Multiple Linear Regression - Estimated Regression Equation |
RFC[t] = -1661.60468215782 + 664.67899217393Logins[t] + 906.083891796237Computations[t] + 246.974391885102Feedback[t] + 0.613986602873893`characters `[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) | -1661.60468215782 | 3174.469508 | -0.5234 | 0.60151 | 0.300755 |
Logins | 664.67899217393 | 100.51958 | 6.6124 | 0 | 0 |
Computations | 906.083891796237 | 139.570288 | 6.492 | 0 | 0 |
Feedback | 246.974391885102 | 99.715369 | 2.4768 | 0.014457 | 0.007228 |
`characters ` | 0.613986602873893 | 0.160734 | 3.8199 | 0.000201 | 1e-04 |
Multiple Linear Regression - Regression Statistics | |
Multiple R | 0.881794968281067 |
R-squared | 0.777562366085809 |
Adjusted R-squared | 0.771161283095472 |
F-TEST (value) | 121.473564279619 |
F-TEST (DF numerator) | 4 |
F-TEST (DF denominator) | 139 |
p-value | 0 |
Multiple Linear Regression - Residual Statistics | |
Residual Standard Deviation | 16881.3398854582 |
Sum Squared Residuals | 39612169449.6424 |
Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
1 | 58198 | 53977.9357721483 | 4220.06422785173 |
2 | 65968 | 55574.6174063021 | 10393.3825936979 |
3 | 7176 | 10511.6411206885 | -3335.64112068852 |
4 | 78306 | 97921.719860808 | -19615.7198608079 |
5 | 127587 | 120793.516148028 | 6793.48385197171 |
6 | 250877 | 226771.751564682 | 24105.2484353184 |
7 | 65878 | 56887.7607176032 | 8990.23928239684 |
8 | 72513 | 70712.292070834 | 1800.70792916599 |
9 | 72507 | 77951.3970594703 | -5444.39705947028 |
10 | 168544 | 102759.920017797 | 65784.079982203 |
11 | 66288 | 72304.7011503182 | -6016.70115031816 |
12 | 94815 | 98123.5145189705 | -3308.51451897047 |
13 | 45496 | 73032.5736796694 | -27536.5736796694 |
14 | 78277 | 76562.2251101535 | 1714.77488984652 |
15 | 66960 | 49741.4401373277 | 17218.5598626723 |
16 | 72377 | 62580.6445542167 | 9796.35544578333 |
17 | 61175 | 98982.6655244954 | -37807.6655244954 |
18 | 15580 | 19604.8253159583 | -4024.82531595834 |
19 | 71693 | 103548.678251582 | -31855.6782515825 |
20 | 13397 | 40106.7871690701 | -26709.7871690701 |
21 | 38921 | 46839.6214700063 | -7918.6214700063 |
22 | 97709 | 114048.54207443 | -16339.5420744304 |
23 | 47899 | 35445.3119080073 | 12453.6880919927 |
24 | 61674 | 57898.6461245757 | 3775.35387542435 |
25 | 77395 | 83109.5844585827 | -5714.58445858271 |
26 | 65152 | 37889.0482262194 | 27262.9517737806 |
27 | 85842 | 106315.903381357 | -20473.9033813567 |
28 | 75108 | 87215.9471753442 | -12107.9471753442 |
29 | 182314 | 123122.638600342 | 59191.3613996584 |
30 | 91493 | 46305.1560278286 | 45187.8439721714 |
31 | 56374 | 56017.4101196467 | 356.589880353314 |
32 | 104756 | 62877.0478124901 | 41878.9521875099 |
33 | 50485 | 74510.8780830175 | -24025.8780830175 |
34 | 29013 | 47232.5157606798 | -18219.5157606798 |
35 | 90349 | 64827.3864696562 | 25521.6135303438 |
36 | 0 | -1661.60468215782 | 1661.60468215782 |
37 | 61484 | 45272.371104802 | 16211.628895198 |
