Multiple Linear Regression - Estimated Regression Equation |
Y_t[t] = + 775.693886285818 + 0.916318386195141X_1t[t] + 1.56228856777394X_2t[t] + 1.42711750419291X_3t[t] + 0.907997375332752X_4t[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) | 775.693886285818 | 220.748375 | 3.5139 | 0.000596 | 0.000298 |
X_1t | 0.916318386195141 | 0.073374 | 12.4884 | 0 | 0 |
X_2t | 1.56228856777394 | 0.113646 | 13.7469 | 0 | 0 |
X_3t | 1.42711750419291 | 0.029479 | 48.4116 | 0 | 0 |
X_4t | 0.907997375332752 | 0.04934 | 18.4027 | 0 | 0 |
Multiple Linear Regression - Regression Statistics | |
Multiple R | 0.994595397681047 |
R-squared | 0.989220005088319 |
Adjusted R-squared | 0.988909789407408 |
F-TEST (value) | 3188.81367370326 |
F-TEST (DF numerator) | 4 |
F-TEST (DF denominator) | 139 |
p-value | 0 |
Multiple Linear Regression - Residual Statistics | |
Residual Standard Deviation | 93.6772246649449 |
Sum Squared Residuals | 1219783.71650879 |
Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
1 | 14915 | 14840.571339868 | 74.4286601319822 |
2 | 11773 | 11841.1809307555 | -68.180930755464 |
3 | 11608 | 11774.1217474668 | -166.121747466848 |
4 | 11468 | 11623.7509979764 | -155.750997976379 |
5 | 11511 | 11532.4969605465 | -21.4969605464614 |
6 | 11200 | 11181.9725192747 | 18.027480725304 |
7 | 11164 | 11214.4104885719 | -50.4104885719231 |
8 | 10960 | 10967.686678045 | -7.68667804504588 |
9 | 10667 | 10750.3928551887 | -83.392855188651 |
10 | 11556 | 11658.3981511137 | -102.39815111374 |
11 | 11372 | 11490.8255284269 | -118.825528426926 |
12 | 12333 | 12049.3846431253 | 283.615356874716 |
13 | 13102 | 12937.1433435503 | 164.856656449743 |
14 | 11115 | 11091.4069671528 | 23.5930328471609 |
15 | 12572 | 12522.183968337 | 49.8160316630354 |
16 | 11557 | 11593.7673440598 | -36.7673440597625 |
17 | 12059 | 12067.5192432049 | -8.51924320487507 |
18 | 11420 | 11350.9721617467 | 69.0278382533336 |
19 | 11185 | 10944.5545459952 | 240.445454004825 |
20 | 11113 | 10780.5398656995 | 332.46013430046 |
21 | 10706 | 10476.5527348706 | 229.447265129416 |
22 | 11523 | 11367.3404136122 | 155.659586387847 |
23 | 11391 | 11284.9046027184 | 106.095397281621 |
24 | 12634 | 12447.5814640324 | 186.418535967597 |
25 | 13469 | 13256.318978831 | 212.68102116898 |
26 | 11735 | 11682.7552020176 | 52.244797982449 |
27 | 13281 | 13216.2535854467 | 64.7464145533103 |
28 | 11968 | 12037.0911657944 | -69.0911657944415 |
29 | 11623 | 11622.8921063615 | 0.107893638537695 |
30 | 11084 | 11064.6154868958 | 19.3845131041764 |
31 | 11509 | 11401.381179301 | 107.618820698955 |
32 | 11134 | 11142.8264669125 | -8.82646691247861 |
33 | 10438 | 10370.2761497171 | 67.7238502829115 |
34 | 11530 | 11598.3277234299 | -68.3277234298999 |
35 | 11491 | 11495.935139987 | -4.93513998696291 |
36 | 13093 | 13107.4863027177 | -14.4863027177239 |
37 | 13106 | 13087.9497385491 | 18.0502614508547 |
38 | 11305 | 11430.294128928 | -125.29412892803 |
39 | 13113 | 13172.5957817635 | -59.5957817634641 |
