Multiple Linear Regression - Estimated Regression Equation |
y[t] = + 0.798651349529265 + 0.00472531567739815x1[t] + 0.207076583341754x2[t] + 0.157771782945949x3[t] + 0.149637329469757x4[t] + 0.173326753875179x5[t] + 0.0319795163326446x6[t] -0.0387105943596768M1[t] + 0.0768735256343226M2[t] + 0.112509114385824M3[t] -0.132101853134254M4[t] -0.157713147188171M5[t] + 0.217054121005734M6[t] + 0.16140957424235M7[t] -0.554040474802723M8[t] -0.206280916205303M9[t] + 0.107726425781439M10[t] + 0.377411731782024M11[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) | 0.798651349529265 | 0.446895 | 1.7871 | 0.07618 | 0.03809 |
x1 | 0.00472531567739815 | 0.063896 | 0.074 | 0.941158 | 0.470579 |
x2 | 0.207076583341754 | 0.072053 | 2.8739 | 0.004716 | 0.002358 |
x3 | 0.157771782945949 | 0.066102 | 2.3868 | 0.018393 | 0.009197 |
x4 | 0.149637329469757 | 0.083208 | 1.7984 | 0.074371 | 0.037186 |
x5 | 0.173326753875179 | 0.073206 | 2.3677 | 0.01933 | 0.009665 |
x6 | 0.0319795163326446 | 0.063865 | 0.5007 | 0.617379 | 0.308689 |
M1 | -0.0387105943596768 | 0.259658 | -0.1491 | 0.881712 | 0.440856 |
M2 | 0.0768735256343226 | 0.253947 | 0.3027 | 0.762577 | 0.381288 |
M3 | 0.112509114385824 | 0.254616 | 0.4419 | 0.65929 | 0.329645 |
M4 | -0.132101853134254 | 0.261175 | -0.5058 | 0.613829 | 0.306914 |
M5 | -0.157713147188171 | 0.253138 | -0.623 | 0.534322 | 0.267161 |
M6 | 0.217054121005734 | 0.255342 | 0.8501 | 0.396812 | 0.198406 |
M7 | 0.16140957424235 | 0.255943 | 0.6306 | 0.529345 | 0.264673 |
M8 | -0.554040474802723 | 0.254923 | -2.1734 | 0.031511 | 0.015755 |
M9 | -0.206280916205303 | 0.258109 | -0.7992 | 0.425588 | 0.212794 |
M10 | 0.107726425781439 | 0.260012 | 0.4143 | 0.679308 | 0.339654 |
M11 | 0.377411731782024 | 0.258872 | 1.4579 | 0.147205 | 0.073602 |
Multiple Linear Regression - Regression Statistics | |
Multiple R | 0.631888676545997 |
R-squared | 0.399283299547052 |
Adjusted R-squared | 0.323072971877648 |
F-TEST (value) | 5.23922822217902 |
F-TEST (DF numerator) | 17 |
F-TEST (DF denominator) | 134 |
p-value | 1.00962128657400e-08 |
Multiple Linear Regression - Residual Statistics | |
Residual Standard Deviation | 0.624867951380325 |
Sum Squared Residuals | 52.3216341927407 |
Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
1 | 4 | 3.86508646508212 | 0.134913534917875 |
2 | 4 | 3.62395667226457 | 0.376043327735434 |
3 | 5 | 4.13691898950816 | 0.863081010491836 |
4 | 3 | 2.95598884132625 | 0.0440111586737519 |
5 | 2 | 2.63110288833281 | -0.63110288833281 |
6 | 5 | 3.72225298469321 | 1.27774701530679 |
7 | 4 | 3.33891903890749 | 0.66108096109251 |
8 | 2 | 2.77472099401507 | -0.774720994015071 |
9 | 4 | 3.42471021409548 | 0.575289785904525 |
10 | 4 | 2.54988895355206 | 1.45011104644794 |
11 | 4 | 3.65525372552112 | 0.344746274478885 |
12 | 2 | 2.74128154825911 | -0.741281548259107 |
13 | 5 | 3.7245925813477 | 1.27540741865230 |
