Multiple Linear Regression - Estimated Regression Equation |
YT[t] = -1.97155708164814 + 0.810124516285502X1[t] + 0.251253601241107X2[t] + 0.188518804715737X3[t] + 0.566064813317673X4[t] -0.115718741599822`X5\r`[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) | -1.97155708164814 | 3.052906 | -0.6458 | 0.519378 | 0.259689 |
X1 | 0.810124516285502 | 0.130335 | 6.2157 | 0 | 0 |
X2 | 0.251253601241107 | 0.13276 | 1.8925 | 0.060307 | 0.030154 |
X3 | 0.188518804715737 | 0.168259 | 1.1204 | 0.264294 | 0.132147 |
X4 | 0.566064813317673 | 0.095813 | 5.908 | 0 | 0 |
`X5\r` | -0.115718741599822 | 0.103024 | -1.1232 | 0.263103 | 0.131551 |
Multiple Linear Regression - Regression Statistics | |
Multiple R | 0.638102890589065 |
R-squared | 0.40717529897812 |
Adjusted R-squared | 0.387801942735575 |
F-TEST (value) | 21.0172823893021 |
F-TEST (DF numerator) | 5 |
F-TEST (DF denominator) | 153 |
p-value | 5.55111512312578e-16 |
Multiple Linear Regression - Residual Statistics | |
Residual Standard Deviation | 4.47771018087769 |
Sum Squared Residuals | 3067.63293498216 |
Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
1 | 24 | 24.9730696546186 | -0.973069654618644 |
2 | 25 | 21.6968275200519 | 3.30317247994805 |
3 | 17 | 22.7576275344242 | -5.75762753442423 |
4 | 18 | 19.8643239601547 | -1.86432396015473 |
5 | 18 | 19.475921308563 | -1.47592130856298 |
6 | 16 | 19.5619453157043 | -3.56194531570428 |
7 | 20 | 20.9062047066683 | -0.906204706668275 |
8 | 16 | 22.3667061957279 | -6.36670619572788 |
9 | 18 | 22.4023995380277 | -4.40239953802769 |
10 | 17 | 20.5201335863125 | -3.52013358631251 |
11 | 23 | 22.3178193586678 | 0.682180641332218 |
12 | 30 | 22.327476885032 | 7.67252311496805 |
13 | 23 | 15.1035765940144 | 7.89642340598557 |
14 | 18 | 19.0918794530003 | -1.09187945300029 |
15 | 15 | 21.6854310399808 | -6.68543103998085 |
16 | 12 | 17.8354454157556 | -5.83544541575557 |
17 | 21 | 19.4165662795253 | 1.58343372047466 |
18 | 15 | 15.3176615872635 | -0.317661587263506 |
19 | 20 | 19.7765579973379 | 0.223442002662073 |
20 | 31 | 26.4203200936308 | 4.57967990636915 |
21 | 27 | 25.2301666514384 | 1.76983334856159 |
22 | 34 | 27.1596931008076 | 6.84030689919239 |
23 | 21 | 19.612996323041 | 1.38700367695902 |
24 | 31 | 20.9185081794081 | 10.0814918205919 |
25 | 19 | 19.2929241504289 | -0.292924150428892 |
26 | 16 | 20.2171532176049 | -4.21715321760486 |
27 | 20 | 21.5938509463785 | -1.5938509463785 |
28 | 21 | 18.2605112781375 | 2.73948872186254 |
29 | 22 | 21.960314890049 | 0.0396851099510344 |
30 | 17 | 19.5088680455431 | -2.50886804554309 |
31 | 24 | 20.3178601472182 | 3.68213985278175 |
32 | 25 | 30.4697362245754 | -5.46973622457538 |
33 | 26 | 26.7379136808267 | -0.737913680826712 |
34 | 25 | 24.0652193827093 | 0.934780617290695 |
35 | 17 | 23.0090707878074 | -6.00907078780739 |
36 | 32 | 27.7900227230014 | 4.20997727699858 |
37 | 33 | 23.6362102946555 | 9.36378970534447 |
38 | 13 | 22.0253619285962 | -9.02536192859621 |
