Multiple Linear Regression - Estimated Regression Equation |
Ihavemanyfriends[t] = + 0.0496203608625268 -0.0502689740190555sum[t] + 0.282977054518711Popularity[t] + 0.0269440633049747KnowingPeople[t] -0.0242599319071114Liked[t] -0.0409210098415009Celebrity[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) | 0.0496203608625268 | 0.202278 | 0.2453 | 0.806556 | 0.403278 |
sum | -0.0502689740190555 | 0.032126 | -1.5648 | 0.119761 | 0.059881 |
Popularity | 0.282977054518711 | 0.015892 | 17.8068 | 0 | 0 |
KnowingPeople | 0.0269440633049747 | 0.016869 | 1.5973 | 0.11232 | 0.05616 |
Liked | -0.0242599319071114 | 0.019572 | -1.2395 | 0.217109 | 0.108555 |
Celebrity | -0.0409210098415009 | 0.031395 | -1.3034 | 0.194445 | 0.097222 |
Multiple Linear Regression - Regression Statistics | |
Multiple R | 0.895389490189128 |
R-squared | 0.801722339141146 |
Adjusted R-squared | 0.795068726360648 |
F-TEST (value) | 120.494288680425 |
F-TEST (DF numerator) | 5 |
F-TEST (DF denominator) | 149 |
p-value | 0 |
Multiple Linear Regression - Residual Statistics | |
Residual Standard Deviation | 0.404795214699169 |
Sum Squared Residuals | 24.4150157106586 |
Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
1 | 3 | 3.53991480021537 | -0.539914800215375 |
2 | 3 | 3.06370032020287 | -0.0637003202028701 |
3 | 4 | 3.93003184213015 | 0.0699681578698532 |
4 | 3 | 3.00038942084032 | -0.000389420840319157 |
5 | 2 | 2.52656031685648 | -0.526560316856485 |
6 | 3 | 3.14285820848801 | -0.142858208488009 |
7 | 4 | 3.78358335310063 | 0.216416646899371 |
8 | 2 | 2.38504222021739 | -0.385042220217386 |
9 | 3 | 3.11816291921492 | -0.118162919214916 |
10 | 4 | 2.91506485056321 | 1.08493514943679 |
11 | 3 | 2.83055688233723 | 0.169443117662766 |
12 | 3 | 2.79462540364564 | 0.205374596354361 |
13 | 4 | 4.05284099526083 | -0.0528409952608306 |
14 | 2 | 1.77512242114967 | 0.224877578850334 |
15 | 2 | 2.71285819253768 | -0.712858192537684 |
16 | 3 | 3.00488445586476 | -0.00488445586475642 |
17 | 2 | 2.51164834912693 | -0.511648349126928 |
18 | 4 | 3.63096818207914 | 0.369031817920857 |
19 | 2 | 2.60876288533042 | -0.60876288533042 |
20 | 1 | 1.48222293005130 | -0.482222930051305 |
21 | 3 | 2.88016138449458 | 0.119838615505419 |
22 | 4 | 3.84339603205351 | 0.156603967946485 |
23 | 2 | 2.91824864578812 | -0.918248645788125 |
24 | 3 | 3.10287221983954 | -0.102872219839538 |
25 | 3 | 3.72345373592366 | -0.723453735923664 |
26 | 4 | 3.96421421061691 | 0.0357857893830908 |
27 | 3 | 2.19580267896031 | 0.804197321039694 |
28 | 3 | 3.3871630271971 | -0.387163027197100 |
29 | 4 | 3.39289183878376 | 0.607108161216239 |
30 | 4 | 4.16561979478394 | -0.165619794783941 |
31 | 4 | 3.46224822267048 | 0.537751777329523 |
32 | 3 | 3.09687285892156 | -0.0968728589215549 |
33 | 4 | 3.53709406682072 | 0.462905933179277 |
34 | 3 | 2.82526342811655 | 0.174736571883446 |
35 | 2 | 2.30782918289336 | -0.307829182893356 |
36 | 4 | 4.19785731230960 | -0.197857312309595 |
37 | 3 | 3.00844181503391 | -0.008441815033909 |
38 | 2 | 2.52481120665165 | -0.524811206651652 |
