Multiple Linear Regression - Estimated Regression Equation |
Y[t] = + 0.530179124767959 + 0.08203483012131X1t[t] + 0.382220352569239X2t[t] + 0.125417786702747X3t[t] -0.120826659285732X4t[t] -0.0412507968502131X5t[t] + 0.165388840699340X6t[t] + 0.139655817303533X7t[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) | 0.530179124767959 | 0.542822 | 0.9767 | 0.330307 | 0.165154 |
X1t | 0.08203483012131 | 0.072922 | 1.125 | 0.262422 | 0.131211 |
X2t | 0.382220352569239 | 0.082671 | 4.6234 | 8e-06 | 4e-06 |
X3t | 0.125417786702747 | 0.074841 | 1.6758 | 0.095892 | 0.047946 |
X4t | -0.120826659285732 | 0.082196 | -1.47 | 0.143687 | 0.071844 |
X5t | -0.0412507968502131 | 0.087366 | -0.4722 | 0.637508 | 0.318754 |
X6t | 0.165388840699340 | 0.080641 | 2.0509 | 0.042039 | 0.021019 |
X7t | 0.139655817303533 | 0.07695 | 1.8149 | 0.071565 | 0.035783 |
Multiple Linear Regression - Regression Statistics | |
Multiple R | 0.455185301715151 |
R-squared | 0.207193658897513 |
Adjusted R-squared | 0.169696061683206 |
F-TEST (value) | 5.52551828090096 |
F-TEST (DF numerator) | 7 |
F-TEST (DF denominator) | 148 |
p-value | 1.15362556940557e-05 |
Multiple Linear Regression - Residual Statistics | |
Residual Standard Deviation | 0.781193377548189 |
Sum Squared Residuals | 90.3189377825218 |
Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
1 | 2 | 2.00704188999157 | -0.00704188999156803 |
2 | 3 | 2.93687143582941 | 0.0631285641705947 |
3 | 3 | 2.43122550066409 | 0.568774499335907 |
4 | 3 | 2.60268185184588 | 0.397318148154119 |
5 | 3 | 2.08208542482673 | 0.91791457517327 |
6 | 3 | 2.00218275443664 | 0.997817245563357 |
7 | 2 | 3.75154643721094 | -1.75154643721094 |
8 | 3 | 2.41168388139324 | 0.588316118606763 |
9 | 3 | 2.10304674257575 | 0.896953257424245 |
10 | 4 | 1.99545946728840 | 2.00454053271160 |
11 | 3 | 2.64879178425104 | 0.351208215748962 |
12 | 3 | 2.89476822210159 | 0.105231777898412 |
13 | 2 | 2.30921961654619 | -0.309219616546191 |
14 | 3 | 2.30804039171402 | 0.69195960828598 |
15 | 3 | 3.45128954683689 | -0.451289546836892 |
16 | 2 | 3.02497377643316 | -1.02497377643316 |
17 | 3 | 2.72809963854863 | 0.271900361451372 |
18 | 3 | 2.93400450438114 | 0.0659954956188643 |
19 | 2 | 3.03921180703395 | -1.03921180703395 |
20 | 2 | 2.42592191199402 | -0.425921911994024 |
21 | 1 | 2.64120567287237 | -1.64120567287237 |
22 | 4 | 3.07366032168467 | 0.926339678315331 |
23 | 3 | 3.06953595784677 | -0.06953595784677 |
24 | 2 | 2.7644912998439 | -0.764491299843897 |
25 | 3 | 2.8498375145286 | 0.150162485471398 |
26 | 3 | 3.2133161389882 | -0.213316138988202 |
27 | 4 | 3.34104666365194 | 0.658953336348061 |
28 | 3 | 2.77148259513007 | 0.228517404869935 |
29 | 3 | 2.71386160794784 | 0.286138392052158 |
30 | 2 | 2.96589246816755 | -0.965892468167552 |
31 | 2 | 2.27568231858971 | -0.275682318589713 |
32 | 4 | 3.13605301451367 | 0.863946985486327 |
33 | 4 | 3.35987582166974 | 0.64012417833026 |
34 | 2 | 3.14911182028229 | -1.14911182028229 |