39 | 32 | 27.8387300504054 | 4.16126994959459 |
40 | 25 | 25.8389604910979 | -0.838960491097935 |
41 | 29 | 27.024061914111 | 1.97593808588899 |
42 | 22 | 22.0238725008844 | -0.0238725008844256 |
43 | 18 | 17.3643313167998 | 0.635668683200175 |
44 | 17 | 21.7723044845037 | -4.77230448450369 |
45 | 20 | 22.2065286208074 | -2.20652862080744 |
46 | 15 | 20.4502048915139 | -5.45020489151386 |
47 | 20 | 22.1848414522041 | -2.18484145220414 |
48 | 33 | 28.0994056135831 | 4.90059438641692 |
49 | 29 | 22.142971009972 | 6.85702899002803 |
50 | 23 | 26.6826557598034 | -3.68265575980342 |
51 | 26 | 23.2430193118991 | 2.75698068810088 |
52 | 18 | 18.952868498816 | -0.952868498815959 |
53 | 20 | 18.7340532353845 | 1.2659467646155 |
54 | 11 | 11.7902591765424 | -0.790259176542405 |
55 | 28 | 28.9774711402709 | -0.977471140270937 |
56 | 26 | 23.3129672959119 | 2.68703270408813 |
57 | 22 | 22.2461608568904 | -0.24616085689036 |
58 | 17 | 20.1978454987339 | -3.19784549873386 |
59 | 12 | 15.4254660880949 | -3.42546608809486 |
60 | 14 | 21.0281654373449 | -7.02816543734494 |
61 | 17 | 20.7238630018849 | -3.72386300188489 |
62 | 21 | 21.3354034468641 | -0.335403446864113 |
63 | 19 | 22.9325499189927 | -3.93254991899267 |
64 | 18 | 23.0750654036623 | -5.0750654036623 |
65 | 10 | 17.9297721146776 | -7.92977211467762 |
66 | 29 | 24.2201359970942 | 4.77986400290577 |
67 | 31 | 18.457555194607 | 12.542444805393 |
68 | 19 | 22.9476672047626 | -3.94766720476257 |
69 | 9 | 20.0659733838091 | -11.0659733838091 |
70 | 20 | 22.4704044418167 | -2.47040444181673 |
71 | 28 | 17.6195978476967 | 10.3804021523033 |
72 | 19 | 18.1263076319767 | 0.873692368023276 |
73 | 30 | 23.0600995039614 | 6.93990049603859 |
74 | 29 | 27.134541986358 | 1.86545801364201 |
75 | 26 | 21.4781322047787 | 4.52186779522132 |
76 | 23 | 19.5440844265833 | 3.45591557341674 |
77 | 13 | 22.7619883304533 | -9.76198833045328 |
78 | 21 | 22.6403328681881 | -1.64033286818809 |
79 | 19 | 21.4342707638265 | -2.43427076382648 |
80 | 28 | 22.9430302596669 | 5.05696974033307 |
81 | 23 | 25.5488853193873 | -2.54888531938728 |
82 | 18 | 13.775544612248 | 4.22445538775199 |
83 | 21 | 20.7338035054779 | 0.266196494522131 |
84 | 20 | 21.7890552501971 | -1.78905525019705 |
85 | 23 | 19.953634409697 | 3.04636559030299 |
86 | 21 | 20.823548318318 | 0.176451681682022 |
87 | 21 | 21.7765070663015 | -0.776507066301509 |
88 | 15 | 22.8032661951564 | -7.80326619515638 |
89 | 28 | 27.147195644037 | 0.852804355963 |
90 | 19 | 17.6573711819145 | 1.3426288180855 |
91 | 26 | 21.241739029455 | 4.75826097054501 |
92 | 10 | 13.1981887926427 | -3.1981887926427 |
93 | 16 | 17.1052598018456 | -1.10525980184556 |
94 | 22 | 21.1686559891103 | 0.831344010889731 |
95 | 19 | 18.7314962822069 | 0.26850371779314 |
96 | 31 | 28.7736261084291 | 2.22637389157087 |
97 | 31 | 25.1990473784126 | 5.8009526215874 |
98 | 29 | 24.802119615067 | 4.19788038493298 |
99 | 19 | 17.4133114789467 | 1.58668852105333 |
