Multiple Linear Regression - Estimated Regression Equation |
PS[t] = + 6.96722882487706 + 0.338739169615999CM[t] -0.370733791378405D[t] + 0.173454693435831PE[t] + 0.048155789305374PC[t] + 0.414415238664376O[t] + 0.0195267114176807`H `[t] -0.00254732860272504t + 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) | 6.96722882487706 | 3.106557 | 2.2427 | 0.026369 | 0.013185 |
CM | 0.338739169615999 | 0.057193 | 5.9228 | 0 | 0 |
D | -0.370733791378405 | 0.116406 | -3.1848 | 0.00176 | 0.00088 |
PE | 0.173454693435831 | 0.101683 | 1.7058 | 0.090095 | 0.045047 |
PC | 0.048155789305374 | 0.128585 | 0.3745 | 0.708553 | 0.354276 |
O | 0.414415238664376 | 0.075193 | 5.5113 | 0 | 0 |
`H ` | 0.0195267114176807 | 0.127692 | 0.1529 | 0.878666 | 0.439333 |
t | -0.00254732860272504 | 0.006168 | -0.413 | 0.680182 | 0.340091 |
Multiple Linear Regression - Regression Statistics | |
Multiple R | 0.614545793502647 |
R-squared | 0.377666532311799 |
Adjusted R-squared | 0.348816636458703 |
F-TEST (value) | 13.0907416177475 |
F-TEST (DF numerator) | 7 |
F-TEST (DF denominator) | 151 |
p-value | 4.10338429901458e-13 |
Multiple Linear Regression - Residual Statistics | |
Residual Standard Deviation | 3.4353914418521 |
Sum Squared Residuals | 1782.08906817135 |
Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
1 | 24 | 23.3600829066697 | 0.6399170933303 |
2 | 25 | 22.7568953205311 | 2.24310467946888 |
3 | 30 | 24.5395878492502 | 5.46041215074979 |
4 | 19 | 20.5497834763604 | -1.54978347636043 |
5 | 22 | 20.8261556690439 | 1.1738443309561 |
6 | 22 | 23.3158162465616 | -1.31581624656163 |
7 | 25 | 22.8098028489195 | 2.19019715108048 |
8 | 23 | 19.8000480437899 | 3.19995195621013 |
9 | 17 | 18.7822363353937 | -1.78223633539366 |
10 | 21 | 21.8089527605843 | -0.80895276058432 |
11 | 19 | 23.1167179796368 | -4.11671797963679 |
12 | 19 | 23.6592384288345 | -4.65923842883448 |
13 | 15 | 23.5393128544941 | -8.53931285449405 |
14 | 16 | 17.1894615696005 | -1.18946156960050 |
15 | 23 | 19.65484531045 | 3.34515468955 |
16 | 27 | 24.2189040611562 | 2.7810959388438 |
17 | 22 | 21.2179623331316 | 0.782037666868405 |
18 | 14 | 16.5371454664626 | -2.53714546646256 |
19 | 22 | 24.2133759326396 | -2.21337593263964 |
20 | 23 | 24.3060990583595 | -1.30609905835951 |
21 | 23 | 21.7185497794293 | 1.28145022057074 |
22 | 19 | 22.6600108417653 | -3.66001084176532 |
23 | 18 | 24.1049457209068 | -6.1049457209068 |
24 | 20 | 23.3757339063873 | -3.37573390638733 |
25 | 23 | 22.6120641857161 | 0.387935814283944 |
26 | 25 | 23.5273792219535 | 1.47262077804648 |
27 | 19 | 23.5244420640875 | -4.52444206408749 |
28 | 24 | 24.0251628809969 | -0.0251628809969272 |
29 | 22 | 21.7226683903436 | 0.277331609656368 |
30 | 26 | 23.5005109208289 | 2.49948907917106 |
31 | 29 | 22.7132200272242 | 6.28677997277577 |
32 | 32 | 25.4406249917871 | 6.5593750082129 |
33 | 25 | 21.6828813174281 | 3.31711868257193 |
34 | 29 | 24.6281494256649 | 4.37185057433512 |
35 | 28 | 25.2384561145834 | 2.7615438854166 |
36 | 17 | 17.0601380163531 | -0.0601380163531021 |
