Multiple Linear Regression - Estimated Regression Equation |
D[t] = + 7.47561072472881 + 0.248860445943252CM[t] -0.105949734415458PE[t] + 0.147529539189439PC[t] -0.192213547252973PS[t] + 0.109733980302453`O `[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) | 7.47561072472881 | 1.582911 | 4.7227 | 5e-06 | 3e-06 |
CM | 0.248860445943252 | 0.040037 | 6.2157 | 0 | 0 |
PE | -0.105949734415458 | 0.073943 | -1.4329 | 0.153941 | 0.07697 |
PC | 0.147529539189439 | 0.092876 | 1.5885 | 0.114246 | 0.057123 |
PS | -0.192213547252973 | 0.056762 | -3.3863 | 9e-04 | 0.00045 |
`O ` | 0.109733980302453 | 0.056645 | 1.9372 | 0.05456 | 0.02728 |
Multiple Linear Regression - Regression Statistics | |
Multiple R | 0.489435601598432 |
R-squared | 0.239547208112019 |
Adjusted R-squared | 0.214695809684307 |
F-TEST (value) | 9.63918424183727 |
F-TEST (DF numerator) | 5 |
F-TEST (DF denominator) | 153 |
p-value | 5.12764863902504e-08 |
Multiple Linear Regression - Residual Statistics | |
Residual Standard Deviation | 2.48174999937267 |
Sum Squared Residuals | 942.339708086094 |
Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
1 | 14 | 12.2931271728623 | 1.7068728271377 |
2 | 11 | 11.8542529115495 | -0.85425291154948 |
3 | 6 | 8.06227222418893 | -2.06227222418893 |
4 | 12 | 10.9476618702182 | 1.05233812978182 |
5 | 8 | 9.86771537760797 | -1.86771537760797 |
6 | 10 | 10.1722752103671 | -0.172275210367124 |
7 | 10 | 9.81550154801854 | 0.184498451981458 |
8 | 11 | 9.79825771186774 | 1.20174228813226 |
9 | 16 | 10.8629259764013 | 5.13707402359868 |
10 | 11 | 10.0684635479381 | 0.93153645206192 |
11 | 13 | 12.4680172993328 | 0.53198270066718 |
12 | 12 | 13.0446779919111 | -1.04467799191107 |
13 | 8 | 13.0401936526073 | -5.0401936526073 |
14 | 12 | 10.6464306695575 | 1.35356933044252 |
15 | 11 | 9.21654262865863 | 1.78345737134137 |
16 | 4 | 7.34559388921211 | -3.34559388921211 |
17 | 9 | 11.0418798989866 | -2.04187989898656 |
18 | 8 | 9.84912475091086 | -1.84912475091086 |
19 | 8 | 10.0892984205506 | -2.08929842055058 |
20 | 14 | 12.7857320142213 | 1.21426798577868 |
21 | 15 | 12.2406635388646 | 2.75933646113537 |
22 | 16 | 13.8107907121416 | 2.18920928785844 |
23 | 9 | 11.7886240057284 | -2.7886240057284 |
24 | 14 | 14.3750612147334 | -0.375061214733429 |
25 | 11 | 11.4470289360053 | -0.44702893600527 |
26 | 8 | 9.4086016367344 | -1.40860163673439 |
27 | 9 | 9.57702770843313 | -0.577027708433134 |
28 | 9 | 11.6336575242935 | -2.63365752429346 |
29 | 9 | 10.4938670504230 | -1.49386705042302 |
30 | 9 | 9.50925250089076 | -0.509252500890762 |
31 | 10 | 11.7568378002112 | -1.75683780021115 |
32 | 16 | 11.7865625795444 | 4.21343742045556 |
33 | 11 | 9.17755357083022 | 1.82244642916978 |
34 | 8 | 10.0509478301168 | -2.05094783011685 |
35 | 9 | 8.73193357843342 | 0.268066421566578 |
36 | 16 | 12.6496652378379 | 3.35033476216208 |
37 | 11 | 12.6518033098243 | -1.65180330982433 |
38 | 16 | 9.32356466830619 | 6.67643533169381 |
39 | 12 | 12.3345724892786 | -0.334572489278588 |
40 | 12 | 10.4081205112709 | 1.59187948872914 |
