Multiple Linear Regression - Estimated Regression Equation |
i[t] = -84.0731978333051 -0.0541036915164171w[t] + 2.04918398266427f[t] + 0.320926779095698s[t] + 0.0764278391768203c[t] + 0.00107723090722604b[t] + 7.41164214900091e-05h[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) | -84.0731978333051 | 10.847935 | -7.7502 | 0 | 0 |
w | -0.0541036915164171 | 0.008085 | -6.6916 | 0 | 0 |
f | 2.04918398266427 | 0.188384 | 10.8777 | 0 | 0 |
s | 0.320926779095698 | 0.122378 | 2.6224 | 0.009727 | 0.004863 |
c | 0.0764278391768203 | 0.139559 | 0.5476 | 0.584837 | 0.292418 |
b | 0.00107723090722604 | 0.00023 | 4.6906 | 7e-06 | 3e-06 |
h | 7.41164214900091e-05 | 0.000509 | 0.1456 | 0.884442 | 0.442221 |
Multiple Linear Regression - Regression Statistics | |
Multiple R | 0.865040444862777 |
R-squared | 0.748294971248391 |
Adjusted R-squared | 0.737190337626996 |
F-TEST (value) | 67.3858316051691 |
F-TEST (DF numerator) | 6 |
F-TEST (DF denominator) | 136 |
p-value | 0 |
Multiple Linear Regression - Residual Statistics | |
Residual Standard Deviation | 3.84278730448689 |
Sum Squared Residuals | 2008.31394038349 |
Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
1 | 14 | 8.47080048063266 | 5.52919951936734 |
2 | 14 | 8.92758634403241 | 5.07241365596759 |
3 | 15 | 9.69923377043439 | 5.30076622956561 |
4 | 13 | 9.01366639041246 | 3.98633360958754 |
5 | 8 | 10.0467669297353 | -2.04676692973535 |
6 | 7 | 6.37594629508048 | 0.624053704919523 |
7 | 3 | 3.61910451251079 | -0.619104512510785 |
8 | 3 | 0.177226225666602 | 2.8227737743334 |
9 | 4 | 2.32640437418886 | 1.67359562581114 |
10 | 4 | 5.83965205394121 | -1.83965205394121 |
11 | 0 | -1.14615542297038 | 1.14615542297038 |
12 | -4 | -5.14651466472646 | 1.14651466472646 |
13 | -14 | -13.5805941047635 | -0.419405895236472 |
14 | -18 | -10.7123598358821 | -7.2876401641179 |
15 | -8 | -9.36567205233476 | 1.36567205233476 |
16 | -1 | 0.311830639634532 | -1.31183063963453 |
17 | 1 | 3.48499450294894 | -2.48499450294894 |
18 | 2 | 1.52961850276615 | 0.470381497233852 |
19 | 0 | 0.462376594402993 | -0.462376594402993 |
20 | 1 | 0.217489342740743 | 0.782510657259257 |
21 | 0 | -0.77836452757882 | 0.77836452757882 |
22 | -1 | 4.08898518013437 | -5.08898518013437 |
23 | -3 | -5.2669672439582 | 2.2669672439582 |
24 | -3 | -5.90181066693502 | 2.90181066693502 |
25 | -3 | -5.06380593282068 | 2.06380593282068 |
26 | -4 | -7.58693802944875 | 3.58693802944875 |
27 | -8 | -7.46347520539161 | -0.536524794608393 |
28 | -9 | -5.46866249163329 | -3.53133750836671 |
29 | -13 | -13.1258619400512 | 0.125861940051202 |
30 | -18 | -19.0088157013959 | 1.00881570139586 |
31 | -11 | -10.0417192423105 | -0.958280757689514 |
32 | -9 | -8.61735928754664 | -0.38264071245336 |
33 | -10 | -9.55116172565187 | -0.44883827434813 |
34 | -13 | -11.8158017093635 | -1.18419829063653 |
35 | -11 | -16.8943949431163 | 5.89439494311627 |
36 | -5 | -9.93708860067008 | 4.93708860067008 |
37 | -15 | -13.2188075766277 | -1.78119242337228 |
38 | -6 | -7.47444859204463 | 1.47444859204463 |
39 | -6 | -5.46271734380575 | -0.537282656194248 |
40 | -3 | -4.76181320568204 | 1.76181320568204 |
41 | -1 | -3.38785585755192 | 2.38785585755192 |
42 | -3 | -4.27735896272192 | 1.27735896272192 |
43 | -4 | -2.40489980525548 | -1.59510019474452 |
44 | -6 | -4.13514786366207 | -1.86485213633793 |
45 | 0 | -0.804396154766398 | 0.804396154766398 |
46 | -4 | -3.03288476382807 | -0.967115236171931 |
