Multiple Linear Regression - Estimated Regression Equation |
time[t] = + 5775.58331422066 + 173.865493156532comp[t] + 1023.22174823199blog[t] -1814.33730391916review[t] + 908.942471267879fbm[t] + 0.991895416208138charac[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) | 5775.58331422066 | 3946.898059 | 1.4633 | 0.145653 | 0.072827 |
comp | 173.865493156532 | 59.319625 | 2.931 | 0.003956 | 0.001978 |
blog | 1023.22174823199 | 160.10877 | 6.3908 | 0 | 0 |
review | -1814.33730391916 | 804.303041 | -2.2558 | 0.025657 | 0.012828 |
fbm | 908.942471267879 | 228.217886 | 3.9828 | 0.00011 | 5.5e-05 |
charac | 0.991895416208138 | 0.183678 | 5.4002 | 0 | 0 |
Multiple Linear Regression - Regression Statistics | |
Multiple R | 0.854757040874396 |
R-squared | 0.730609598924355 |
Adjusted R-squared | 0.720849077146251 |
F-TEST (value) | 74.8535391379809 |
F-TEST (DF numerator) | 5 |
F-TEST (DF denominator) | 138 |
p-value | 0 |
Multiple Linear Regression - Residual Statistics | |
Residual Standard Deviation | 20012.4760735035 |
Sum Squared Residuals | 55268889405.7721 |
Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
1 | 63031 | 50268.6405623156 | 12762.3594376844 |
2 | 66751 | 59186.7955142815 | 7564.20448571853 |
3 | 7176 | 7360.91598464139 | -184.915984641393 |
4 | 78306 | 87021.2988620928 | -8715.29886209282 |
5 | 137944 | 117836.859145619 | 20107.1408543808 |
6 | 261308 | 230272.021950602 | 31035.9780493983 |
7 | 69266 | 63347.7734036871 | 5918.22659631292 |
8 | 80226 | 85043.6593101671 | -4817.65931016709 |
9 | 73226 | 70768.2266961951 | 2457.77330380492 |
10 | 178519 | 112113.098843598 | 66405.9011564025 |
11 | 66476 | 87558.7923030032 | -21082.7923030032 |
12 | 98606 | 100461.959499427 | -1855.95949942691 |
13 | 50001 | 44910.6833909095 | 5090.31660909051 |
14 | 91093 | 98791.0878648494 | -7698.08786484942 |
15 | 73884 | 63201.9059120467 | 10682.0940879533 |
16 | 72961 | 69419.3384932411 | 3541.66150675886 |
17 | 69388 | 130429.280152815 | -61041.2801528152 |
18 | 15629 | 20658.8572843779 | -5029.85728437793 |
19 | 71693 | 107472.887695069 | -35779.8876950685 |
20 | 19920 | 56726.8531213656 | -36806.8531213656 |
21 | 39403 | 34788.299519973 | 4614.70048002698 |
22 | 99933 | 122353.193157977 | -22420.1931579772 |
23 | 56088 | 38275.4624893315 | 17812.5375106685 |
24 | 62006 | 72153.6650431447 | -10147.6650431447 |
25 | 81665 | 70273.275704157 | 11391.724295843 |
26 | 65223 | 57608.8596653331 | 7614.14033466694 |
27 | 88794 | 84195.8399217537 | 4598.16007824631 |
28 | 90642 | 78837.4441586631 | 11804.5558413369 |
29 | 203699 | 135019.485937422 | 68679.514062578 |
30 | 99340 | 57091.6042446224 | 42248.3957553776 |
31 | 56695 | 59716.2417043044 | -3021.24170430442 |
32 | 108143 | 83461.7705714529 | 24681.2294285471 |
33 | 58313 | 67341.3599338616 | -9028.35993386157 |
34 | 29101 | 41005.9523144089 | -11904.9523144089 |
35 | 113060 | 75343.4201660737 | 37716.5798339262 |
36 | 0 | 5775.58331422066 | -5775.58331422066 |