41 | 14 | 12.5552310099955 | 1.44476899000448 |
42 | 9 | 10.5135529720010 | -1.51355297200096 |
43 | 10 | 10.7205770525910 | -0.720577052591042 |
44 | 9 | 8.46723311669603 | 0.53276688330397 |
45 | 10 | 10.0998879313339 | -0.0998879313338787 |
46 | 12 | 10.1223852113249 | 1.87761478867509 |
47 | 14 | 11.6185904303772 | 2.38140956962284 |
48 | 14 | 12.1024170814173 | 1.89758291858266 |
49 | 10 | 12.3199460232452 | -2.3199460232452 |
50 | 14 | 9.93003717571405 | 4.06996282428595 |
51 | 16 | 12.2190557443743 | 3.7809442556257 |
52 | 9 | 10.4610692871838 | -1.46106928718378 |
53 | 10 | 11.5899396475331 | -1.58993964753306 |
54 | 6 | 9.04003585641422 | -3.04003585641422 |
55 | 8 | 11.2797735574175 | -3.27977355741749 |
56 | 13 | 12.4239821144831 | 0.576017885516867 |
57 | 10 | 10.8246452755993 | -0.824645275599276 |
58 | 8 | 8.9091416916669 | -0.909141691666905 |
59 | 7 | 9.15425950080064 | -2.15425950080064 |
60 | 15 | 9.8273007573465 | 5.1726992426535 |
61 | 9 | 9.8928317189735 | -0.892831718973498 |
62 | 10 | 10.2300011704603 | -0.230001170460275 |
63 | 12 | 10.2127960045576 | 1.78720399544244 |
64 | 13 | 10.4557571222761 | 2.54424287772387 |
65 | 10 | 8.4082399506884 | 1.59176004931160 |
66 | 11 | 11.8100631875226 | -0.810063187522588 |
67 | 8 | 13.6099912716085 | -5.60999127160853 |
68 | 9 | 9.12149677428637 | -0.121496774286373 |
69 | 13 | 8.63232673895495 | 4.36767326104505 |
70 | 11 | 10.4056197047763 | 0.594380295223702 |
71 | 8 | 12.7748897940749 | -4.77488979407492 |
72 | 9 | 10.7705154168815 | -1.77051541688151 |
73 | 9 | 12.3432616515329 | -3.34326165153293 |
74 | 15 | 12.5112633288267 | 2.48873667117329 |
75 | 9 | 11.1799243643951 | -2.17992436439510 |
76 | 10 | 11.5683831232456 | -1.56838312324565 |
77 | 14 | 8.92549222497563 | 5.07450777502436 |
78 | 12 | 10.9510671481191 | 1.04893285188092 |
79 | 12 | 11.0860720089643 | 0.913927991035738 |
80 | 11 | 11.5603427842052 | -0.560342784205158 |
81 | 14 | 11.4548286127589 | 2.54517138724108 |
82 | 6 | 11.5553411712160 | -5.55534117121603 |
83 | 12 | 11.2666600244991 | 0.733339975500887 |
84 | 8 | 10.0611961307754 | -2.06119613077543 |
85 | 14 | 12.4002108724069 | 1.59978912759315 |
86 | 11 | 10.8285356954152 | 0.171464304584769 |
87 | 10 | 9.90994400559581 | 0.0900559944041932 |
88 | 14 | 10.1965799596067 | 3.80342004039329 |
89 | 12 | 12.0383027999684 | -0.0383027999683501 |
90 | 10 | 11.0020524420421 | -1.00205244204212 |
91 | 14 | 13.0089075749108 | 0.991092425089237 |
92 | 5 | 8.98335267342666 | -3.98335267342666 |
93 | 11 | 10.4977291896848 | 0.502270810315231 |
94 | 10 | 10.2124533208687 | -0.212453320868745 |
95 | 9 | 11.4401404868287 | -2.44014048682872 |
96 | 10 | 11.4379445722869 | -1.43794457228688 |
97 | 16 | 13.7416191351070 | 2.25838086489298 |
98 | 13 | 12.8237520019172 | 0.176247998082808 |
99 | 9 | 10.8098388947891 | -1.80983889478915 |
100 | 10 | 11.3785320767880 | -1.37853207678798 |
101 | 10 | 10.9689523566192 | -0.968952356619233 |
102 | 7 | 9.47465402457373 | -2.47465402457373 |
103 | 9 | 9.8265428213743 | -0.8265428213743 |