35 | 2 | 2.91105098252544 | -0.911050982525436 |
36 | 3 | 3.23904916238401 | -0.239049162384009 |
37 | 3 | 3.06906919426765 | -0.0690691942676537 |
38 | 3 | 2.51733563716118 | 0.482664362838824 |
39 | 3 | 2.97066417381433 | 0.0293358261856662 |
40 | 4 | 3.23904916238401 | 0.760950837615991 |
41 | 3 | 2.66893090037486 | 0.331069099625144 |
42 | 2 | 2.41158336337179 | -0.411583363371789 |
43 | 1 | 2.20527053377680 | -1.20527053377680 |
44 | 2 | 2.72596747881740 | -0.725967478817404 |
45 | 3 | 2.65898365857138 | 0.341016341428616 |
46 | 3 | 3.11113297039237 | -0.111132970392371 |
47 | 2 | 3.13686599378818 | -1.13686599378818 |
48 | 2 | 2.57234163905101 | -0.572341639051014 |
49 | 3 | 2.52391896868487 | 0.476081031315134 |
50 | 3 | 3.07152816195345 | -0.071528161953445 |
51 | 3 | 2.86893468068433 | 0.131065319315668 |
52 | 2 | 2.63934152127908 | -0.639341521279079 |
53 | 2 | 3.17683704778477 | -1.17683704778477 |
54 | 2 | 2.54506086466366 | -0.545060864663658 |
55 | 3 | 2.83668047134025 | 0.163319528659751 |
56 | 3 | 2.83586749206574 | 0.164132507934255 |
57 | 2 | 2.80895524383777 | -0.808955243837767 |
58 | 3 | 2.95973752777694 | 0.0402624722230577 |
59 | 1 | 3.01114998369511 | -2.01114998369511 |
60 | 3 | 3.18142817520179 | -0.181428175201785 |
61 | 1 | 2.43516085141532 | -1.43516085141532 |
62 | 3 | 3.33660176595972 | -0.336601765959725 |
63 | 2 | 2.82778440185557 | -0.827784401855569 |
64 | 2 | 2.97525530123135 | -0.97525530123135 |
65 | 3 | 2.47726406514313 | 0.522735934856866 |
66 | 2 | 2.89430145852247 | -0.894301458522472 |
67 | 3 | 2.85138526552015 | 0.148614734479849 |
68 | 2 | 2.68599642482081 | -0.685996424820811 |
69 | 3 | 2.65955200532901 | 0.340447994670987 |
70 | 1 | 2.41787944438907 | -1.41787944438907 |
71 | 2 | 2.69143996911543 | -0.69143996911543 |
72 | 2 | 2.81344585323333 | -0.813445853233333 |
73 | 2 | 3.08458696772206 | -1.08458696772206 |
74 | 2 | 2.70246485257256 | -0.70246485257256 |
75 | 3 | 2.94979028597347 | 0.0502097140265289 |
76 | 2 | 2.81013446866994 | -0.810134468669938 |
77 | 2 | 2.89216929879125 | -0.892169298791248 |
78 | 2 | 2.34561127784146 | -0.345611277841461 |
79 | 2 | 2.91635457119551 | -0.916354571195506 |
80 | 1 | 2.24406236294123 | -1.24406236294123 |
81 | 2 | 2.85138526552015 | -0.85138526552015 |
82 | 3 | 2.98858211513789 | 0.0114178848621071 |
83 | 4 | 3.11277895880366 | 0.887221041196342 |
84 | 3 | 2.07059043203171 | 0.929409567968291 |
85 | 3 | 3.34624866914350 | -0.346248669143496 |
86 | 3 | 2.46430577739597 | 0.535694222604032 |
87 | 3 | 1.83338201115246 | 1.16661798884754 |
88 | 4 | 3.49494051155626 | 0.505059488443742 |
89 | 4 | 3.08704593540785 | 0.912954064592148 |
90 | 3 | 2.72809963854863 | 0.271900361451372 |
91 | 4 | 3.21118397925698 | 0.788816020743022 |
92 | 4 | 3.45496945755967 | 0.545030542440335 |
93 | 4 | 3.57825508453119 | 0.421744915468811 |
94 | 3 | 3.11645886952643 | -0.116458869526431 |
95 | 3 | 2.74361741200303 | 0.256382587996965 |
96 | 2 | 2.76321155699028 | -0.763211556990277 |