14 | 3 | 3.05203172263511 | -0.0520317226351052 |
15 | 4 | 3.80450427480842 | 0.195495725191577 |
16 | 4 | 3.52614347782177 | 0.473856522178231 |
17 | 3 | 2.80976473159175 | 0.190235268408255 |
18 | 4 | 3.91377459710573 | 0.086225402894269 |
19 | 2 | 2.76047431048474 | -0.760474310484738 |
20 | 4 | 2.98359204047272 | 1.01640795952728 |
21 | 3 | 3.03958156120114 | -0.0395815612011431 |
22 | 3 | 3.32239485771194 | -0.322394857711944 |
23 | 4 | 3.65997904119851 | 0.340020958801487 |
24 | 4 | 3.48964389275824 | 0.510356107241757 |
25 | 4 | 3.65800988174032 | 0.34199011825968 |
26 | 4 | 3.38017525691276 | 0.619824743087236 |
27 | 5 | 3.80922959048582 | 1.19077040951418 |
28 | 3 | 3.04199847373209 | -0.0419984737320906 |
29 | 1 | 3.53900732891183 | -2.53900732891183 |
30 | 4 | 3.73099721187576 | 0.269002788124245 |
31 | 4 | 3.84867941898755 | 0.15132058101245 |
32 | 3 | 2.62005985206362 | 0.379940147936378 |
33 | 3 | 3.30766217466472 | -0.307662174664718 |
34 | 4 | 3.95880954702859 | 0.0411904529714089 |
35 | 4 | 4.07413220788202 | -0.0741322078820209 |
36 | 4 | 3.72869999243264 | 0.271300007567358 |
37 | 3 | 3.43334821356758 | -0.433348213567577 |
38 | 4 | 3.76414337037952 | 0.235856629620477 |
39 | 3 | 3.43965590852072 | -0.439655908520720 |
40 | 4 | 3.37014200800975 | 0.62985799199025 |
41 | 3 | 3.05827146262094 | -0.0582714626209402 |
42 | 4 | 3.69204378149449 | 0.307956218505508 |
43 | 3 | 2.76580939986849 | 0.234190600131508 |
44 | 2 | 2.21596709044127 | -0.215967090441266 |
45 | 3 | 3.64007688936445 | -0.640076889364452 |
46 | 4 | 3.52088285232218 | 0.479117147677818 |
47 | 4 | 4.39709629122696 | -0.397096291226957 |
48 | 3 | 3.6872698447452 | -0.6872698447452 |
49 | 3 | 3.32218602924179 | -0.322186029241793 |
50 | 4 | 3.79612288671217 | 0.203877113287833 |
51 | 4 | 3.76779944279838 | 0.23220055720162 |
52 | 3 | 2.96248447013757 | 0.0375155298624292 |
53 | 2 | 2.65153881339047 | -0.651538813390471 |
54 | 4 | 3.91377459710573 | 0.0862254028942692 |
55 | 4 | 3.61611894812448 | 0.383881051875521 |
56 | 3 | 2.58985064886491 | 0.410149351135093 |
57 | 2 | 2.41881463524633 | -0.418814635246328 |
58 | 4 | 3.80444690188144 | 0.195553098118565 |
59 | 3 | 4.07413220788202 | -1.07413220788202 |
60 | 3 | 3.5069691768214 | -0.506969176821403 |
61 | 4 | 3.43627906612908 | 0.563720933870918 |
62 | 3 | 2.91042468432474 | 0.0895753156752582 |
63 | 4 | 3.84120910681847 | 0.158790893181534 |
64 | 3 | 3.24907505707384 | -0.249075057073844 |
65 | 4 | 3.56626152956707 | 0.433738470432928 |
66 | 4 | 4.60158704673837 | -0.601587046738371 |
67 | 4 | 3.65892811970896 | 0.341071880291044 |
68 | 3 | 2.56307473344695 | 0.43692526655305 |
69 | 3 | 2.46207794208613 | 0.537922057913871 |
70 | 3 | 3.77246738554879 | -0.77246738554879 |
71 | 4 | 3.14089951823272 | 0.859100481767279 |
72 | 3 | 2.52344684449907 | 0.476553155500927 |