104 | 8 | 10.2188112017114 | -2.21881120171137 |
105 | 14 | 12.8472637784596 | 1.15273622154039 |
106 | 14 | 11.6477018919235 | 2.35229810807650 |
107 | 8 | 11.0805233342968 | -3.08052333429676 |
108 | 9 | 11.5401625785906 | -2.54016257859058 |
109 | 14 | 11.8064163349481 | 2.19358366505185 |
110 | 14 | 10.7412291054721 | 3.25877089452788 |
111 | 8 | 9.86606244753663 | -1.86606244753663 |
112 | 8 | 13.6926336074711 | -5.69263360747113 |
113 | 8 | 10.9525118828595 | -2.95251188285949 |
114 | 7 | 8.55085509620331 | -1.55085509620331 |
115 | 6 | 7.44027047059843 | -1.44027047059843 |
116 | 8 | 9.4148100433135 | -1.41481004331350 |
117 | 6 | 8.31398706901332 | -2.31398706901332 |
118 | 11 | 9.87854261184873 | 1.12145738815127 |
119 | 14 | 11.8405591974766 | 2.15944080252337 |
120 | 11 | 11.1231055546712 | -0.123105554671159 |
121 | 11 | 11.9576290110093 | -0.957629011009308 |
122 | 11 | 9.2090803108136 | 1.7909196891864 |
123 | 14 | 10.3696761291700 | 3.63032387082997 |
124 | 8 | 10.3570748050233 | -2.35707480502332 |
125 | 20 | 11.4803602064078 | 8.51963979359218 |
126 | 11 | 10.3193075266905 | 0.680692473309466 |
127 | 8 | 9.14405571417421 | -1.14405571417421 |
128 | 11 | 10.7075672323317 | 0.292432767668276 |
129 | 10 | 10.6161673181472 | -0.616167318147203 |
130 | 14 | 13.4485919547856 | 0.551408045214404 |
131 | 11 | 10.558105430536 | 0.441894569463994 |
132 | 9 | 10.5952141906548 | -1.59521419065478 |
133 | 9 | 9.71061082418663 | -0.710610824186625 |
134 | 8 | 10.1579861032424 | -2.15798610324236 |
135 | 10 | 12.0589843809759 | -2.05898438097594 |
136 | 13 | 10.7188783609152 | 2.28112163908477 |
137 | 13 | 10.1115013821010 | 2.88849861789897 |
138 | 12 | 9.29557530863078 | 2.70442469136922 |
139 | 8 | 10.3597383804300 | -2.35973838042996 |
140 | 13 | 11.0143393969289 | 1.98566060307107 |
141 | 14 | 12.4310064834081 | 1.56899351659186 |
142 | 12 | 11.6674281750066 | 0.332571824993391 |
143 | 14 | 10.9169138958967 | 3.08308610410328 |
144 | 15 | 11.2948106795225 | 3.70518932047750 |
145 | 13 | 10.5165955153937 | 2.48340448460630 |
146 | 16 | 11.8561435650783 | 4.14385643492171 |
147 | 9 | 11.9965118610340 | -2.99651186103404 |
148 | 9 | 10.4782744530865 | -1.47827445308649 |
149 | 9 | 11.0181531709424 | -2.01815317094243 |
150 | 8 | 11.2929483065479 | -3.29294830654791 |
151 | 7 | 10.0317337558054 | -3.03173375580541 |
152 | 16 | 11.9492341671955 | 4.05076583280446 |
153 | 11 | 13.3481625806087 | -2.34816258060872 |
154 | 9 | 10.0171718546235 | -1.0171718546235 |
155 | 11 | 9.83326343672508 | 1.16673656327492 |
156 | 9 | 9.86642518204478 | -0.866425182044775 |
157 | 14 | 12.4789828392728 | 1.52101716072717 |
158 | 13 | 11.0220394382314 | 1.97796056176859 |
159 | 16 | 14.4647615248554 | 1.53523847514457 |
Goldfeld-Quandt test for Heteroskedasticity | |||
p-values | Alternative Hypothesis | ||
breakpoint index | greater | 2-sided | less |
9 | 0.476091055083597 | 0.952182110167194 | 0.523908944916403 |
10 | 0.320155027094972 | 0.640310054189944 | 0.679844972905028 |