97 | 3 | 3.05777295691382 | -0.0577729569138207 |
98 | 3 | 2.6157406576145 | 0.384259342385504 |
99 | 4 | 3.16794097830009 | 0.83205902169991 |
100 | 3 | 3.32955167085692 | -0.329551670856919 |
101 | 4 | 3.53700428768098 | 0.462995712319024 |
102 | 3 | 3.47166645584624 | -0.471666455846243 |
103 | 3 | 3.71337857423435 | -0.713378574234345 |
104 | 3 | 2.55259378532763 | 0.447406214672374 |
105 | 3 | 2.69781492533891 | 0.302185074661094 |
106 | 4 | 2.69996644728367 | 1.30003355271633 |
107 | 3 | 3.37411385227053 | -0.374113852270527 |
108 | 4 | 3.04707488141126 | 0.952925118588741 |
109 | 3 | 2.79755848846248 | 0.202441511537515 |
110 | 3 | 3.23492479854611 | -0.234924798546110 |
111 | 2 | 2.68930780938421 | -0.689307809384206 |
112 | 3 | 3.27570883181721 | -0.275708831817207 |
113 | 3 | 2.97552330936928 | 0.0244766906307223 |
114 | 4 | 3.25115503325357 | 0.748844966746429 |
115 | 4 | 3.47729057837063 | 0.522709421629372 |
116 | 4 | 2.85010552266653 | 1.14989447733347 |
117 | 4 | 2.98976133997006 | 1.01023866002994 |
118 | 2 | 2.72468773596378 | -0.724687735963784 |
119 | 3 | 3.01218297880248 | -0.0121829788024757 |
120 | 3 | 3.05556593538391 | -0.0555659353839127 |
121 | 3 | 3.09634996865501 | -0.0963499686550095 |
122 | 4 | 3.18098372208666 | 0.81901627791334 |
123 | 3 | 2.81391261681245 | 0.186087383187551 |
124 | 4 | 3.3719816925393 | 0.628018307460697 |
125 | 4 | 3.09634996865501 | 0.90365003134499 |
126 | 3 | 2.44546353126488 | 0.55453646873512 |
127 | 4 | 3.35774366193852 | 0.642256338061484 |
128 | 3 | 2.98858211513789 | 0.0114178848621071 |
129 | 3 | 2.61049921451984 | 0.38950078548016 |
130 | 1 | 1.81713868833171 | -0.817138688331712 |
131 | 4 | 3.23232587523577 | 0.76767412476423 |
132 | 4 | 3.19522175268745 | 0.804778247312554 |
133 | 2 | 2.56169906313360 | -0.561699063133597 |
134 | 2 | 2.73295877410357 | -0.732958774103572 |
135 | 4 | 3.43778628795315 | 0.562213712046848 |
136 | 3 | 2.97552330936928 | 0.0244766906307223 |
137 | 4 | 3.68648970162742 | 0.313510298372578 |
138 | 2 | 2.31805354045546 | -0.318053540455458 |
139 | 5 | 3.10818783138664 | 1.89181216861336 |
140 | 3 | 3.5632040746559 | -0.563204074655898 |
141 | 4 | 2.76807069254522 | 1.23192930745478 |
142 | 3 | 3.15183879610601 | -0.151838796106009 |
143 | 4 | 3.12336273490444 | 0.876637265095563 |
144 | 2 | 2.59131075269336 | -0.591310752693364 |
145 | 3 | 2.89348847924797 | 0.106511520752032 |
146 | 1 | 3.13973292523645 | -2.13973292523645 |
147 | 2 | 2.80804174654181 | -0.808041746541814 |
148 | 5 | 3.31436070535708 | 1.68563929464292 |
149 | 4 | 3.20990423640336 | 0.790095763596642 |
150 | 4 | 2.85469665008355 | 1.14530334991645 |
151 | 3 | 2.78689985056302 | 0.213100149436978 |
152 | 4 | 3.35443227737512 | 0.645567722624878 |
153 | 2 | 2.48553510328292 | -0.485535103282922 |
154 | 4 | 2.97552330936928 | 1.02447669063072 |
155 | 4 | 3.51650973351107 | 0.483490266488933 |
156 | 3 | 2.67121342308345 | 0.32878657691655 |
Goldfeld-Quandt test for Heteroskedasticity | |||
