Multiple Linear Regression - Estimated Regression Equation |
X_2t[t] = + 31.3471573638543 + 0.444702753166022X_1t[t] -0.362675102423084X_3t[t] -0.262539402740327X_4t[t] -0.207318027182089X_5t[t] -0.274389035067997X_6t[t] -0.327297113875413X_7t[t] -0.209605852221708X_8t[t] + 0.0459801204750859X_9t[t] + 0.887743425105732X_10t[t] -0.000478451727605654X_11t[t] -0.241762602800191X_12t[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) | 31.3471573638543 | 9.23636 | 3.3939 | 0.001138 | 0.000569 |
X_1t | 0.444702753166022 | 0.053459 | 8.3185 | 0 | 0 |
X_3t | -0.362675102423084 | 0.058971 | -6.1501 | 0 | 0 |
X_4t | -0.262539402740327 | 0.059547 | -4.4089 | 3.7e-05 | 1.8e-05 |
X_5t | -0.207318027182089 | 0.056577 | -3.6644 | 0.000478 | 0.000239 |
X_6t | -0.274389035067997 | 0.079743 | -3.4409 | 0.000982 | 0.000491 |
X_7t | -0.327297113875413 | 0.136247 | -2.4022 | 0.018952 | 0.009476 |
X_8t | -0.209605852221708 | 0.269963 | -0.7764 | 0.440115 | 0.220057 |
X_9t | 0.0459801204750859 | 0.297767 | 0.1544 | 0.877726 | 0.438863 |
X_10t | 0.887743425105732 | 0.312265 | 2.8429 | 0.005854 | 0.002927 |
X_11t | -0.000478451727605654 | 0.066048 | -0.0072 | 0.994241 | 0.49712 |
X_12t | -0.241762602800191 | 0.158891 | -1.5216 | 0.132624 | 0.066312 |
Multiple Linear Regression - Regression Statistics | |
Multiple R | 0.957117519497325 |
R-squared | 0.916073946128713 |
Adjusted R-squared | 0.902885566234654 |
F-TEST (value) | 69.460688385338 |
F-TEST (DF numerator) | 11 |
F-TEST (DF denominator) | 70 |
p-value | 0 |
Multiple Linear Regression - Residual Statistics | |
Residual Standard Deviation | 3.0240654350445 |
Sum Squared Residuals | 640.148022880163 |
Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
1 | -3 | -4.94808082486269 | 1.94808082486269 |
2 | -4 | -2.14131446342658 | -1.85868553657342 |
3 | -7 | -6.51154590698915 | -0.488454093010852 |
4 | -7 | -4.20445493251037 | -2.79554506748963 |
5 | -7 | -4.77415776825536 | -2.22584223174464 |
6 | -3 | -2.18641994553898 | -0.813580054461025 |
7 | 0 | -1.78500251453288 | 1.78500251453288 |
8 | -5 | -1.86842044012433 | -3.13157955987567 |
9 | -3 | -3.07434783929724 | 0.0743478392972435 |
10 | 3 | 0.564505095473401 | 2.4354949045266 |
11 | 2 | -0.632129383592598 | 2.6321293835926 |
12 | -7 | -11.1663388195651 | 4.16633881956507 |
13 | -1 | 1.69080317608383 | -2.69080317608383 |
14 | 0 | 1.94923548223378 | -1.94923548223378 |
15 | -3 | -0.948930336808768 | -2.05106966319123 |
16 | 4 | 7.10114994268736 | -3.10114994268736 |
17 | 2 | 2.58329321015519 | -0.583293210155192 |
18 | 3 | 1.21672499531602 | 1.78327500468398 |
19 | 0 | -3.04277854650954 | 3.04277854650954 |
20 | -10 | -7.42122418583962 | -2.57877581416038 |
21 | -10 | -8.49030488148799 | -1.50969511851201 |
22 | -9 | -7.54308200443584 | -1.45691799556416 |
23 | -22 | -18.1955557988583 | -3.80444420114172 |
24 | -16 | -16.823827801967 | 0.823827801967045 |
25 | -18 | -21.377552846466 | 3.37755284646597 |
26 | -14 | -14.2583025565495 | 0.258302556549502 |
27 | -12 | -16.1476454519459 | 4.14764545194594 |
28 | -17 | -18.5571169442532 | 1.55711694425317 |
29 | -23 | -20.6407854145687 | -2.35921458543134 |
30 | -28 | -24.2630396191683 | -3.73696038083171 |
31 | -31 | -28.0235085879537 | -2.97649141204635 |
