | 0.286531515637121 |
81 | 0.701840431196502 | 0.596319137606996 | 0.298159568803498 |
82 | 0.696500947725774 | 0.606998104548452 | 0.303499052274226 |
83 | 0.686594290300823 | 0.626811419398353 | 0.313405709699177 |
84 | 0.667299126034075 | 0.665401747931849 | 0.332700873965925 |
85 | 0.649608555323119 | 0.700782889353762 | 0.350391444676881 |
86 | 0.620381478826637 | 0.759237042346725 | 0.379618521173363 |
87 | 0.61228751293628 | 0.77542497412744 | 0.38771248706372 |
88 | 0.782452751209485 | 0.435094497581030 | 0.217547248790515 |
89 | 0.748220379185291 | 0.503559241629418 | 0.251779620814709 |
90 | 0.727431742720123 | 0.545136514559755 | 0.272568257279877 |
91 | 0.693856048870889 | 0.612287902258222 | 0.306143951129111 |
92 | 0.668646395856595 | 0.66270720828681 | 0.331353604143405 |
93 | 0.627738304215607 | 0.744523391568786 | 0.372261695784393 |
94 | 0.626286904447698 | 0.747426191104604 | 0.373713095552302 |
95 | 0.613733056178541 | 0.772533887642918 | 0.386266943821459 |
96 | 0.5904429346509 | 0.8191141306982 | 0.4095570653491 |
97 | 0.562254893327149 | 0.875490213345701 | 0.437745106672851 |
98 | 0.553524507806981 | 0.892950984386037 | 0.446475492193019 |
99 | 0.719168058351071 | 0.561663883297858 | 0.280831941648929 |
100 | 0.680262405213606 | 0.639475189572788 | 0.319737594786394 |
101 | 0.638056217641328 | 0.723887564717344 | 0.361943782358672 |
102 | 0.593615643948824 | 0.812768712102352 | 0.406384356051176 |
103 | 0.560210636220262 | 0.879578727559476 | 0.439789363779738 |
104 | 0.526496558357452 | 0.947006883285096 | 0.473503441642548 |
105 | 0.477883345033489 | 0.955766690066978 | 0.522116654966511 |
106 | 0.433944770863013 | 0.867889541726025 | 0.566055229136987 |
107 | 0.395148229834862 | 0.790296459669723 | 0.604851770165138 |
108 | 0.354207343482538 | 0.708414686965075 | 0.645792656517462 |
109 | 0.324388081106625 | 0.64877616221325 | 0.675611918893375 |
110 | 0.484132160246792 | 0.968264320493584 | 0.515867839753208 |
111 | 0.489212877763361 | 0.978425755526722 | 0.510787122236639 |
112 | 0.715847164375938 | 0.568305671248123 | 0.284152835624062 |
113 | 0.691476278063712 | 0.617047443872575 | 0.308523721936288 |
114 | 0.652209701041188 | 0.695580597917623 | 0.347790298958812 |
115 | 0.611637443734608 | 0.776725112530784 | 0.388362556265392 |
116 | 0.998812492191953 | 0.00237501561609453 | 0.00118750780804726 |
117 | 0.998148427554467 | 0.00370314489106532 | 0.00185157244553266 |
118 | 0.997187080765923 | 0.00562583846815396 | 0.00281291923407698 |
119 | 0.995744183731565 | 0.00851163253687024 | 0.00425581626843512 |
120 | 0.997542483385526 | 0.00491503322894708 | 0.00245751661447354 |
121 | 0.99621665443561 | 0.00756669112877881 | 0.00378334556438941 |
122 | 0.994198020597923 | 0.0116039588041545 | 0.00580197940207724 |
123 | 0.99268974708467 | 0.0146205058306607 | 0.00731025291533033 |
124 | 0.98997168317269 | 0.0200566336546183 | 0.0100283168273091 |
125 | 0.98491482855799 | 0.0301703428840192 | 0.0150851714420096 |
126 | 0.978098692090386 | 0.0438026158192273 | 0.0219013079096137 |
127 | 0.968231221712965 | 0.0635375565740699 | 0.0317687782870350 |
128 | 0.954798132654633 | 0.0904037346907345 | 0.0452018673453672 |
129 | 0.952573594227903 | 0.094852811544194 | 0.047426405772097 |
130 | 0.943831522226333 | 0.112336955547334 | 0.0561684777736671 |
131 | 0.920941157633583 | 0.158117684732835 | 0.0790588423664175 |
132 | 0.890430997140396 | 0.219138005719209 | 0.109569002859604 |
133 | 0.854373763550198 | 0.291252472899604 | 0.145626236449802 |
134 | 0.81198347173201 | 0.376033056535981 | 0.188016528267991 |
135 | 0.755497399817756 | 0.489005200364488 | 0.244502600182244 |
136 | 0.692269707089683 | 0.615460585820634 | 0.307730292910317 |
137 | 0.618983590165047 | 0.762032819669906 | 0.381016409834953 |
138 | 0.600023653080147 | 0.799952693839705 | 0.399976346919853 |
139 | 0.521219579628738 | 0.957560840742523 | 0.478780420371262 |
140 | 0.503045959925915 | 0.99390808014817 | 0.496954040074085 |
141 | 0.612660138258753 | 0.774679723482494 | 0.387339861741247 |
142 | 0.517213119128132 | 0.965573761743735 | 0.482786880871868 |
143 | 0.418983553607387 | 0.837967107214775 | 0.581016446392613 |
144 | 0.994687631700698 | 0.0106247365986042 | 0.00531236829930212 |
145 | 0.985249614623504 | 0.029500770752991 | 0.0147503853764955 |
146 | 0.971534389344233 | 0.0569312213115334 | 0.0284656106557667 |
147 | 0.935481603909209 | 0.129036792181582 | 0.064518396090791 |
148 | 1 | 3.89377133056926e-45 | 1.94688566528463e-45 |
Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
Description | # significant tests | % significant tests | OK/NOK |
1% type I error level | 7 | 0.049645390070922 | NOK |
5% type I error level | 14 | 0.099290780141844 | NOK |
10% type I error level | 18 | 0.127659574468085 | NOK |