100 | 22 | 18.8946458843887 | 3.10535411561134 |
101 | 23 | 22.3730772796911 | 0.62692272030893 |
102 | 15 | 16.1706084549776 | -1.1706084549776 |
103 | 20 | 21.4483664364161 | -1.44836643641609 |
104 | 18 | 19.5049798788849 | -1.5049798788849 |
105 | 23 | 21.9846165671171 | 1.01538343288295 |
106 | 25 | 20.9638904859829 | 4.03610951401714 |
107 | 21 | 16.5635547265782 | 4.43644527342176 |
108 | 24 | 19.4904987572516 | 4.5095012427484 |
109 | 25 | 25.2360293362311 | -0.23602933623114 |
110 | 17 | 19.5772208157054 | -2.57722081570542 |
111 | 13 | 14.5703651925901 | -1.57036519259012 |
112 | 28 | 18.2036391664048 | 9.79636083359519 |
113 | 21 | 20.1156089993067 | 0.88439100069334 |
114 | 25 | 28.140636065485 | -3.14063606548499 |
115 | 9 | 20.7272742072835 | -11.7272742072834 |
116 | 16 | 17.8284411696244 | -1.82844116962435 |
117 | 19 | 21.2002096254339 | -2.20020962543391 |
118 | 17 | 19.4548480129136 | -2.45484801291361 |
119 | 25 | 24.5118355020002 | 0.488164497999802 |
120 | 20 | 15.5584155586162 | 4.44158444138375 |
121 | 29 | 21.6245358561065 | 7.37546414389351 |
122 | 14 | 19.0460894061991 | -5.04608940619911 |
123 | 22 | 26.9144076581427 | -4.9144076581427 |
124 | 15 | 15.5764012107348 | -0.576401210734847 |
125 | 19 | 25.4228566000411 | -6.42285660004114 |
126 | 20 | 21.9451042791923 | -1.94510427919232 |
127 | 15 | 17.452226374503 | -2.45222637450297 |
128 | 20 | 21.7886208868992 | -1.78862088689923 |
129 | 18 | 20.2225815390998 | -2.22258153909977 |
130 | 33 | 25.4668428039909 | 7.5331571960091 |
131 | 22 | 23.7824344363272 | -1.78243443632724 |
132 | 16 | 16.4697006570271 | -0.46970065702706 |
133 | 17 | 19.0367506268633 | -2.03675062686334 |
134 | 16 | 15.052432261591 | 0.947567738409009 |
135 | 21 | 17.0483876901129 | 3.95161230988708 |
136 | 26 | 27.6421945331063 | -1.64219453310631 |
137 | 18 | 21.1470742942904 | -3.14707429429044 |
138 | 18 | 23.0959206112274 | -5.09592061122736 |
139 | 17 | 18.3312627872462 | -1.3312627872462 |
140 | 22 | 24.7434940752527 | -2.74349407525273 |
141 | 30 | 24.7275661238695 | 5.27243387613054 |
142 | 30 | 27.2739964505683 | 2.72600354943171 |
143 | 24 | 29.9008223341231 | -5.90082233412311 |
144 | 21 | 21.9917911761762 | -0.991791176176224 |
145 | 21 | 25.3787580941457 | -4.3787580941457 |
146 | 29 | 27.3918377820479 | 1.60816221795207 |
147 | 31 | 23.240508271007 | 7.75949172899297 |
148 | 20 | 18.9759710592584 | 1.0240289407416 |
149 | 16 | 14.1875805146353 | 1.81241948536466 |
150 | 22 | 18.9190989475258 | 3.08090105247424 |
151 | 20 | 20.3316462195076 | -0.331646219507597 |
152 | 28 | 27.3269489577319 | 0.673051042268083 |
153 | 38 | 26.5958059363835 | 11.4041940636165 |
154 | 22 | 19.3348333644292 | 2.66516663557078 |
155 | 20 | 25.6868097712468 | -5.68680977124681 |
156 | 17 | 18.0421110887897 | -1.04211108878971 |
157 | 28 | 24.4504319189554 | 3.54956808104462 |
158 | 22 | 24.1216672736301 | -2.12166727363008 |
159 | 31 | 26.0892814723567 | 4.91071852764329 |