32 | -21 | -21.1020592383068 | 0.102059238306841 |
33 | -19 | -17.4096709779125 | -1.59032902208746 |
34 | -22 | -25.0019751407929 | 3.0019751407929 |
35 | -22 | -23.8570898503263 | 1.85708985032628 |
36 | -25 | -22.0598870066226 | -2.94011299337739 |
37 | -16 | -18.4456709644692 | 2.44567096446921 |
38 | -22 | -17.8341257308486 | -4.16587426915142 |
39 | -21 | -16.7685618316674 | -4.23143816833263 |
40 | -10 | -11.0306703421397 | 1.0306703421397 |
41 | -7 | -6.4366553049305 | -0.563344695069504 |
42 | -5 | -8.40780507108695 | 3.40780507108696 |
43 | -4 | -5.61479460237621 | 1.61479460237621 |
44 | 7 | 2.14591340850389 | 4.85408659149611 |
45 | 6 | 1.42993911934804 | 4.57006088065196 |
46 | 3 | 2.62980878894998 | 0.370191211050021 |
47 | 10 | 7.87258694746923 | 2.12741305253077 |
48 | 0 | 5.80434527654845 | -5.80434527654845 |
49 | -2 | -0.288555804068115 | -1.71144419593188 |
50 | -1 | 1.20563724070957 | -2.20563724070957 |
51 | 2 | 0.900108328206155 | 1.09989167179384 |
52 | 8 | 6.0843590203522 | 1.9156409796478 |
53 | -6 | -4.3397445194819 | -1.6602554805181 |
54 | -4 | -1.01767324966563 | -2.98232675033437 |
55 | 4 | 4.81947387797566 | -0.819473877975659 |
56 | 7 | 3.39324563089569 | 3.60675436910431 |
57 | 3 | 2.09695799721404 | 0.903042002785955 |
58 | 3 | -0.0809167571807361 | 3.08091675718074 |
59 | 8 | 3.01423765824375 | 4.98576234175625 |
60 | 3 | 0.551300428954482 | 2.44869957104552 |
61 | -3 | -2.56320995451276 | -0.436790045487237 |
62 | 4 | 3.3630497294552 | 0.6369502705448 |
63 | -5 | -8.21313854701562 | 3.21313854701562 |
64 | -1 | 1.21843408563981 | -2.21843408563981 |
65 | 5 | 5.34078981836698 | -0.340789818366985 |
66 | 0 | -2.70501667147466 | 2.70501667147466 |
67 | -6 | -3.85489205975439 | -2.14510794024561 |
68 | -13 | -9.50176898800993 | -3.49823101199007 |
69 | -15 | -9.3952163369065 | -5.6047836630935 |
70 | -8 | -7.28536732264578 | -0.714632677354223 |
71 | -20 | -20.4896206863158 | 0.489620686315809 |
72 | -10 | -19.3364214441201 | 9.33642144412008 |
73 | -22 | -23.2399015742188 | 1.23990157421877 |
74 | -25 | -24.4844514739612 | -0.515548526038803 |
75 | -10 | -11.8386881013632 | 1.83868810136319 |
76 | -8 | -11.8417462537851 | 3.84174625378515 |
77 | -9 | -6.64717552975094 | -2.35282447024906 |
78 | -5 | -2.76587485556428 | -2.23412514443572 |
79 | -7 | -3.20421652514465 | -3.79578347485535 |
80 | -11 | -9.4522647182309 | -1.5477352817691 |
81 | -11 | -9.42543491839396 | -1.57456508160604 |
82 | -16 | -17.0097690902306 | 1.0097690902306 |
Goldfeld-Quandt test for Heteroskedasticity | |||
p-values | Alternative Hypothesis | ||
breakpoint index | greater | 2-sided | less |
15 | 0.0741143161522709 | 0.148228632304542 | 0.925885683847729 |
16 | 0.0253620827609327 | 0.0507241655218654 | 0.974637917239067 |
17 | 0.00877390077065663 | 0.0175478015413133 | 0.991226099229343 |
18 | 0.0254040871517831 | 0.0508081743035662 | 0.974595912848217 |
19 | 0.0553521026135038 | 0.110704205227008 | 0.944647897386496 |
20 | 0.1000504580198 | 0.200100916039599 | 0.8999495419802 |
21 | 0.0586157084572817 | 0.117231416914563 | 0.941384291542718 |
22 | 0.0336030093583597 | 0.0672060187167194 | 0.96639699064164 |
23 | 0.0211145434170726 | 0.0422290868341452 | 0.978885456582927 |
