Multiple Linear Regression - Estimated Regression Equation |
YT[t] = + 1.29605226452594 + 0.0689248642585393X1[t] + 0.252916716305925X2[t] + 0.363828375948588X3[t] -0.118420136069921X4[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) | 1.29605226452594 | 0.431979 | 3.0003 | 0.003153 | 0.001577 |
X1 | 0.0689248642585393 | 0.073619 | 0.9362 | 0.350634 | 0.175317 |
X2 | 0.252916716305925 | 0.0826 | 3.0619 | 0.002601 | 0.001301 |
X3 | 0.363828375948588 | 0.072444 | 5.0222 | 1e-06 | 1e-06 |
X4 | -0.118420136069921 | 0.089782 | -1.319 | 0.189163 | 0.094582 |
Multiple Linear Regression - Regression Statistics | |
Multiple R | 0.456901675014126 |
R-squared | 0.208759140630714 |
Adjusted R-squared | 0.187937012752575 |
F-TEST (value) | 10.0258312624181 |
F-TEST (DF numerator) | 4 |
F-TEST (DF denominator) | 152 |
p-value | 3.15112685944641e-07 |
Multiple Linear Regression - Residual Statistics | |
Residual Standard Deviation | 0.866596311038476 |
Sum Squared Residuals | 114.150353278435 |
Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
1 | 4 | 3.79853867015723 | 0.201461329842773 |
2 | 4 | 3.30021371397264 | 0.699786286027362 |
3 | 5 | 3.07423506654113 | 1.92576493345887 |
4 | 3 | 2.93638533802405 | 0.0636146619759458 |
5 | 4 | 2.49947676967074 | 1.50052323032926 |
6 | 3 | 3.32715178284706 | -0.327151782847056 |
7 | 4 | 3.6220552945371 | 0.377944705462896 |
8 | 3 | 3.12373033835251 | -0.123730338352512 |
9 | 2 | 2.38856511002808 | -0.388565110028079 |
10 | 4 | 2.93638533802405 | 1.06361466197595 |
11 | 2 | 3.07423506654113 | -1.07423506654113 |
12 | 2 | 2.75239348597667 | -0.752393485976667 |
13 | 1 | 2.75239348597667 | -1.75239348597667 |
14 | 4 | 3.07423506654113 | 0.925764933458869 |
15 | 4 | 3.08174354296839 | 0.918256457031611 |
16 | 2 | 3.00531020228259 | -1.00531020228259 |
17 | 2 | 2.61789690574066 | -0.617896905740663 |
18 | 3 | 3.36913857823118 | -0.369138578231179 |
19 | 3 | 3.80189181843831 | -0.801891818438307 |
20 | 3 | 3.66404208992123 | -0.664042089921228 |
21 | 4 | 3.63397641055700 | 0.366023589442996 |
22 | 3 | 3.80189181843831 | -0.801891818438307 |
23 | 2 | 3.42720181778139 | -1.42720181778139 |
24 | 2 | 3.25822691858852 | -1.25822691858852 |
25 | 4 | 3.07423506654113 | 0.925764933458869 |
26 | 4 | 3.80189181843831 | 0.198108181561693 |
27 | 3 | 3.00531020228259 | -0.00531020228259128 |
28 | 4 | 3.43806344248972 | 0.561936557510281 |
29 | 2 | 3.07423506654113 | -1.07423506654113 |
30 | 4 | 3.59511722566269 | 0.404882774337312 |
31 | 4 | 3.3196433064198 | 0.680356693580202 |
32 | 5 | 3.364983250085 | 1.63501674991500 |
33 | 5 | 2.93638533802405 | 2.06361466197595 |
34 | 4 | 3.07423506654113 | 0.925764933458869 |
35 | 4 | 3.86746353441577 | 0.132536465584229 |
36 | 4 | 4.0439469100359 | -0.0439469100358984 |
37 | 2 | 3.19265520261105 | -1.19265520261105 |
38 | 4 | 3.61789996639092 | 0.382100033609078 |
39 | 4 | 3.68347168236839 | 0.316528317631614 |
40 | 4 | 4.3002167746229 | -0.300216774622899 |
41 | 3 | 3.43806344248972 | -0.438063442489719 |