47 | -2 | -3.7558614535465 | 1.7558614535465 |
48 | -2 | -5.67243642601728 | 3.67243642601728 |
49 | -6 | -1.57740860532381 | -4.42259139467619 |
50 | -7 | -8.28797177864238 | 1.28797177864238 |
51 | -6 | -4.43172511450308 | -1.56827488549692 |
52 | -6 | -2.62253191097893 | -3.37746808902107 |
53 | -3 | -0.647518338537184 | -2.35248166146282 |
54 | -2 | -3.48640858908786 | 1.48640858908786 |
55 | -5 | -7.01492314091372 | 2.01492314091372 |
56 | -11 | -10.0884828658382 | -0.911517134161775 |
57 | -11 | -7.05531662918239 | -3.94468337081761 |
58 | -11 | -7.16157336818934 | -3.83842663181066 |
59 | -10 | -12.3345942854641 | 2.33459428546406 |
60 | -14 | -18.3261284174035 | 4.32612841740353 |
61 | -8 | -8.78290216109875 | 0.782902161098753 |
62 | -9 | -8.96654656693183 | -0.0334534330681684 |
63 | -5 | -3.19944405593501 | -1.80055594406499 |
64 | -1 | 0.065773067508206 | -1.06577306750821 |
65 | -2 | -0.787952459527467 | -1.21204754047253 |
66 | -5 | -2.99726286484738 | -2.00273713515262 |
67 | -4 | -1.36045137748009 | -2.63954862251991 |
68 | -6 | -6.02222911347798 | 0.0222291134779818 |
69 | -2 | -0.575800416796943 | -1.42419958320306 |
70 | -2 | -0.589987516375699 | -1.4100124836243 |
71 | -2 | -4.09819273549509 | 2.09819273549509 |
72 | -2 | -8.10256924072034 | 6.10256924072034 |
73 | 2 | -0.606519447014608 | 2.60651944701461 |
74 | 1 | -0.469113459195329 | 1.46911345919533 |
75 | -8 | -2.14213168359047 | -5.85786831640953 |
76 | -1 | 2.5601490737742 | -3.5601490737742 |
77 | 1 | 1.7892852108143 | -0.7892852108143 |
78 | -1 | 0.0764891463011801 | -1.07648914630118 |
79 | 2 | 1.71035156708909 | 0.289648432910911 |
80 | 2 | 4.57857861500768 | -2.57857861500768 |
81 | 1 | 2.75008816724462 | -1.75008816724462 |
82 | -1 | 0.524229823972655 | -1.52422982397266 |
83 | -2 | -4.47475146849554 | 2.47475146849554 |
84 | -2 | -2.93851703897486 | 0.938517038974855 |
85 | -1 | -3.0429880640968 | 2.0429880640968 |
86 | -8 | -10.9267307693712 | 2.92673076937123 |
87 | -4 | -7.04307925131394 | 3.04307925131394 |
88 | -6 | -11.9127845528597 | 5.91278455285972 |
89 | -3 | -5.94843527533398 | 2.94843527533398 |
90 | -3 | -11.6180860354547 | 8.61808603545474 |
91 | -7 | -11.0794528839099 | 4.07945288390992 |
92 | -9 | -9.20047240968194 | 0.20047240968194 |
93 | -11 | -16.8506321812825 | 5.85063218128254 |
94 | -13 | -12.716763704099 | -0.283236295900996 |
95 | -11 | -11.7057299070294 | 0.705729907029424 |
96 | -9 | -5.61472512636117 | -3.38527487363883 |
97 | -17 | -17.3644313824676 | 0.364431382467596 |
98 | -22 | -15.7458478071383 | -6.25415219286171 |
99 | -25 | -17.5898217921382 | -7.41017820786181 |
100 | -20 | -10.0712366925351 | -9.92876330746487 |
101 | -24 | -13.4758075524005 | -10.5241924475995 |
102 | -24 | -18.2427851136007 | -5.75721488639928 |
103 | -22 | -15.1280414302386 | -6.8719585697614 |
104 | -19 | -10.4664740963955 | -8.53352590360452 |
105 | -18 | -8.1463550807264 | -9.8536449192736 |
106 | -17 | -15.3064374581534 | -1.6935625418466 |
107 | -11 | -10.8958867691393 | -0.104113230860703 |
108 | -11 | -11.0758505477448 | 0.0758505477448361 |
109 | -12 | -5.18586696895028 | -6.81413303104972 |
110 | -10 | -5.15580211789459 | -4.84419788210541 |
111 | -15 | -8.65941515084279 | -6.34058484915721 |
112 | -15 | -8.04450162759061 | -6.95549837240939 |
113 | -15 | -10.7670032983128 | -4.23299670168717 |
114 | -13 | -6.0079680021063 | -6.9920319978937 |