39 | 4 | 3.41715177069087 | 0.582848229309127 |
40 | 4 | 4.1093514598469 | -0.109351459846902 |
41 | 4 | 3.64985985119053 | 0.350140148809472 |
42 | 4 | 3.98910524064628 | 0.0108947593537228 |
43 | 2 | 1.16201882685703 | 0.837981173142966 |
44 | 2 | 2.05086117048659 | -0.050861170486589 |
45 | 3 | 2.76768134034066 | 0.232318659659336 |
46 | 4 | 4.15063301847934 | -0.150633018479337 |
47 | 5 | 4.40244669170154 | 0.597553308298461 |
48 | 2 | 2.3733706734329 | -0.373370673432902 |
49 | 3 | 2.29198219397077 | 0.708017806029232 |
50 | 3 | 3.37131603827451 | -0.371316038274513 |
51 | 2 | 2.37961216399992 | -0.379612163999918 |
52 | 2 | 1.46150734216004 | 0.53849265783996 |
53 | 3 | 3.09332851490571 | -0.093328514905708 |
54 | 2 | 1.94938820125545 | 0.0506117987445524 |
55 | 4 | 3.73381152986930 | 0.266188470130704 |
56 | 3 | 3.10512099387142 | -0.105120993871420 |
57 | 3 | 2.93035554993859 | 0.0696444500614104 |
58 | 4 | 4.17359738040248 | -0.173597380402484 |
59 | 1 | 2.01327357302010 | -1.01327357302010 |
60 | 4 | 3.89939381765923 | 0.100606182340769 |
61 | 2 | 1.77824190991351 | 0.221758090086489 |
62 | 4 | 4.22211724421671 | -0.222117244216706 |
63 | 4 | 3.8285458577457 | 0.171454142254301 |
64 | 4 | 4.21394391784189 | -0.213943917841888 |
65 | 2 | 2.14211029310663 | -0.142110293106632 |
66 | 4 | 3.71410577174611 | 0.285894228253891 |
67 | 2 | 2.8288077721324 | -0.828807772132401 |
68 | 4 | 3.37093730662869 | 0.629062693371308 |
69 | 4 | 3.90951199499516 | 0.0904880050048423 |
70 | 1 | 1.29554632272428 | -0.295546322724285 |
71 | 4 | 3.92710809412258 | 0.0728919058774222 |
72 | 4 | 3.35753483249426 | 0.642465167505738 |
73 | 3 | 2.76732079154973 | 0.23267920845027 |
74 | 3 | 2.68056404929187 | 0.319435950708131 |
75 | 3 | 3.03363676813405 | -0.0336367681340510 |
76 | 3 | 3.11084980545808 | -0.110849805458081 |
77 | 3 | 3.14908668390172 | -0.149086683901719 |
78 | 3 | 3.09788268868963 | -0.0978826886896326 |
79 | 4 | 3.64993465976557 | 0.350065340234425 |
80 | 1 | 1.48323275981938 | -0.483232759819382 |
81 | 3 | 1.71399598935793 | 1.28600401064207 |
82 | 4 | 3.62746996166948 | 0.372530038330522 |
83 | 3 | 3.55375514475511 | -0.553755144755113 |
84 | 3 | 2.55256935896843 | 0.447430641031571 |
85 | 4 | 3.35224137827358 | 0.647758621726417 |
86 | 3 | 3.10454652146932 | -0.104546521469324 |
87 | 2 | 2.30514505149549 | -0.305145051495492 |
88 | 3 | 3.04574367228452 | -0.045743672284516 |
89 | 4 | 4.10877698744481 | -0.108776987444805 |
90 | 3 | 2.54322139479087 | 0.456778605209126 |
91 | 4 | 3.54651683957333 | 0.453483160426675 |
92 | 3 | 2.46943176930146 | 0.530568230698538 |
93 | 4 | 4.13267637056098 | -0.132676370560983 |
94 | 4 | 3.98672503231919 | 0.0132749676808122 |
95 | 3 | 3.06825449398679 | -0.0682544939867946 |
96 | 2 | 2.61051199553525 | -0.610511995535253 |
97 | 1 | 1.81003890237160 | -0.810038902371603 |
98 | 2 | 2.03614494351331 | -0.0361449435133078 |
99 | 2 | 2.81665474437575 | -0.816654744375754 |
100 | 3 | 3.31299467006187 | -0.312994670061868 |