42 | 2 | 3.00531020228259 | -1.00531020228259 |
43 | 3 | 3.69098015879564 | -0.690980158795644 |
44 | 4 | 2.93638533802405 | 1.06361466197595 |
45 | 3 | 2.82547367838139 | 0.174526321618612 |
46 | 2 | 3.07423506654113 | -1.07423506654113 |
47 | 4 | 3.42720181778139 | 0.572798182218614 |
48 | 4 | 3.56505154629846 | 0.434948453701535 |
49 | 3 | 3.54897510213238 | -0.548975102132382 |
50 | 4 | 3.47669708959277 | 0.523302910407233 |
51 | 3 | 3.07423506654113 | -0.0742350665411309 |
52 | 4 | 2.93638533802405 | 1.06361466197595 |
53 | 2 | 2.11621880127500 | -0.116218801274996 |
54 | 4 | 3.43055496606246 | 0.569445033937539 |
55 | 4 | 3.02138664644867 | 0.978613353551326 |
56 | 4 | 3.66404208992123 | 0.335957910078772 |
57 | 4 | 3.07423506654113 | 0.925764933458869 |
58 | 3 | 3.37664705465844 | -0.376647054658437 |
59 | 1 | 2.31964024576954 | -1.31964024576954 |
60 | 3 | 3.18930205432998 | -0.189302054329976 |
61 | 3 | 3.00531020228259 | -0.00531020228259128 |
62 | 4 | 3.18930205432998 | 0.810697945670024 |
63 | 2 | 2.86746047376551 | -0.867460473765512 |
64 | 3 | 2.75990196240392 | 0.240098037596076 |
65 | 5 | 4.28078718217574 | 0.719212817824259 |
66 | 4 | 3.25071844216126 | 0.749281557838742 |
67 | 4 | 3.00531020228259 | 0.99468979771741 |
68 | 3 | 3.01281867870985 | -0.0128186787098493 |
69 | 4 | 2.93638533802405 | 1.06361466197595 |
70 | 2 | 3.243209965734 | -1.243209965734 |
71 | 3 | 2.93638533802405 | 0.0636146619759482 |
72 | 4 | 4.3002167746229 | -0.300216774622899 |
73 | 3 | 3.81796826260439 | -0.81796826260439 |
74 | 4 | 3.69098015879564 | 0.309019841204356 |
75 | 4 | 2.69954506588421 | 1.30045493411579 |
76 | 3 | 3.12373033835251 | -0.123730338352512 |
77 | 3 | 3.32715178284706 | -0.327151782847056 |
78 | 2 | 3.25822691858852 | -1.25822691858852 |
79 | 4 | 3.56505154629846 | 0.434948453701535 |
80 | 3 | 3.07088191826006 | -0.0708819182600554 |
81 | 2 | 2.75239348597667 | -0.752393485976667 |
82 | 2 | 3.73296695417977 | -1.73296695417977 |
83 | 3 | 3.80189181843831 | -0.801891818438307 |
84 | 2 | 2.81796520195413 | -0.81796520195413 |
85 | 2 | 3.07423506654113 | -1.07423506654113 |
86 | 4 | 3.30021371397264 | 0.69978628602736 |
87 | 4 | 3.3077221903999 | 0.692277809600103 |
88 | 4 | 3.80189181843831 | 0.198108181561693 |
89 | 2 | 3.00531020228259 | -1.00531020228259 |
90 | 2 | 3.56505154629846 | -1.56505154629846 |
91 | 4 | 2.94389381445131 | 1.05610618554869 |
92 | 2 | 2.68346862171813 | -0.683468621718127 |
93 | 3 | 3.11622186192525 | -0.116221861925255 |
94 | 3 | 3.25822691858852 | -0.258226918588516 |
95 | 5 | 3.88689312686293 | 1.11310687313707 |
96 | 3 | 2.69954506588421 | 0.300454934115790 |
97 | 4 | 3.25071844216126 | 0.749281557838742 |
98 | 3 | 3.07423506654113 | -0.0742350665411309 |
99 | 2 | 2.88689006621267 | -0.88689006621267 |
100 | 4 | 3.07423506654113 | 0.925764933458869 |
101 | 3 | 3.12373033835251 | -0.123730338352512 |
102 | 3 | 3.00531020228259 | -0.00531020228259128 |
103 | 3 | 2.93638533802405 | 0.0636146619759482 |
104 | 4 | 3.6220552945371 | 0.377944705462896 |