38 | 65245 | 69308.8949843993 | -4063.89498439926 |
39 | 35361 | 39164.6813727921 | -3803.68137279212 |
40 | 106880 | 104593.47804231 | 2286.52195768986 |
41 | 82577 | 78276.6883540434 | 4300.31164595658 |
42 | 53655 | 44647.2905991497 | 9007.70940085028 |
43 | 40064 | 37628.6644410673 | 2435.33555893273 |
44 | 58619 | 78212.7141046896 | -19593.7141046896 |
45 | 55561 | 70186.8507063693 | -14625.8507063693 |
46 | 31331 | 34103.8692724008 | -2772.86927240079 |
47 | 31350 | 37242.2396053643 | -5892.23960536434 |
48 | 93341 | 80945.9329466148 | 12395.0670533852 |
49 | 57002 | 57802.3734144606 | -800.373414460552 |
50 | 60206 | 57933.6555870875 | 2272.34441291247 |
51 | 33820 | 35260.4950092918 | -1440.49500929185 |
52 | 49791 | 50075.3172705395 | -284.317270539452 |
53 | 108716 | 70564.3346413525 | 38151.6653586475 |
54 | 87699 | 73976.9218196718 | 13722.0781803282 |
55 | 89612 | 77832.7305909414 | 11779.2694090586 |
56 | 62529 | 48501.67994551 | 14027.32005449 |
57 | 64319 | 58096.2535078215 | 6222.74649217847 |
58 | 25090 | 27688.1896442821 | -2598.18964428214 |
59 | 59080 | 69132.929912771 | -10052.929912771 |
60 | 19608 | 35559.9237849468 | -15951.9237849468 |
61 | 31969 | 29431.0751326411 | 2537.92486735888 |
62 | 29728 | 43751.7675949973 | -14023.7675949973 |
63 | 27697 | 34866.7540056763 | -7169.75400567626 |
64 | 42406 | 41628.3356874388 | 777.664312561204 |
65 | 47859 | 27043.3673667343 | 20815.6326332657 |
66 | 55240 | 55626.6769527127 | -386.67695271267 |
67 | 64606 | 78366.7816662382 | -13760.7816662382 |
68 | 61854 | 80245.9953506234 | -18391.9953506234 |
69 | 35185 | 44833.3979237933 | -9648.39792379328 |
70 | 12207 | 8550.50094740954 | 3656.49905259046 |
71 | 112537 | 97753.4047073906 | 14783.5952926094 |
72 | 43601 | 46596.4987952958 | -2995.49879529577 |
73 | 46737 | 66142.84214202 | -19405.8421420201 |
74 | 40699 | 63021.9296576701 | -22322.9296576701 |
75 | 46357 | 56223.2455179852 | -9866.24551798521 |
76 | 17667 | 19717.425857088 | -2050.425857088 |
77 | 59058 | 59915.9182891271 | -857.918289127137 |
78 | 54106 | 67358.9569528749 | -13252.9569528749 |
79 | 23795 | 35737.4449934916 | -11942.4449934916 |
80 | 34323 | 63148.5665208959 | -28825.5665208959 |
81 | 37071 | 65823.6879756895 | -28752.6879756895 |
82 | 78258 | 46417.5719358294 | 31840.4280641706 |
83 | 32392 | 37982.8282067482 | -5590.82820674817 |
84 | 55020 | 53680.0952219472 | 1339.90477805277 |
85 | 29613 | 44394.3282751208 | -14781.3282751208 |
86 | 56879 | 54299.4358922393 | 2579.56410776067 |
87 | 100802 | 120847.553543942 | -20045.5535439421 |
88 | 24612 | 44930.331702946 | -20318.331702946 |
89 | 37664 | 41975.7016975998 | -4311.70169759982 |
90 | 53398 | 47989.9706320036 | 5408.02936799637 |
91 | 54198 | 52446.3620204535 | 1751.63797954648 |
92 | 66038 | 82961.0714581114 | -16923.0714581114 |
93 | 61352 | 47552.0575477139 | 13799.9424522861 |
94 | 48096 | 45991.1751217747 | 2104.82487822527 |
95 | 25189 | 38980.6990382963 | -13791.6990382963 |