37 | 28 | 26.2958086274675 | 1.70419137253245 |
38 | 29 | 23.0745219544930 | 5.92547804550697 |
39 | 26 | 27.8691994778676 | -1.86919947786763 |
40 | 25 | 23.6672122623102 | 1.33278773768976 |
41 | 14 | 19.4606216675032 | -5.46062166750324 |
42 | 25 | 22.1422346980926 | 2.85776530190735 |
43 | 26 | 21.8303301600076 | 4.16966983999239 |
44 | 20 | 20.433957994168 | -0.433957994168018 |
45 | 18 | 21.5077925054716 | -3.50779250547162 |
46 | 32 | 24.8294310460586 | 7.17056895394144 |
47 | 25 | 25.2742828932654 | -0.274282893265404 |
48 | 25 | 21.6880724477451 | 3.31192755225495 |
49 | 23 | 20.8994902264098 | 2.10050977359018 |
50 | 21 | 22.2866056488887 | -1.28660564888866 |
51 | 20 | 24.2875172456324 | -4.28751724563239 |
52 | 15 | 16.4933916627726 | -1.49339166277261 |
53 | 30 | 27.0387539888558 | 2.96124601114416 |
54 | 24 | 25.5559440077963 | -1.55594400779633 |
55 | 26 | 24.5013376089538 | 1.49866239104625 |
56 | 24 | 21.7641370528022 | 2.23586294719776 |
57 | 22 | 21.5950979554049 | 0.404902044595074 |
58 | 14 | 15.5840538002886 | -1.58405380028861 |
59 | 24 | 22.4070382612356 | 1.59296173876444 |
60 | 24 | 22.9642324837384 | 1.03576751626160 |
61 | 24 | 23.3829572477102 | 0.617042752289785 |
62 | 24 | 20.1664929785397 | 3.83350702146025 |
63 | 19 | 18.4990860629835 | 0.500913937016457 |
64 | 31 | 26.9791594695616 | 4.02084053043840 |
65 | 22 | 26.9078641570514 | -4.90786415705139 |
66 | 27 | 21.4562164040507 | 5.54378359594928 |
67 | 19 | 17.6829076437667 | 1.31709235623332 |
68 | 25 | 22.437251747161 | 2.56274825283898 |
69 | 20 | 25.1583990491765 | -5.15839904917651 |
70 | 21 | 21.6109898495906 | -0.610989849590591 |
71 | 27 | 27.7343855534004 | -0.734385553400403 |
72 | 23 | 24.5225995384187 | -1.52259953841868 |
73 | 25 | 25.7763981883151 | -0.776398188315096 |
74 | 20 | 22.3637662373848 | -2.36376623738476 |
75 | 22 | 22.482950321875 | -0.482950321874988 |
76 | 23 | 23.1330262843134 | -0.133026284313445 |
77 | 25 | 24.0144309704262 | 0.98556902957381 |
78 | 25 | 23.5292659044047 | 1.47073409559533 |
79 | 17 | 24.0388904116908 | -7.03889041169081 |
80 | 19 | 21.4002460073737 | -2.40024600737372 |
81 | 25 | 24.085034368004 | 0.914965631995982 |
82 | 19 | 22.3524440420347 | -3.35244404203470 |
83 | 20 | 23.1424834269455 | -3.14248342694555 |
84 | 26 | 22.5861382667667 | 3.41386173323331 |
85 | 23 | 20.9378549293207 | 2.06214507067932 |
86 | 27 | 24.5849617506268 | 2.41503824937321 |
87 | 17 | 20.8884850749446 | -3.88848507494460 |
88 | 17 | 23.4710677945635 | -6.47106779456346 |
89 | 17 | 19.6695405130879 | -2.66954051308790 |
90 | 22 | 21.9548536503222 | 0.0451463496778307 |
91 | 21 | 23.7260603697963 | -2.72606036979633 |
92 | 32 | 28.8536192709296 | 3.14638072907044 |
93 | 21 | 24.8145503105897 | -3.81455031058973 |
94 | 21 | 24.3882977810568 | -3.38829778105680 |
95 | 18 | 21.1802601032482 | -3.18026010324816 |
96 | 18 | 21.1964497861098 | -3.19644978610981 |
97 | 23 | 22.8827999156050 | 0.117200084395035 |
98 | 19 | 20.5695533666805 | -1.56955336668047 |
99 | 20 | 20.8539641213514 | -0.853964121351367 |