105 | 1 | 2.19371163327236 | -1.19371163327236 |
106 | 3 | 3.00531020228259 | -0.00531020228259128 |
107 | 2 | 3.03978852123946 | -1.03978852123946 |
108 | 3 | 3.3196433064198 | -0.319643306419798 |
109 | 2 | 3.18930205432998 | -1.18930205432998 |
110 | 2 | 2.57591011035654 | -0.575910110356539 |
111 | 2 | 2.83739479440129 | -0.837394794401289 |
112 | 4 | 2.61454375745959 | 1.38545624254041 |
113 | 5 | 4.23464505864543 | 0.765354941354565 |
114 | 5 | 2.69097709814538 | 2.30902290185462 |
115 | 3 | 3.00531020228259 | -0.00531020228259128 |
116 | 4 | 2.56840163392928 | 1.43159836607072 |
117 | 4 | 2.10871032484774 | 1.89128967515226 |
118 | 3 | 3.02473979472975 | -0.0247397947297494 |
119 | 2 | 2.87081362204659 | -0.870813622046588 |
120 | 4 | 3.97837519405843 | 0.0216248059415657 |
121 | 2 | 2.75239348597667 | -0.752393485976667 |
122 | 3 | 2.63397334990675 | 0.366026650093254 |
123 | 2 | 3.3077221903999 | -1.30772219039990 |
124 | 2 | 2.93638533802405 | -0.936385338024052 |
125 | 2 | 2.70289821416528 | -0.702898214165285 |
126 | 4 | 3.19265520261105 | 0.807344797388948 |
127 | 4 | 3.36913857823118 | 0.630861421768821 |
128 | 4 | 3.00531020228259 | 0.99468979771741 |
129 | 4 | 3.61454681810985 | 0.385453181890154 |
130 | 3 | 3.54897510213238 | -0.548975102132382 |
131 | 2 | 3.00531020228259 | -1.00531020228259 |
132 | 4 | 3.80189181843831 | 0.198108181561693 |
133 | 3 | 3.80189181843831 | -0.801891818438307 |
134 | 2 | 2.93638533802405 | -0.936385338024052 |
135 | 4 | 3.80189181843831 | 0.198108181561693 |
136 | 3 | 2.92887686159679 | 0.0711231384032061 |
137 | 3 | 3.07423506654113 | -0.0742350665411309 |
138 | 3 | 3.00531020228259 | -0.00531020228259128 |
139 | 3 | 2.74488500954941 | 0.255114990450591 |
140 | 3 | 3.15820865730938 | -0.158208657309378 |
141 | 4 | 3.66404208992123 | 0.335957910078772 |
142 | 5 | 3.84723176210351 | 1.15276823789649 |
143 | 2 | 3.05480547409397 | -1.05480547409397 |
144 | 4 | 3.13229830609134 | 0.867701693908663 |
145 | 3 | 3.72545847775251 | -0.72545847775251 |
146 | 3 | 2.38105663360082 | 0.61894336639918 |
147 | 1 | 2.49947676967074 | -1.49947676967074 |
148 | 2 | 3.07423506654113 | -1.07423506654113 |
149 | 4 | 2.82131835023521 | 1.17868164976479 |
150 | 4 | 2.83739479440129 | 1.16260520559871 |
151 | 5 | 4.04730005831697 | 0.952699941683026 |
152 | 2 | 2.81380987380795 | -0.813809873807948 |
153 | 4 | 3.39607664710560 | 0.603923352894405 |
154 | 3 | 3.00531020228259 | -0.00531020228259128 |
155 | 2 | 3.36913857823118 | -1.36913857823118 |
156 | 4 | 3.3196433064198 | 0.680356693580202 |
157 | 2 | 2.46605794202544 | -0.466057942025443 |
Goldfeld-Quandt test for Heteroskedasticity | |||
p-values | Alternative Hypothesis | ||
breakpoint index | greater | 2-sided | less |
8 | 0.472229617660685 | 0.94445923532137 | 0.527770382339315 |
9 | 0.417243607614547 | 0.834487215229093 | 0.582756392385453 |
10 | 0.581513620444951 | 0.836972759110097 | 0.418486379555049 |
11 | 0.773498499251351 | 0.453003001497298 | 0.226501500748649 |
