Multiple Linear Regression - Estimated Regression Equation |
a[t] = + 54.6896103726068 -31.4214447834521b[t] + 31.5139663075632c[t] + 0.384318238038688d[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) | 54.6896103726068 | 9.810049 | 5.5749 | 0 | 0 |
b | -31.4214447834521 | 6.81932 | -4.6077 | 9e-06 | 4e-06 |
c | 31.5139663075632 | 6.741798 | 4.6744 | 7e-06 | 3e-06 |
d | 0.384318238038688 | 0.02944 | 13.0545 | 0 | 0 |
Multiple Linear Regression - Regression Statistics | |
Multiple R | 0.871229340532814 |
R-squared | 0.759040563805242 |
Adjusted R-squared | 0.754156250909402 |
F-TEST (value) | 155.403754835561 |
F-TEST (DF numerator) | 3 |
F-TEST (DF denominator) | 148 |
p-value | 0 |
Multiple Linear Regression - Residual Statistics | |
Residual Standard Deviation | 6.70804072902335 |
Sum Squared Residuals | 6659.67594249095 |
Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
1 | 93.7 | 88.4100388579105 | 5.28996114208951 |
2 | 114.7 | 107.023829705601 | 7.67617029439873 |
3 | 121.2 | 110.528972572665 | 10.6710274273351 |
4 | 98.6 | 96.383933210889 | 2.21606678911099 |
5 | 111.5 | 106.870130773457 | 4.62986922654309 |
6 | 107.5 | 100.200784868951 | 7.29921513104851 |
7 | 69.1 | 70.4595281924414 | -1.35952819244142 |
8 | 88.3 | 98.8535324334527 | -10.5535324334527 |
9 | 114.7 | 109.282057678368 | 5.41794232163222 |
10 | 115.5 | 107.156221709586 | 8.34377829041392 |
11 | 109.5 | 102.883883543264 | 6.61611645673599 |
12 | 97.7 | 94.0168050903914 | 3.68319490960864 |
13 | 102 | 94.2203549641856 | 7.77964503581437 |
14 | 107.5 | 107.571116990855 | -0.071116990855209 |
15 | 120.5 | 106.565501810522 | 13.934498189478 |
16 | 101.9 | 94.9171077818382 | 6.98289221816184 |
17 | 107.6 | 101.234176989927 | 6.36582301007292 |
18 | 113.9 | 108.371084661849 | 5.52891533815063 |
19 | 70.9 | 73.2059970825439 | -2.30599708254393 |
20 | 93.4 | 94.9071686042948 | -1.5071686042948 |
21 | 114.8 | 103.753570427998 | 11.0464295720021 |
22 | 117.8 | 113.106015006816 | 4.6939849931842 |
23 | 105.2 | 102.554354951826 | 2.64564504817371 |
24 | 95.1 | 85.637244286989 | 9.46275571301102 |
25 | 97.5 | 95.1747448351897 | 2.32525516481034 |
26 | 103.2 | 99.380168931859 | 3.81983106814098 |
27 | 111.6 | 107.129167719396 | 4.47083228060441 |
28 | 105.4 | 104.128636513625 | 1.27136348637454 |
29 | 97.8 | 100.850556177433 | -3.05055617743273 |
30 | 104.4 | 111.801453637188 | -7.40145363718759 |
31 | 75 | 71.7925614075069 | 3.20743859249312 |
32 | 82.2 | 86.1575346256084 | -3.95753462560839 |
33 | 116.2 | 104.735732198146 | 11.4642678018542 |
34 | 115 | 109.4763579205 | 5.52364207950009 |
35 | 91.5 | 99.8000880072928 | -8.30008800729285 |
36 | 89.5 | 82.1947638097596 | 7.30523619024034 |
37 | 90.7 | 92.5713458363926 | -1.8713458363926 |
38 | 100.1 | 100.131726838023 | -0.0317268380231115 |
39 | 100.1 | 107.735537615301 | -7.63553761530083 |
40 | 93.5 | 101.481125755547 | -7.98112575554741 |
41 | 84.4 | 98.4450091542923 | -14.0450091542923 |
42 | 101.2 | 103.495238469852 | -2.29523846985191 |
