Multiple Linear Regression - Estimated Regression Equation |
y[t] = + 0.85901483403914 + 0.00480364594500278x1[t] + 0.248974358803874x2[t] + 0.147059243206037x3[t] + 0.162154471874077x4[t] + 0.163836595619903x5[t] + 0.0504204407030673x6[t] -0.00332137712527254t + 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) | 0.85901483403914 | 0.411478 | 2.0876 | 0.038592 | 0.019296 |
x1 | 0.00480364594500278 | 0.061118 | 0.0786 | 0.937463 | 0.468732 |
x2 | 0.248974358803874 | 0.071657 | 3.4745 | 0.000676 | 0.000338 |
x3 | 0.147059243206037 | 0.06461 | 2.2761 | 0.024315 | 0.012158 |
x4 | 0.162154471874077 | 0.082937 | 1.9551 | 0.052503 | 0.026251 |
x5 | 0.163836595619903 | 0.073467 | 2.2301 | 0.02729 | 0.013645 |
x6 | 0.0504204407030673 | 0.061045 | 0.826 | 0.410197 | 0.205098 |
t | -0.00332137712527254 | 0.00124 | -2.6794 | 0.008234 | 0.004117 |
Multiple Linear Regression - Regression Statistics | |
Multiple R | 0.585208926340266 |
R-squared | 0.342469487468327 |
Adjusted R-squared | 0.310506198664704 |
F-TEST (value) | 10.7144633824260 |
F-TEST (DF numerator) | 7 |
F-TEST (DF denominator) | 144 |
p-value | 7.9982798162348e-11 |
Multiple Linear Regression - Residual Statistics | |
Residual Standard Deviation | 0.630641441916382 |
Sum Squared Residuals | 57.2700424697817 |
Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
1 | 4 | 4.21366284032564 | -0.213662840325641 |
2 | 4 | 3.79921263252237 | 0.200787367477632 |
3 | 5 | 4.28884044071016 | 0.711159559289841 |
4 | 3 | 3.25449230268405 | -0.254492302684047 |
5 | 2 | 2.92686198181061 | -0.926861981810613 |
6 | 5 | 3.71588458950534 | 1.28411541049466 |
7 | 4 | 3.38176849894109 | 0.618231501058912 |
8 | 2 | 3.51148537054551 | -1.51148537054551 |
9 | 4 | 3.80255926063250 | 0.197440739367505 |
10 | 4 | 2.58258190494444 | 1.41741809505556 |
11 | 4 | 3.42872234671624 | 0.571277653283762 |
12 | 2 | 2.83641454881677 | -0.836414548816773 |
13 | 5 | 3.89993354911071 | 1.10006645088929 |
14 | 3 | 3.11434814620531 | -0.114348146205308 |
15 | 4 | 3.9133855558229 | 0.0866144441771042 |
16 | 4 | 3.82492641551365 | 0.175073584486348 |
17 | 3 | 3.12949404542039 | -0.129494045420389 |
18 | 4 | 3.90822507039208 | 0.0917749296079187 |
19 | 2 | 2.68288301814769 | -0.682883018147693 |
20 | 4 | 3.72982055237745 | 0.270179447622548 |
21 | 3 | 3.34508813476045 | -0.345088134760445 |
22 | 3 | 3.39718673063293 | -0.397186730632927 |
23 | 4 | 3.39366946715797 | 0.60633053284203 |
24 | 4 | 3.63932244883657 | 0.360677551163428 |
25 | 4 | 3.88497543051517 | 0.115024569484827 |
26 | 4 | 3.41530113606388 | 0.584698863936121 |
27 | 5 | 3.87833267626463 | 1.12166732373537 |
28 | 3 | 3.33191845392341 | -0.331918453923407 |
29 | 1 | 3.87168992201408 | -2.87168992201408 |
30 | 4 | 3.6949246573789 | 0.305075342621098 |
31 | 4 | 3.85543987587353 | 0.144560124126468 |
32 | 3 | 3.31863294542232 | -0.318632945422317 |
33 | 3 | 3.68496052600308 | -0.684960526003084 |
34 | 4 | 4.0220411542068 | -0.0220411542068012 |