37 | 65773 | 39382.3901526758 | 26390.6098473242 |
38 | 67047 | 82035.0437416088 | -14988.0437416088 |
39 | 41953 | 85727.0045585381 | -43774.0045585381 |
40 | 109835 | 130493.935931375 | -20658.935931375 |
41 | 86584 | 89281.3977456786 | -2697.39774567864 |
42 | 59588 | 56354.1806780322 | 3233.8193219678 |
43 | 40064 | 52856.311755492 | -12792.311755492 |
44 | 70227 | 77307.3702841582 | -7080.37028415819 |
45 | 60437 | 85590.1811864581 | -25153.1811864581 |
46 | 47000 | 33509.6727680644 | 13490.3272319356 |
47 | 40295 | 34169.1391953431 | 6125.86080465687 |
48 | 103397 | 81900.7796261689 | 21496.2203738311 |
49 | 78982 | 77379.1871803793 | 1602.81281962068 |
50 | 60206 | 65494.5863924308 | -5288.58639243084 |
51 | 39887 | 27712.9739449396 | 12174.0260550604 |
52 | 49791 | 45030.7481275355 | 4760.25187246446 |
53 | 129283 | 81386.7269990981 | 47896.2730009019 |
54 | 104816 | 76382.0496565205 | 28433.9503434795 |
55 | 101395 | 96904.6215953017 | 4490.37840469827 |
56 | 72824 | 51380.0547299485 | 21443.9452700515 |
57 | 76018 | 64256.1090892268 | 11761.8909107732 |
58 | 33891 | 37711.1679986913 | -3820.16799869127 |
59 | 62164 | 73448.361748893 | -11284.361748893 |
60 | 28266 | 40496.294482568 | -12230.294482568 |
61 | 35093 | 40377.9271585077 | -5284.92715850772 |
62 | 35252 | 47471.3255235597 | -12219.3255235597 |
63 | 36977 | 54019.9437960304 | -17042.9437960304 |
64 | 42406 | 45525.3488024528 | -3119.34880245282 |
65 | 56353 | 40560.6969144332 | 15792.3030855668 |
66 | 58817 | 71908.7755500857 | -13091.7755500857 |
67 | 76053 | 93951.055360313 | -17898.055360313 |
68 | 70872 | 87477.8480591587 | -16605.8480591587 |
69 | 42372 | 57867.29886896 | -15495.29886896 |
70 | 19144 | 18043.8456874707 | 1100.15431252926 |
71 | 114177 | 84472.7482183416 | 29704.2517816584 |
72 | 53544 | 55002.4203839811 | -1458.42038398113 |
73 | 51379 | 81515.6668711758 | -30136.6668711758 |
74 | 40756 | 56597.3196840283 | -15841.3196840283 |
75 | 46956 | 76009.4976520011 | -29053.4976520011 |
76 | 17799 | 21828.3158249529 | -4029.31582495295 |
77 | 71154 | 70019.4332141587 | 1134.5667858413 |
78 | 58305 | 79273.9710949755 | -20968.9710949755 |
79 | 27454 | 41237.1270495946 | -13783.1270495946 |
80 | 34323 | 59211.1510071441 | -24888.1510071441 |
81 | 44761 | 69269.8132902699 | -24508.8132902699 |
82 | 113862 | 51583.9186016354 | 62278.0813983646 |
83 | 35027 | 25905.8009350148 | 9121.19906498515 |
84 | 62396 | 66879.0256867169 | -4483.02568671694 |
85 | 29613 | 43729.921715756 | -14116.921715756 |
86 | 65559 | 52437.3290705051 | 13121.6709294949 |
87 | 110811 | 91443.2878865363 | 19367.7121134637 |
88 | 27883 | 43137.6848157147 | -15254.6848157147 |
89 | 40181 | 48984.8620085005 | -8803.86200850049 |
90 | 53398 | 58865.5685889982 | -5467.56858899817 |
91 | 56435 | 56797.8309603107 | -362.830960310744 |
92 | 77283 | 90395.6622872887 | -13112.6622872887 |
93 | 71738 | 56071.3452160167 | 15666.6547839833 |
94 | 48503 | 50565.5171554839 | -2062.51715548387 |