11 | 0.324803577006545 | 0.64960715401309 | 0.675196422993455 |
12 | 0.233266213547837 | 0.466532427095675 | 0.766733786452163 |
13 | 0.793564934243949 | 0.412870131512102 | 0.206435065756051 |
14 | 0.718291593016648 | 0.563416813966704 | 0.281708406983352 |
15 | 0.641167940924177 | 0.717664118151647 | 0.358832059075823 |
16 | 0.687698101596045 | 0.624603796807909 | 0.312301898403955 |
17 | 0.667142450692695 | 0.66571509861461 | 0.332857549307305 |
18 | 0.645049844354672 | 0.709900311290656 | 0.354950155645328 |
19 | 0.57631975918551 | 0.84736048162898 | 0.42368024081449 |
20 | 0.575099313020188 | 0.849801373959624 | 0.424900686979812 |
21 | 0.585405060746221 | 0.829189878507558 | 0.414594939253779 |
22 | 0.555126722745432 | 0.889746554509136 | 0.444873277254568 |
23 | 0.558017709223827 | 0.883964581552347 | 0.441982290776173 |
24 | 0.510035987515598 | 0.979928024968803 | 0.489964012484402 |
25 | 0.43954334372347 | 0.87908668744694 | 0.56045665627653 |
26 | 0.377278219139064 | 0.754556438278127 | 0.622721780860936 |
27 | 0.314096897330082 | 0.628193794660164 | 0.685903102669918 |
28 | 0.306692912841130 | 0.613385825682259 | 0.69330708715887 |
29 | 0.260229892083154 | 0.520459784166308 | 0.739770107916846 |
30 | 0.210038175247729 | 0.420076350495459 | 0.78996182475227 |
31 | 0.192881445825193 | 0.385762891650385 | 0.807118554174807 |
32 | 0.262884027930576 | 0.525768055861151 | 0.737115972069424 |
33 | 0.235396766876013 | 0.470793533752027 | 0.764603233123987 |
34 | 0.235007038463068 | 0.470014076926136 | 0.764992961536932 |
35 | 0.19140588032168 | 0.38281176064336 | 0.80859411967832 |
36 | 0.212302642451889 | 0.424605284903778 | 0.787697357548111 |
37 | 0.209648116699031 | 0.419296233398062 | 0.790351883300969 |
38 | 0.606540921417603 | 0.786918157164794 | 0.393459078582397 |
39 | 0.554135704077907 | 0.891728591844186 | 0.445864295922093 |
40 | 0.520990964978723 | 0.958018070042555 | 0.479009035021278 |
41 | 0.481258183394213 | 0.962516366788426 | 0.518741816605787 |
42 | 0.446585909193591 | 0.893171818387181 | 0.553414090806409 |
43 | 0.399113225350086 | 0.798226450700173 | 0.600886774649914 |
44 | 0.350418690892097 | 0.700837381784193 | 0.649581309107903 |
45 | 0.301831574820829 | 0.603663149641658 | 0.69816842517917 |
46 | 0.28530085662361 | 0.57060171324722 | 0.71469914337639 |
47 | 0.276880642043234 | 0.553761284086469 | 0.723119357956766 |
48 | 0.255998886010795 | 0.51199777202159 | 0.744001113989205 |
49 | 0.256699729798469 | 0.513399459596937 | 0.743300270201531 |
50 | 0.320245094302186 | 0.640490188604372 | 0.679754905697814 |
51 | 0.370824888458201 | 0.741649776916403 | 0.629175111541799 |
52 | 0.340837659367933 | 0.681675318735867 | 0.659162340632067 |
53 | 0.3149336797837 | 0.6298673595674 | 0.6850663202163 |
54 | 0.33176099422921 | 0.66352198845842 | 0.66823900577079 |
55 | 0.351662726969555 | 0.703325453939111 | 0.648337273030445 |
56 | 0.307841980911196 | 0.615683961822393 | 0.692158019088804 |
57 | 0.270238986480131 | 0.540477972960263 | 0.729761013519869 |