100 | 21 | 22.395925037391 | -1.39592503739102 |
101 | 20 | 24.0307052826698 | -4.03070528266981 |
102 | 17 | 18.5849371598002 | -1.58493715980023 |
103 | 18 | 20.2816301091783 | -2.28163010917832 |
104 | 19 | 20.7410407575224 | -1.74104075752237 |
105 | 22 | 22.1051202498069 | -0.105120249806918 |
106 | 15 | 18.6315165374418 | -3.63151653744184 |
107 | 14 | 18.7567940134575 | -4.75679401345753 |
108 | 18 | 26.8029547198515 | -8.8029547198515 |
109 | 24 | 21.4701801830877 | 2.52981981691228 |
110 | 35 | 23.5697499835098 | 11.4302500164902 |
111 | 29 | 19.2114740958044 | 9.7885259041956 |
112 | 21 | 21.8313873417681 | -0.831387341768137 |
113 | 20 | 18.3766920537217 | 1.62330794627827 |
114 | 22 | 23.1900750069294 | -1.19007500692941 |
115 | 13 | 16.6510839127491 | -3.65108391274912 |
116 | 26 | 23.2144181423986 | 2.78558185760142 |
117 | 17 | 16.6755593840826 | 0.324440615917431 |
118 | 25 | 19.9753954526882 | 5.02460454731181 |
119 | 20 | 20.7622584686874 | -0.762258468687355 |
120 | 19 | 18.0414007867671 | 0.958599213232875 |
121 | 21 | 22.4946143030851 | -1.49461430308515 |
122 | 22 | 20.9767618621827 | 1.02323813781726 |
123 | 24 | 22.7115639126755 | 1.28843608732448 |
124 | 21 | 22.9512651944144 | -1.95126519441439 |
125 | 26 | 25.5834618476785 | 0.416538152321532 |
126 | 24 | 20.5184016887368 | 3.48159831126324 |
127 | 16 | 20.1892640026714 | -4.18926400267138 |
128 | 23 | 22.2991366870723 | 0.700863312927737 |
129 | 18 | 20.6121662423911 | -2.61216624239106 |
130 | 16 | 22.3138878394759 | -6.31388783947587 |
131 | 26 | 23.9233154494156 | 2.07668455058441 |
132 | 19 | 18.8408170046833 | 0.159182995316669 |
133 | 21 | 16.6260188581603 | 4.37398114183967 |
134 | 21 | 22.1723071687452 | -1.17230716874521 |
135 | 22 | 18.4336193177372 | 3.56638068226279 |
136 | 23 | 19.6819025013261 | 3.31809749867393 |
137 | 29 | 24.8445553261332 | 4.1554446738668 |
138 | 21 | 19.0206123985753 | 1.9793876014247 |
139 | 21 | 19.7228070602223 | 1.27719293977767 |
140 | 23 | 21.793065487162 | 1.20693451283801 |
141 | 27 | 22.9160268001213 | 4.08397319987874 |
142 | 25 | 25.2796869741909 | -0.279686974190913 |
143 | 21 | 20.8674377020862 | 0.132562297913804 |
144 | 10 | 16.8397398735801 | -6.83973987358006 |
145 | 20 | 22.5558599122971 | -2.55585991229709 |
146 | 26 | 22.6045122006451 | 3.39548779935495 |
147 | 24 | 23.5841688389319 | 0.415831161068146 |
148 | 29 | 31.6943493231591 | -2.69434932315913 |
149 | 19 | 18.7060451628066 | 0.293954837193363 |
150 | 24 | 21.9386390844474 | 2.06136091555264 |
151 | 19 | 20.485430266394 | -1.48543026639402 |
152 | 24 | 23.3675194658252 | 0.632480534174842 |
153 | 22 | 21.6840974973478 | 0.315902502652156 |
154 | 17 | 23.7914510648184 | -6.7914510648184 |
155 | 24 | 22.9677943018502 | 1.03220569814981 |
156 | 25 | 22.3646067157115 | 2.63539328428855 |
157 | 30 | 24.1472992444305 | 5.85270075556945 |
158 | 19 | 20.1574948715408 | -1.15749487154078 |
159 | 22 | 20.4338670642242 | 1.56613293577575 |
Goldfeld-Quandt test for Heteroskedasticity | |||