95 | 25214 | 31686.7580383669 | -6472.75803836693 |
96 | 119424 | 72230.4260835502 | 47193.5739164498 |
97 | 79201 | 98305.7438935657 | -19104.7438935657 |
98 | 19349 | 23734.5437807961 | -4385.54378079607 |
99 | 78760 | 56399.0459510378 | 22360.9540489622 |
100 | 54133 | 40696.2441396359 | 13436.7558603641 |
101 | 21623 | 16579.1777622049 | 5043.82223779505 |
102 | 25497 | 53745.2437837112 | -28248.2437837112 |
103 | 69535 | 56486.8853733704 | 13048.1146266296 |
104 | 30709 | 29068.7882105971 | 1640.21178940294 |
105 | 37043 | 30470.8089593055 | 6572.19104069455 |
106 | 24716 | 6214.64095684346 | 18501.3590431565 |
107 | 54865 | 82421.7903452315 | -27556.7903452315 |
108 | 27246 | 18550.3782642992 | 8695.62173570082 |
109 | 0 | 5775.58331422066 | -5775.58331422066 |
110 | 38814 | 51069.4992047509 | -12255.4992047509 |
111 | 27646 | 52604.4419430386 | -24958.4419430386 |
112 | 65373 | 67423.2980120096 | -2050.29801200959 |
113 | 43021 | 70140.4451085056 | -27119.4451085056 |
114 | 43116 | 51142.1035710851 | -8026.10357108514 |
115 | 3058 | 5775.58331422066 | -2717.58331422066 |
116 | 0 | 5775.58331422066 | -5775.58331422066 |
117 | 96347 | 78006.7070897158 | 18340.2929102842 |
118 | 48626 | 58432.4605639345 | -9806.46056393446 |
119 | 73073 | 44837.7745340923 | 28235.2254659077 |
120 | 45266 | 64260.0690481919 | -18994.0690481919 |
121 | 43410 | 27562.6128830654 | 15847.3871169346 |
122 | 83842 | 92600.5303341165 | -8758.53033411649 |
123 | 39296 | 41253.6447585796 | -1957.64475857962 |
124 | 38490 | 47070.0384413327 | -8580.03844133266 |
125 | 39841 | 30874.8627657007 | 8966.13723429933 |
126 | 19764 | 24891.8007874214 | -5127.8007874214 |
127 | 59975 | 72715.0405989864 | -12740.0405989864 |
128 | 64589 | 50789.7728399886 | 13799.2271600114 |
129 | 63339 | 81663.0709655445 | -18324.0709655444 |
130 | 11796 | 7904.11377532591 | 3891.88622467409 |
131 | 7627 | 6992.64176631638 | 634.358233683618 |
132 | 68998 | 44836.7157641437 | 24161.2842358563 |
133 | 6836 | 4830.57347608416 | 2005.42652391584 |
134 | 33365 | 34079.8441978869 | -714.844197886868 |
135 | 5118 | 11065.5575485371 | -5947.55754853715 |
136 | 20898 | 15190.0670789489 | 5707.93292105109 |
137 | 0 | 5775.58331422066 | -5775.58331422066 |
138 | 42690 | 47236.4824639751 | -4546.48246397507 |
139 | 14507 | 17786.3479500538 | -3279.34795005376 |
140 | 7131 | 5775.58331422066 | 1355.41668577934 |
141 | 4194 | 6471.04528684679 | -2277.04528684679 |
142 | 21416 | 35277.7669687875 | -13861.7669687875 |
143 | 30591 | 34642.7417165379 | -4051.74171653792 |
144 | 42419 | 35812.5680966739 | 6606.43190332609 |
Goldfeld-Quandt test for Heteroskedasticity | |||
p-values | Alternative Hypothesis | ||
breakpoint index | greater | 2-sided | less |
9 | 0.202622781053404 | 0.405245562106808 | 0.797377218946596 |
10 | 0.847663387253608 | 0.304673225492784 | 0.152336612746392 |
11 | 0.830084211759345 | 0.33983157648131 | 0.169915788240655 |
12 | 0.742576363091858 | 0.514847273816284 | 0.257423636908142 |