101 | 4 | 4.15962043386596 | -0.159620433865957 |
102 | 4 | 4.12999223916312 | -0.129992239163119 |
103 | 3 | 3.68298626630303 | -0.682986266303031 |
104 | 3 | 2.75840818473816 | 0.241591815261844 |
105 | 1 | 0.891269608670017 | 0.108730391329983 |
106 | 3 | 3.44134990917624 | -0.441349909176243 |
107 | 3 | 2.33079354481650 | 0.669206455183498 |
108 | 4 | 3.54644203099828 | 0.453557969001722 |
109 | 2 | 2.04326231651387 | -0.0432623165138671 |
110 | 2 | 1.97808137476525 | 0.0219186252347451 |
111 | 3 | 2.86423958699695 | 0.135760413003053 |
112 | 3 | 3.11657861704474 | -0.116578617044742 |
113 | 3 | 2.73618310325176 | 0.263816896748235 |
114 | 4 | 3.64798980880447 | 0.352010191195533 |
115 | 4 | 3.79219203684143 | 0.207807963158571 |
116 | 4 | 4.21849809162581 | -0.218498091625812 |
117 | 4 | 4.26152876046308 | -0.26152876046308 |
118 | 2 | 2.64369754940724 | -0.643697549407243 |
119 | 3 | 3.60589416116023 | -0.605894161160229 |
120 | 4 | 3.72539858688477 | 0.274601413115228 |
121 | 3 | 3.13880369853113 | -0.138803698531134 |
122 | 4 | 3.76892891954909 | 0.231071080450911 |
123 | 2 | 1.90367340102032 | 0.0963265989796834 |
124 | 4 | 3.3462420173556 | 0.6537579826444 |
125 | 4 | 4.22211724421671 | -0.222117244216706 |
126 | 3 | 3.00887717239989 | -0.00887717239989009 |
127 | 4 | 4.08813620812859 | -0.0881362081285879 |
128 | 3 | 3.18082453760032 | -0.180824537600323 |
129 | 3 | 2.78702654967292 | 0.212973450327083 |
130 | 1 | 1.05552512846779 | -0.0555251284677942 |
131 | 4 | 4.04510553929132 | -0.0451055392913202 |
132 | 4 | 3.87894877909929 | 0.121051220900711 |
133 | 2 | 2.46588742528562 | -0.465887425285616 |
134 | 3 | 3.22144413741038 | -0.221444137410377 |
135 | 4 | 3.93190188451621 | 0.0680981154837921 |
136 | 3 | 3.13156539334935 | -0.131565393349346 |
137 | 4 | 3.65254398258839 | 0.347456017411609 |
138 | 2 | 1.86269325241933 | 0.137306747580671 |
139 | 5 | 5.06649423398891 | -0.0664942339889137 |
140 | 3 | 3.10418597267839 | -0.104185972678390 |
141 | 4 | 3.26628570987422 | 0.733714290125781 |
142 | 3 | 3.36594777547879 | -0.365947775478786 |
143 | 4 | 4.03881792511812 | -0.0388179251181231 |
144 | 2 | 2.10312111907293 | -0.103121119072934 |
145 | 3 | 3.13518454594024 | -0.135184545940240 |
146 | 3 | 2.37599301140902 | 0.624006988590976 |
147 | 2 | 1.90753217022092 | 0.092467829779084 |
148 | NA | NA | 0.0375348995879236 |
149 | 4 | 4.12848274556799 | -0.128482745567992 |
150 | 4 | 4.29901772352534 | -0.299017723525342 |
151 | 3 | 3.12905721797009 | -0.129057217970089 |
152 | 4 | 4.33021907241441 | -0.330219072414406 |
153 | 2 | 1.57077677148044 | 0.429223228519564 |
154 | 4 | 3.65441402497445 | 0.345585975025548 |
155 | 4 | 4.21971069702110 | -0.219710697021105 |
156 | 3 | NA | NA |
Goldfeld-Quandt test for Heteroskedasticity | |||
p-values | Alternative Hypothesis | ||
breakpoint index | greater | 2-sided | less |
9 | 0.0763749284487003 | 0.152749856897401 | 0.9236250715513 |
10 | 0.789713070269334 | 0.420573859461331 | 0.210286929730666 |
11 | 0.773561564484629 | 0.452876871030743 | 0.226438435515371 |