35 | 4 | 3.85176165926245 | 0.148238340737552 |
36 | 4 | 3.89886072284024 | 0.101139277159757 |
37 | 3 | 3.60163248298606 | -0.601632482986063 |
38 | 4 | 3.83219023599662 | 0.167809764003376 |
39 | 3 | 3.43763890280644 | -0.437638902806443 |
40 | 4 | 3.63287144378198 | 0.367128556218022 |
41 | 3 | 3.35878308581080 | -0.358783085810795 |
42 | 4 | 3.58061189477337 | 0.419388105226632 |
43 | 3 | 2.68182196063430 | 0.318178039365705 |
44 | 2 | 2.86428334174944 | -0.864283341749444 |
45 | 3 | 3.9807023598838 | -0.9807023598838 |
46 | 4 | 3.57152846517544 | 0.428471534824557 |
47 | 4 | 4.13789620125316 | -0.137896201253158 |
48 | 3 | 3.7989764647439 | -0.798976464743899 |
49 | 3 | 3.48956289473769 | -0.489562894737689 |
50 | 4 | 3.84275415119642 | 0.157245848803579 |
51 | 4 | 3.73859189266501 | 0.261408107334986 |
52 | 3 | 3.13458716909687 | -0.134587169096866 |
53 | 2 | 2.85285042378168 | -0.852850423781682 |
54 | 4 | 3.78865549388227 | 0.211344506117730 |
55 | 4 | 3.51585299378596 | 0.484147006214043 |
56 | 3 | 3.22321677619361 | -0.223216776193613 |
57 | 2 | 2.66375461319183 | -0.663754613191827 |
58 | 4 | 3.77536998538118 | 0.224630014618820 |
59 | 3 | 3.77204860825591 | -0.772048608255907 |
60 | 3 | 3.57124754722153 | -0.57124754722153 |
61 | 4 | 3.51750572939319 | 0.48249427060681 |
62 | 3 | 2.89848850094819 | 0.101511499051806 |
63 | 4 | 3.80918354045788 | 0.190816459542116 |
64 | 3 | 3.46132323621747 | -0.46132323621747 |
65 | 4 | 3.79773714026234 | 0.202262859737664 |
66 | 4 | 4.47082363788289 | -0.470823637882891 |
67 | 4 | 3.53839061545462 | 0.461609384545384 |
68 | 3 | 3.12225828390557 | -0.122258283905566 |
69 | 3 | 2.69630703678334 | 0.303692963216657 |
70 | 3 | 3.68509301917484 | -0.685093019174842 |
71 | 4 | 2.76058516489075 | 1.23941483510925 |
72 | 3 | 2.52899207947845 | 0.471007920521548 |
73 | 2 | 2.54578120064939 | -0.54578120064939 |
74 | 4 | 3.92519557206396 | 0.0748044279360424 |
75 | 4 | 3.90677896627064 | 0.0932210337293552 |
76 | 4 | 4.04637991056526 | -0.0463799105652571 |
77 | 3 | 2.48078939357036 | 0.519210606429637 |
78 | 5 | 4.01983828170167 | 0.980161718298331 |
79 | 3 | 3.35147484674531 | -0.351474846745308 |
80 | 2 | 2.92024728652822 | -0.920247286528218 |
81 | 3 | 3.28616735707613 | -0.286167357076134 |
82 | 3 | 3.29962333236473 | -0.299623332364727 |
83 | 4 | 3.34779663013422 | 0.652203369865776 |
84 | 4 | 3.12914398249428 | 0.87085601750572 |
85 | 3 | 3.37669071160187 | -0.376690711601873 |
86 | 2 | 2.35554405481481 | -0.355544054814809 |
87 | 4 | 3.49666559350721 | 0.503334406492789 |
88 | 4 | 3.11212906223989 | 0.887870937760112 |
89 | 3 | 2.7405392912572 | 0.259460708742799 |
90 | 4 | 3.46199894157335 | 0.538001058426653 |
91 | 3 | 3.12267169503124 | -0.122671695031237 |
92 | 2 | 3.03253043097617 | -1.03253043097617 |
93 | 3 | 3.44006110372867 | -0.440061103728667 |
94 | 3 | 3.04550977053849 | -0.0455097705384864 |
95 | 3 | 2.7618141206773 | 0.238185879322702 |