43 | 75.3 | 78.3074567489307 | -3.00745674893069 |
44 | 76.5 | 84.3640503550114 | -7.8640503550114 |
45 | 105.6 | 111.165934953711 | -5.56593495371071 |
46 | 110.4 | 110.015116321209 | 0.38488367879148 |
47 | 91.5 | 99.6954549812911 | -8.19545498129113 |
48 | 88.1 | 93.4196819879849 | -5.31968198798496 |
49 | 88.2 | 94.305047550045 | -6.10504755004503 |
50 | 99.3 | 101.552281104607 | -2.25228110460682 |
51 | 117.1 | 114.797020295685 | 2.3029797043151 |
52 | 100.5 | 103.974911739159 | -3.47491173915944 |
53 | 83.9 | 97.4827903450362 | -13.5827903450361 |
54 | 110.7 | 111.045659493116 | -0.345659493115766 |
55 | 66.9 | 75.2300644163023 | -8.33006441630229 |
56 | 85.9 | 93.0973161104891 | -7.19731611048909 |
57 | 112.1 | 113.615596256881 | -1.5155962568811 |
58 | 105.5 | 108.113452649997 | -2.61345264999673 |
59 | 104 | 105.641701903909 | -1.64170190390903 |
60 | 97.8 | 97.047220955347 | 0.752779044653035 |
61 | 91.4 | 93.901501739318 | -2.50150173931804 |
62 | 104.4 | 103.550012674542 | 0.849987325457665 |
63 | 111.2 | 104.409765423231 | 6.79023457676909 |
64 | 102.3 | 112.634160275348 | -10.3341602753483 |
65 | 94.6 | 99.9281949268893 | -5.32819492688933 |
66 | 109.4 | 112.353054369902 | -2.95305436990173 |
67 | 69.1 | 72.5562049732402 | -3.45620497324025 |
68 | 86.9 | 98.1340081892487 | -11.2340081892487 |
69 | 118.3 | 115.716537638659 | 2.58346236134064 |
70 | 102.3 | 109.235078689945 | -6.93507868994548 |
71 | 108.8 | 108.614476652445 | 0.185523347554633 |
72 | 101.2 | 97.459295650619 | 3.74070434938103 |
73 | 99.1 | 93.716474133006 | 5.38352586699398 |
74 | 105.5 | 101.659750158516 | 3.84024984148379 |
75 | 119.8 | 114.881002534839 | 4.91899746516068 |
76 | 94.5 | 99.8000880072928 | -5.30008800729285 |
77 | 101.4 | 109.13118437372 | -7.73118437371954 |
78 | 116.5 | 112.637735013032 | 3.86226498696784 |
79 | 66.7 | 67.3700706836532 | -0.670070683653173 |
80 | 91.6 | 102.57287217781 | -10.9728721778096 |
81 | 119.8 | 115.621169686229 | 4.1788303137706 |
82 | 116.4 | 112.770098653946 | 3.62990134605415 |
83 | 111.7 | 111.28406645303 | 0.415933546970458 |
84 | 102.4 | 96.315593088914 | 6.084406911086 |
85 | 99.3 | 104.500137944567 | -5.20013794456694 |
86 | 109.3 | 108.610207009967 | 0.689792990032528 |
87 | 119 | 115.553560711782 | 3.44643928821777 |
88 | 102.5 | 100.546665924274 | 1.953334075726 |
89 | 104.9 | 106.30502337035 | -1.40502337035045 |
90 | 122.4 | 114.488145011844 | 7.91185498815554 |
91 | 76.4 | 79.7941914168894 | -3.39419141688939 |
92 | 103.2 | 106.696455158437 | -3.49645515843693 |
93 | 120.8 | 111.469109501252 | 9.33089049874835 |
94 | 124.9 | 120.405212263069 | 4.49478773693083 |
95 | 110.2 | 113.609892999832 | -3.4098929998321 |
96 | 99.7 | 92.4966078699871 | 7.20339213001289 |
97 | 97.1 | 112.306057418819 | -15.206057418819 |
98 | 109.3 | 115.576321737922 | -6.27632173792166 |
99 | 109.4 | 107.484288005968 | 1.91571199403191 |
100 | 117 | 123.555896026371 | -6.55589602637123 |
101 | 107.1 | 106.772610980089 | 0.327389019910907 |