p-values | Alternative Hypothesis | ||
breakpoint index | greater | 2-sided | less |
11 | 0.219061366264004 | 0.438122732528007 | 0.780938633735996 |
12 | 0.113594601725804 | 0.227189203451608 | 0.886405398274196 |
13 | 0.0566016437835751 | 0.113203287567150 | 0.943398356216425 |
14 | 0.119064967999433 | 0.238129935998866 | 0.880935032000567 |
15 | 0.085622263545484 | 0.171244527090968 | 0.914377736454516 |
16 | 0.233827267302907 | 0.467654534605813 | 0.766172732697094 |
17 | 0.160401121287444 | 0.320802242574889 | 0.839598878712556 |
18 | 0.103812198999344 | 0.207624397998687 | 0.896187801000656 |
19 | 0.0845104391564942 | 0.169020878312988 | 0.915489560843506 |
20 | 0.0937323724112021 | 0.187464744822404 | 0.906267627588798 |
21 | 0.352331579731186 | 0.704663159462371 | 0.647668420268814 |
22 | 0.551708856173536 | 0.896582287652927 | 0.448291143826464 |
23 | 0.5367320243319 | 0.926535951336201 | 0.463267975668100 |
24 | 0.54587822376117 | 0.908243552477661 | 0.454121776238830 |
25 | 0.470823027238813 | 0.941646054477627 | 0.529176972761187 |
26 | 0.427772292710612 | 0.855544585421223 | 0.572227707289388 |
27 | 0.407448449517653 | 0.814896899035305 | 0.592551550482347 |
28 | 0.369369568769656 | 0.738739137539312 | 0.630630431230344 |
29 | 0.317493893541252 | 0.634987787082503 | 0.682506106458748 |
30 | 0.275073647518494 | 0.550147295036988 | 0.724926352481506 |
31 | 0.222267217741837 | 0.444534435483675 | 0.777732782258163 |
32 | 0.233009020603464 | 0.466018041206927 | 0.766990979396536 |
33 | 0.244253254465605 | 0.48850650893121 | 0.755746745534395 |
34 | 0.267832729778613 | 0.535665459557226 | 0.732167270221387 |
35 | 0.339259192303685 | 0.67851838460737 | 0.660740807696315 |
36 | 0.287080585730714 | 0.574161171461429 | 0.712919414269286 |
37 | 0.238851185009731 | 0.477702370019461 | 0.76114881499027 |
38 | 0.215484489935692 | 0.430968979871384 | 0.784515510064308 |
39 | 0.175675008372211 | 0.351350016744422 | 0.82432499162779 |
40 | 0.212651204342366 | 0.425302408684732 | 0.787348795657634 |
41 | 0.184856064464405 | 0.36971212892881 | 0.815143935535595 |
42 | 0.212815264981890 | 0.425630529963781 | 0.78718473501811 |
43 | 0.405999414357531 | 0.811998828715062 | 0.594000585642469 |
44 | 0.386256696482876 | 0.772513392965752 | 0.613743303517124 |
45 | 0.341238535960547 | 0.682477071921093 | 0.658761464039453 |
46 | 0.311825140227965 | 0.62365028045593 | 0.688174859772035 |
47 | 0.415824219781884 | 0.831648439563768 | 0.584175780218116 |
48 | 0.396060702459234 | 0.792121404918469 | 0.603939297540766 |
49 | 0.368242104329974 | 0.736484208659947 | 0.631757895670026 |
50 | 0.328114524661846 | 0.656229049323693 | 0.671885475338154 |
51 | 0.294903926602249 | 0.589807853204499 | 0.705096073397751 |
52 | 0.270638791205819 | 0.541277582411638 | 0.729361208794181 |
53 | 0.324744643790586 | 0.649489287581173 | 0.675255356209414 |
54 | 0.303650215385106 | 0.607300430770212 | 0.696349784614894 |
55 | 0.262096897462054 | 0.524193794924108 | 0.737903102537946 |