115 | -8 | -6.81836056716142 | -1.18163943283858 |
116 | -13 | -11.6923215495444 | -1.30767845045562 |
117 | -9 | -5.75357185174232 | -3.24642814825768 |
118 | -7 | -9.34959365347747 | 2.34959365347747 |
119 | -4 | -9.28268621346491 | 5.28268621346491 |
120 | -4 | -9.01532940908673 | 5.01532940908673 |
121 | -2 | -2.50837938263743 | 0.508379382637432 |
122 | 0 | -3.72848718750272 | 3.72848718750272 |
123 | -2 | -7.01905309212264 | 5.01905309212264 |
124 | -3 | -6.7636448479557 | 3.7636448479557 |
125 | 1 | -0.617868629131816 | 1.61786862913182 |
126 | -2 | -11.6747558203145 | 9.67475582031451 |
127 | -1 | -6.32447117836902 | 5.32447117836902 |
128 | 1 | -3.81149035712205 | 4.81149035712205 |
129 | -3 | -6.98897923680259 | 3.98897923680259 |
130 | -4 | -10.1332189803902 | 6.13321898039024 |
131 | -9 | -11.956462769946 | 2.95646276994597 |
132 | -9 | -9.76961678273619 | 0.769616782736188 |
133 | -7 | -4.30931707871153 | -2.69068292128847 |
134 | -14 | -10.3275014984174 | -3.67249850158259 |
135 | -12 | -17.3360674346795 | 5.33606743467947 |
136 | -16 | -18.5191067505051 | 2.5191067505051 |
137 | -20 | -20.1374007694266 | 0.13740076942665 |
138 | -12 | -16.165729457326 | 4.16572945732599 |
139 | -12 | -13.1670149900208 | 1.16701499002082 |
140 | -10 | -11.3389955142556 | 1.33899551425563 |
141 | -10 | -7.1123090117547 | -2.8876909882453 |
142 | -13 | -11.8036443271922 | -1.19635567280779 |
143 | -16 | -16.2207294359258 | 0.220729435925833 |
Goldfeld-Quandt test for Heteroskedasticity | |||
p-values | Alternative Hypothesis | ||
breakpoint index | greater | 2-sided | less |
10 | 0.110655678946208 | 0.221311357892415 | 0.889344321053792 |
11 | 0.0535156150978646 | 0.107031230195729 | 0.946484384902135 |
12 | 0.0430459103255239 | 0.0860918206510477 | 0.956954089674476 |
13 | 0.112647052078738 | 0.225294104157477 | 0.887352947921262 |
14 | 0.446999820729367 | 0.893999641458733 | 0.553000179270633 |
15 | 0.365919671113597 | 0.731839342227194 | 0.634080328886403 |
16 | 0.317334479081425 | 0.63466895816285 | 0.682665520918575 |
17 | 0.279549589438369 | 0.559099178876738 | 0.720450410561631 |
18 | 0.210675955235049 | 0.421351910470098 | 0.789324044764951 |
19 | 0.176275575869785 | 0.35255115173957 | 0.823724424130215 |
20 | 0.150005087385452 | 0.300010174770904 | 0.849994912614548 |
21 | 0.121011700821828 | 0.242023401643656 | 0.878988299178172 |
22 | 0.0956656616199818 | 0.191331323239964 | 0.904334338380018 |
23 | 0.09346979174588 | 0.18693958349176 | 0.90653020825412 |
24 | 0.0953616835325865 | 0.190723367065173 | 0.904638316467414 |
25 | 0.0757631445894694 | 0.151526289178939 | 0.924236855410531 |
26 | 0.0698272795511077 | 0.139654559102215 | 0.930172720448892 |
27 | 0.0594096195303283 | 0.118819239060657 | 0.940590380469672 |
28 | 0.0464088959385104 | 0.0928177918770208 | 0.95359110406149 |
29 | 0.0359397422426379 | 0.0718794844852758 | 0.964060257757362 |
30 | 0.0290105617205811 | 0.0580211234411623 | 0.970989438279419 |
31 | 0.022229804546305 | 0.04445960909261 | 0.977770195453695 |
32 | 0.0171894540017453 | 0.0343789080034907 | 0.982810545998255 |
33 | 0.0113454851296203 | 0.0226909702592407 | 0.98865451487038 |
34 | 0.00720629583239052 | 0.014412591664781 | 0.992793704167609 |
35 | 0.0088574471972527 | 0.0177148943945054 | 0.991142552802747 |
36 | 0.00726436647294272 | 0.0145287329458854 | 0.992735633527057 |
37 | 0.0110465855319583 | 0.0220931710639166 | 0.988953414468042 |