12 | 0.671250629349592 | 0.657498741300815 | 0.328749370650408 |
13 | 0.634216858277358 | 0.731566283445284 | 0.365783141722642 |
14 | 0.681095170509505 | 0.63780965898099 | 0.318904829490495 |
15 | 0.851903168816455 | 0.296193662367089 | 0.148096831183545 |
16 | 0.803045120986422 | 0.393909758027157 | 0.196954879013578 |
17 | 0.830575960252561 | 0.338848079494877 | 0.169424039747439 |
18 | 0.8279082456424 | 0.344183508715199 | 0.172091754357600 |
19 | 0.847965735160502 | 0.304068529678995 | 0.152034264839498 |
20 | 0.815465792583215 | 0.36906841483357 | 0.184534207416785 |
21 | 0.80012958859045 | 0.399740822819101 | 0.199870411409551 |
22 | 0.746681961471968 | 0.506636077056064 | 0.253318038528032 |
23 | 0.848045648319572 | 0.303908703360856 | 0.151954351680428 |
24 | 0.803885839275634 | 0.392228321448732 | 0.196114160724366 |
25 | 0.8798740169682 | 0.240251966063599 | 0.120125983031799 |
26 | 0.842937157865523 | 0.314125684268953 | 0.157062842134477 |
27 | 0.921914273702845 | 0.156171452594310 | 0.0780857262971552 |
28 | 0.90918772149562 | 0.18162455700876 | 0.09081227850438 |
29 | 0.931392376398512 | 0.137215247202976 | 0.0686076236014878 |
30 | 0.910003493657766 | 0.179993012684469 | 0.0899965063422344 |
31 | 0.955124210110826 | 0.0897515797783478 | 0.0448757898891739 |
32 | 0.939825551384247 | 0.120348897231505 | 0.0601744486157527 |
33 | 0.939675582170525 | 0.120648835658951 | 0.0603244178294754 |
34 | 0.92581244327636 | 0.148375113447280 | 0.0741875567236399 |
35 | 0.910122278888943 | 0.179755442222115 | 0.0898777211110573 |
36 | 0.891902670430846 | 0.216194659138308 | 0.108097329569154 |
37 | 0.863524165216835 | 0.27295166956633 | 0.136475834783165 |
38 | 0.860812425501872 | 0.278375148996256 | 0.139187574498128 |
39 | 0.884521206254842 | 0.230957587490316 | 0.115478793745158 |
40 | 0.858462371487166 | 0.283075257025669 | 0.141537628512834 |
41 | 0.848499669821338 | 0.303000660357325 | 0.151500330178662 |
42 | 0.815494672574335 | 0.36901065485133 | 0.184505327425665 |
43 | 0.910313564579187 | 0.179372870841626 | 0.089686435420813 |
44 | 0.887780004099082 | 0.224439991801837 | 0.112219995900918 |
45 | 0.86822918519644 | 0.263541629607119 | 0.131770814803560 |
46 | 0.842971451061006 | 0.314057097877989 | 0.157028548938994 |
47 | 0.885598825348103 | 0.228802349303794 | 0.114401174651897 |
48 | 0.87516670589592 | 0.249666588208160 | 0.124833294104080 |
49 | 0.91398597078595 | 0.172028058428098 | 0.0860140292140492 |
50 | 0.915388270401751 | 0.169223459196498 | 0.084611729598249 |
51 | 0.917484135712949 | 0.165031728574103 | 0.0825158642870515 |
52 | 0.93261429037956 | 0.134771419240879 | 0.0673857096204395 |
53 | 0.916270029297047 | 0.167459941405905 | 0.0837299707029527 |
54 | 0.895952673377351 | 0.208094653245298 | 0.104047326622649 |
55 | 0.882816675350097 | 0.234366649299805 | 0.117183324649903 |
56 | 0.858549216596162 | 0.282901566807677 | 0.141450783403838 |
57 | 0.83017606095505 | 0.3396478780899 | 0.16982393904495 |
58 | 0.805686491052923 | 0.388627017894154 | 0.194313508947077 |