56 | 0.226898041491313 | 0.453796082982627 | 0.773101958508687 |
57 | 0.231136329975702 | 0.462272659951404 | 0.768863670024298 |
58 | 0.194415959529781 | 0.388831919059562 | 0.805584040470219 |
59 | 0.290714546131109 | 0.581429092262219 | 0.70928545386889 |
60 | 0.250787806905219 | 0.501575613810437 | 0.749212193094781 |
61 | 0.330295542369995 | 0.66059108473999 | 0.669704457630005 |
62 | 0.304059377718023 | 0.608118755436047 | 0.695940622281977 |
63 | 0.293913179150870 | 0.587826358301739 | 0.70608682084913 |
64 | 0.309487252385291 | 0.618974504770583 | 0.690512747614709 |
65 | 0.283779173144273 | 0.567558346288546 | 0.716220826855727 |
66 | 0.302796160424538 | 0.605592320849076 | 0.697203839575462 |
67 | 0.289560855256110 | 0.579121710512219 | 0.71043914474389 |
68 | 0.269167826132222 | 0.538335652264444 | 0.730832173867778 |
69 | 0.234258457851073 | 0.468516915702146 | 0.765741542148927 |
70 | 0.310734785200184 | 0.621469570400367 | 0.689265214799816 |
71 | 0.315794556963739 | 0.631589113927477 | 0.684205443036261 |
72 | 0.328361004480882 | 0.656722008961764 | 0.671638995519118 |
73 | 0.370367332856197 | 0.740734665712394 | 0.629632667143803 |
74 | 0.363855042326008 | 0.727710084652017 | 0.636144957673991 |
75 | 0.336270409055539 | 0.672540818111079 | 0.66372959094446 |
76 | 0.344902677005711 | 0.689805354011423 | 0.655097322994289 |
77 | 0.37801923130177 | 0.75603846260354 | 0.62198076869823 |
78 | 0.356113064730377 | 0.712226129460754 | 0.643886935269623 |
79 | 0.453871400312344 | 0.907742800624689 | 0.546128599687656 |
80 | 0.61328730489843 | 0.77342539020314 | 0.38671269510157 |
81 | 0.659739745241175 | 0.68052050951765 | 0.340260254758825 |
82 | 0.618371082495634 | 0.763257835008732 | 0.381628917504366 |
83 | 0.71429815487167 | 0.571403690256658 | 0.285701845128329 |
84 | 0.733430008712301 | 0.533139982575398 | 0.266569991287699 |
85 | 0.722810125360003 | 0.554379749279995 | 0.277189874639998 |
86 | 0.703054199613637 | 0.593891600772727 | 0.296945800386363 |
87 | 0.715029877826584 | 0.569940244346832 | 0.284970122173416 |
88 | 0.708596583112666 | 0.582806833774668 | 0.291403416887334 |
89 | 0.765806629737936 | 0.468386740524128 | 0.234193370262064 |
90 | 0.730911691265942 | 0.538176617468116 | 0.269088308734058 |
91 | 0.744496413096532 | 0.511007173806935 | 0.255503586903468 |
92 | 0.737179914049654 | 0.525640171900692 | 0.262820085950346 |
93 | 0.726822472591432 | 0.546355054817136 | 0.273177527408568 |
94 | 0.690392388714387 | 0.619215222571226 | 0.309607611285613 |
95 | 0.653146767680221 | 0.693706464639559 | 0.346853232319779 |
96 | 0.721356267148736 | 0.557287465702528 | 0.278643732851264 |
97 | 0.690137614971164 | 0.619724770057672 | 0.309862385028836 |
98 | 0.657452674619465 | 0.68509465076107 | 0.342547325380535 |
99 | 0.684654940049855 | 0.63069011990029 | 0.315345059950145 |
100 | 0.646700244019385 | 0.70659951196123 | 0.353299755980615 |
101 | 0.626550436464428 | 0.746899127071143 | 0.373449563535572 |
