Multiple Linear Regression - Estimated Regression Equation |
D[t] = + 7.47561072472881 + 0.248860445943252CM[t] -0.105949734415458PE[t] + 0.147529539189438PC[t] -0.192213547252973PS[t] + 0.109733980302452`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 | 0.147529539189438 | 0.092876 | 1.5885 | 0.114246 | 0.057123 |
PS | -0.192213547252973 | 0.056762 | -3.3863 | 9e-04 | 0.00045 |
`O ` | 0.109733980302452 | 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) | 9.63918424183728 |
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 | 942.339708086093 |
Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
1 | 14 | 12.2931271728625 | 1.7068728271375 |
2 | 11 | 11.8542529115495 | -0.854252911549478 |
3 | 6 | 8.06227222418893 | -2.06227222418893 |
4 | 12 | 10.9476618702182 | 1.05233812978182 |
5 | 8 | 9.86771537760798 | -1.86771537760798 |
6 | 10 | 10.1722752103671 | -0.172275210367121 |
7 | 10 | 9.81550154801854 | 0.184498451981456 |
8 | 11 | 9.79825771186774 | 1.20174228813226 |
9 | 16 | 10.8629259764013 | 5.13707402359868 |
10 | 11 | 10.0684635479381 | 0.931536452061921 |
11 | 13 | 12.4680172993328 | 0.531982700667187 |
12 | 12 | 13.0446779919111 | -1.04467799191107 |
13 | 8 | 13.0401936526073 | -5.0401936526073 |
14 | 12 | 10.6464306695575 | 1.35356933044252 |
15 | 11 | 9.21654262865862 | 1.78345737134138 |
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 | 1.21426798577869 |
21 | 15 | 12.2406635388646 | 2.75933646113537 |
22 | 16 | 13.8107907121416 | 2.18920928785844 |
23 | 9 | 11.7886240057284 | -2.78862400572839 |
24 | 14 | 14.3750612147334 | -0.375061214733427 |
25 | 11 | 11.4470289360053 | -0.447028936005265 |
26 | 8 | 9.40860163673439 | -1.40860163673439 |
27 | 9 | 9.57702770843314 | -0.577027708433137 |
28 | 9 | 11.6336575242935 | -2.63365752429345 |
29 | 9 | 10.493867050423 | -1.49386705042302 |
30 | 9 | 9.50925250089076 | -0.509252500890763 |
31 | 10 | 11.7568378002112 | -1.75683780021115 |
32 | 16 | 11.7865625795444 | 4.21343742045558 |
33 | 11 | 9.17755357083023 | 1.82244642916977 |
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 | -0.334572489278586 |
40 | 12 | 10.4081205112709 | 1.59187948872914 |
41 | 14 | 12.5552310099955 | 1.44476899000448 |
42 | 9 | 10.513552972001 | -1.51355297200096 |
43 | 10 | 10.720577052591 | -0.720577052591046 |
44 | 9 | 8.46723311669603 | 0.532766883303966 |
45 | 10 | 10.0998879313339 | -0.0998879313338744 |
46 | 12 | 10.1223852113249 | 1.8776147886751 |
47 | 14 | 11.6185904303772 | 2.38140956962285 |
48 | 14 | 12.1024170814173 | 1.89758291858266 |
49 | 10 | 12.3199460232452 | -2.3199460232452 |
50 | 14 | 9.93003717571406 | 4.06996282428594 |
51 | 16 | 12.2190557443743 | 3.78094425562571 |
52 | 9 | 10.4610692871838 | -1.46106928718377 |
53 | 10 | 11.5899396475331 | -1.58993964753306 |
54 | 6 | 9.04003585641423 | -3.04003585641423 |
55 | 8 | 11.2797735574175 | -3.27977355741748 |
56 | 13 | 12.4239821144831 | 0.576017885516871 |
57 | 10 | 10.8246452755993 | -0.824645275599272 |
58 | 8 | 8.90914169166691 | -0.909141691666908 |
59 | 7 | 9.15425950080064 | -2.15425950080064 |
60 | 15 | 9.8273007573465 | 5.1726992426535 |
61 | 9 | 9.89283171897349 | -0.892831718973492 |
62 | 10 | 10.2300011704603 | -0.230001170460277 |
63 | 12 | 10.2127960045576 | 1.78720399544244 |
64 | 13 | 10.4557571222761 | 2.54424287772388 |
65 | 10 | 8.4082399506884 | 1.5917600493116 |