40 | 12203 | 12164.2734598677 | 38.7265401322715 |
41 | 11309 | 11409.7844902639 | -100.784490263859 |
42 | 11088 | 11030.5636414463 | 57.4363585537328 |
43 | 11234 | 11059.4023402686 | 174.597659731435 |
44 | 11619 | 11449.4833536045 | 169.516646395505 |
45 | 10942 | 10939.2885331224 | 2.7114668775962 |
46 | 11445 | 11401.9382135657 | 43.0617864342789 |
47 | 11291 | 11354.133840284 | -63.13384028404 |
48 | 13281 | 13257.6430743902 | 23.35692560981 |
49 | 13726 | 13691.0038860688 | 34.9961139311973 |
50 | 11300 | 11390.6686290806 | -90.6686290805906 |
51 | 11983 | 12030.5619663303 | -47.5619663302737 |
52 | 11092 | 11151.0243078667 | -59.024307866742 |
53 | 11093 | 11226.2229368949 | -133.222936894946 |
54 | 10692 | 10847.6828909527 | -155.682890952738 |
55 | 10786 | 10746.7629475621 | 39.2370524378782 |
56 | 11166 | 11099.1452507643 | 66.8547492357246 |
57 | 10553 | 10598.0438631066 | -45.043863106577 |
58 | 11103 | 11129.4174416403 | -26.4174416403328 |
59 | 10969 | 11056.3756924693 | -87.3756924692754 |
60 | 12090 | 12116.1818844861 | -26.1818844860736 |
61 | 12544 | 12583.0874452549 | -39.087445254887 |
62 | 12264 | 12277.9673981225 | -13.9673981225449 |
63 | 13783 | 13899.4657936815 | -116.465793681492 |
64 | 11214 | 11265.6185904704 | -51.6185904704077 |
65 | 11453 | 11429.6853714251 | 23.3146285749203 |
66 | 10883 | 10884.0300532352 | -1.03005323520424 |
67 | 10381 | 10330.3590418924 | 50.640958107603 |
68 | 10348 | 10287.5334012139 | 60.466598786125 |
69 | 10024 | 9945.7741358421 | 78.2258641578999 |
70 | 10805 | 10841.6276060119 | -36.6276060119076 |
71 | 10796 | 10970.4013529371 | -174.401352937098 |
72 | 11907 | 12059.6499664798 | -152.649966479839 |
73 | 12261 | 12212.6999283581 | 48.3000716419311 |
74 | 11377 | 11492.5711179 | -115.571117899968 |
75 | 12689 | 12713.844479414 | -24.8444794140396 |
76 | 11474 | 11577.6440236049 | -103.644023604864 |
77 | 10992 | 10957.0768759239 | 34.9231240761476 |
78 | 10764 | 10787.6003747297 | -23.6003747296566 |
79 | 12164 | 11999.861017101 | 164.138982898958 |
80 | 10409 | 10246.3401535826 | 162.659846417354 |
81 | 10398 | 10352.2934915682 | 45.7065084318393 |
82 | 10349 | 10445.2656537495 | -96.2656537495402 |
83 | 10865 | 10913.962753703 | -48.9627537029582 |
84 | 11630 | 11698.1797353716 | -68.1797353715746 |
85 | 12221 | 12231.2553059977 | -10.2553059976532 |
86 | 10884 | 11016.8067526524 | -132.806752652364 |
87 | 12019 | 12022.7687641779 | -3.76876417786747 |
88 | 11021 | 11129.6844203677 | -108.684420367724 |
89 | 10799 | 10821.8715778835 | -22.8715778834547 |
90 | 10423 | 10489.3938745884 | -66.393874588422 |
91 | 10484 | 10407.2825011378 | 76.7174988621639 |
92 | 10450 | 10422.4509923466 | 27.5490076534501 |
93 | 9906 | 9955.66740790896 | -49.6674079089563 |
94 | 11049 | 11056.2955896803 | -7.29558968034399 |
95 | 11281 | 11344.0265487158 | -63.0265487158106 |
96 | 12485 | 12536.2980173046 | -51.2980173045924 |