12 | 0.839907386007692 | 0.320185227984615 | 0.160092613992308 |
13 | 0.958567373770467 | 0.0828652524590654 | 0.0414326262295327 |
14 | 0.95367933502914 | 0.0926413299417217 | 0.0463206649708608 |
15 | 0.944736877159966 | 0.110526245680067 | 0.0552631228400336 |
16 | 0.950054109948924 | 0.0998917801021516 | 0.0499458900510758 |
17 | 0.93764045957818 | 0.124719080843638 | 0.0623595404218189 |
18 | 0.916592744509712 | 0.166814510980577 | 0.0834072554902883 |
19 | 0.8967140702546 | 0.206571859490798 | 0.103285929745399 |
20 | 0.868059672172746 | 0.263880655654509 | 0.131940327827254 |
21 | 0.832705912575118 | 0.334588174849764 | 0.167294087424882 |
22 | 0.795358060813185 | 0.409283878373630 | 0.204641939186815 |
23 | 0.839660680348203 | 0.320678639303594 | 0.160339319651797 |
24 | 0.886869022248661 | 0.226261955502678 | 0.113130977751339 |
25 | 0.880999036365217 | 0.238001927269565 | 0.119000963634783 |
26 | 0.853051723651679 | 0.293896552696643 | 0.146948276348321 |
27 | 0.81269123652185 | 0.374617526956301 | 0.187308763478151 |
28 | 0.784927419159922 | 0.430145161680156 | 0.215072580840078 |
29 | 0.81379556419361 | 0.372408871612780 | 0.186204435806390 |
30 | 0.799003740513366 | 0.401992518973268 | 0.200996259486634 |
31 | 0.786268021932328 | 0.427463956135345 | 0.213731978067672 |
32 | 0.847840709388467 | 0.304318581223065 | 0.152159290611533 |
33 | 0.953237238800319 | 0.0935255223993624 | 0.0467627611996812 |
34 | 0.950223607719392 | 0.0995527845612164 | 0.0497763922806082 |
35 | 0.935028002050801 | 0.129943995898398 | 0.0649719979491991 |
36 | 0.916662742587525 | 0.166674514824951 | 0.0833372574124753 |
37 | 0.934852722701419 | 0.130294554597162 | 0.065147277298581 |
38 | 0.917711409081531 | 0.164577181836938 | 0.0822885909184688 |
39 | 0.896871468016046 | 0.206257063967908 | 0.103128531983954 |
40 | 0.873389069959593 | 0.253221860080814 | 0.126610930040407 |
41 | 0.852176397269945 | 0.295647205460109 | 0.147823602730055 |
42 | 0.859852108439239 | 0.280295783121523 | 0.140147891560762 |
43 | 0.844315718471663 | 0.311368563056674 | 0.155684281528337 |
44 | 0.856577886873351 | 0.286844226253298 | 0.143422113126649 |
45 | 0.82673474469639 | 0.346530510607219 | 0.173265255303610 |
46 | 0.842192167908972 | 0.315615664182055 | 0.157807832091028 |
47 | 0.818831451895815 | 0.36233709620837 | 0.181168548104185 |
48 | 0.788326526763531 | 0.423346946472937 | 0.211673473236469 |
49 | 0.765999427414306 | 0.468001145171387 | 0.234000572585693 |
50 | 0.736666344684264 | 0.526667310631471 | 0.263333655315736 |
51 | 0.694385415700725 | 0.611229168598551 | 0.305614584299276 |
52 | 0.706325001418897 | 0.587349997162206 | 0.293674998581103 |
53 | 0.669164775003665 | 0.661670449992669 | 0.330835224996335 |
54 | 0.636485429109733 | 0.727029141780533 | 0.363514570890266 |
55 | 0.627315138766855 | 0.745369722466289 | 0.372684861233145 |
56 | 0.589655106853709 | 0.820689786292582 | 0.410344893146291 |
57 | 0.590247620938251 | 0.819504758123498 | 0.409752379061749 |
58 | 0.54665065565443 | 0.90669868869114 | 0.45334934434557 |