66 | 11 | 11.8100631875226 | -0.810063187522585 |
67 | 8 | 13.6099912716085 | -5.60999127160853 |
68 | 9 | 9.12149677428637 | -0.121496774286372 |
69 | 13 | 8.63232673895495 | 4.36767326104505 |
70 | 11 | 10.4056197047763 | 0.594380295223706 |
71 | 8 | 12.7748897940749 | -4.77488979407492 |
72 | 9 | 10.7705154168815 | -1.77051541688151 |
73 | 9 | 12.3432616515329 | -3.34326165153292 |
74 | 15 | 12.5112633288267 | 2.48873667117329 |
75 | 9 | 11.1799243643951 | -2.1799243643951 |
76 | 10 | 11.5683831232456 | -1.56838312324565 |
77 | 14 | 8.92549222497563 | 5.07450777502436 |
78 | 12 | 10.9510671481191 | 1.04893285188092 |
79 | 12 | 11.0860720089643 | 0.913927991035744 |
80 | 11 | 11.5603427842052 | -0.560342784205161 |
81 | 14 | 11.4548286127589 | 2.54517138724109 |
82 | 6 | 11.555341171216 | -5.55534117121603 |
83 | 12 | 11.2666600244991 | 0.733339975500888 |
84 | 8 | 10.0611961307754 | -2.06119613077543 |
85 | 14 | 12.4002108724069 | 1.59978912759315 |
86 | 11 | 10.8285356954152 | 0.171464304584766 |
87 | 10 | 9.90994400559581 | 0.0900559944041917 |
88 | 14 | 10.1965799596067 | 3.80342004039329 |
89 | 12 | 12.0383027999683 | -0.0383027999683423 |
90 | 10 | 11.0020524420421 | -1.00205244204212 |
91 | 14 | 13.0089075749108 | 0.991092425089236 |
92 | 5 | 8.98335267342666 | -3.98335267342666 |
93 | 11 | 10.4977291896848 | 0.50227081031523 |
94 | 10 | 10.2124533208688 | -0.21245332086875 |
95 | 9 | 11.4401404868287 | -2.44014048682871 |
96 | 10 | 11.4379445722869 | -1.43794457228688 |
97 | 16 | 13.741619135107 | 2.25838086489298 |
98 | 13 | 12.8237520019172 | 0.17624799808281 |
99 | 9 | 10.8098388947891 | -1.80983889478915 |
100 | 10 | 11.378532076788 | -1.37853207678798 |
101 | 10 | 10.9689523566192 | -0.968952356619231 |
102 | 7 | 9.47465402457373 | -2.47465402457373 |
103 | 9 | 9.8265428213743 | -0.826542821374303 |
104 | 8 | 10.2188112017114 | -2.21881120171137 |
105 | 14 | 12.8472637784596 | 1.1527362215404 |
106 | 14 | 11.6477018919235 | 2.3522981080765 |
107 | 8 | 11.0805233342968 | -3.08052333429676 |
108 | 9 | 11.5401625785906 | -2.54016257859058 |
109 | 14 | 11.8064163349481 | 2.19358366505186 |
110 | 14 | 10.7412291054721 | 3.25877089452787 |
111 | 8 | 9.86606244753663 | -1.86606244753663 |
112 | 8 | 13.6926336074711 | -5.69263360747113 |
113 | 8 | 10.9525118828595 | -2.95251188285948 |
114 | 7 | 8.55085509620331 | -1.55085509620331 |
115 | 6 | 7.44027047059842 | -1.44027047059841 |
116 | 8 | 9.4148100433135 | -1.4148100433135 |
117 | 6 | 8.31398706901332 | -2.31398706901332 |
118 | 11 | 9.87854261184873 | 1.12145738815127 |
119 | 14 | 11.8405591974766 | 2.15944080252337 |
120 | 11 | 11.1231055546712 | -0.123105554671166 |
121 | 11 | 11.9576290110093 | -0.95762901100931 |
122 | 11 | 9.2090803108136 | 1.7909196891864 |
123 | 14 | 10.36967612917 | 3.63032387082998 |
124 | 8 | 10.3570748050233 | -2.35707480502331 |
125 | 20 | 11.4803602064078 | 8.51963979359219 |
126 | 11 | 10.3193075266905 | 0.680692473309463 |
127 | 8 | 9.14405571417421 | -1.14405571417421 |
128 | 11 | 10.7075672323317 | 0.29243276766828 |
129 | 10 | 10.6161673181472 | -0.616167318147201 |
130 | 14 | 13.4485919547856 | 0.551408045214407 |
131 | 11 | 10.558105430536 | 0.441894569463998 |
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 | 10.111501382101 | 2.88849861789897 |
138 | 12 | 9.29557530863078 | 2.70442469136922 |
139 | 8 | 10.35973838043 | -2.35973838042996 |