73 | 2 | 2.54022949372711 | -0.540229493727114 |
74 | 4 | 3.94576021618192 | 0.0542397838180752 |
75 | 4 | 3.98953025840962 | 0.0104697415903816 |
76 | 4 | 3.89230802198808 | 0.107691978011922 |
77 | 3 | 2.34499927544895 | 0.655000724551051 |
78 | 5 | 4.24487313392686 | 0.75512686607314 |
79 | 3 | 3.50115633676301 | -0.501156336763007 |
80 | 2 | 2.41343740397719 | -0.413437403977192 |
81 | 3 | 3.11003622267776 | -0.110036222677761 |
82 | 3 | 3.43959853559373 | -0.439598535593732 |
83 | 4 | 3.72660912565748 | 0.273390874342522 |
84 | 4 | 3.15854535593711 | 0.841454644062886 |
85 | 3 | 3.40950315071112 | -0.409503150711124 |
86 | 2 | 2.49804183077516 | -0.498041830775164 |
87 | 4 | 3.61134383773104 | 0.388656162268964 |
88 | 4 | 3.00706395485598 | 0.992936045144022 |
89 | 3 | 2.64295775650986 | 0.357042243490141 |
90 | 4 | 3.71457266647234 | 0.28542733352766 |
91 | 3 | 3.33550990110869 | -0.335509901108695 |
92 | 2 | 2.56262059819162 | -0.562620598191625 |
93 | 3 | 3.28040797400947 | -0.280407974009472 |
94 | 3 | 3.23429226538591 | -0.234292265385908 |
95 | 3 | 3.20826768869680 | -0.208267688696803 |
96 | 4 | 3.31159182320567 | 0.688408176794335 |
97 | 4 | 3.65978019487425 | 0.34021980512575 |
98 | 4 | 3.07941741175942 | 0.920582588240582 |
99 | 3 | 3.22917018738017 | -0.229170187380173 |
100 | 4 | 3.65029691977021 | 0.349703080229789 |
101 | 4 | 2.99610689307154 | 1.00389310692845 |
102 | 3 | 2.83742435677997 | 0.162575643220034 |
103 | 4 | 3.99831674845731 | 0.00168325154269271 |
104 | 3 | 3.16179974847633 | -0.161799748476328 |
105 | 4 | 3.33089746381482 | 0.669102536185184 |
106 | 4 | 4.15466518588162 | -0.154665185881618 |
107 | 3 | 3.91163510925867 | -0.911635109258673 |
108 | 3 | 3.51394309087002 | -0.513943090870021 |
109 | 3 | 3.45880795110693 | -0.458807951106929 |
110 | 3 | 3.54241255476828 | -0.542412554768284 |
111 | 3 | 3.10544673070509 | -0.105446730705092 |
112 | 2 | 2.48826838263998 | -0.488268382639978 |
113 | 4 | 3.47301818234478 | 0.526981817655222 |
114 | 2 | 3.02335107904091 | -1.02335107904091 |
115 | 3 | 3.33550990110869 | -0.335509901108695 |
116 | 3 | 2.80685614879875 | 0.193143851201253 |
117 | 3 | 2.94753912405441 | 0.0524608759455865 |
118 | 4 | 3.82000187281067 | 0.179998127189335 |
119 | 4 | 3.52294168011452 | 0.477058319885483 |
120 | 3 | 2.99132294163637 | 0.00867705836363157 |
121 | 4 | 3.62130504973028 | 0.378694950269723 |
122 | 3 | 3.09188589167611 | -0.0918858916761129 |
123 | 3 | 3.64673249186247 | -0.646732491862474 |
124 | 3 | 3.3494075861478 | -0.349407586147797 |
125 | 4 | 3.61996031003890 | 0.380039689961104 |
126 | 2 | 3.21946651866176 | -1.21946651866176 |
127 | 4 | 3.67489852985705 | 0.325101470142954 |
128 | 3 | 2.94347807066388 | 0.0565219293361169 |
129 | 3 | 2.89527932111514 | 0.104720678884860 |
130 | 4 | 3.79143149427681 | 0.208568505723186 |
131 | 4 | 3.55492119644716 | 0.445078803552838 |