59 | 0.925656367704867 | 0.148687264590265 | 0.0743436322951327 |
60 | 0.910044201991837 | 0.179911596016326 | 0.0899557980081628 |
61 | 0.89708585227742 | 0.205828295445161 | 0.102914147722581 |
62 | 0.881511298356415 | 0.236977403287170 | 0.118488701643585 |
63 | 0.860945574072868 | 0.278108851854264 | 0.139054425927132 |
64 | 0.842349003721778 | 0.315301992556444 | 0.157650996278222 |
65 | 0.81530528983106 | 0.369389420337879 | 0.184694710168940 |
66 | 0.798038226457291 | 0.403923547085418 | 0.201961773542709 |
67 | 0.88133163439869 | 0.237336731202619 | 0.118668365601309 |
68 | 0.908424402132488 | 0.183151195735024 | 0.0915755978675119 |
69 | 0.888340809244507 | 0.223318381510985 | 0.111659190755493 |
70 | 0.88067448510066 | 0.238651029798681 | 0.119325514899341 |
71 | 0.857851362442107 | 0.284297275115785 | 0.142148637557893 |
72 | 0.891857536305409 | 0.216284927389182 | 0.108142463694591 |
73 | 0.875968734277982 | 0.248062531444035 | 0.124031265722018 |
74 | 0.86772173860457 | 0.264556522790861 | 0.132278261395431 |
75 | 0.84084805243443 | 0.31830389513114 | 0.15915194756557 |
76 | 0.812552221847998 | 0.374895556304005 | 0.187447778152002 |
77 | 0.784449868480701 | 0.431100263038598 | 0.215550131519299 |
78 | 0.750874065734973 | 0.498251868530054 | 0.249125934265027 |
79 | 0.735944331218349 | 0.528111337563302 | 0.264055668781651 |
80 | 0.757474274172372 | 0.485051451655256 | 0.242525725827628 |
81 | 0.963958300244643 | 0.072083399510713 | 0.0360416997553565 |
82 | 0.961520212558959 | 0.0769595748820821 | 0.0384797874410411 |
83 | 0.970376601027835 | 0.0592467979443306 | 0.0296233989721653 |
84 | 0.972711635262402 | 0.0545767294751955 | 0.0272883647375977 |
85 | 0.980235020329632 | 0.0395299593407357 | 0.0197649796703678 |
86 | 0.974144766852205 | 0.0517104662955894 | 0.0258552331477947 |
87 | 0.97152230557127 | 0.05695538885746 | 0.02847769442873 |
88 | 0.962931897682224 | 0.0741362046355526 | 0.0370681023177763 |
89 | 0.953403980355778 | 0.0931920392884437 | 0.0465960196442218 |
90 | 0.955995927673701 | 0.088008144652598 | 0.044004072326299 |
91 | 0.961551917517628 | 0.0768961649647442 | 0.0384480824823721 |
92 | 0.972712850406384 | 0.0545742991872327 | 0.0272871495936164 |
93 | 0.964863989937818 | 0.0702720201243633 | 0.0351360100621817 |
94 | 0.95411218627097 | 0.09177562745806 | 0.04588781372903 |
95 | 0.941451392658435 | 0.117097214683129 | 0.0585486073415647 |
96 | 0.96183449344205 | 0.0763310131159009 | 0.0381655065579505 |
97 | 0.984312812341865 | 0.0313743753162702 | 0.0156871876581351 |
98 | 0.979342614449367 | 0.0413147711012653 | 0.0206573855506326 |
99 | 0.992589362119093 | 0.0148212757618141 | 0.00741063788090707 |
100 | 0.991903017676194 | 0.0161939646476113 | 0.00809698232380563 |
101 | 0.988899297352491 | 0.0222014052950179 | 0.0111007026475090 |
102 | 0.984899801919942 | 0.0302003961601151 | 0.0151001980800575 |
103 | 0.991648954829349 | 0.0167020903413029 | 0.00835104517065145 |
104 | 0.989750883984274 | 0.020498232031451 | 0.0102491160157255 |