140 | 13 | 11.0143393969289 | 1.98566060307108 |
141 | 14 | 12.4310064834081 | 1.56899351659187 |
142 | 12 | 11.6674281750066 | 0.332571824993393 |
143 | 14 | 10.9169138958967 | 3.08308610410329 |
144 | 15 | 11.2948106795225 | 3.7051893204775 |
145 | 13 | 10.5165955153937 | 2.4834044846063 |
146 | 16 | 11.8561435650783 | 4.14385643492171 |
147 | 9 | 11.996511861034 | -2.99651186103404 |
148 | 9 | 10.4782744530865 | -1.47827445308649 |
149 | 9 | 11.0181531709424 | -2.01815317094244 |
150 | 8 | 11.2929483065479 | -3.2929483065479 |
151 | 7 | 10.0317337558054 | -3.0317337558054 |
152 | 16 | 11.9492341671955 | 4.05076583280446 |
153 | 11 | 13.3481625806087 | -2.34816258060873 |
154 | 9 | 10.0171718546235 | -1.01717185462351 |
155 | 11 | 9.83326343672508 | 1.16673656327492 |
156 | 9 | 9.86642518204478 | -0.866425182044778 |
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 | 0.952182110167193 | 0.523908944916403 |
10 | 0.320155027094973 | 0.640310054189945 | 0.679844972905027 |
11 | 0.324803577006544 | 0.649607154013089 | 0.675196422993456 |
12 | 0.233266213547837 | 0.466532427095673 | 0.766733786452163 |
13 | 0.793564934243949 | 0.412870131512103 | 0.206435065756051 |
14 | 0.718291593016648 | 0.563416813966704 | 0.281708406983352 |
15 | 0.641167940924178 | 0.717664118151645 | 0.358832059075822 |
16 | 0.687698101596045 | 0.624603796807909 | 0.312301898403955 |
17 | 0.667142450692695 | 0.66571509861461 | 0.332857549307305 |
18 | 0.645049844354671 | 0.709900311290659 | 0.354950155645329 |
19 | 0.57631975918551 | 0.84736048162898 | 0.42368024081449 |
20 | 0.575099313020188 | 0.849801373959624 | 0.424900686979812 |
21 | 0.585405060746221 | 0.829189878507557 | 0.414594939253779 |
22 | 0.555126722745431 | 0.889746554509138 | 0.444873277254569 |
23 | 0.558017709223827 | 0.883964581552346 | 0.441982290776173 |
24 | 0.510035987515598 | 0.979928024968805 | 0.489964012484402 |
25 | 0.43954334372347 | 0.87908668744694 | 0.56045665627653 |
26 | 0.377278219139064 | 0.754556438278127 | 0.622721780860936 |
27 | 0.314096897330081 | 0.628193794660162 | 0.685903102669919 |
28 | 0.306692912841129 | 0.613385825682259 | 0.693307087158871 |
29 | 0.260229892083154 | 0.520459784166307 | 0.739770107916846 |
30 | 0.21003817524773 | 0.420076350495459 | 0.78996182475227 |
31 | 0.192881445825191 | 0.385762891650382 | 0.807118554174809 |
32 | 0.262884027930576 | 0.525768055861152 | 0.737115972069424 |
33 | 0.235396766876013 | 0.470793533752026 | 0.764603233123987 |
34 | 0.235007038463068 | 0.470014076926136 | 0.764992961536932 |
35 | 0.191405880321681 | 0.382811760643362 | 0.808594119678319 |
36 | 0.212302642451889 | 0.424605284903778 | 0.787697357548111 |
37 | 0.20964811669903 | 0.41929623339806 | 0.79035188330097 |
38 | 0.606540921417601 | 0.786918157164798 | 0.393459078582399 |
39 | 0.554135704077906 | 0.891728591844188 | 0.445864295922094 |
40 | 0.520990964978722 | 0.958018070042556 | 0.479009035021278 |
41 | 0.481258183394213 | 0.962516366788426 | 0.518741816605787 |
42 | 0.446585909193592 | 0.893171818387184 | 0.553414090806408 |
43 | 0.399113225350086 | 0.798226450700172 | 0.600886774649914 |
44 | 0.350418690892097 | 0.700837381784193 | 0.649581309107903 |
45 | 0.30183157482083 | 0.603663149641659 | 0.69816842517917 |
46 | 0.285300856623609 | 0.570601713247218 | 0.714699143376391 |
47 | 0.276880642043234 | 0.553761284086469 | 0.723119357956766 |