102 | 118.5 | 120.049347907808 | -1.54934790780769 |
103 | 85.1 | 86.2286638149326 | -1.12866381493261 |
104 | 85.3 | 97.7788592221911 | -12.4788592221911 |
105 | 129.7 | 118.917756847993 | 10.7822431520067 |
106 | 128 | 119.397430117302 | 8.60256988269822 |
107 | 103.3 | 100.533128687474 | 2.76687131252598 |
108 | 103.9 | 93.5520585500593 | 10.3479414499407 |
109 | 96.2 | 89.8619139190058 | 6.33808608099424 |
110 | 106.3 | 105.37694625901 | 0.923053740989636 |
111 | 114.8 | 108.790277948668 | 6.00972205133195 |
112 | 101.9 | 101.849060328467 | 0.0509396715327991 |
113 | 90.9 | 97.9190622017677 | -7.01906220176768 |
114 | 108.5 | 107.991751454493 | 0.508248545507101 |
115 | 75.6 | 77.26125822127 | -1.66125822127002 |
116 | 90.6 | 92.6396805994549 | -2.03968059945489 |
117 | 121.1 | 113.076840376922 | 8.02315962307761 |
118 | 116.6 | 113.125947567297 | 3.47405243270318 |
119 | 105.7 | 100.596457619031 | 5.10354238096878 |
120 | 101.1 | 89.9216731543784 | 11.1783268456216 |
121 | 97 | 88.7025430803863 | 8.29745691961369 |
122 | 105.4 | 96.1768108027474 | 9.22318919725259 |
123 | 117.9 | 114.910895073687 | 2.98910492631299 |
124 | 104.5 | 105.294394796264 | -0.794394796263757 |
125 | 97.4 | 98.295543621893 | -0.895543621892971 |
126 | 115.8 | 113.100329712426 | 2.69967028757361 |
127 | 73.1 | 75.9140108272697 | -2.81401082726974 |
128 | 90.6 | 98.2677975650713 | -7.66779756507131 |
129 | 124.1 | 115.594826042744 | 8.50517395725617 |
130 | 110.1 | 109.86564826806 | 0.234351731940278 |
131 | 103.4 | 102.858244887571 | 0.541755112428868 |
132 | 109.4 | 86.7218718002907 | 22.6781281997093 |
133 | 92.1 | 95.8522776424031 | -3.75227764240314 |
134 | 107.8 | 114.584907815362 | -6.78490781536215 |
135 | 116.2 | 126.178504317783 | -9.97850431778322 |
136 | 97.5 | 103.304481764169 | -5.8044817641687 |
137 | 104.8 | 112.301090350797 | -7.50109035079676 |
138 | 106.2 | 111.31608215233 | -5.11608215232999 |
139 | 73.6 | 76.7808487629353 | -3.1808487629353 |
140 | 100.7 | 106.118544186808 | -5.41854418680778 |
141 | 123.4 | 120.44790080819 | 2.9520991918098 |
142 | 109.1 | 111.136021614041 | -2.03602161404062 |
143 | 100.1 | 114.105934492348 | -14.005934492348 |
144 | 105.9 | 98.0257975874002 | 7.87420241259978 |
145 | 104.8 | 101.068317391998 | 3.73168260800237 |
146 | 110.8 | 105.130702481183 | 5.66929751881682 |
147 | 118.4 | 127.516520360195 | -9.11652036019488 |
148 | 93.1 | 108.746140347065 | -15.6461403470653 |
149 | 105.4 | 109.010183124509 | -3.61018312450946 |
150 | 113.6 | 110.871281411053 | 2.728718588947 |
151 | 75 | 82.4851165087045 | -7.48511650870454 |
152 | 94 | 103.859616267748 | -9.85961626774784 |
Goldfeld-Quandt test for Heteroskedasticity | |||
p-values | Alternative Hypothesis | ||
breakpoint index | greater | 2-sided | less |
7 | 0.0820442618929551 | 0.16408852378591 | 0.917955738107045 |
8 | 0.412666985743787 | 0.825333971487574 | 0.587333014256213 |
9 | 0.339459708061187 | 0.678919416122374 | 0.660540291938813 |