132 | 4 | 3.66001564408995 | 0.339984355910046 |
133 | 3 | 3.28495552714287 | -0.284955527142873 |
134 | 2 | 2.25662186492651 | -0.256621864926505 |
135 | 4 | 3.80922959048582 | 0.190770409514178 |
136 | 2 | 3.50065959030045 | -1.50065959030045 |
137 | 3 | 3.16943364694672 | -0.169433646946724 |
138 | 4 | 3.87366062729689 | 0.126339372703106 |
139 | 3 | 3.4427921942493 | -0.4427921942493 |
140 | 3 | 2.52932490398038 | 0.470675096019625 |
141 | 3 | 3.14291647767015 | -0.142916477670151 |
142 | 3 | 3.63112014800626 | -0.631120148006256 |
143 | 4 | 4.07413220788202 | -0.0741322078820209 |
144 | 3 | 3.6872698447452 | -0.6872698447452 |
145 | 3 | 3.58591639559884 | -0.585916395598839 |
146 | 2 | 3.05900563668372 | -1.05900563668372 |
147 | 2 | 3.80922959048582 | -1.80922959048582 |
148 | 3 | 3.00616321619623 | -0.00616321619623199 |
149 | 4 | 3.49757718122438 | 0.502422818775616 |
150 | 3 | 3.51222139880798 | -0.512221398807985 |
151 | 4 | 3.72288715237425 | 0.277112847625754 |
152 | 3 | 3.83521776660731 | -0.835217766607312 |
Goldfeld-Quandt test for Heteroskedasticity | |||
p-values | Alternative Hypothesis | ||
breakpoint index | greater | 2-sided | less |
21 | 0.120596712705617 | 0.241193425411233 | 0.879403287294383 |
22 | 0.819856175840086 | 0.360287648319828 | 0.180143824159914 |
23 | 0.727401674404558 | 0.545196651190883 | 0.272598325595442 |
24 | 0.735848125168934 | 0.528303749662131 | 0.264151874831066 |
25 | 0.638881711980294 | 0.722236576039413 | 0.361118288019706 |
26 | 0.643761144904137 | 0.712477710191725 | 0.356238855095863 |
27 | 0.73866996609184 | 0.522660067816321 | 0.261330033908161 |
28 | 0.672574882863675 | 0.65485023427265 | 0.327425117136325 |
29 | 0.99330949522015 | 0.0133810095597004 | 0.00669050477985021 |
30 | 0.99048206995373 | 0.0190358600925384 | 0.0095179300462692 |
31 | 0.984573306334867 | 0.0308533873302671 | 0.0154266936651335 |
32 | 0.983138752393599 | 0.0337224952128017 | 0.0168612476064009 |
33 | 0.97675997981445 | 0.0464800403711017 | 0.0232400201855508 |
34 | 0.966455276605355 | 0.0670894467892901 | 0.0335447233946450 |
35 | 0.955293405905152 | 0.0894131881896969 | 0.0447065940948484 |
36 | 0.938572472350592 | 0.122855055298816 | 0.061427527649408 |
37 | 0.970152101179867 | 0.0596957976402661 | 0.0298478988201331 |
38 | 0.959394330785664 | 0.0812113384286721 | 0.0406056692143361 |
39 | 0.976981205785999 | 0.0460375884280023 | 0.0230187942140011 |
40 | 0.984166388725778 | 0.0316672225484445 | 0.0158336112742222 |
41 | 0.98614695217077 | 0.0277060956584599 | 0.0138530478292299 |
42 | 0.982259337610773 | 0.0354813247784547 | 0.0177406623892274 |
43 | 0.977170465385994 | 0.0456590692280118 | 0.0228295346140059 |
44 | 0.975495878550832 | 0.0490082428983365 | 0.0245041214491682 |
45 | 0.973904518549158 | 0.0521909629016847 | 0.0260954814508423 |