48 | 0.255998886010793 | 0.511997772021586 | 0.744001113989207 |
49 | 0.256699729798468 | 0.513399459596937 | 0.743300270201532 |
50 | 0.320245094302186 | 0.640490188604372 | 0.679754905697814 |
51 | 0.370824888458202 | 0.741649776916405 | 0.629175111541798 |
52 | 0.340837659367932 | 0.681675318735864 | 0.659162340632068 |
53 | 0.314933679783701 | 0.629867359567403 | 0.685066320216299 |
54 | 0.331760994229209 | 0.663521988458418 | 0.668239005770791 |
55 | 0.351662726969555 | 0.70332545393911 | 0.648337273030445 |
56 | 0.307841980911196 | 0.615683961822393 | 0.692158019088804 |
57 | 0.270238986480131 | 0.540477972960262 | 0.729761013519869 |
58 | 0.23566569897297 | 0.47133139794594 | 0.76433430102703 |
59 | 0.223294194809293 | 0.446588389618586 | 0.776705805190707 |
60 | 0.357926992174277 | 0.715853984348554 | 0.642073007825723 |
61 | 0.317418096385377 | 0.634836192770754 | 0.682581903614623 |
62 | 0.276394366413777 | 0.552788732827555 | 0.723605633586223 |
63 | 0.256535513703847 | 0.513071027407694 | 0.743464486296153 |
64 | 0.26782826652585 | 0.535656533051701 | 0.73217173347415 |
65 | 0.24401030728983 | 0.48802061457966 | 0.75598969271017 |
66 | 0.212324329654128 | 0.424648659308257 | 0.787675670345872 |
67 | 0.390040519480441 | 0.780081038960882 | 0.609959480519559 |
68 | 0.345224833395202 | 0.690449666790405 | 0.654775166604798 |
69 | 0.434822332802387 | 0.869644665604774 | 0.565177667197613 |
70 | 0.391410429384713 | 0.782820858769426 | 0.608589570615287 |
71 | 0.518949159678525 | 0.962101680642951 | 0.481050840321475 |
72 | 0.496464134882848 | 0.992928269765697 | 0.503535865117152 |
73 | 0.531641361916029 | 0.936717276167943 | 0.468358638083971 |
74 | 0.53179254264969 | 0.93641491470062 | 0.46820745735031 |
75 | 0.519911999650483 | 0.960176000699034 | 0.480088000349517 |
76 | 0.492426975651176 | 0.984853951302352 | 0.507573024348824 |
77 | 0.644457793217583 | 0.711084413564833 | 0.355542206782417 |
78 | 0.608445607100601 | 0.783108785798797 | 0.391554392899399 |
79 | 0.569031770874919 | 0.861936458250163 | 0.430968229125081 |
80 | 0.526201024255373 | 0.947597951489254 | 0.473798975744627 |
81 | 0.527674227423092 | 0.944651545153816 | 0.472325772576908 |
82 | 0.69949315770858 | 0.601013684582841 | 0.30050684229142 |
83 | 0.661288799796887 | 0.677422400406225 | 0.338711200203113 |
84 | 0.644279313401495 | 0.71144137319701 | 0.355720686598505 |
85 | 0.615843118427675 | 0.76831376314465 | 0.384156881572325 |
86 | 0.57143247127669 | 0.85713505744662 | 0.42856752872331 |
87 | 0.525199918237691 | 0.949600163524618 | 0.474800081762309 |
88 | 0.594703454276607 | 0.810593091446787 | 0.405296545723393 |
89 | 0.550132002192165 | 0.89973599561567 | 0.449867997807835 |
90 | 0.509575972582257 | 0.980848054835487 | 0.490424027417743 |
91 | 0.469521789478772 | 0.939043578957544 | 0.530478210521228 |
92 | 0.528056279019302 | 0.943887441961397 | 0.471943720980698 |
93 | 0.4842672576452 | 0.968534515290399 | 0.5157327423548 |
94 | 0.437200214778865 | 0.87440042955773 | 0.562799785221135 |
95 | 0.43393139693459 | 0.86786279386918 | 0.56606860306541 |
96 | 0.40410087586012 | 0.80820175172024 | 0.59589912413988 |
97 | 0.388194529491105 | 0.776389058982209 | 0.611805470508895 |
98 | 0.34359498074084 | 0.687189961481681 | 0.65640501925916 |
99 | 0.320168074584797 | 0.640336149169595 | 0.679831925415203 |