102 | 0.590583410021479 | 0.818833179957042 | 0.409416589978521 |
103 | 0.770481622943952 | 0.459036754112097 | 0.229518377056048 |
104 | 0.755679110373303 | 0.488641779253393 | 0.244320889626696 |
105 | 0.781802002669819 | 0.436395994660362 | 0.218197997330181 |
106 | 0.792814420902784 | 0.414371158194432 | 0.207185579097216 |
107 | 0.759391568470667 | 0.481216863058667 | 0.240608431529333 |
108 | 0.744747668129819 | 0.510504663740362 | 0.255252331870181 |
109 | 0.70972270101648 | 0.580554597967041 | 0.290277298983520 |
110 | 0.671147580601953 | 0.657704838796094 | 0.328852419398047 |
111 | 0.811461712274039 | 0.377076575451922 | 0.188538287725961 |
112 | 0.800051260475284 | 0.399897479049432 | 0.199948739524716 |
113 | 0.773851572332001 | 0.452296855335998 | 0.226148427667999 |
114 | 0.762394869877905 | 0.47521026024419 | 0.237605130122095 |
115 | 0.76497352440381 | 0.470052951192381 | 0.235026475596190 |
116 | 0.784134835274588 | 0.431730329450824 | 0.215865164725412 |
117 | 0.794238979117772 | 0.411522041764457 | 0.205761020882228 |
118 | 0.889091998228402 | 0.221816003543197 | 0.110908001771598 |
119 | 0.874030415042673 | 0.251939169914654 | 0.125969584957327 |
120 | 0.839585731921186 | 0.320828536157629 | 0.160414268078814 |
121 | 0.799892130792768 | 0.400215738414464 | 0.200107869207232 |
122 | 0.878153352288745 | 0.24369329542251 | 0.121846647711255 |
123 | 0.872008832359527 | 0.255982335280946 | 0.127991167640473 |
124 | 0.842824699359343 | 0.314350601281315 | 0.157175300640657 |
125 | 0.90149025329758 | 0.19701949340484 | 0.09850974670242 |
126 | 0.875263726072645 | 0.249472547854710 | 0.124736273927355 |
127 | 0.843888324675184 | 0.312223350649632 | 0.156111675324816 |
128 | 0.819053852760545 | 0.36189229447891 | 0.180946147239455 |
129 | 0.771706618154377 | 0.456586763691247 | 0.228293381845623 |
130 | 0.744148151195922 | 0.511703697608157 | 0.255851848804078 |
131 | 0.698913733191317 | 0.602172533617366 | 0.301086266808683 |
132 | 0.937353676217425 | 0.125292647565149 | 0.0626463237825747 |
133 | 0.921878131053439 | 0.156243737893123 | 0.0781218689465615 |
134 | 0.888705137457152 | 0.222589725085696 | 0.111294862542848 |
135 | 0.899308135140525 | 0.201383729718950 | 0.100691864859475 |
136 | 0.875605681509956 | 0.248788636980087 | 0.124394318490044 |
137 | 0.826277523359027 | 0.347444953281947 | 0.173722476640973 |
138 | 0.783066374073857 | 0.433867251852285 | 0.216933625926142 |
139 | 0.761065976846048 | 0.477868046307903 | 0.238934023153952 |
140 | 0.68376168132573 | 0.632476637348541 | 0.316238318674271 |
141 | 0.769028448020252 | 0.461943103959496 | 0.230971551979748 |
142 | 0.719872519883976 | 0.560254960232047 | 0.280127480116024 |
143 | 0.618836037620859 | 0.762327924758282 | 0.381163962379141 |
144 | 0.783760743265517 | 0.432478513468966 | 0.216239256734483 |
145 | 0.77481947716183 | 0.45036104567634 | 0.22518052283817 |
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 | 0 | 0 | OK |
10% type I error level | 0 | 0 | OK |