46 | 0.967146601747463 | 0.0657067965050747 | 0.0328533982525373 |
47 | 0.957083165969415 | 0.0858336680611691 | 0.0429168340305845 |
48 | 0.952182861345168 | 0.0956342773096631 | 0.0478171386548316 |
49 | 0.941524501758432 | 0.116950996483136 | 0.058475498241568 |
50 | 0.926049613564687 | 0.147900772870627 | 0.0739503864353135 |
51 | 0.908420096191636 | 0.183159807616728 | 0.0915799038083639 |
52 | 0.883230656703387 | 0.233538686593227 | 0.116769343296613 |
53 | 0.883411297158847 | 0.233177405682306 | 0.116588702841153 |
54 | 0.86924869124371 | 0.261502617512579 | 0.130751308756290 |
55 | 0.856483577678623 | 0.287032844642753 | 0.143516422321377 |
56 | 0.849155743059736 | 0.301688513880529 | 0.150844256940264 |
57 | 0.83271123126086 | 0.334577537478281 | 0.167288768739141 |
58 | 0.807411985876758 | 0.385176028246483 | 0.192588014123242 |
59 | 0.859369637245766 | 0.281260725508467 | 0.140630362754234 |
60 | 0.847495277775198 | 0.305009444449604 | 0.152504722224802 |
61 | 0.846762583873187 | 0.306474832253626 | 0.153237416126813 |
62 | 0.815113733276374 | 0.369772533447251 | 0.184886266723626 |
63 | 0.79223040931662 | 0.41553918136676 | 0.20776959068338 |
64 | 0.757286198925834 | 0.485427602148331 | 0.242713801074166 |
65 | 0.783937270501097 | 0.432125458997806 | 0.216062729498903 |
66 | 0.805787907124655 | 0.388424185750691 | 0.194212092875345 |
67 | 0.782982094870347 | 0.434035810259305 | 0.217017905129653 |
68 | 0.765323296550487 | 0.469353406899025 | 0.234676703449512 |
69 | 0.771401649667709 | 0.457196700664582 | 0.228598350332291 |
70 | 0.796798855444865 | 0.40640228911027 | 0.203201144555135 |
71 | 0.84449706690231 | 0.311005866195381 | 0.155502933097691 |
72 | 0.825385359882324 | 0.349229280235352 | 0.174614640117676 |
73 | 0.831855635545813 | 0.336288728908374 | 0.168144364454187 |
74 | 0.801690506769823 | 0.396618986460354 | 0.198309493230177 |
75 | 0.787899529816719 | 0.424200940366563 | 0.212100470183281 |
76 | 0.750945190553662 | 0.498109618892675 | 0.249054809446338 |
77 | 0.741645312636007 | 0.516709374727986 | 0.258354687363993 |
78 | 0.801405604114154 | 0.397188791771693 | 0.198594395885846 |
79 | 0.787628222180902 | 0.424743555638197 | 0.212371777819098 |
80 | 0.769852713627121 | 0.460294572745759 | 0.230147286372879 |
81 | 0.729591412716395 | 0.540817174567209 | 0.270408587283605 |
82 | 0.710059745462653 | 0.579880509074694 | 0.289940254537347 |
83 | 0.674788046638109 | 0.650423906723782 | 0.325211953361891 |
84 | 0.702947639459116 | 0.594104721081769 | 0.297052360540884 |
85 | 0.66654717251719 | 0.66690565496562 | 0.33345282748281 |
86 | 0.662217412151691 | 0.675565175696618 | 0.337782587848309 |
87 | 0.648043746358969 | 0.703912507282062 | 0.351956253641031 |
88 | 0.735880262832959 | 0.528239474334082 | 0.264119737167041 |
89 | 0.703999993592751 | 0.592000012814497 | 0.296000006407249 |