100 | 0.290385090765841 | 0.580770181531681 | 0.709614909234159 |
101 | 0.256352317706483 | 0.512704635412965 | 0.743647682293518 |
102 | 0.248521505838521 | 0.497043011677043 | 0.751478494161479 |
103 | 0.213854846463103 | 0.427709692926206 | 0.786145153536897 |
104 | 0.204088309924542 | 0.408176619849085 | 0.795911690075458 |
105 | 0.175105319691062 | 0.350210639382124 | 0.824894680308938 |
106 | 0.170558236007088 | 0.341116472014177 | 0.829441763992912 |
107 | 0.184578417463128 | 0.369156834926256 | 0.815421582536872 |
108 | 0.189248434454485 | 0.37849686890897 | 0.810751565545515 |
109 | 0.176721115775724 | 0.353442231551448 | 0.823278884224276 |
110 | 0.202029085947166 | 0.404058171894331 | 0.797970914052834 |
111 | 0.181318748782535 | 0.36263749756507 | 0.818681251217465 |
112 | 0.406498565425634 | 0.812997130851268 | 0.593501434574366 |
113 | 0.465486153700663 | 0.930972307401327 | 0.534513846299337 |
114 | 0.429649070419864 | 0.859298140839728 | 0.570350929580136 |
115 | 0.422135996081516 | 0.844271992163031 | 0.577864003918484 |
116 | 0.379739971174427 | 0.759479942348855 | 0.620260028825573 |
117 | 0.365472859961179 | 0.730945719922357 | 0.634527140038821 |
118 | 0.323420729234327 | 0.646841458468653 | 0.676579270765673 |
119 | 0.302331410044504 | 0.604662820089008 | 0.697668589955496 |
120 | 0.257541358270713 | 0.515082716541425 | 0.742458641729287 |
121 | 0.229217140864474 | 0.458434281728948 | 0.770782859135526 |
122 | 0.215962894307203 | 0.431925788614407 | 0.784037105692797 |
123 | 0.22788116252121 | 0.45576232504242 | 0.77211883747879 |
124 | 0.241452989526193 | 0.482905979052387 | 0.758547010473807 |
125 | 0.790956538438538 | 0.418086923122925 | 0.209043461561462 |
126 | 0.754537021129096 | 0.490925957741809 | 0.245462978870904 |
127 | 0.70723225485574 | 0.58553549028852 | 0.29276774514426 |
128 | 0.650610707546916 | 0.698778584906168 | 0.349389292453084 |
129 | 0.591211562681127 | 0.817576874637746 | 0.408788437318873 |
130 | 0.529775510485169 | 0.940448979029663 | 0.470224489514831 |
131 | 0.473593931496003 | 0.947187862992005 | 0.526406068503997 |
132 | 0.418388363759168 | 0.836776727518335 | 0.581611636240832 |
133 | 0.356258908378721 | 0.712517816757443 | 0.643741091621279 |
134 | 0.316736189482038 | 0.633472378964076 | 0.683263810517962 |
135 | 0.285367565123948 | 0.570735130247895 | 0.714632434876052 |
136 | 0.262690626270164 | 0.525381252540329 | 0.737309373729836 |
137 | 0.298957615224637 | 0.597915230449275 | 0.701042384775363 |
138 | 0.307974903567051 | 0.615949807134102 | 0.692025096432949 |
139 | 0.328331373504198 | 0.656662747008396 | 0.671668626495802 |
140 | 0.265316978126099 | 0.530633956252198 | 0.734683021873901 |
141 | 0.208208703930898 | 0.416417407861796 | 0.791791296069102 |
142 | 0.158048550232565 | 0.316097100465129 | 0.841951449767435 |
143 | 0.184447031478692 | 0.368894062957383 | 0.815552968521309 |
144 | 0.173591647090987 | 0.347183294181975 | 0.826408352909013 |
145 | 0.156255031298021 | 0.312510062596041 | 0.843744968701979 |
146 | 0.273200771077995 | 0.54640154215599 | 0.726799228922005 |
147 | 0.239791906503731 | 0.479583813007461 | 0.760208093496269 |
148 | 0.159221051012305 | 0.318442102024611 | 0.840778948987695 |
149 | 0.11258941786019 | 0.225178835720379 | 0.88741058213981 |
150 | 0.16099946030146 | 0.32199892060292 | 0.83900053969854 |
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 |