24 | 0.0164307125408822 | 0.0328614250817644 | 0.983569287459118 |
25 | 0.0280633313748781 | 0.0561266627497562 | 0.971936668625122 |
26 | 0.0155890959247563 | 0.0311781918495127 | 0.984410904075244 |
27 | 0.0133487425923854 | 0.0266974851847709 | 0.986651257407615 |
28 | 0.00929601318827876 | 0.0185920263765575 | 0.990703986811721 |
29 | 0.0161399666002963 | 0.0322799332005925 | 0.983860033399704 |
30 | 0.0100745091734642 | 0.0201490183469283 | 0.989925490826536 |
31 | 0.00781561502283006 | 0.0156312300456601 | 0.99218438497717 |
32 | 0.00470037848446664 | 0.00940075696893327 | 0.995299621515533 |
33 | 0.0116631883000758 | 0.0233263766001515 | 0.988336811699924 |
34 | 0.0117053180674745 | 0.023410636134949 | 0.988294681932525 |
35 | 0.009240704058513 | 0.018481408117026 | 0.990759295941487 |
36 | 0.00774941278745622 | 0.0154988255749124 | 0.992250587212544 |
37 | 0.00724668500111486 | 0.0144933700022297 | 0.992753314998885 |
38 | 0.00541078194070677 | 0.0108215638814135 | 0.994589218059293 |
39 | 0.00570400820515442 | 0.0114080164103088 | 0.994295991794846 |
40 | 0.0325294026801224 | 0.0650588053602447 | 0.967470597319878 |
41 | 0.0297138626415149 | 0.0594277252830298 | 0.970286137358485 |
42 | 0.0405883907468361 | 0.0811767814936721 | 0.959411609253164 |
43 | 0.0348204535985992 | 0.0696409071971984 | 0.965179546401401 |
44 | 0.0747439114389706 | 0.149487822877941 | 0.925256088561029 |
45 | 0.0930186480294168 | 0.186037296058834 | 0.906981351970583 |
46 | 0.0744304430106978 | 0.148860886021396 | 0.925569556989302 |
47 | 0.0938599557445632 | 0.187719911489126 | 0.906140044255437 |
48 | 0.139953662581018 | 0.279907325162036 | 0.860046337418982 |
49 | 0.107320665921514 | 0.214641331843028 | 0.892679334078486 |
50 | 0.0862695243668577 | 0.172539048733715 | 0.913730475633142 |
51 | 0.100900766394863 | 0.201801532789727 | 0.899099233605137 |
52 | 0.0949751643016268 | 0.189950328603254 | 0.905024835698373 |
53 | 0.0669311509394632 | 0.133862301878926 | 0.933068849060537 |
54 | 0.0542209966355915 | 0.108441993271183 | 0.945779003364408 |
55 | 0.0355366176755716 | 0.0710732353511432 | 0.964463382324428 |
56 | 0.0645225754149818 | 0.129045150829964 | 0.935477424585018 |
57 | 0.0781532294627625 | 0.156306458925525 | 0.921846770537238 |
58 | 0.121677561436078 | 0.243355122872156 | 0.878322438563922 |
59 | 0.314813956661577 | 0.629627913323153 | 0.685186043338423 |
60 | 0.456350402270769 | 0.912700804541538 | 0.543649597729231 |
61 | 0.497488019579318 | 0.994976039158636 | 0.502511980420682 |
62 | 0.394176270478748 | 0.788352540957497 | 0.605823729521252 |
63 | 0.396688838118127 | 0.793377676236255 | 0.603311161881873 |
64 | 0.318758845135975 | 0.63751769027195 | 0.681241154864025 |
65 | 0.219708795491874 | 0.439417590983748 | 0.780291204508126 |
66 | 0.144992213304209 | 0.289984426608417 | 0.855007786695791 |
67 | 0.0868847089595174 | 0.173769417919035 | 0.913115291040483 |
Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
Description | # significant tests | % significant tests | OK/NOK |
1% type I error level | 1 | 0.0188679245283019 | NOK |
5% type I error level | 17 | 0.320754716981132 | NOK |
10% type I error level | 26 | 0.490566037735849 | NOK |