Goldfeld-Quandt test for Heteroskedasticity | |||
p-values | Alternative Hypothesis | ||
breakpoint index | greater | 2-sided | less |
9 | 0.211396023302327 | 0.422792046604654 | 0.788603976697673 |
10 | 0.102076375342588 | 0.204152750685175 | 0.897923624657412 |
11 | 0.227238038192074 | 0.454476076384148 | 0.772761961807926 |
12 | 0.651688236191951 | 0.696623527616098 | 0.348311763808049 |
13 | 0.667307232542331 | 0.665385534915337 | 0.332692767457669 |
14 | 0.642015414981076 | 0.715969170037849 | 0.357984585018924 |
15 | 0.647421329942228 | 0.705157340115543 | 0.352578670057772 |
16 | 0.58200717018021 | 0.83598565963958 | 0.41799282981979 |
17 | 0.497441679833797 | 0.994883359667593 | 0.502558320166203 |
18 | 0.466853717517482 | 0.933707435034964 | 0.533146282482518 |
19 | 0.40318515945476 | 0.806370318909521 | 0.59681484054524 |
20 | 0.437609217255157 | 0.875218434510315 | 0.562390782744843 |
21 | 0.396901525097771 | 0.793803050195542 | 0.603098474902229 |
22 | 0.400777969653792 | 0.801555939307584 | 0.599222030346208 |
23 | 0.338769951631692 | 0.677539903263384 | 0.661230048368308 |
24 | 0.603341567728286 | 0.793316864543428 | 0.396658432271714 |
25 | 0.53355120104486 | 0.932897597910281 | 0.46644879895514 |
26 | 0.503544024150427 | 0.992911951699147 | 0.496455975849573 |
27 | 0.441730998369871 | 0.883461996739741 | 0.558269001630129 |
28 | 0.395183167548785 | 0.790366335097569 | 0.604816832451215 |
29 | 0.334977520412384 | 0.669955040824767 | 0.665022479587617 |
30 | 0.282918967778749 | 0.565837935557497 | 0.717081032221251 |
31 | 0.342901815128517 | 0.685803630257033 | 0.657098184871483 |
32 | 0.404232070072038 | 0.808464140144077 | 0.595767929927962 |
33 | 0.360398880532785 | 0.72079776106557 | 0.639601119467215 |
34 | 0.370631372835848 | 0.741262745671697 | 0.629368627164152 |
35 | 0.385307154342616 | 0.770614308685232 | 0.614692845657384 |
36 | 0.375949698359978 | 0.751899396719955 | 0.624050301640022 |
37 | 0.554989703390057 | 0.890020593219885 | 0.445010296609943 |
38 | 0.758465746223827 | 0.483068507552346 | 0.241534253776173 |
39 | 0.754517941616512 | 0.490964116766976 | 0.245482058383488 |
40 | 0.712620047429136 | 0.574759905141728 | 0.287379952570864 |
41 | 0.68761372332183 | 0.624772553356341 | 0.31238627667817 |
42 | 0.638173577653739 | 0.723652844692523 | 0.361826422346261 |
43 | 0.589575343770854 | 0.820849312458293 | 0.410424656229147 |
44 | 0.57618726679963 | 0.84762546640074 | 0.42381273320037 |
45 | 0.541737547166001 | 0.916524905667998 | 0.458262452833999 |
46 | 0.56383048884673 | 0.87233902230654 | 0.43616951115327 |
47 | 0.522810428163516 | 0.954379143672967 | 0.477189571836484 |
48 | 0.513226336040152 | 0.973547327919696 | 0.486773663959848 |
49 | 0.578119098257291 | 0.843761803485418 | 0.421880901742709 |
50 | 0.557204565171353 | 0.885590869657294 | 0.442795434828647 |
51 | 0.521832610252995 | 0.95633477949401 | 0.478167389747005 |
52 | 0.472518698692183 | 0.945037397384366 | 0.527481301307817 |