96 | 118291 | 76155.48357099 | 42135.51642901 |
97 | 71853 | 75932.3670750375 | -4079.36707503753 |
98 | 19349 | 20314.3814270705 | -965.381427070508 |
99 | 67369 | 61067.9817208808 | 6301.01827911924 |
100 | 51588 | 43902.1485539093 | 7685.85144609069 |
101 | 19719 | 16396.3353778103 | 3322.66462218973 |
102 | 25497 | 42188.9431435786 | -16691.9431435786 |
103 | 55049 | 55713.4618330049 | -664.461833004925 |
104 | 24912 | 29481.7430148783 | -4569.74301487826 |
105 | 28591 | 34200.4052848028 | -5609.40528480284 |
106 | 24716 | 22348.2903273605 | 2367.70967263947 |
107 | 52452 | 57935.7869298869 | -5483.78692988688 |
108 | 17850 | 15798.7605731489 | 2051.23942685114 |
109 | 0 | -1661.60468215782 | 1661.60468215782 |
110 | 35269 | 49871.6617036333 | -14602.6617036333 |
111 | 27554 | 47858.3989668524 | -20304.3989668524 |
112 | 55167 | 56014.3222901645 | -847.32229016446 |
113 | 42982 | 67986.3205561975 | -25004.3205561975 |
114 | 40920 | 56923.2238905813 | -16003.2238905813 |
115 | 3058 | 997.111286537898 | 2060.8887134621 |
116 | 0 | -1661.60468215782 | 1661.60468215782 |
117 | 96347 | 61991.0294659438 | 34355.9705340562 |
118 | 37559 | 56415.2803343093 | -18856.2803343093 |
119 | 62694 | 55038.1928603794 | 7655.80713962056 |
120 | 36901 | 44694.6891208965 | -7793.68912089654 |
121 | 43410 | 19758.3033299681 | 23651.6966700319 |
122 | 78320 | 77788.0383630755 | 531.961636924454 |
123 | 37972 | 40621.0211516494 | -2649.02115164936 |
124 | 34563 | 51188.3059814548 | -16625.3059814548 |
125 | 39841 | 27583.6687555464 | 12257.3312444536 |
126 | 16145 | 17819.2334544587 | -1674.23345445873 |
127 | 45310 | 51087.6202144095 | -5777.62021440952 |
128 | 57938 | 29149.0942192069 | 28788.9057807931 |
129 | 48187 | 49197.0536552618 | -1010.0536552618 |
130 | 11796 | 7202.3852742846 | 4593.6147257154 |
131 | 7627 | 3655.82725523362 | 3971.17274476638 |
132 | 62522 | 45701.3605420252 | 16820.6394579748 |
133 | 6836 | 1320.32986190438 | 5515.67013809562 |
134 | 28834 | 32185.2693499343 | -3351.26934993431 |
135 | 5118 | 4862.85175334515 | 255.148246654848 |
136 | 20825 | 12905.344748174 | 7919.65525182604 |
137 | 0 | -1661.60468215782 | 1661.60468215782 |
138 | 34363 | 29561.6689172549 | 4801.33108274509 |
139 | 12137 | 22988.7070194351 | -10851.7070194351 |
140 | 7131 | 997.111286537898 | 6133.8887134621 |
141 | 4194 | 5649.86423175541 | -1455.86423175541 |
142 | 21416 | 25224.938421731 | -3808.93842173098 |
143 | 19205 | 20018.6059520466 | -813.605952046624 |
144 | 38232 | 27463.0138445767 | 10768.9861554233 |
Goldfeld-Quandt test for Heteroskedasticity | |||
p-values | Alternative Hypothesis | ||
breakpoint index | greater | 2-sided | less |
8 | 0.244744295230888 | 0.489488590461775 | 0.755255704769112 |
9 | 0.275959041033676 | 0.551918082067351 | 0.724040958966324 |
10 | 0.957581243699603 | 0.0848375126007947 | 0.0424187563003974 |
11 | 0.931308624552857 | 0.137382750894285 | 0.0686913754471426 |
12 | 0.892576774044263 | 0.214846451911474 | 0.107423225955737 |