p-values | Alternative Hypothesis | ||
breakpoint index | greater | 2-sided | less |
11 | 0.421146350042458 | 0.842292700084915 | 0.578853649957543 |
12 | 0.295393138892056 | 0.590786277784113 | 0.704606861107944 |
13 | 0.225860318043728 | 0.451720636087456 | 0.774139681956272 |
14 | 0.205436981507734 | 0.410873963015468 | 0.794563018492266 |
15 | 0.340962780348358 | 0.681925560696716 | 0.659037219651642 |
16 | 0.320482413861828 | 0.640964827723657 | 0.679517586138171 |
17 | 0.486097858965602 | 0.972195717931203 | 0.513902141034398 |
18 | 0.394749320578378 | 0.789498641156757 | 0.605250679421622 |
19 | 0.313747794781716 | 0.627495589563432 | 0.686252205218284 |
20 | 0.298788533982462 | 0.597577067964924 | 0.701211466017538 |
21 | 0.39711395930483 | 0.79422791860966 | 0.60288604069517 |
22 | 0.331106194863779 | 0.662212389727558 | 0.668893805136221 |
23 | 0.363088305040966 | 0.726176610081933 | 0.636911694959034 |
24 | 0.317283364123517 | 0.634566728247035 | 0.682716635876483 |
25 | 0.264923137368998 | 0.529846274737996 | 0.735076862631002 |
26 | 0.210987285544443 | 0.421974571088885 | 0.789012714455557 |
27 | 0.180463264630792 | 0.360926529261584 | 0.819536735369208 |
28 | 0.156733072571073 | 0.313466145142147 | 0.843266927428927 |
29 | 0.118860350394266 | 0.237720700788533 | 0.881139649605734 |
30 | 0.135720868931431 | 0.271441737862862 | 0.864279131068569 |
31 | 0.307043266187303 | 0.614086532374606 | 0.692956733812697 |
32 | 0.579580582283763 | 0.840838835432473 | 0.420419417716237 |
33 | 0.540862786469022 | 0.918274427061956 | 0.459137213530978 |
34 | 0.546668381628682 | 0.906663236742636 | 0.453331618371318 |
35 | 0.499756390346927 | 0.999512780693855 | 0.500243609653073 |
36 | 0.516992028848683 | 0.966015942302634 | 0.483007971151317 |
37 | 0.480865569466204 | 0.961731138932408 | 0.519134430533796 |
38 | 0.543130356129887 | 0.913739287740226 | 0.456869643870113 |
39 | 0.598670958322274 | 0.802658083355452 | 0.401329041677726 |
40 | 0.545451377188666 | 0.909097245622667 | 0.454548622811334 |
41 | 0.607236772453054 | 0.785526455093892 | 0.392763227546946 |
42 | 0.57265822216421 | 0.85468355567158 | 0.42734177783579 |
43 | 0.56872346802615 | 0.8625530639477 | 0.43127653197385 |
44 | 0.538472712743044 | 0.923054574513912 | 0.461527287256956 |
45 | 0.539398182562411 | 0.921203634875177 | 0.460601817437589 |
46 | 0.639536237547459 | 0.720927524905083 | 0.360463762452541 |
47 | 0.622799660682211 | 0.754400678635578 | 0.377200339317789 |
48 | 0.605645706147193 | 0.788708587705614 | 0.394354293852807 |
49 | 0.563511641985517 | 0.872976716028967 | 0.436488358014483 |
50 | 0.530944543431120 | 0.93811091313776 | 0.46905545656888 |
51 | 0.604229408324064 | 0.791541183351872 | 0.395770591675936 |
52 | 0.56694348011788 | 0.86611303976424 | 0.43305651988212 |
53 | 0.607906669687226 | 0.784186660625548 | 0.392093330312774 |
54 | 0.582268362204929 | 0.835463275590141 | 0.417731637795071 |
55 | 0.539110909374918 | 0.921778181250163 | 0.460889090625082 |
56 | 0.507567995615684 | 0.984864008768631 | 0.492432004384316 |