105 | 0.985708342069768 | 0.0285833158604648 | 0.0142916579302324 |
106 | 0.986631541418253 | 0.026736917163494 | 0.013368458581747 |
107 | 0.993866510223154 | 0.0122669795536914 | 0.00613348977684568 |
108 | 0.994705443515149 | 0.0105891129697023 | 0.00529455648485116 |
109 | 0.992173072798675 | 0.0156538544026504 | 0.00782692720132518 |
110 | 0.988672001971102 | 0.0226559960577966 | 0.0113279980288983 |
111 | 0.984504421430063 | 0.0309911571398732 | 0.0154955785699366 |
112 | 0.979170155006539 | 0.0416596899869225 | 0.0208298449934613 |
113 | 0.975163696818487 | 0.0496726063630258 | 0.0248363031815129 |
114 | 0.974562604155848 | 0.0508747916883043 | 0.0254373958441522 |
115 | 0.969821273392215 | 0.0603574532155691 | 0.0301787266077846 |
116 | 0.962539117322857 | 0.0749217653542856 | 0.0374608826771428 |
117 | 0.95735229074297 | 0.0852954185140595 | 0.0426477092570298 |
118 | 0.97283609428868 | 0.0543278114226409 | 0.0271639057113204 |
119 | 0.986312300722303 | 0.0273753985553933 | 0.0136876992776967 |
120 | 0.98365626694285 | 0.0326874661142997 | 0.0163437330571498 |
121 | 0.97724605071211 | 0.0455078985757805 | 0.0227539492878903 |
122 | 0.970315779960979 | 0.0593684400780423 | 0.0296842200390212 |
123 | 0.958059820746089 | 0.0838803585078225 | 0.0419401792539112 |
124 | 0.981241726597376 | 0.0375165468052485 | 0.0187582734026242 |
125 | 0.975752161024939 | 0.0484956779501219 | 0.0242478389750609 |
126 | 0.963951071365013 | 0.0720978572699748 | 0.0360489286349874 |
127 | 0.94913075939428 | 0.101738481211438 | 0.0508692406057192 |
128 | 0.938177663914962 | 0.123644672170077 | 0.0618223360850384 |
129 | 0.923105483373853 | 0.153789033252294 | 0.0768945166261469 |
130 | 0.905011637956625 | 0.18997672408675 | 0.094988362043375 |
131 | 0.868804878913017 | 0.262390242173965 | 0.131195121086983 |
132 | 0.828327647201064 | 0.343344705597873 | 0.171672352798936 |
133 | 0.834751347894708 | 0.330497304210584 | 0.165248652105292 |
134 | 0.799149769344368 | 0.401700461311265 | 0.200850230655632 |
135 | 0.736814273240063 | 0.526371453519874 | 0.263185726759937 |
136 | 0.672395696115575 | 0.655208607768851 | 0.327604303884425 |
137 | 0.645922343167185 | 0.70815531366563 | 0.354077656832815 |
138 | 0.564176351308381 | 0.871647297383238 | 0.435823648691619 |
139 | 0.472545068849117 | 0.945090137698234 | 0.527454931150883 |
140 | 0.384484334567115 | 0.76896866913423 | 0.615515665432885 |
141 | 0.909975348645885 | 0.180049302708231 | 0.0900246513541153 |
142 | 0.876851552632096 | 0.246296894735808 | 0.123148447367904 |
143 | 0.870657074919597 | 0.258685850160805 | 0.129342925080403 |
144 | 0.786667940667247 | 0.426664118665506 | 0.213332059332753 |
145 | 0.69051518749708 | 0.61896962500584 | 0.30948481250292 |
146 | 0.538535189692523 | 0.922929620614954 | 0.461464810307477 |
147 | 0.429948419982576 | 0.859896839965152 | 0.570051580017424 |
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 | 23 | 0.165467625899281 | NOK |
10% type I error level | 46 | 0.330935251798561 | NOK |