13 | 0.669319665646952 | 0.661360668706096 | 0.330680334353048 |
14 | 0.786738973671693 | 0.426522052656613 | 0.213261026328307 |
15 | 0.722568642750069 | 0.554862714499862 | 0.277431357249931 |
16 | 0.677002045876475 | 0.64599590824705 | 0.322997954123525 |
17 | 0.990000500725752 | 0.0199989985484955 | 0.00999949927424777 |
18 | 0.983972110526751 | 0.0320557789464981 | 0.016027889473249 |
19 | 0.988066187907606 | 0.0238676241847877 | 0.0119338120923938 |
20 | 0.992785875697204 | 0.0144282486055916 | 0.0072141243027958 |
21 | 0.991999698873801 | 0.0160006022523989 | 0.00800030112619944 |
22 | 0.99135517168819 | 0.0172896566236206 | 0.00864482831181032 |
23 | 0.990816870915988 | 0.0183662581680236 | 0.0091831290840118 |
24 | 0.988238091365701 | 0.0235238172685972 | 0.0117619086342986 |
25 | 0.984094378990116 | 0.0318112420197681 | 0.0159056210098841 |
26 | 0.976865183183128 | 0.0462696336337438 | 0.0231348168168719 |
27 | 0.968405604112731 | 0.0631887917745386 | 0.0315943958872693 |
28 | 0.963369158412972 | 0.0732616831740555 | 0.0366308415870278 |
29 | 0.999025389066572 | 0.00194922186685664 | 0.000974610933428322 |
30 | 0.999752212084442 | 0.000495575831116455 | 0.000247787915558228 |
31 | 0.999581459514137 | 0.000837080971726902 | 0.000418540485863451 |
32 | 0.999660819806693 | 0.000678360386615055 | 0.000339180193307527 |
33 | 0.999560422697837 | 0.000879154604325678 | 0.000439577302162839 |
34 | 0.999406720224764 | 0.00118655955047264 | 0.00059327977523632 |
35 | 0.999786964132062 | 0.000426071735876246 | 0.000213035867938123 |
36 | 0.999671712089239 | 0.000656575821522231 | 0.000328287910761116 |
37 | 0.999737183394841 | 0.000525633210318206 | 0.000262816605159103 |
38 | 0.999644211324849 | 0.000711577350302541 | 0.00035578867515127 |
39 | 0.999940663523152 | 0.000118672953695627 | 5.93364768478133e-05 |
40 | 0.999947456361668 | 0.00010508727666314 | 5.25436383315699e-05 |
41 | 0.999914922690756 | 0.000170154618488391 | 8.50773092441954e-05 |
42 | 0.999858854428095 | 0.00028229114380964 | 0.00014114557190482 |
43 | 0.999818057413686 | 0.00036388517262768 | 0.00018194258631384 |
44 | 0.999723545013477 | 0.0005529099730451 | 0.00027645498652255 |
45 | 0.999765961672208 | 0.0004680766555834 | 0.0002340383277917 |
46 | 0.999698791754697 | 0.000602416490606612 | 0.000301208245303306 |
47 | 0.999540363712343 | 0.000919272575313212 | 0.000459636287656606 |
48 | 0.99960835385356 | 0.00078329229288042 | 0.00039164614644021 |
49 | 0.999384710136094 | 0.00123057972781138 | 0.000615289863905691 |
50 | 0.999101189144408 | 0.00179762171118297 | 0.000898810855591485 |
51 | 0.9988036963718 | 0.00239260725640092 | 0.00119630362820046 |
52 | 0.998213253208315 | 0.00357349358336959 | 0.00178674679168479 |
53 | 0.999838241206902 | 0.000323517586196085 | 0.000161758793098042 |
54 | 0.999945839954699 | 0.00010832009060281 | 5.41600453014051e-05 |
55 | 0.999936242191276 | 0.000127515617448187 | 6.37578087240934e-05 |