38 | 0.00884831558214533 | 0.0176966311642907 | 0.991151684417855 |
39 | 0.0104703610303207 | 0.0209407220606413 | 0.989529638969679 |
40 | 0.00828134820392309 | 0.0165626964078462 | 0.991718651796077 |
41 | 0.00717245426434951 | 0.014344908528699 | 0.99282754573565 |
42 | 0.00630620660287696 | 0.0126124132057539 | 0.993693793397123 |
43 | 0.0050011441138625 | 0.010002288227725 | 0.994998855886137 |
44 | 0.00362802461298067 | 0.00725604922596135 | 0.996371975387019 |
45 | 0.00421426718582344 | 0.00842853437164688 | 0.995785732814177 |
46 | 0.00333342385718418 | 0.00666684771436836 | 0.996666576142816 |
47 | 0.00322786357621244 | 0.00645572715242488 | 0.996772136423788 |
48 | 0.00339438276051062 | 0.00678876552102123 | 0.996605617239489 |
49 | 0.00656782753846692 | 0.0131356550769338 | 0.993432172461533 |
50 | 0.00491100243392733 | 0.00982200486785465 | 0.995088997566073 |
51 | 0.00373172168685447 | 0.00746344337370895 | 0.996268278313146 |
52 | 0.00315858347001369 | 0.00631716694002738 | 0.996841416529986 |
53 | 0.00227013674523304 | 0.00454027349046608 | 0.997729863254767 |
54 | 0.00248863502625361 | 0.00497727005250723 | 0.997511364973746 |
55 | 0.00347367305202194 | 0.00694734610404388 | 0.996526326947978 |
56 | 0.0026574948232219 | 0.00531498964644381 | 0.997342505176778 |
57 | 0.00220137661185477 | 0.00440275322370955 | 0.997798623388145 |
58 | 0.00147428106452197 | 0.00294856212904395 | 0.998525718935478 |
59 | 0.00130695922482382 | 0.00261391844964763 | 0.998693040775176 |
60 | 0.00262506753929826 | 0.00525013507859653 | 0.997374932460702 |
61 | 0.00182526873694721 | 0.00365053747389442 | 0.998174731263053 |
62 | 0.00129999957255799 | 0.00259999914511599 | 0.998700000427442 |
63 | 0.00125285804593617 | 0.00250571609187233 | 0.998747141954064 |
64 | 0.000872626694062139 | 0.00174525338812428 | 0.999127373305938 |
65 | 0.000656026327459295 | 0.00131205265491859 | 0.999343973672541 |
66 | 0.000469959484867828 | 0.000939918969735657 | 0.999530040515132 |
67 | 0.000305819996095217 | 0.000611639992190433 | 0.999694180003905 |
68 | 0.000344056562742105 | 0.00068811312548421 | 0.999655943437258 |
69 | 0.000268011358804318 | 0.000536022717608637 | 0.999731988641196 |
70 | 0.000196902907461637 | 0.000393805814923274 | 0.999803097092538 |
71 | 0.000197047889167346 | 0.000394095778334691 | 0.999802952110833 |
72 | 0.00126460060712006 | 0.00252920121424012 | 0.99873539939288 |
73 | 0.00128257731302715 | 0.0025651546260543 | 0.998717422686973 |
74 | 0.0010914697573763 | 0.00218293951475261 | 0.998908530242624 |
75 | 0.00105560123978471 | 0.00211120247956942 | 0.998944398760215 |
76 | 0.00079505885978197 | 0.00159011771956394 | 0.999204941140218 |
77 | 0.000613562805435247 | 0.00122712561087049 | 0.999386437194565 |
78 | 0.000471155147793443 | 0.000942310295586885 | 0.999528844852207 |
79 | 0.00039397557476814 | 0.00078795114953628 | 0.999606024425232 |
80 | 0.000260586196129024 | 0.000521172392258049 | 0.999739413803871 |
81 | 0.000183477577934631 | 0.000366955155869263 | 0.999816522422065 |
82 | 0.000142629663837628 | 0.000285259327675256 | 0.999857370336162 |
83 | 0.000180873526786191 | 0.000361747053572382 | 0.999819126473214 |
84 | 0.000138564636037073 | 0.000277129272074145 | 0.999861435363963 |
85 | 0.000141261915115715 | 0.00028252383023143 | 0.999858738084884 |
86 | 0.000132648645648313 | 0.000265297291296626 | 0.999867351354352 |