13 | 0.912255571561214 | 0.175488856877571 | 0.0877444284387856 |
14 | 0.870343638454781 | 0.259312723090438 | 0.129656361545219 |
15 | 0.830270283174593 | 0.339459433650813 | 0.169729716825407 |
16 | 0.854170527001455 | 0.291658945997089 | 0.145829472998545 |
17 | 0.973461641733585 | 0.0530767165328297 | 0.0265383582664149 |
18 | 0.966117105882544 | 0.0677657882349128 | 0.0338828941174564 |
19 | 0.99257134482676 | 0.0148573103464815 | 0.00742865517324075 |
20 | 0.996764584578133 | 0.0064708308437347 | 0.00323541542186735 |
21 | 0.99491546635388 | 0.010169067292242 | 0.00508453364612098 |
22 | 0.993477598317706 | 0.0130448033645884 | 0.00652240168229419 |
23 | 0.991538693359752 | 0.0169226132804961 | 0.00846130664024803 |
24 | 0.987820900331794 | 0.0243581993364112 | 0.0121790996682056 |
25 | 0.981788425738046 | 0.0364231485239074 | 0.0182115742619537 |
26 | 0.99176145941136 | 0.0164770811772809 | 0.00823854058864044 |
27 | 0.993749148566697 | 0.0125017028666049 | 0.00625085143330246 |
28 | 0.991607024129352 | 0.0167859517412952 | 0.0083929758706476 |
29 | 0.999820498948266 | 0.000359002103468241 | 0.000179501051734121 |
30 | 0.999992658391487 | 1.46832170255802e-05 | 7.3416085127901e-06 |
31 | 0.999986285958994 | 2.7428082012983e-05 | 1.37140410064915e-05 |
32 | 0.999999342092267 | 1.31581546493668e-06 | 6.5790773246834e-07 |
33 | 0.999999603289516 | 7.9342096784639e-07 | 3.96710483923195e-07 |
34 | 0.99999962808522 | 7.43829561580955e-07 | 3.71914780790478e-07 |
35 | 0.99999981596422 | 3.68071561061702e-07 | 1.84035780530851e-07 |
36 | 0.99999963171213 | 7.3657573967279e-07 | 3.68287869836395e-07 |
37 | 0.99999957590468 | 8.48190640023737e-07 | 4.24095320011868e-07 |
38 | 0.999999214298673 | 1.57140265420789e-06 | 7.85701327103943e-07 |
39 | 0.999998643763057 | 2.71247388615232e-06 | 1.35623694307616e-06 |
40 | 0.999998096874446 | 3.80625110901885e-06 | 1.90312555450942e-06 |
41 | 0.99999680809461 | 6.38381078100466e-06 | 3.19190539050233e-06 |
42 | 0.999994827738003 | 1.03445239938134e-05 | 5.17226199690671e-06 |
43 | 0.999991995143841 | 1.60097123174435e-05 | 8.00485615872175e-06 |
44 | 0.9999927875688 | 1.44248624019466e-05 | 7.21243120097328e-06 |
45 | 0.999991628168152 | 1.67436636951068e-05 | 8.3718318475534e-06 |
46 | 0.99998554523711 | 2.89095257818392e-05 | 1.44547628909196e-05 |
47 | 0.99997738343539 | 4.52331292186241e-05 | 2.2616564609312e-05 |
48 | 0.99997342083871 | 5.31583225788196e-05 | 2.65791612894098e-05 |
49 | 0.999955814244468 | 8.83715110638244e-05 | 4.41857555319122e-05 |
50 | 0.999927154304121 | 0.000145691391757301 | 7.28456958786504e-05 |
51 | 0.99988285649318 | 0.000234287013640606 | 0.000117143506820303 |
52 | 0.999811989845716 | 0.000376020308567377 | 0.000188010154283689 |
53 | 0.99998635596386 | 2.7288072281258e-05 | 1.3644036140629e-05 |
54 | 0.999987129775644 | 2.57404487122641e-05 | 1.28702243561321e-05 |
55 | 0.999985840850648 | 2.83182987042797e-05 | 1.41591493521399e-05 |