90 | 0.703659138826989 | 0.592681722346022 | 0.296340861173011 |
91 | 0.677949620345982 | 0.644100759308036 | 0.322050379654018 |
92 | 0.68339459499325 | 0.6332108100135 | 0.31660540500675 |
93 | 0.643897711988507 | 0.712204576022987 | 0.356102288011494 |
94 | 0.606882229452262 | 0.786235541095476 | 0.393117770547738 |
95 | 0.573204019539217 | 0.853591960921567 | 0.426795980460783 |
96 | 0.602573801277901 | 0.794852397444197 | 0.397426198722099 |
97 | 0.586697120191213 | 0.826605759617575 | 0.413302879808787 |
98 | 0.710569357695275 | 0.578861284609449 | 0.289430642304725 |
99 | 0.670143463027311 | 0.659713073945378 | 0.329856536972689 |
100 | 0.724426389279881 | 0.551147221440238 | 0.275573610720119 |
101 | 0.76469760201538 | 0.470604795969241 | 0.235302397984620 |
102 | 0.779314272746687 | 0.441371454506625 | 0.220685727253313 |
103 | 0.732233845075927 | 0.535532309848147 | 0.267766154924073 |
104 | 0.680532817891012 | 0.638934364217977 | 0.319467182108988 |
105 | 0.698733599563034 | 0.602532800873932 | 0.301266400436966 |
106 | 0.642487211312252 | 0.715025577375497 | 0.357512788687748 |
107 | 0.748784658643063 | 0.502430682713874 | 0.251215341356937 |
108 | 0.715939337396693 | 0.568121325206613 | 0.284060662603307 |
109 | 0.700794109408353 | 0.598411781183294 | 0.299205890591647 |
110 | 0.651488387910083 | 0.697023224179833 | 0.348511612089916 |
111 | 0.61893901688278 | 0.762121966234439 | 0.381060983117219 |
112 | 0.588115304762031 | 0.823769390475938 | 0.411884695237969 |
113 | 0.558650887538726 | 0.882698224922548 | 0.441349112461274 |
114 | 0.622825255048906 | 0.754349489902188 | 0.377174744951094 |
115 | 0.574159335992738 | 0.851681328014525 | 0.425840664007262 |
116 | 0.50687250666637 | 0.98625498666726 | 0.49312749333363 |
117 | 0.433558984155095 | 0.86711796831019 | 0.566441015844905 |
118 | 0.367958298520107 | 0.735916597040215 | 0.632041701479893 |
119 | 0.308700802634704 | 0.617401605269408 | 0.691299197365296 |
120 | 0.260660853414836 | 0.521321706829672 | 0.739339146585164 |
121 | 0.308626994152307 | 0.617253988304614 | 0.691373005847693 |
122 | 0.243650467065881 | 0.487300934131762 | 0.756349532934119 |
123 | 0.196359537422571 | 0.392719074845142 | 0.803640462577429 |
124 | 0.145048158830950 | 0.290096317661900 | 0.85495184116905 |
125 | 0.100800168028716 | 0.201600336057433 | 0.899199831971284 |
126 | 0.133044094542255 | 0.26608818908451 | 0.866955905457745 |
127 | 0.0946326899678296 | 0.189265379935659 | 0.90536731003217 |
128 | 0.0571646801305799 | 0.114329360261160 | 0.94283531986942 |
129 | 0.0313533158994947 | 0.0627066317989893 | 0.968646684100505 |
130 | 0.0314363100635211 | 0.0628726201270423 | 0.968563689936479 |
131 | 0.0153812784353617 | 0.0307625568707234 | 0.984618721564638 |
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 | 12 | 0.108108108108108 | NOK |
10% type I error level | 22 | 0.198198198198198 | NOK |