59 | 0.630615303125799 | 0.738769393748402 | 0.369384696874201 |
60 | 0.585656769231592 | 0.828686461536816 | 0.414343230768408 |
61 | 0.538118583182334 | 0.923762833635332 | 0.461881416817666 |
62 | 0.532827337165651 | 0.934345325668698 | 0.467172662834349 |
63 | 0.532345631541649 | 0.935308736916703 | 0.467654368458351 |
64 | 0.489559581201966 | 0.979119162403932 | 0.510440418798034 |
65 | 0.482348949898236 | 0.964697899796471 | 0.517651050101764 |
66 | 0.464751986816671 | 0.929503973633341 | 0.535248013183329 |
67 | 0.47547825139185 | 0.9509565027837 | 0.52452174860815 |
68 | 0.428658797783253 | 0.857317595566505 | 0.571341202216747 |
69 | 0.449108218469997 | 0.898216436939995 | 0.550891781530003 |
70 | 0.512417235725819 | 0.975165528548361 | 0.487582764274181 |
71 | 0.466086199724719 | 0.932172399449439 | 0.533913800275281 |
72 | 0.425135270148557 | 0.850270540297115 | 0.574864729851443 |
73 | 0.421354985797159 | 0.842709971594318 | 0.578645014202841 |
74 | 0.382035179059019 | 0.764070358118037 | 0.617964820940981 |
75 | 0.431099941899274 | 0.862199883798548 | 0.568900058100726 |
76 | 0.386194662790985 | 0.77238932558197 | 0.613805337209015 |
77 | 0.348338181156095 | 0.69667636231219 | 0.651661818843905 |
78 | 0.392849216610069 | 0.785698433220138 | 0.607150783389931 |
79 | 0.359282093106964 | 0.718564186213927 | 0.640717906893036 |
80 | 0.318627588443937 | 0.637255176887874 | 0.681372411556063 |
81 | 0.311096470401163 | 0.622192940802325 | 0.688903529598837 |
82 | 0.429723702009406 | 0.859447404018812 | 0.570276297990594 |
83 | 0.420712624977346 | 0.841425249954692 | 0.579287375022654 |
84 | 0.417434877220091 | 0.834869754440182 | 0.582565122779909 |
85 | 0.443155021463674 | 0.886310042927347 | 0.556844978536326 |
86 | 0.428706742356588 | 0.857413484713176 | 0.571293257643412 |
87 | 0.414969065036804 | 0.829938130073607 | 0.585030934963196 |
88 | 0.372598995908807 | 0.745197991817614 | 0.627401004091193 |
89 | 0.386107220383383 | 0.772214440766766 | 0.613892779616617 |
90 | 0.486703147628042 | 0.973406295256083 | 0.513296852371959 |
91 | 0.516801745912969 | 0.966396508174062 | 0.483198254087031 |
92 | 0.494623252251818 | 0.989246504503635 | 0.505376747748182 |
93 | 0.448150734791354 | 0.896301469582708 | 0.551849265208646 |
94 | 0.404503602155672 | 0.809007204311345 | 0.595496397844328 |
95 | 0.42868704578385 | 0.8573740915677 | 0.57131295421615 |
96 | 0.394720044159487 | 0.789440088318974 | 0.605279955840513 |
97 | 0.387926370232582 | 0.775852740465163 | 0.612073629767419 |
98 | 0.342954055782698 | 0.685908111565396 | 0.657045944217302 |
99 | 0.337652406257229 | 0.675304812514459 | 0.662347593742771 |
100 | 0.340500857342996 | 0.681001714685992 | 0.659499142657004 |
101 | 0.297611508987224 | 0.595223017974449 | 0.702388491012776 |
102 | 0.256684503404764 | 0.513369006809528 | 0.743315496595236 |
103 | 0.220218822965077 | 0.440437645930155 | 0.779781177034923 |
104 | 0.195206404686730 | 0.390412809373461 | 0.80479359531327 |