96 | 4 | 3.23154305425204 | 0.768456945747957 |
97 | 4 | 3.68055359997645 | 0.319446400023546 |
98 | 4 | 2.97030278201533 | 1.02969721798467 |
99 | 3 | 3.00928079109926 | -0.00928079109925973 |
100 | 4 | 3.69718573658768 | 0.302814263412324 |
101 | 4 | 3.06787692541964 | 0.932123074580357 |
102 | 3 | 2.50948899660956 | 0.490511003390441 |
103 | 4 | 3.77845519472799 | 0.221544805272014 |
104 | 3 | 3.68329866104475 | -0.683298661044747 |
105 | 4 | 3.43748869480643 | 0.562511305193571 |
106 | 4 | 3.98755174562014 | 0.0124482543798581 |
107 | 3 | 3.46075961709178 | -0.460759617091784 |
108 | 3 | 3.43585724160764 | -0.435857241607643 |
109 | 3 | 3.39889277619317 | -0.398892776193169 |
110 | 3 | 3.34515095836483 | -0.345150958364829 |
111 | 3 | 2.8536840418715 | 0.146315958128501 |
112 | 2 | 2.47627522535683 | -0.476275225356834 |
113 | 4 | 3.51411865127695 | 0.485881348723046 |
114 | 2 | 2.68016009567596 | -0.680160095675958 |
115 | 3 | 3.04295864402470 | -0.0429586440246957 |
116 | 3 | 3.26703062734443 | -0.267030627344429 |
117 | 3 | 3.01473489141528 | -0.0147348914152821 |
118 | 4 | 3.59286471027869 | 0.407135289721308 |
119 | 4 | 2.95935382020749 | 1.04064617979251 |
120 | 3 | 2.85290787088842 | 0.147092129111576 |
121 | 4 | 3.51089913984094 | 0.489100860159061 |
122 | 3 | 2.84794724038370 | 0.152052759616296 |
123 | 3 | 3.40761758308742 | -0.407617583087424 |
124 | 3 | 3.32227996497736 | -0.322279964977358 |
125 | 4 | 3.60934766251086 | 0.390652337489141 |
126 | 2 | 2.78797070293285 | -0.787970702932848 |
127 | 4 | 3.36273627430461 | 0.637263725695393 |
128 | 3 | 3.33578661081299 | -0.335786610812991 |
129 | 3 | 2.90287692685008 | 0.0971230731499242 |
130 | 4 | 3.48268886945931 | 0.517311130540689 |
131 | 4 | 2.96991773540729 | 1.03008226459271 |
132 | 4 | 3.47436399146294 | 0.525636008537059 |
133 | 3 | 2.9925201041931 | 0.00747989580690048 |
134 | 2 | 1.96547982993585 | 0.0345201700641528 |
135 | 4 | 3.51962394673519 | 0.480376053264806 |
136 | 2 | 3.41546168820379 | -1.41546168820379 |
137 | 3 | 3.11214394452973 | -0.112143944529734 |
138 | 4 | 3.47433460332435 | 0.525665396675651 |
139 | 3 | 3.07302071964316 | -0.0730207196431601 |
140 | 3 | 2.79798136770197 | 0.202018632298028 |
141 | 3 | 3.15515675686842 | -0.155156756868416 |
142 | 3 | 3.33253771123838 | -0.332537711238383 |
143 | 4 | 3.49305292973301 | 0.506947070266987 |
144 | 3 | 3.48012426071773 | -0.480124260717735 |
145 | 3 | 3.40066452274437 | -0.400664522744374 |
146 | 2 | 2.69996216206853 | -0.699962162068528 |
147 | 2 | 3.47976742123192 | -1.47976742123192 |
148 | 3 | 2.89499484811797 | 0.105005151882032 |
149 | 4 | 3.41309693438830 | 0.586903065611695 |
150 | 3 | 3.01854560119812 | -0.0185456011981236 |
151 | 4 | 3.36023581833786 | 0.639764181662143 |
152 | 3 | 4.18998885105445 | -1.18998885105446 |
Goldfeld-Quandt test for Heteroskedasticity | |||
p-values | Alternative Hypothesis | ||
breakpoint index | greater | 2-sided | less |