56 | 0.999984226817158 | 3.15463656848589e-05 | 1.57731828424294e-05 |
57 | 0.999979451273889 | 4.10974522225569e-05 | 2.05487261112785e-05 |
58 | 0.999966279970998 | 6.74400580034527e-05 | 3.37200290017263e-05 |
59 | 0.999951704854774 | 9.65902904520035e-05 | 4.82951452260017e-05 |
60 | 0.999949577482155 | 0.000100845035689584 | 5.04225178447921e-05 |
61 | 0.999927368725782 | 0.000145262548436759 | 7.26312742183796e-05 |
62 | 0.999923511092559 | 0.00015297781488302 | 7.64889074415102e-05 |
63 | 0.99988459533336 | 0.000230809333278937 | 0.000115404666639469 |
64 | 0.9998141909589 | 0.000371618082201705 | 0.000185809041100853 |
65 | 0.99987201749407 | 0.000255965011860962 | 0.000127982505930481 |
66 | 0.999802220882412 | 0.000395558235175913 | 0.000197779117587957 |
67 | 0.999730487378683 | 0.000539025242633448 | 0.000269512621316724 |
68 | 0.999731804451089 | 0.000536391097822946 | 0.000268195548911473 |
69 | 0.999628823347645 | 0.000742353304710563 | 0.000371176652355282 |
70 | 0.999428516703944 | 0.00114296659211235 | 0.000571483296056175 |
71 | 0.99950297807401 | 0.00099404385198241 | 0.000497021925991205 |
72 | 0.999332464040765 | 0.00133507191847063 | 0.000667535959235315 |
73 | 0.999330039995854 | 0.00133992000829215 | 0.000669960004146074 |
74 | 0.99946231437891 | 0.00107537124217961 | 0.000537685621089807 |
75 | 0.999378914003 | 0.00124217199400127 | 0.000621085997000637 |
76 | 0.999238866472647 | 0.00152226705470686 | 0.000761133527353428 |
77 | 0.99891485665131 | 0.00217028669737864 | 0.00108514334868932 |
78 | 0.998602880342134 | 0.00279423931573232 | 0.00139711965786616 |
79 | 0.998330585836655 | 0.00333882832669076 | 0.00166941416334538 |
80 | 0.998705419437805 | 0.00258916112439082 | 0.00129458056219541 |
81 | 0.999316334040948 | 0.00136733191810307 | 0.000683665959051536 |
82 | 0.9997950233152 | 0.000409953369599545 | 0.000204976684799772 |
83 | 0.999708251781632 | 0.00058349643673576 | 0.00029174821836788 |
84 | 0.999534379008836 | 0.000931241982327697 | 0.000465620991163848 |
85 | 0.999565248330782 | 0.000869503338435767 | 0.000434751669217884 |
86 | 0.999335927180011 | 0.00132814563997747 | 0.000664072819988733 |
87 | 0.999634495546946 | 0.000731008906107985 | 0.000365504453053993 |
88 | 0.999840334196221 | 0.000319331607557811 | 0.000159665803778906 |
89 | 0.999740470243805 | 0.00051905951238919 | 0.000259529756194595 |
90 | 0.999585051852437 | 0.00082989629512699 | 0.000414948147563495 |
91 | 0.999406696747982 | 0.00118660650403583 | 0.000593303252017914 |
92 | 0.999314634235811 | 0.0013707315283771 | 0.000685365764188548 |
93 | 0.999233704829848 | 0.00153259034030387 | 0.000766295170151934 |
94 | 0.99880059548027 | 0.00239880903945993 | 0.00119940451972997 |
95 | 0.998565939239948 | 0.00286812152010496 | 0.00143406076005248 |
96 | 0.999884579680994 | 0.000230840638012816 | 0.000115420319006408 |
97 | 0.9998152106608 | 0.000369578678400123 | 0.000184789339200062 |