97 | 12849 | 12766.7904188958 | 82.2095811042217 |
98 | 11380 | 11475.9982429686 | -95.9982429686162 |
99 | 12079 | 12069.8420014599 | 9.15799854007095 |
100 | 11366 | 11449.3945275831 | -83.3945275830799 |
101 | 11328 | 11293.1048481195 | 34.8951518804523 |
102 | 10444 | 10477.3530942891 | -33.3530942891457 |
103 | 10854 | 10698.9136373229 | 155.08636267708 |
104 | 10434 | 10332.9356668164 | 101.064333183616 |
105 | 10137 | 10214.2657421827 | -77.2657421827146 |
106 | 10992 | 11059.5230305627 | -67.523030562716 |
107 | 10906 | 10977.0104041609 | -71.0104041609395 |
108 | 12367 | 12368.6376173806 | -1.63761738061016 |
109 | 14371 | 14286.4660655018 | 84.5339344982182 |
110 | 11695 | 11680.9066693453 | 14.0933306546689 |
111 | 11546 | 11600.5497864892 | -54.5497864891688 |
112 | 10922 | 10993.3945993698 | -71.3945993698458 |
113 | 10670 | 10723.9170444561 | -53.9170444561261 |
114 | 10254 | 10231.9972526252 | 22.0027473747995 |
115 | 10573 | 10563.0838119921 | 9.91618800791597 |
116 | 10239 | 10223.7166941297 | 15.2833058703227 |
117 | 10253 | 10230.4232149388 | 22.5767850611705 |
118 | 11176 | 11201.7644253184 | -25.7644253184023 |
119 | 10719 | 10751.5201905532 | -32.5201905531648 |
120 | 11817 | 11926.2996717004 | -109.299671700439 |
121 | 12487 | 12500.2195591343 | -13.2195591342678 |
122 | 11519 | 11619.3074185674 | -100.307418567356 |
123 | 12025 | 11993.8911209586 | 31.1088790413822 |
124 | 10976 | 10882.7564722411 | 93.2435277589249 |
125 | 11276 | 11115.4155570427 | 160.584442957324 |
126 | 10657 | 10658.1260498722 | -1.12604987217184 |
127 | 11141 | 11031.3054396996 | 109.694560300379 |
128 | 10423 | 10390.5052111585 | 32.4947888414552 |
129 | 10640 | 10572.6050765534 | 67.3949234465655 |
130 | 11426 | 11474.9749899867 | -48.9749899866593 |
131 | 10948 | 10995.3846696817 | -47.3846696817359 |
132 | 12540 | 12686.2239661366 | -146.223966136599 |
133 | 12200 | 12269.5226385143 | -69.5226385142654 |
134 | 10644 | 10726.608564358 | -82.6085643580297 |
135 | 12044 | 11969.2364114309 | 74.763588569128 |
136 | 11338 | 11390.3998042779 | -52.3998042778618 |
137 | 11292 | 11292.1140465825 | -0.114046582543401 |
138 | 10612 | 10586.8091086886 | 25.1908913113688 |
139 | 10995 | 10988.1390120473 | 6.86098795267519 |
140 | 10686 | 10747.2726539137 | -61.2726539137333 |
141 | 10635 | 10629.3684798811 | 5.63152011890151 |
142 | 11285 | 11309.5905135295 | -24.5905135294764 |
143 | 11475 | 11472.1078368437 | 2.89216315627486 |
144 | 12535 | 12581.7039503746 | -46.7039503745898 |
Goldfeld-Quandt test for Heteroskedasticity | |||
p-values | Alternative Hypothesis | ||
breakpoint index | greater | 2-sided | less |
8 | 0.11457449114237 | 0.229148982284739 | 0.88542550885763 |
9 | 0.05151189924811 | 0.10302379849622 | 0.94848810075189 |
10 | 0.0417519888749158 | 0.0835039777498317 | 0.958248011125084 |
11 | 0.021790229111613 | 0.043580458223226 | 0.978209770888387 |
12 | 0.61745970613415 | 0.765080587731701 | 0.38254029386585 |