11 | 0.171952217541052 | 0.343904435082104 | 0.828047782458948 |
12 | 0.122609118576654 | 0.245218237153309 | 0.877390881423346 |
13 | 0.0884975763171005 | 0.176995152634201 | 0.9115024236829 |
14 | 0.864129903246083 | 0.271740193507834 | 0.135870096753917 |
15 | 0.812716356780949 | 0.374567286438103 | 0.187283643219051 |
16 | 0.739543708471578 | 0.520912583056843 | 0.260456291528422 |
17 | 0.652891574501867 | 0.694216850996266 | 0.347108425498133 |
18 | 0.60224129147102 | 0.795517417057959 | 0.397758708528979 |
19 | 0.529346735804414 | 0.941306528391173 | 0.470653264195586 |
20 | 0.50818580142493 | 0.98362839715014 | 0.49181419857507 |
21 | 0.474390299473599 | 0.948780598947198 | 0.525609700526401 |
22 | 0.412646721492868 | 0.825293442985736 | 0.587353278507132 |
23 | 0.351690068910916 | 0.703380137821833 | 0.648309931089084 |
24 | 0.288544200715735 | 0.57708840143147 | 0.711455799284265 |
25 | 0.228119103657113 | 0.456238207314227 | 0.771880896342887 |
26 | 0.357174673592138 | 0.714349347184275 | 0.642825326407862 |
27 | 0.407080731445707 | 0.814161462891415 | 0.592919268554293 |
28 | 0.489657432809911 | 0.979314865619823 | 0.510342567190089 |
29 | 0.998661607589402 | 0.00267678482119516 | 0.00133839241059758 |
30 | 0.997995973661821 | 0.00400805267635788 | 0.00200402633817894 |
31 | 0.996982898656564 | 0.00603420268687135 | 0.00301710134343568 |
32 | 0.99543792770544 | 0.00912414458911856 | 0.00456207229455928 |
33 | 0.995419718137902 | 0.0091605637241967 | 0.00458028186209835 |
34 | 0.993334758378006 | 0.0133304832439876 | 0.0066652416219938 |
35 | 0.991612878733668 | 0.0167742425326644 | 0.0083871212663322 |
36 | 0.987915226609526 | 0.0241695467809488 | 0.0120847733904744 |
37 | 0.985895165266602 | 0.0282096694667962 | 0.0141048347333981 |
38 | 0.98346462926298 | 0.0330707414740427 | 0.0165353707370213 |
39 | 0.977973517389443 | 0.0440529652211136 | 0.0220264826105568 |
40 | 0.987544593616975 | 0.0249108127660503 | 0.0124554063830252 |
41 | 0.983614645702218 | 0.0327707085955645 | 0.0163853542977823 |
42 | 0.98982576289816 | 0.0203484742036824 | 0.0101742371018412 |
43 | 0.98887567309613 | 0.0222486538077394 | 0.0111243269038697 |
44 | 0.993153669777963 | 0.0136926604440741 | 0.00684633022203705 |
45 | 0.994843843211456 | 0.0103123135770884 | 0.00515615678854418 |
46 | 0.99413759961897 | 0.0117248007620601 | 0.00586240038103003 |
47 | 0.991573215597037 | 0.0168535688059254 | 0.0084267844029627 |
48 | 0.99165275804185 | 0.0166944839163013 | 0.00834724195815066 |
49 | 0.989637084013514 | 0.0207258319729718 | 0.0103629159864859 |
50 | 0.986277479025604 | 0.0274450419487917 | 0.0137225209743958 |
51 | 0.984620675116844 | 0.030758649766313 | 0.0153793248831565 |
52 | 0.980283129338784 | 0.0394337413224317 | 0.0197168706612159 |
53 | 0.981626092849136 | 0.0367478143017269 | 0.0183739071508635 |
54 | 0.977454785925086 | 0.0450904281498283 | 0.0225452140749141 |
55 | 0.977416470880393 | 0.0451670582392141 | 0.0225835291196071 |