56 | 0.999945956434655 | 0.000108087130690248 | 5.40435653451238e-05 |
57 | 0.999949424010823 | 0.000101151978353525 | 5.05759891767623e-05 |
58 | 0.999922600762738 | 0.000154798474524989 | 7.73992372624943e-05 |
59 | 0.999893208759068 | 0.000213582481863468 | 0.000106791240931734 |
60 | 0.999861496241456 | 0.000277007517088781 | 0.000138503758544391 |
61 | 0.999823114921531 | 0.000353770156937168 | 0.000176885078468584 |
62 | 0.999810213105994 | 0.000379573788012644 | 0.000189786894006322 |
63 | 0.999848723501168 | 0.000302552997663202 | 0.000151276498831601 |
64 | 0.999762434518311 | 0.000475130963378551 | 0.000237565481689276 |
65 | 0.999741737970752 | 0.000516524058495478 | 0.000258262029247739 |
66 | 0.999642370804475 | 0.000715258391049 | 0.0003576291955245 |
67 | 0.999553449457523 | 0.000893101084953214 | 0.000446550542476607 |
68 | 0.999790959141755 | 0.000418081716489706 | 0.000209040858244853 |
69 | 0.999740223197898 | 0.00051955360420358 | 0.00025977680210179 |
70 | 0.999621036980361 | 0.000757926039277822 | 0.000378963019638911 |
71 | 0.999639224927372 | 0.000721550145255721 | 0.00036077507262786 |
72 | 0.999471318224547 | 0.00105736355090597 | 0.000528681775452985 |
73 | 0.999581208449583 | 0.000837583100834687 | 0.000418791550417343 |
74 | 0.999616002398229 | 0.000767995203541286 | 0.000383997601770643 |
75 | 0.999862002070897 | 0.00027599585820643 | 0.000137997929103215 |
76 | 0.999865724216188 | 0.00026855156762339 | 0.000134275783811695 |
77 | 0.999848363133536 | 0.000303273732928773 | 0.000151636866464387 |
78 | 0.999818304866462 | 0.000363390267075977 | 0.000181695133537988 |
79 | 0.999837292966505 | 0.000325414066989707 | 0.000162707033494853 |
80 | 0.999827023429037 | 0.000345953141925905 | 0.000172976570962953 |
81 | 0.999828508542839 | 0.000342982914321512 | 0.000171491457160756 |
82 | 0.999999948344777 | 1.0331044677711e-07 | 5.16552233885551e-08 |
83 | 0.999999921303012 | 1.57393977004045e-07 | 7.86969885020225e-08 |
84 | 0.999999894309518 | 2.11380963140561e-07 | 1.05690481570281e-07 |
85 | 0.999999870367279 | 2.59265441032603e-07 | 1.29632720516302e-07 |
86 | 0.9999997777707 | 4.44458599962497e-07 | 2.22229299981248e-07 |
87 | 0.999999867195637 | 2.65608725998228e-07 | 1.32804362999114e-07 |
88 | 0.999999891916992 | 2.16166016545933e-07 | 1.08083008272967e-07 |
89 | 0.999999781562272 | 4.36875455336347e-07 | 2.18437727668174e-07 |
90 | 0.999999689828019 | 6.20343962883763e-07 | 3.10171981441881e-07 |
91 | 0.99999957062488 | 8.58750239091515e-07 | 4.29375119545758e-07 |
92 | 0.999999260516175 | 1.4789676497518e-06 | 7.39483824875901e-07 |
93 | 0.999999385692792 | 1.22861441502819e-06 | 6.14307207514094e-07 |
94 | 0.999998811828507 | 2.37634298511778e-06 | 1.18817149255889e-06 |
95 | 0.999997847007471 | 4.305985057581e-06 | 2.1529925287905e-06 |
96 | 0.999999550407986 | 8.99184028505108e-07 | 4.49592014252554e-07 |
97 | 0.99999918577519 | 1.62844962005364e-06 | 8.14224810026822e-07 |