58 | 0.235665698972970 | 0.471331397945941 | 0.76433430102703 |
59 | 0.223294194809294 | 0.446588389618588 | 0.776705805190706 |
60 | 0.357926992174277 | 0.715853984348554 | 0.642073007825723 |
61 | 0.317418096385376 | 0.634836192770752 | 0.682581903614624 |
62 | 0.276394366413775 | 0.552788732827549 | 0.723605633586225 |
63 | 0.256535513703847 | 0.513071027407694 | 0.743464486296153 |
64 | 0.267828266525851 | 0.535656533051701 | 0.732171733474149 |
65 | 0.244010307289830 | 0.488020614579659 | 0.75598969271017 |
66 | 0.212324329654130 | 0.424648659308259 | 0.78767567034587 |
67 | 0.390040519480441 | 0.780081038960882 | 0.609959480519559 |
68 | 0.345224833395200 | 0.690449666790401 | 0.6547751666048 |
69 | 0.434822332802387 | 0.869644665604773 | 0.565177667197613 |
70 | 0.39141042938471 | 0.78282085876942 | 0.60858957061529 |
71 | 0.518949159678523 | 0.962101680642954 | 0.481050840321477 |
72 | 0.496464134882847 | 0.992928269765694 | 0.503535865117153 |
73 | 0.53164136191603 | 0.93671727616794 | 0.46835863808397 |
74 | 0.531792542649688 | 0.936414914700624 | 0.468207457350312 |
75 | 0.519911999650482 | 0.960176000699036 | 0.480088000349518 |
76 | 0.492426975651176 | 0.984853951302352 | 0.507573024348824 |
77 | 0.644457793217581 | 0.711084413564838 | 0.355542206782419 |
78 | 0.608445607100602 | 0.783108785798796 | 0.391554392899398 |
79 | 0.569031770874919 | 0.861936458250163 | 0.430968229125081 |
80 | 0.526201024255375 | 0.94759795148925 | 0.473798975744625 |
81 | 0.527674227423092 | 0.944651545153816 | 0.472325772576908 |
82 | 0.699493157708578 | 0.601013684582844 | 0.300506842291422 |
83 | 0.661288799796887 | 0.677422400406225 | 0.338711200203113 |
84 | 0.644279313401498 | 0.711441373197005 | 0.355720686598502 |
85 | 0.615843118427673 | 0.768313763144654 | 0.384156881572327 |
86 | 0.57143247127669 | 0.85713505744662 | 0.42856752872331 |
87 | 0.52519991823769 | 0.949600163524619 | 0.474800081762309 |
88 | 0.594703454276606 | 0.810593091446787 | 0.405296545723394 |
89 | 0.550132002192165 | 0.89973599561567 | 0.449867997807835 |
90 | 0.509575972582258 | 0.980848054835484 | 0.490424027417742 |
91 | 0.469521789478772 | 0.939043578957543 | 0.530478210521228 |
92 | 0.528056279019302 | 0.943887441961396 | 0.471943720980698 |
93 | 0.484267257645203 | 0.968534515290406 | 0.515732742354797 |
94 | 0.43720021477886 | 0.87440042955772 | 0.56279978522114 |
95 | 0.433931396934589 | 0.867862793869179 | 0.566068603065411 |
96 | 0.404100875860118 | 0.808201751720235 | 0.595899124139882 |
97 | 0.388194529491107 | 0.776389058982214 | 0.611805470508893 |
98 | 0.343594980740843 | 0.687189961481687 | 0.656405019259157 |
99 | 0.320168074584798 | 0.640336149169595 | 0.679831925415202 |
100 | 0.290385090765841 | 0.580770181531682 | 0.709614909234159 |
101 | 0.256352317706483 | 0.512704635412967 | 0.743647682293517 |
102 | 0.248521505838521 | 0.497043011677043 | 0.751478494161478 |
103 | 0.213854846463106 | 0.427709692926211 | 0.786145153536894 |
104 | 0.204088309924541 | 0.408176619849081 | 0.79591169007546 |