57 | 0.458760197252434 | 0.917520394504867 | 0.541239802747566 |
58 | 0.420459780269622 | 0.840919560539244 | 0.579540219730378 |
59 | 0.383570965101833 | 0.767141930203666 | 0.616429034898167 |
60 | 0.343540995370397 | 0.687081990740794 | 0.656459004629603 |
61 | 0.301215273961807 | 0.602430547923614 | 0.698784726038193 |
62 | 0.313398097265309 | 0.626796194530619 | 0.686601902734691 |
63 | 0.278419004074647 | 0.556838008149294 | 0.721580995925353 |
64 | 0.282885927504942 | 0.565771855009884 | 0.717114072495058 |
65 | 0.389109909231050 | 0.778219818462101 | 0.610890090768950 |
66 | 0.48120580502645 | 0.9624116100529 | 0.51879419497355 |
67 | 0.447292343030426 | 0.894584686060853 | 0.552707656969574 |
68 | 0.432427489975911 | 0.864854979951822 | 0.567572510024089 |
69 | 0.519696187875784 | 0.960607624248433 | 0.480303812124216 |
70 | 0.475411471183907 | 0.950822942367815 | 0.524588528816093 |
71 | 0.438655174228514 | 0.877310348457028 | 0.561344825771486 |
72 | 0.408198960760971 | 0.816397921521943 | 0.591801039239029 |
73 | 0.377419684136791 | 0.754839368273582 | 0.622580315863209 |
74 | 0.350308189929836 | 0.700616379859673 | 0.649691810070164 |
75 | 0.309599783942413 | 0.619199567884827 | 0.690400216057587 |
76 | 0.271429423838847 | 0.542858847677694 | 0.728570576161153 |
77 | 0.246968209176075 | 0.49393641835215 | 0.753031790823925 |
78 | 0.226404816809047 | 0.452809633618093 | 0.773595183190953 |
79 | 0.328189711110747 | 0.656379422221494 | 0.671810288889253 |
80 | 0.297592619014268 | 0.595185238028536 | 0.702407380985732 |
81 | 0.267302330728723 | 0.534604661457445 | 0.732697669271277 |
82 | 0.255787399255827 | 0.511574798511653 | 0.744212600744173 |
83 | 0.243580420587619 | 0.487160841175239 | 0.75641957941238 |
84 | 0.263906824767243 | 0.527813649534486 | 0.736093175232757 |
85 | 0.254973348887600 | 0.509946697775201 | 0.7450266511124 |
86 | 0.254562874707113 | 0.509125749414226 | 0.745437125292887 |
87 | 0.246497125758044 | 0.492994251516088 | 0.753502874241956 |
88 | 0.320202052190444 | 0.640404104380888 | 0.679797947809556 |
89 | 0.288355514860942 | 0.576711029721884 | 0.711644485139058 |
90 | 0.255484079708122 | 0.510968159416243 | 0.744515920291878 |
91 | 0.229815081047294 | 0.459630162094588 | 0.770184918952706 |
92 | 0.247007679096849 | 0.494015358193698 | 0.752992320903151 |
93 | 0.235749236100587 | 0.471498472201174 | 0.764250763899413 |
94 | 0.214642500705125 | 0.42928500141025 | 0.785357499294875 |
95 | 0.192504816899054 | 0.385009633798109 | 0.807495183100946 |
96 | 0.173170305306774 | 0.346340610613549 | 0.826829694693226 |
97 | 0.146938903046447 | 0.293877806092894 | 0.853061096953553 |
98 | 0.121406558941832 | 0.242813117883664 | 0.878593441058168 |
99 | 0.098807662794169 | 0.197615325588338 | 0.90119233720583 |
100 | 0.0798317917117787 | 0.159663583423557 | 0.920168208288221 |
101 | 0.080994253781883 | 0.161988507563766 | 0.919005746218117 |
102 | 0.0644416655442469 | 0.128883331088494 | 0.935558334455753 |
103 | 0.0547264281508925 | 0.109452856301785 | 0.945273571849108 |