10 | 0.230998369373002 | 0.461996738746004 | 0.769001630626998 |
11 | 0.154398171160195 | 0.30879634232039 | 0.845601828839805 |
12 | 0.100341439092093 | 0.200682878184185 | 0.899658560907907 |
13 | 0.0779136983364417 | 0.155827396672883 | 0.922086301663558 |
14 | 0.116616769657023 | 0.233233539314046 | 0.883383230342977 |
15 | 0.0841889929726907 | 0.168377985945381 | 0.915811007027309 |
16 | 0.0556864752214236 | 0.111372950442847 | 0.944313524778576 |
17 | 0.0436648486464139 | 0.0873296972928278 | 0.956335151353586 |
18 | 0.0418718014243214 | 0.0837436028486428 | 0.958128198575679 |
19 | 0.0412435020541831 | 0.0824870041083661 | 0.958756497945817 |
20 | 0.0315480892491857 | 0.0630961784983714 | 0.968451910750814 |
21 | 0.0258196012582443 | 0.0516392025164886 | 0.974180398741756 |
22 | 0.0300293411787511 | 0.0600586823575021 | 0.969970658821249 |
23 | 0.0276338295868386 | 0.0552676591736772 | 0.972366170413161 |
24 | 0.0340247716837248 | 0.0680495433674496 | 0.965975228316275 |
25 | 0.0286542876634252 | 0.0573085753268505 | 0.971345712336575 |
26 | 0.0212232358066106 | 0.0424464716132212 | 0.978776764193389 |
27 | 0.0200053022863499 | 0.0400106045726998 | 0.97999469771365 |
28 | 0.0206850261203344 | 0.0413700522406687 | 0.979314973879666 |
29 | 0.0331015670881829 | 0.0662031341763659 | 0.966898432911817 |
30 | 0.101455231803149 | 0.202910463606298 | 0.898544768196851 |
31 | 0.0784342006960504 | 0.156868401392101 | 0.92156579930395 |
32 | 0.0810778943107335 | 0.162155788621467 | 0.918922105689266 |
33 | 0.086264381798984 | 0.172528763597968 | 0.913735618201016 |
34 | 0.078543721288246 | 0.157087442576492 | 0.921456278711754 |
35 | 0.211091219918638 | 0.422182439837276 | 0.788908780081362 |
36 | 0.202846152268831 | 0.405692304537662 | 0.797153847731169 |
37 | 0.205957041185611 | 0.411914082371222 | 0.794042958814389 |
38 | 0.187811590935444 | 0.375623181870889 | 0.812188409064556 |
39 | 0.320334000512196 | 0.640668001024391 | 0.679665999487804 |
40 | 0.430590926781557 | 0.861181853563114 | 0.569409073218443 |
41 | 0.679221749222223 | 0.641556501555553 | 0.320778250777777 |
42 | 0.652554877258664 | 0.694890245482672 | 0.347445122741336 |
43 | 0.614141796194339 | 0.771716407611321 | 0.385858203805661 |
44 | 0.624290598085964 | 0.751418803828073 | 0.375709401914036 |
45 | 0.634128505136005 | 0.73174298972799 | 0.365871494863995 |
46 | 0.587043258820451 | 0.825913482359099 | 0.412956741179549 |
47 | 0.624529461001763 | 0.750941077996473 | 0.375470538998237 |
48 | 0.604122749540031 | 0.791754500919937 | 0.395877250459969 |
49 | 0.591940117653428 | 0.816119764693143 | 0.408059882346571 |
50 | 0.55322132882589 | 0.89355734234822 | 0.44677867117411 |
51 | 0.509081861144911 | 0.981836277710177 | 0.490918138855088 |
52 | 0.473348169198512 | 0.946696338397024 | 0.526651830801488 |
53 | 0.613937057689491 | 0.772125884621018 | 0.386062942310509 |
54 | 0.565666512000626 | 0.868666975998748 | 0.434333487999374 |
55 | 0.566077495514428 | 0.867845008971144 | 0.433922504485572 |