105 | 0.219153698653581 | 0.438307397307163 | 0.780846301346419 |
106 | 0.184309419261686 | 0.368618838523371 | 0.815690580738314 |
107 | 0.203692599681598 | 0.407385199363196 | 0.796307400318402 |
108 | 0.173235725146631 | 0.346471450293263 | 0.826764274853369 |
109 | 0.187516905197643 | 0.375033810395286 | 0.812483094802357 |
110 | 0.170465448874449 | 0.340930897748899 | 0.82953455112555 |
111 | 0.166005322209869 | 0.332010644419738 | 0.833994677790131 |
112 | 0.222208057889540 | 0.444416115779081 | 0.77779194211046 |
113 | 0.207683680499927 | 0.415367360999855 | 0.792316319500073 |
114 | 0.566859173561306 | 0.866281652877388 | 0.433140826438694 |
115 | 0.516318069751983 | 0.967363860496035 | 0.483681930248017 |
116 | 0.587318581075517 | 0.825362837848966 | 0.412681418924483 |
117 | 0.87908804795162 | 0.241823904096761 | 0.120911952048381 |
118 | 0.857706390559669 | 0.284587218880662 | 0.142293609440331 |
119 | 0.836553393509502 | 0.326893212980997 | 0.163446606490498 |
120 | 0.800542086119869 | 0.398915827760263 | 0.199457913880131 |
121 | 0.772374914463799 | 0.455250171072402 | 0.227625085536201 |
122 | 0.745423930048809 | 0.509152139902383 | 0.254576069951191 |
123 | 0.749959339338505 | 0.50008132132299 | 0.250040660661495 |
124 | 0.724689775634267 | 0.550620448731466 | 0.275310224365733 |
125 | 0.715895904801093 | 0.568208190397813 | 0.284104095198907 |
126 | 0.722272399995635 | 0.555455200008731 | 0.277727600004365 |
127 | 0.710527200675484 | 0.578945598649032 | 0.289472799324516 |
128 | 0.780718141983957 | 0.438563716032086 | 0.219281858016043 |
129 | 0.734716139690558 | 0.530567720618883 | 0.265283860309442 |
130 | 0.715874259806147 | 0.568251480387707 | 0.284125740193853 |
131 | 0.697981123721364 | 0.604037752557272 | 0.302018876278636 |
132 | 0.635372477163432 | 0.729255045673135 | 0.364627522836568 |
133 | 0.67846002434435 | 0.6430799513113 | 0.32153997565565 |
134 | 0.630875170292535 | 0.73824965941493 | 0.369124829707465 |
135 | 0.563849109525387 | 0.872301780949227 | 0.436150890474613 |
136 | 0.506010842922659 | 0.987978314154681 | 0.493989157077341 |
137 | 0.431152514684984 | 0.862305029369968 | 0.568847485315016 |
138 | 0.361846104788853 | 0.723692209577706 | 0.638153895211147 |
139 | 0.307912055508669 | 0.615824111017337 | 0.692087944491331 |
140 | 0.258239923707795 | 0.51647984741559 | 0.741760076292205 |
141 | 0.250993082784963 | 0.501986165569925 | 0.749006917215037 |
142 | 0.260772806539506 | 0.521545613079013 | 0.739227193460494 |
143 | 0.199184763047546 | 0.398369526095091 | 0.800815236952454 |
144 | 0.173159443295815 | 0.346318886591629 | 0.826840556704185 |
145 | 0.125738879765476 | 0.251477759530952 | 0.874261120234524 |
146 | 0.202731199659177 | 0.405462399318353 | 0.797268800340823 |
147 | 0.141861585929578 | 0.283723171859155 | 0.858138414070422 |
148 | 0.186646559806457 | 0.373293119612915 | 0.813353440193542 |
149 | 0.367052722357574 | 0.734105444715149 | 0.632947277642426 |
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 | 5 | 0.0352112676056338 | OK |