13 | 0.5960129542276 | 0.8079740915448 | 0.4039870457724 |
14 | 0.525801767919398 | 0.948396464161204 | 0.474198232080602 |
15 | 0.460731321034924 | 0.921462642069847 | 0.539268678965076 |
16 | 0.561712273265014 | 0.876575453469973 | 0.438287726734986 |
17 | 0.719127284137368 | 0.561745431725264 | 0.280872715862632 |
18 | 0.662711457966124 | 0.674577084067751 | 0.337288542033876 |
19 | 0.679927208092082 | 0.640145583815836 | 0.320072791907918 |
20 | 0.919340329797022 | 0.161319340405957 | 0.0806596702029783 |
21 | 0.977000720573517 | 0.045998558852966 | 0.022999279426483 |
22 | 0.982991341536001 | 0.0340173169279987 | 0.0170086584639993 |
23 | 0.982602842827837 | 0.0347943143443262 | 0.0173971571721631 |
24 | 0.99799507725929 | 0.00400984548141969 | 0.00200492274070984 |
25 | 0.998959331475445 | 0.0020813370491091 | 0.00104066852455455 |
26 | 0.998862358842265 | 0.00227528231546952 | 0.00113764115773476 |
27 | 0.998986176042141 | 0.00202764791571826 | 0.00101382395785913 |
28 | 0.999669454433154 | 0.00066109113369196 | 0.00033054556684598 |
29 | 0.999647041188481 | 0.000705917623037497 | 0.000352958811518749 |
30 | 0.999850039364239 | 0.000299921271522174 | 0.000149960635761087 |
31 | 0.999847018574588 | 0.000305962850823322 | 0.000152981425411661 |
32 | 0.999951095477677 | 9.78090446457179e-05 | 4.89045223228589e-05 |
33 | 0.99993576076104 | 0.00012847847791997 | 6.42392389599848e-05 |
34 | 0.999926792088162 | 0.000146415823676095 | 7.32079118380475e-05 |
35 | 0.999891072048558 | 0.000217855902883542 | 0.000108927951441771 |
36 | 0.999862292474007 | 0.000275415051986762 | 0.000137707525993381 |
37 | 0.999818315034855 | 0.000363369930290738 | 0.000181684965145369 |
38 | 0.999891700663899 | 0.000216598672202888 | 0.000108299336101444 |
39 | 0.999880935038921 | 0.000238129922158848 | 0.000119064961079424 |
40 | 0.999852250805002 | 0.000295498389995656 | 0.000147749194997828 |
41 | 0.999916668014608 | 0.00016666397078472 | 8.33319853923599e-05 |
42 | 0.999893787661831 | 0.000212424676338833 | 0.000106212338169416 |
43 | 0.999958313841946 | 8.33723161088337e-05 | 4.16861580544169e-05 |
44 | 0.99998568624374 | 2.86275125203961e-05 | 1.43137562601981e-05 |
45 | 0.999982263653115 | 3.54726937703253e-05 | 1.77363468851626e-05 |
46 | 0.999982698473587 | 3.46030528262901e-05 | 1.73015264131451e-05 |
47 | 0.999984280429696 | 3.14391406077948e-05 | 1.57195703038974e-05 |
48 | 0.999984450583328 | 3.10988333439271e-05 | 1.55494166719636e-05 |
49 | 0.999985843834144 | 2.83123317126718e-05 | 1.41561658563359e-05 |
50 | 0.999984126853902 | 3.17462921963465e-05 | 1.58731460981733e-05 |
51 | 0.999982030918666 | 3.59381626689184e-05 | 1.79690813344592e-05 |
52 | 0.99997977943247 | 4.04411350609844e-05 | 2.02205675304922e-05 |
53 | 0.999987432722113 | 2.51345557737996e-05 | 1.25672778868998e-05 |
54 | 0.99999594811634 | 8.10376731969542e-06 | 4.05188365984771e-06 |
55 | 0.999994391337988 | 1.12173240250601e-05 | 5.60866201253005e-06 |