104 | 0.0467699720392488 | 0.0935399440784976 | 0.953230027960751 |
105 | 0.0368775495268784 | 0.0737550990537567 | 0.963122450473122 |
106 | 0.0346701229874316 | 0.0693402459748633 | 0.965329877012568 |
107 | 0.0443808027390602 | 0.0887616054781203 | 0.95561919726094 |
108 | 0.230469097454290 | 0.460938194908580 | 0.76953090254571 |
109 | 0.239402047361746 | 0.478804094723493 | 0.760597952638254 |
110 | 0.646307414314944 | 0.707385171370112 | 0.353692585685056 |
111 | 0.884187389093037 | 0.231625221813926 | 0.115812610906963 |
112 | 0.855728278249613 | 0.288543443500775 | 0.144271721750387 |
113 | 0.83080921614876 | 0.338381567702479 | 0.169190783851240 |
114 | 0.80024093637436 | 0.39951812725128 | 0.19975906362564 |
115 | 0.828529488635187 | 0.342941022729626 | 0.171470511364813 |
116 | 0.808526422949083 | 0.382947154101835 | 0.191473577050918 |
117 | 0.769899402415356 | 0.460201195169288 | 0.230100597584644 |
118 | 0.819902891773485 | 0.360194216453029 | 0.180097108226515 |
119 | 0.780671272713017 | 0.438657454573967 | 0.219328727286983 |
120 | 0.741672920352702 | 0.516654159294595 | 0.258327079647298 |
121 | 0.697287739875408 | 0.605424520249184 | 0.302712260124592 |
122 | 0.64657485499902 | 0.706850290001961 | 0.353425145000980 |
123 | 0.596467327486696 | 0.807065345026609 | 0.403532672513304 |
124 | 0.547679472659693 | 0.904641054680614 | 0.452320527340307 |
125 | 0.489880368107411 | 0.979760736214821 | 0.510119631892589 |
126 | 0.489690975739743 | 0.979381951479486 | 0.510309024260257 |
127 | 0.522494103228841 | 0.955011793542318 | 0.477505896771159 |
128 | 0.4588394063328 | 0.9176788126656 | 0.5411605936672 |
129 | 0.421374640504679 | 0.842749281009358 | 0.578625359495321 |
130 | 0.675995728072305 | 0.64800854385539 | 0.324004271927695 |
131 | 0.62536132496651 | 0.749277350066981 | 0.374638675033490 |
132 | 0.585362152162429 | 0.829275695675141 | 0.414637847837571 |
133 | 0.567074606788364 | 0.865850786423272 | 0.432925393211636 |
134 | 0.634671445341941 | 0.730657109316118 | 0.365328554658059 |
135 | 0.579697889559414 | 0.840604220881171 | 0.420302110440586 |
136 | 0.554960304679724 | 0.890079390640552 | 0.445039695320276 |
137 | 0.52795320090575 | 0.9440935981885 | 0.47204679909425 |
138 | 0.757730231129452 | 0.484539537741095 | 0.242269768870548 |
139 | 0.683885079907542 | 0.632229840184915 | 0.316114920092458 |
140 | 0.60493691427425 | 0.7901261714515 | 0.39506308572575 |
141 | 0.65930375533992 | 0.681392489320159 | 0.340696244660080 |
142 | 0.663954574708272 | 0.672090850583456 | 0.336045425291728 |
143 | 0.563430695215875 | 0.87313860956825 | 0.436569304784125 |
144 | 0.671504060067124 | 0.656991879865751 | 0.328495939932876 |
145 | 0.680080703079928 | 0.639838593840143 | 0.319919296920072 |
146 | 0.877286159321744 | 0.245427681356513 | 0.122713840678256 |
147 | 0.840559488182601 | 0.318881023634798 | 0.159440511817399 |
148 | 0.756735015975613 | 0.486529968048773 | 0.243264984024387 |
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 | 4 | 0.0289855072463768 | OK |