98 | 0.999683735434515 | 0.000632529130969972 | 0.000316264565484986 |
99 | 0.999479471449403 | 0.00104105710119392 | 0.000520528550596962 |
100 | 0.999235904963571 | 0.00152819007285714 | 0.000764095036428571 |
101 | 0.998767057322735 | 0.00246588535452991 | 0.00123294267726496 |
102 | 0.998518387220156 | 0.00296322555968799 | 0.00148161277984399 |
103 | 0.997664290355212 | 0.00467141928957613 | 0.00233570964478807 |
104 | 0.996647415236568 | 0.00670516952686435 | 0.00335258476343217 |
105 | 0.99551363962119 | 0.00897272075762221 | 0.00448636037881111 |
106 | 0.993723408213304 | 0.0125531835733925 | 0.00627659178669627 |
107 | 0.990519262145393 | 0.0189614757092144 | 0.0094807378546072 |
108 | 0.985859944791332 | 0.0282801104173369 | 0.0141400552086685 |
109 | 0.97950326036375 | 0.0409934792724983 | 0.0204967396362491 |
110 | 0.975842655987685 | 0.0483146880246297 | 0.0241573440123149 |
111 | 0.979729722015696 | 0.0405405559686081 | 0.0202702779843041 |
112 | 0.971602652057116 | 0.0567946958857672 | 0.0283973479428836 |
113 | 0.993274843028725 | 0.0134503139425489 | 0.00672515697127447 |
114 | 0.992508407140422 | 0.0149831857191555 | 0.00749159285957773 |
115 | 0.988139040144285 | 0.0237219197114293 | 0.0118609598557146 |
116 | 0.981523480152062 | 0.0369530396958767 | 0.0184765198479383 |
117 | 0.998206790649449 | 0.003586418701102 | 0.001793209350551 |
118 | 0.99900648454626 | 0.00198703090747873 | 0.000993515453739367 |
119 | 0.999009280379753 | 0.00198143924049413 | 0.000990719620247067 |
120 | 0.998892557293374 | 0.00221488541325199 | 0.00110744270662599 |
121 | 0.999222393639295 | 0.00155521272141 | 0.000777606360705002 |
122 | 0.998700098860286 | 0.00259980227942862 | 0.00129990113971431 |
123 | 0.997383011169978 | 0.00523397766004385 | 0.00261698883002193 |
124 | 0.99934770731085 | 0.00130458537829934 | 0.00065229268914967 |
125 | 0.998561187198627 | 0.00287762560274539 | 0.0014388128013727 |
126 | 0.99685138301025 | 0.0062972339795019 | 0.00314861698975095 |
127 | 0.99700014725478 | 0.00599970549044087 | 0.00299985274522044 |
128 | 0.999814174710643 | 0.000371650578713646 | 0.000185825289356823 |
129 | 0.999449009378844 | 0.00110198124231115 | 0.000550990621155576 |
130 | 0.998515252631887 | 0.0029694947362262 | 0.0014847473681131 |
131 | 0.995910769066954 | 0.00817846186609284 | 0.00408923093304642 |
132 | 0.999136926783993 | 0.00172614643201326 | 0.000863073216006628 |
133 | 0.996961213904752 | 0.00607757219049673 | 0.00303878609524836 |
134 | 0.989489468505661 | 0.021021062988677 | 0.0105105314943385 |
135 | 0.967846637903721 | 0.0643067241925573 | 0.0321533620962786 |
136 | 0.920298586675009 | 0.159402826649983 | 0.0797014133249914 |
Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
Description | # significant tests | % significant tests | OK/NOK |
1% type I error level | 95 | 0.736434108527132 | NOK |
5% type I error level | 115 | 0.891472868217054 | NOK |
10% type I error level | 120 | 0.930232558139535 | NOK |