105 | 0.175105319691062 | 0.350210639382124 | 0.824894680308938 |
106 | 0.170558236007089 | 0.341116472014178 | 0.829441763992911 |
107 | 0.184578417463128 | 0.369156834926255 | 0.815421582536872 |
108 | 0.189248434454485 | 0.378496868908969 | 0.810751565545515 |
109 | 0.176721115775723 | 0.353442231551446 | 0.823278884224277 |
110 | 0.202029085947166 | 0.404058171894332 | 0.797970914052834 |
111 | 0.181318748782535 | 0.36263749756507 | 0.818681251217465 |
112 | 0.406498565425634 | 0.812997130851268 | 0.593501434574366 |
113 | 0.465486153700664 | 0.930972307401328 | 0.534513846299336 |
114 | 0.429649070419864 | 0.859298140839728 | 0.570350929580136 |
115 | 0.422135996081516 | 0.844271992163032 | 0.577864003918484 |
116 | 0.379739971174427 | 0.759479942348854 | 0.620260028825573 |
117 | 0.365472859961179 | 0.730945719922359 | 0.634527140038821 |
118 | 0.323420729234325 | 0.64684145846865 | 0.676579270765675 |
119 | 0.302331410044504 | 0.604662820089008 | 0.697668589955496 |
120 | 0.257541358270712 | 0.515082716541424 | 0.742458641729288 |
121 | 0.229217140864475 | 0.45843428172895 | 0.770782859135525 |
122 | 0.215962894307202 | 0.431925788614404 | 0.784037105692798 |
123 | 0.227881162521209 | 0.455762325042419 | 0.77211883747879 |
124 | 0.241452989526197 | 0.482905979052395 | 0.758547010473803 |
125 | 0.790956538438538 | 0.418086923122924 | 0.209043461561462 |
126 | 0.754537021129095 | 0.490925957741809 | 0.245462978870905 |
127 | 0.70723225485574 | 0.585535490288521 | 0.292767745144261 |
128 | 0.650610707546915 | 0.698778584906169 | 0.349389292453085 |
129 | 0.591211562681126 | 0.817576874637749 | 0.408788437318874 |
130 | 0.52977551048517 | 0.94044897902966 | 0.47022448951483 |
131 | 0.473593931496003 | 0.947187862992005 | 0.526406068503997 |
132 | 0.418388363759168 | 0.836776727518336 | 0.581611636240832 |
133 | 0.356258908378721 | 0.712517816757442 | 0.643741091621279 |
134 | 0.316736189482038 | 0.633472378964076 | 0.683263810517962 |
135 | 0.285367565123947 | 0.570735130247895 | 0.714632434876053 |
136 | 0.262690626270163 | 0.525381252540327 | 0.737309373729837 |
137 | 0.298957615224636 | 0.597915230449273 | 0.701042384775364 |
138 | 0.307974903567051 | 0.615949807134102 | 0.692025096432949 |
139 | 0.328331373504199 | 0.656662747008399 | 0.671668626495801 |
140 | 0.265316978126099 | 0.530633956252197 | 0.734683021873901 |
141 | 0.208208703930898 | 0.416417407861796 | 0.791791296069102 |
142 | 0.158048550232565 | 0.31609710046513 | 0.841951449767435 |
143 | 0.184447031478692 | 0.368894062957383 | 0.815552968521308 |
144 | 0.173591647090988 | 0.347183294181975 | 0.826408352909012 |
145 | 0.15625503129802 | 0.31251006259604 | 0.84374496870198 |
146 | 0.273200771077996 | 0.546401542155991 | 0.726799228922004 |
147 | 0.239791906503731 | 0.479583813007461 | 0.76020809349627 |
148 | 0.159221051012305 | 0.318442102024611 | 0.840778948987695 |
149 | 0.112589417860190 | 0.225178835720380 | 0.88741058213981 |
150 | 0.160999460301461 | 0.321998920602922 | 0.839000539698539 |
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 |