56 | 0.561284869406256 | 0.877430261187488 | 0.438715130593744 |
57 | 0.516118228201722 | 0.967763543596555 | 0.483881771798278 |
58 | 0.471269432352309 | 0.942538864704619 | 0.528730567647691 |
59 | 0.425678994459365 | 0.851357988918729 | 0.574321005540635 |
60 | 0.384393901559848 | 0.768787803119695 | 0.615606098440152 |
61 | 0.340606258547955 | 0.68121251709591 | 0.659393741452045 |
62 | 0.303957269419491 | 0.607914538838982 | 0.696042730580509 |
63 | 0.319017734302912 | 0.638035468605824 | 0.680982265697088 |
64 | 0.378761980508665 | 0.757523961017329 | 0.621238019491336 |
65 | 0.354568433915263 | 0.709136867830526 | 0.645431566084737 |
66 | 0.317342556059759 | 0.634685112119519 | 0.682657443940241 |
67 | 0.284425379170435 | 0.568850758340871 | 0.715574620829565 |
68 | 0.350103352170636 | 0.700206704341273 | 0.649896647829364 |
69 | 0.315618831763818 | 0.631237663527636 | 0.684381168236182 |
70 | 0.312054268228586 | 0.624108536457173 | 0.687945731771414 |
71 | 0.272042708456164 | 0.544085416912329 | 0.727957291543836 |
72 | 0.253092006276394 | 0.506184012552788 | 0.746907993723606 |
73 | 0.248280064839124 | 0.496560129678248 | 0.751719935160876 |
74 | 0.228483791633755 | 0.45696758326751 | 0.771516208366245 |
75 | 0.213560653055927 | 0.427121306111855 | 0.786439346944073 |
76 | 0.196226807160527 | 0.392453614321053 | 0.803773192839473 |
77 | 0.203808006036618 | 0.407616012073236 | 0.796191993963382 |
78 | 0.183020948756222 | 0.366041897512444 | 0.816979051243778 |
79 | 0.167724755626648 | 0.335449511253295 | 0.832275244373352 |
80 | 0.215245135400299 | 0.430490270800598 | 0.784754864599701 |
81 | 0.195538691831829 | 0.391077383663658 | 0.804461308168171 |
82 | 0.172892722226408 | 0.345785444452815 | 0.827107277773592 |
83 | 0.144572923885175 | 0.28914584777035 | 0.855427076114825 |
84 | 0.139873076837949 | 0.279746153675898 | 0.860126923162051 |
85 | 0.12962114352408 | 0.25924228704816 | 0.87037885647592 |
86 | 0.106744891291066 | 0.213489782582133 | 0.893255108708934 |
87 | 0.0905421637177348 | 0.18108432743547 | 0.909457836282265 |
88 | 0.0739946495995343 | 0.147989299199069 | 0.926005350400466 |
89 | 0.0597605463873278 | 0.119521092774656 | 0.940239453612672 |
90 | 0.063197082542908 | 0.126394165085816 | 0.936802917457092 |
91 | 0.0581046983340513 | 0.116209396668103 | 0.941895301665949 |
92 | 0.0481461315226391 | 0.0962922630452781 | 0.951853868477361 |
93 | 0.0599791913707788 | 0.119958382741558 | 0.940020808629221 |
94 | 0.0520461694179533 | 0.104092338835907 | 0.947953830582047 |
95 | 0.0434672290262084 | 0.0869344580524167 | 0.956532770973792 |
96 | 0.04346846284436 | 0.08693692568872 | 0.95653153715564 |
97 | 0.108892851293016 | 0.217785702586033 | 0.891107148706984 |
98 | 0.103910808739806 | 0.207821617479612 | 0.896089191260194 |
99 | 0.0845262188509536 | 0.169052437701907 | 0.915473781149046 |
100 | 0.0803391841078556 | 0.160678368215711 | 0.919660815892144 |
101 | 0.0634691780405943 | 0.126938356081189 | 0.936530821959406 |
102 | 0.0498248932651873 | 0.0996497865303746 | 0.950175106734813 |