56 | 0.999993598230564 | 1.2803538871074e-05 | 6.40176943553701e-06 |
57 | 0.999990369318335 | 1.92613633310507e-05 | 9.63068166552536e-06 |
58 | 0.999985924629225 | 2.81507415501679e-05 | 1.40753707750839e-05 |
59 | 0.999982178476237 | 3.56430475265571e-05 | 1.78215237632786e-05 |
60 | 0.999977055246859 | 4.58895062816155e-05 | 2.29447531408077e-05 |
61 | 0.999970632197615 | 5.87356047706517e-05 | 2.93678023853259e-05 |
62 | 0.999959821460705 | 8.03570785903168e-05 | 4.01785392951584e-05 |
63 | 0.99996904859771 | 6.19028045801398e-05 | 3.09514022900699e-05 |
64 | 0.999955843644287 | 8.83127114261284e-05 | 4.41563557130642e-05 |
65 | 0.999945528464578 | 0.000108943070843344 | 5.44715354216719e-05 |
66 | 0.999913034295907 | 0.000173931408185031 | 8.69657040925153e-05 |
67 | 0.999894255262457 | 0.00021148947508584 | 0.00010574473754292 |
68 | 0.999906672309242 | 0.000186655381515979 | 9.33276907579896e-05 |
69 | 0.999920132859002 | 0.000159734281995047 | 7.98671409975236e-05 |
70 | 0.9998894360049 | 0.00022112799019966 | 0.00011056399509983 |
71 | 0.999934546139746 | 0.000130907720508273 | 6.54538602541364e-05 |
72 | 0.999944861547455 | 0.00011027690509037 | 5.51384525451852e-05 |
73 | 0.999953173090113 | 9.36538197748401e-05 | 4.682690988742e-05 |
74 | 0.999949471996457 | 0.000101056007085705 | 5.05280035428523e-05 |
75 | 0.999927782997433 | 0.00014443400513342 | 7.22170025667101e-05 |
76 | 0.999920689655878 | 0.000158620688244733 | 7.93103441223666e-05 |
77 | 0.99989764477361 | 0.000204710452780249 | 0.000102355226390124 |
78 | 0.999836447210414 | 0.000327105579172955 | 0.000163552789586478 |
79 | 0.999959315642462 | 8.13687150753267e-05 | 4.06843575376633e-05 |
80 | 0.999997708747089 | 4.58250582152819e-06 | 2.2912529107641e-06 |
81 | 0.999997967690778 | 4.06461844406071e-06 | 2.03230922203036e-06 |
82 | 0.99999814745541 | 3.70508917895582e-06 | 1.85254458947791e-06 |
83 | 0.999996908694755 | 6.18261048965702e-06 | 3.09130524482851e-06 |
84 | 0.999994940374181 | 1.01192516381048e-05 | 5.05962581905242e-06 |
85 | 0.999990853752524 | 1.82924949519551e-05 | 9.14624747597754e-06 |
86 | 0.999994322246428 | 1.13555071448444e-05 | 5.6777535724222e-06 |
87 | 0.999992180900287 | 1.56381994266089e-05 | 7.81909971330447e-06 |
88 | 0.999990865518655 | 1.82689626895187e-05 | 9.13448134475937e-06 |
89 | 0.99998352995071 | 3.29400985799347e-05 | 1.64700492899673e-05 |
90 | 0.999978957721152 | 4.20845576968281e-05 | 2.10422788484141e-05 |
91 | 0.999977214219262 | 4.55715614760864e-05 | 2.27857807380432e-05 |
92 | 0.999969036838904 | 6.19263221919462e-05 | 3.09631610959731e-05 |
93 | 0.999946722563095 | 0.000106554873810515 | 5.32774369052575e-05 |
94 | 0.999926511603464 | 0.000146976793072335 | 7.34883965361674e-05 |
95 | 0.999879683127161 | 0.000240633745678918 | 0.000120316872839459 |
96 | 0.999805960662095 | 0.000388078675809569 | 0.000194039337904784 |
97 | 0.999887568166337 | 0.000224863667327064 | 0.000112431833663532 |