53 | 0.434388024384904 | 0.868776048769809 | 0.565611975615096 |
54 | 0.387597441853447 | 0.775194883706895 | 0.612402558146553 |
55 | 0.344799433006013 | 0.689598866012025 | 0.655200566993987 |
56 | 0.317679472653809 | 0.635358945307619 | 0.682320527346191 |
57 | 0.274752158603493 | 0.549504317206985 | 0.725247841396508 |
58 | 0.251105924453974 | 0.502211848907947 | 0.748894075546026 |
59 | 0.231434319721369 | 0.462868639442737 | 0.768565680278631 |
60 | 0.290144078219362 | 0.580288156438723 | 0.709855921780638 |
61 | 0.278497186524718 | 0.556994373049437 | 0.721502813475282 |
62 | 0.241248961424153 | 0.482497922848305 | 0.758751038575847 |
63 | 0.228675123650197 | 0.457350247300393 | 0.771324876349803 |
64 | 0.262536263897205 | 0.525072527794409 | 0.737463736102795 |
65 | 0.338838414452532 | 0.677676828905065 | 0.661161585547468 |
66 | 0.341559278538762 | 0.683118557077524 | 0.658440721461238 |
67 | 0.67452621767385 | 0.650947564652299 | 0.32547378232615 |
68 | 0.66729814767561 | 0.66540370464878 | 0.33270185232439 |
69 | 0.844206840041378 | 0.311586319917243 | 0.155793159958622 |
70 | 0.824478189179531 | 0.351043621640939 | 0.175521810820469 |
71 | 0.930528498621507 | 0.138943002756987 | 0.0694715013784933 |
72 | 0.914237531913636 | 0.171524936172728 | 0.0857624680863641 |
73 | 0.937422576584964 | 0.125154846830072 | 0.0625774234150359 |
74 | 0.925574321233511 | 0.148851357532979 | 0.0744256787664894 |
75 | 0.927322042553002 | 0.145355914893997 | 0.0726779574469984 |
76 | 0.921002404447875 | 0.157995191104249 | 0.0789975955521247 |
77 | 0.97009612299005 | 0.059807754019899 | 0.0299038770099495 |
78 | 0.962737123434992 | 0.0745257531300151 | 0.0372628765650076 |
79 | 0.955322112720419 | 0.0893557745591628 | 0.0446778872795814 |
80 | 0.958001069235287 | 0.083997861529425 | 0.0419989307647125 |
81 | 0.950327240193387 | 0.0993455196132268 | 0.0496727598066134 |
82 | 0.950009769558878 | 0.0999804608822439 | 0.0499902304411219 |
83 | 0.937189377311647 | 0.125621245376706 | 0.0628106226883528 |
84 | 0.924429516664978 | 0.151140966670043 | 0.0755704833350216 |
85 | 0.915951672892238 | 0.168096654215524 | 0.0840483271077622 |
86 | 0.900653181134239 | 0.198693637731523 | 0.0993468188657613 |
87 | 0.879710042132297 | 0.240579915735407 | 0.120289957867703 |
88 | 0.923727400022814 | 0.152545199954373 | 0.0762725999771865 |
89 | 0.907794947977105 | 0.184410104045791 | 0.0922050520228953 |
90 | 0.88852102833551 | 0.222957943328979 | 0.11147897166449 |
91 | 0.890348508172257 | 0.219302983655487 | 0.109651491827743 |
92 | 0.87972329404173 | 0.240553411916539 | 0.12027670595827 |
93 | 0.858486388567674 | 0.283027222864652 | 0.141513611432326 |
94 | 0.831802333240559 | 0.336395333518881 | 0.168197666759441 |
95 | 0.799891741151273 | 0.400216517697454 | 0.200108258848727 |
96 | 0.771363589009715 | 0.45727282198057 | 0.228636410990285 |
97 | 0.790445706797612 | 0.419108586404776 | 0.209554293202388 |