103 | 0.0412705300107904 | 0.0825410600215808 | 0.95872946998921 |
104 | 0.0718533673227125 | 0.143706734645425 | 0.928146632677288 |
105 | 0.103997532658743 | 0.207995065317486 | 0.896002467341257 |
106 | 0.128584844035052 | 0.257169688070104 | 0.871415155964948 |
107 | 0.107373229832111 | 0.214746459664222 | 0.892626770167889 |
108 | 0.135328306092056 | 0.270656612184112 | 0.864671693907944 |
109 | 0.127498417156164 | 0.254996834312328 | 0.872501582843836 |
110 | 0.109351598719327 | 0.218703197438653 | 0.890648401280673 |
111 | 0.114890688241351 | 0.229781376482701 | 0.885109311758649 |
112 | 0.0954423991849617 | 0.190884798369923 | 0.904557600815038 |
113 | 0.0864743199205911 | 0.172948639841182 | 0.913525680079409 |
114 | 0.0682397007603728 | 0.136479401520746 | 0.931760299239627 |
115 | 0.0592441298525856 | 0.118488259705171 | 0.940755870147414 |
116 | 0.0457073053197423 | 0.0914146106394847 | 0.954292694680258 |
117 | 0.0585733688025083 | 0.117146737605017 | 0.941426631197492 |
118 | 0.053656370593217 | 0.107312741186434 | 0.946343629406783 |
119 | 0.0520164853766991 | 0.104032970753398 | 0.947983514623301 |
120 | 0.0883393540536813 | 0.176678708107363 | 0.911660645946319 |
121 | 0.103796817034456 | 0.207593634068912 | 0.896203182965544 |
122 | 0.145825730481869 | 0.291651460963737 | 0.854174269518131 |
123 | 0.123314954095533 | 0.246629908191066 | 0.876685045904467 |
124 | 0.0979341518892123 | 0.195868303778425 | 0.902065848110788 |
125 | 0.0749502135043169 | 0.149900427008634 | 0.925049786495683 |
126 | 0.0583373175495089 | 0.116674635099018 | 0.941662682450491 |
127 | 0.055930576952556 | 0.111861153905112 | 0.944069423047444 |
128 | 0.0461733876548788 | 0.0923467753097575 | 0.953826612345121 |
129 | 0.0790493722694052 | 0.15809874453881 | 0.920950627730595 |
130 | 0.0617990609658012 | 0.123598121931602 | 0.938200939034199 |
131 | 0.0446663467202856 | 0.0893326934405712 | 0.955333653279714 |
132 | 0.405747095627429 | 0.811494191254858 | 0.594252904372571 |
133 | 0.342738913934462 | 0.685477827868924 | 0.657261086065538 |
134 | 0.28844428452596 | 0.57688856905192 | 0.71155571547404 |
135 | 0.335978048821894 | 0.671956097643789 | 0.664021951178106 |
136 | 0.29417115690069 | 0.588342313801381 | 0.70582884309931 |
137 | 0.472404057038239 | 0.944808114076477 | 0.527595942961761 |
138 | 0.42609928430735 | 0.852198568614699 | 0.57390071569265 |
139 | 0.396064805293307 | 0.792129610586614 | 0.603935194706693 |
140 | 0.33771324928459 | 0.67542649856918 | 0.66228675071541 |
141 | 0.248572772633333 | 0.497145545266665 | 0.751427227366667 |
142 | 0.169855160593073 | 0.339710321186146 | 0.830144839406927 |
143 | 0.191350538131645 | 0.382701076263289 | 0.808649461868355 |
144 | 0.1705075553406 | 0.341015110681199 | 0.8294924446594 |
145 | 0.119697753360919 | 0.239395506721839 | 0.880302246639081 |
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 | 3 | 0.0215827338129496 | OK |
10% type I error level | 21 | 0.151079136690647 | NOK |