98 | 0.999852285443446 | 0.000295429113108695 | 0.000147714556554348 |
99 | 0.999806932160055 | 0.000386135679889238 | 0.000193067839944619 |
100 | 0.999698459476007 | 0.000603081047986184 | 0.000301540523993092 |
101 | 0.999631105163821 | 0.00073778967235728 | 0.00036889483617864 |
102 | 0.999382157274315 | 0.00123568545137065 | 0.000617842725685327 |
103 | 0.999801971480986 | 0.000396057038028414 | 0.000198028519014207 |
104 | 0.999877581122413 | 0.000244837755174922 | 0.000122418877587461 |
105 | 0.999820553801325 | 0.000358892397350019 | 0.000179446198675009 |
106 | 0.999698052622633 | 0.000603894754734848 | 0.000301947377367424 |
107 | 0.99953053107733 | 0.000938937845340183 | 0.000469468922670092 |
108 | 0.999284298898022 | 0.00143140220395548 | 0.000715701101977741 |
109 | 0.999181957586379 | 0.00163608482724301 | 0.000818042413621503 |
110 | 0.998762923840534 | 0.0024741523189329 | 0.00123707615946645 |
111 | 0.99794942283495 | 0.00410115433009962 | 0.00205057716504981 |
112 | 0.997277436382185 | 0.00544512723563047 | 0.00272256361781523 |
113 | 0.996174098222669 | 0.00765180355466214 | 0.00382590177733107 |
114 | 0.993704116682448 | 0.0125917666351037 | 0.00629588331755186 |
115 | 0.989865730163067 | 0.0202685396738664 | 0.0101342698369332 |
116 | 0.984153908840411 | 0.0316921823191778 | 0.0158460911595889 |
117 | 0.975809224819912 | 0.0483815503601754 | 0.0241907751800877 |
118 | 0.968319271331911 | 0.0633614573361775 | 0.0316807286680888 |
119 | 0.95441992557176 | 0.0911601488564794 | 0.0455800744282397 |
120 | 0.948037259672966 | 0.103925480654068 | 0.0519627403270338 |
121 | 0.927394601066034 | 0.145210797867933 | 0.0726053989339664 |
122 | 0.91702796630601 | 0.16594406738798 | 0.0829720336939902 |
123 | 0.900250464723176 | 0.199499070553647 | 0.0997495352768236 |
124 | 0.928180696616327 | 0.143638606767346 | 0.0718193033836729 |
125 | 0.992853086947761 | 0.0142938261044779 | 0.00714691305223894 |
126 | 0.986427261226083 | 0.0271454775478347 | 0.0135727387739174 |
127 | 0.997518562109821 | 0.00496287578035712 | 0.00248143789017856 |
128 | 0.995046529091677 | 0.00990694181664582 | 0.00495347090832291 |
129 | 0.99745863432956 | 0.0050827313408804 | 0.0025413656704402 |
130 | 0.997636747601204 | 0.00472650479759179 | 0.0023632523987959 |
131 | 0.994050359768598 | 0.011899280462803 | 0.00594964023140151 |
132 | 0.990999520890333 | 0.0180009582193347 | 0.00900047910966735 |
133 | 0.977121531624186 | 0.0457569367516271 | 0.0228784683758135 |
134 | 0.947534750264567 | 0.104930499470865 | 0.0524652497354325 |
135 | 0.966102000976562 | 0.0677959980468758 | 0.0338979990234379 |
136 | 0.9659513045165 | 0.0680973909669998 | 0.0340486954834999 |
Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
Description | # significant tests | % significant tests | OK/NOK |
1% type I error level | 94 | 0.728682170542636 | NOK |
5% type I error level | 107 | 0.829457364341085 | NOK |
10% type I error level | 112 | 0.868217054263566 | NOK |