56 | 0.971817047208265 | 0.0563659055834709 | 0.0281829527917355 |
57 | 0.970165735799063 | 0.0596685284018733 | 0.0298342642009366 |
58 | 0.963200628062671 | 0.0735987438746578 | 0.0367993719373289 |
59 | 0.96588616624384 | 0.0682276675123207 | 0.0341138337561604 |
60 | 0.963935117981077 | 0.0721297640378458 | 0.0360648820189229 |
61 | 0.962592942371315 | 0.0748141152573708 | 0.0374070576286854 |
62 | 0.955487125469417 | 0.0890257490611663 | 0.0445128745305831 |
63 | 0.945650881430078 | 0.108698237139844 | 0.0543491185699219 |
64 | 0.940785548401206 | 0.118428903197587 | 0.0592144515987936 |
65 | 0.927727199357135 | 0.144545601285730 | 0.0722728006428651 |
66 | 0.922103371436918 | 0.155793257126164 | 0.0778966285630821 |
67 | 0.915270336887834 | 0.169459326224332 | 0.084729663112166 |
68 | 0.896446753257752 | 0.207106493484497 | 0.103553246742248 |
69 | 0.885043623417094 | 0.229912753165812 | 0.114956376582906 |
70 | 0.895866796891912 | 0.208266406216176 | 0.104133203108088 |
71 | 0.944346857519497 | 0.111306284961007 | 0.0556531424805034 |
72 | 0.939315032681565 | 0.121369934636869 | 0.0606849673184345 |
73 | 0.9368375942779 | 0.126324811444198 | 0.0631624057220992 |
74 | 0.920435886468814 | 0.159128227062372 | 0.079564113531186 |
75 | 0.901180182233299 | 0.197639635533403 | 0.0988198177667015 |
76 | 0.880336791234615 | 0.239326417530771 | 0.119663208765385 |
77 | 0.866903824514382 | 0.266192350971235 | 0.133096175485618 |
78 | 0.88911984389774 | 0.22176031220452 | 0.11088015610226 |
79 | 0.8771983865038 | 0.245603226992400 | 0.122801613496200 |
80 | 0.9171747202338 | 0.1656505595324 | 0.0828252797662 |
81 | 0.905600523837011 | 0.188798952325978 | 0.0943994761629891 |
82 | 0.894719874006029 | 0.210560251987942 | 0.105280125993971 |
83 | 0.891156264943364 | 0.217687470113271 | 0.108843735056636 |
84 | 0.90107892622924 | 0.197842147541522 | 0.098921073770761 |
85 | 0.895943496259109 | 0.208113007481783 | 0.104056503740891 |
86 | 0.889225849796188 | 0.221548300407623 | 0.110774150203811 |
87 | 0.877374326325982 | 0.245251347348036 | 0.122625673674018 |
88 | 0.888462564619943 | 0.223074870760115 | 0.111537435380057 |
89 | 0.864547738287824 | 0.270904523424351 | 0.135452261712176 |
90 | 0.84781372100652 | 0.304372557986959 | 0.152186278993480 |
91 | 0.82033631743037 | 0.359327365139261 | 0.179663682569630 |
92 | 0.88410864455302 | 0.231782710893959 | 0.115891355446980 |
93 | 0.882652288003871 | 0.234695423992257 | 0.117347711996129 |
94 | 0.861214312182143 | 0.277571375635714 | 0.138785687817857 |
95 | 0.832893053920462 | 0.334213892159077 | 0.167106946079538 |
96 | 0.829339954685078 | 0.341320090629844 | 0.170660045314922 |
97 | 0.798449094193552 | 0.403101811612897 | 0.201550905806448 |
98 | 0.84999423586624 | 0.300011528267519 | 0.150005764133759 |
99 | 0.819639922118308 | 0.360720155763383 | 0.180360077881691 |
100 | 0.789569321314826 | 0.420861357370347 | 0.210430678685174 |