98 | 0.999998320796475 | 3.3584070505687e-06 | 1.67920352528435e-06 |
99 | 0.999997808508293 | 4.38298341460878e-06 | 2.19149170730439e-06 |
100 | 0.999997275232449 | 5.44953510131345e-06 | 2.72476755065672e-06 |
101 | 0.999995496842915 | 9.0063141708593e-06 | 4.50315708542965e-06 |
102 | 0.999995993756613 | 8.01248677429138e-06 | 4.00624338714569e-06 |
103 | 0.999993806678919 | 1.23866421620744e-05 | 6.19332108103722e-06 |
104 | 0.999987565460781 | 2.48690784378298e-05 | 1.24345392189149e-05 |
105 | 0.99997879068545 | 4.2418629099387e-05 | 2.12093145496935e-05 |
106 | 0.999962468319 | 7.50633620006575e-05 | 3.75316810003288e-05 |
107 | 0.999976600416937 | 4.6799166126318e-05 | 2.3399583063159e-05 |
108 | 0.99996976871404 | 6.04625719207581e-05 | 3.0231285960379e-05 |
109 | 0.999940665306529 | 0.000118669386941734 | 5.93346934708668e-05 |
110 | 0.999889371527023 | 0.000221256945954091 | 0.000110628472977046 |
111 | 0.999923952045821 | 0.000152095908358188 | 7.60479541790942e-05 |
112 | 0.999900344012036 | 0.000199311975927059 | 9.96559879635293e-05 |
113 | 0.999937696652377 | 0.000124606695246817 | 6.23033476234086e-05 |
114 | 0.999872748388356 | 0.000254503223287502 | 0.000127251611643751 |
115 | 0.999738674944075 | 0.000522650111850294 | 0.000261325055925147 |
116 | 0.999499720031521 | 0.00100055993695803 | 0.000500279968479015 |
117 | 0.999891649695981 | 0.000216700608037061 | 0.000108350304018531 |
118 | 0.999927997234519 | 0.000144005530962173 | 7.20027654810863e-05 |
119 | 0.999934067130343 | 0.000131865739314736 | 6.59328696573681e-05 |
120 | 0.999952638017742 | 9.47239645163063e-05 | 4.73619822581532e-05 |
121 | 0.999920625297405 | 0.000158749405189883 | 7.93747025949414e-05 |
122 | 0.999805366857482 | 0.000389266285035146 | 0.000194633142517573 |
123 | 0.999564823172415 | 0.00087035365516994 | 0.00043517682758497 |
124 | 0.999021867130051 | 0.00195626573989708 | 0.000978132869948538 |
125 | 0.997861036215028 | 0.00427792756994484 | 0.00213896378497242 |
126 | 0.995548591268416 | 0.00890281746316816 | 0.00445140873158408 |
127 | 0.990808500213064 | 0.0183829995738723 | 0.00919149978693613 |
128 | 0.994446164100315 | 0.0111076717993695 | 0.00555383589968476 |
129 | 0.992046445729619 | 0.0159071085407624 | 0.00795355427038118 |
130 | 0.984090431821488 | 0.0318191363570233 | 0.0159095681785116 |
131 | 0.966501204325982 | 0.0669975913480362 | 0.0334987956740181 |
132 | 0.999229769817186 | 0.00154046036562708 | 0.000770230182813541 |
133 | 0.996777276477782 | 0.00644544704443555 | 0.00322272352221777 |
134 | 0.99849684337449 | 0.00300631325102011 | 0.00150315662551005 |
135 | 0.990754900677092 | 0.0184901986458163 | 0.00924509932290817 |
Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
Description | # significant tests | % significant tests | OK/NOK |
1% type I error level | 101 | 0.795275590551181 | NOK |
5% type I error level | 116 | 0.913385826771654 | NOK |
10% type I error level | 119 | 0.937007874015748 | NOK |