87 | 0.000144682198135589 | 0.000289364396271177 | 0.999855317801864 |
88 | 0.000294008087829093 | 0.000588016175658185 | 0.999705991912171 |
89 | 0.000200784302140246 | 0.000401568604280491 | 0.99979921569786 |
90 | 0.00148656611488788 | 0.00297313222977576 | 0.998513433885112 |
91 | 0.00152198979835233 | 0.00304397959670466 | 0.998478010201648 |
92 | 0.0011188880410006 | 0.00223777608200121 | 0.998881111958999 |
93 | 0.00354615205315481 | 0.00709230410630962 | 0.996453847946845 |
94 | 0.00298947347333092 | 0.00597894694666184 | 0.997010526526669 |
95 | 0.00273136124395477 | 0.00546272248790954 | 0.997268638756045 |
96 | 0.00329465467324138 | 0.00658930934648277 | 0.996705345326759 |
97 | 0.00257063610793965 | 0.00514127221587931 | 0.99742936389206 |
98 | 0.00677821599495226 | 0.0135564319899045 | 0.993221784005048 |
99 | 0.0201352659561793 | 0.0402705319123585 | 0.979864734043821 |
100 | 0.062820958785435 | 0.12564191757087 | 0.937179041214565 |
101 | 0.192007350122476 | 0.384014700244952 | 0.807992649877524 |
102 | 0.230043530497202 | 0.460087060994404 | 0.769956469502798 |
103 | 0.214721850407298 | 0.429443700814597 | 0.785278149592702 |
104 | 0.207961095253373 | 0.415922190506745 | 0.792038904746627 |
105 | 0.219563006035974 | 0.439126012071949 | 0.780436993964026 |
106 | 0.183258111273959 | 0.366516222547917 | 0.816741888726041 |
107 | 0.229326653667353 | 0.458653307334707 | 0.770673346332647 |
108 | 0.316403079782238 | 0.632806159564476 | 0.683596920217762 |
109 | 0.297144269303175 | 0.594288538606349 | 0.702855730696825 |
110 | 0.251924206643084 | 0.503848413286168 | 0.748075793356916 |
111 | 0.231502070150351 | 0.463004140300703 | 0.768497929849649 |
112 | 0.436502502624296 | 0.873005005248593 | 0.563497497375704 |
113 | 0.460581288485142 | 0.921162576970285 | 0.539418711514858 |
114 | 0.608687554711052 | 0.782624890577897 | 0.391312445288948 |
115 | 0.570509777089325 | 0.858980445821349 | 0.429490222910675 |
116 | 0.560063257907362 | 0.879873484185275 | 0.439936742092638 |
117 | 0.713644488654047 | 0.572711022691906 | 0.286355511345953 |
118 | 0.826358906827389 | 0.347282186345221 | 0.173641093172611 |
119 | 0.816301822969827 | 0.367396354060345 | 0.183698177030173 |
120 | 0.799490559221305 | 0.40101888155739 | 0.200509440778695 |
121 | 0.768520395059016 | 0.462959209881967 | 0.231479604940984 |
122 | 0.734075087011038 | 0.531849825977924 | 0.265924912988962 |
123 | 0.708848706226928 | 0.582302587546144 | 0.291151293773072 |
124 | 0.725735882362358 | 0.548528235275284 | 0.274264117637642 |
125 | 0.728333928787653 | 0.543332142424695 | 0.271666071212347 |
126 | 0.737079280217398 | 0.525841439565203 | 0.262920719782602 |
127 | 0.734742096415945 | 0.530515807168111 | 0.265257903584055 |
128 | 0.746176930829117 | 0.507646138341765 | 0.253823069170883 |
129 | 0.824481304305479 | 0.351037391389042 | 0.175518695694521 |
130 | 0.884626241023391 | 0.230747517953217 | 0.115373758976609 |
131 | 0.80215137463198 | 0.39569725073604 | 0.19784862536802 |
132 | 0.716792454314253 | 0.566415091371494 | 0.283207545685747 |
133 | 0.793472279624471 | 0.413055440751058 | 0.206527720375529 |
Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
Description | # significant tests | % significant tests | OK/NOK |
1% type I error level | 53 | 0.42741935483871 | NOK |
5% type I error level | 69 | 0.556451612903226 | NOK |
10% type I error level | 73 | 0.588709677419355 | NOK |