101 | 0.826105384703389 | 0.347789230593222 | 0.173894615296611 |
102 | 0.821049605887552 | 0.357900788224896 | 0.178950394112448 |
103 | 0.79111239990415 | 0.417775200191698 | 0.208887600095849 |
104 | 0.78671647085539 | 0.426567058289219 | 0.213283529144610 |
105 | 0.772546098194831 | 0.454907803610338 | 0.227453901805169 |
106 | 0.729961771146403 | 0.540076457707193 | 0.270038228853597 |
107 | 0.705757445696397 | 0.588485108607205 | 0.294242554303603 |
108 | 0.68071270500046 | 0.63857458999908 | 0.31928729499954 |
109 | 0.669802369439678 | 0.660395261120644 | 0.330197630560322 |
110 | 0.663896381707675 | 0.67220723658465 | 0.336103618292325 |
111 | 0.616641466935771 | 0.766717066128458 | 0.383358533064229 |
112 | 0.585890483406649 | 0.828219033186703 | 0.414109516593351 |
113 | 0.541355109894088 | 0.917289780211824 | 0.458644890105912 |
114 | 0.590340185612371 | 0.819319628775258 | 0.409659814387629 |
115 | 0.538605179695526 | 0.922789640608947 | 0.461394820304474 |
116 | 0.508221205461786 | 0.983557589076429 | 0.491778794538214 |
117 | 0.457974135171095 | 0.91594827034219 | 0.542025864828905 |
118 | 0.407186029530148 | 0.814372059060296 | 0.592813970469852 |
119 | 0.448410465601944 | 0.896820931203889 | 0.551589534398056 |
120 | 0.399981239234595 | 0.79996247846919 | 0.600018760765405 |
121 | 0.359704156419390 | 0.719408312838779 | 0.64029584358061 |
122 | 0.306576000530677 | 0.613152001061353 | 0.693423999469323 |
123 | 0.301254374127556 | 0.602508748255112 | 0.698745625872444 |
124 | 0.292515562329718 | 0.585031124659436 | 0.707484437670282 |
125 | 0.238150959045272 | 0.476301918090543 | 0.761849040954728 |
126 | 0.370560505698418 | 0.741121011396837 | 0.629439494301582 |
127 | 0.311506905993472 | 0.623013811986943 | 0.688493094006528 |
128 | 0.412566145678119 | 0.825132291356239 | 0.58743385432188 |
129 | 0.409913423612080 | 0.819826847224159 | 0.59008657638792 |
130 | 0.378498118893802 | 0.756996237787604 | 0.621501881106198 |
131 | 0.445274956058693 | 0.890549912117387 | 0.554725043941307 |
132 | 0.40386260923388 | 0.80772521846776 | 0.59613739076612 |
133 | 0.41056489854262 | 0.82112979708524 | 0.58943510145738 |
134 | 0.328452171705213 | 0.656904343410427 | 0.671547828294787 |
135 | 0.430818719684303 | 0.861637439368607 | 0.569181280315697 |
136 | 0.42622873063782 | 0.85245746127564 | 0.57377126936218 |
137 | 0.33029339348261 | 0.66058678696522 | 0.66970660651739 |
138 | 0.266262642864930 | 0.532525285729861 | 0.73373735713507 |
139 | 0.185401881327281 | 0.370803762654562 | 0.814598118672719 |
140 | 0.134363826447379 | 0.268727652894757 | 0.865636173552621 |
141 | 0.0807869459053985 | 0.161573891810797 | 0.919213054094602 |
Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
Description | # significant tests | % significant tests | OK/NOK |
1% type I error level | 5 | 0.0381679389312977 | NOK |
5% type I error level | 27 | 0.206106870229008 | NOK |
10% type I error level | 34 | 0.259541984732824 | NOK |