98 | 0.785253416561085 | 0.429493166877829 | 0.214746583438915 |
99 | 0.751315699297825 | 0.49736860140435 | 0.248684300702175 |
100 | 0.727772355364809 | 0.544455289270383 | 0.272227644635191 |
101 | 0.686415862962309 | 0.627168274075382 | 0.313584137037691 |
102 | 0.648669584234022 | 0.702660831531957 | 0.351330415765978 |
103 | 0.610688735942807 | 0.778622528114387 | 0.389311264057193 |
104 | 0.568912513183682 | 0.862174973632637 | 0.431087486816318 |
105 | 0.523348261113884 | 0.953303477772232 | 0.476651738886116 |
106 | 0.50374480286819 | 0.99251039426362 | 0.49625519713181 |
107 | 0.500601496808818 | 0.998797006382363 | 0.499398503191182 |
108 | 0.512066888836197 | 0.975866222327606 | 0.487933111163803 |
109 | 0.461970607190606 | 0.923941214381212 | 0.538029392809394 |
110 | 0.438871952745131 | 0.877743905490262 | 0.561128047254869 |
111 | 0.399245111949125 | 0.798490223898249 | 0.600754888050876 |
112 | 0.622464003183592 | 0.755071993632816 | 0.377535996816408 |
113 | 0.6143504316766 | 0.7712991366468 | 0.3856495683234 |
114 | 0.586012234060728 | 0.827975531878544 | 0.413987765939272 |
115 | 0.787995057379245 | 0.424009885241511 | 0.212004942620755 |
116 | 0.766002840747051 | 0.467994318505898 | 0.233997159252949 |
117 | 0.755053282831569 | 0.489893434336862 | 0.244946717168431 |
118 | 0.728310027616057 | 0.543379944767885 | 0.271689972383943 |
119 | 0.680521723246862 | 0.638956553506276 | 0.319478276753138 |
120 | 0.689821686952418 | 0.620356626095164 | 0.310178313047582 |
121 | 0.741250456736066 | 0.517499086527868 | 0.258749543263934 |
122 | 0.746311092056203 | 0.507377815887594 | 0.253688907943797 |
123 | 0.752066455515674 | 0.495867088968652 | 0.247933544484326 |
124 | 0.702722865924083 | 0.594554268151834 | 0.297277134075917 |
125 | 0.746671936072011 | 0.506656127855978 | 0.253328063927989 |
126 | 0.719710175859792 | 0.560579648280415 | 0.280289824140208 |
127 | 0.709720699392157 | 0.580558601215685 | 0.290279300607843 |
128 | 0.676029679145158 | 0.647940641709684 | 0.323970320854842 |
129 | 0.650880955155708 | 0.698238089688583 | 0.349119044844292 |
130 | 0.720462230266049 | 0.559075539467901 | 0.279537769733951 |
131 | 0.666986057099335 | 0.66602788580133 | 0.333013942900665 |
132 | 0.606230214360545 | 0.787539571278909 | 0.393769785639455 |
133 | 0.605895172509633 | 0.788209654980734 | 0.394104827490367 |
134 | 0.546964777920311 | 0.906070444159378 | 0.453035222079689 |
135 | 0.506212479145598 | 0.987575041708804 | 0.493787520854402 |
136 | 0.478869778858994 | 0.957739557717988 | 0.521130221141006 |
137 | 0.485143350871994 | 0.970286701743989 | 0.514856649128006 |
138 | 0.52873348688515 | 0.942533026229701 | 0.47126651311485 |
139 | 0.461648300276759 | 0.923296600553518 | 0.538351699723241 |
140 | 0.387508920972158 | 0.775017841944316 | 0.612491079027842 |
141 | 0.500398992333828 | 0.999202015332345 | 0.499601007666172 |
142 | 0.447731430106021 | 0.895462860212041 | 0.552268569893979 |
143 | 0.377989760724787 | 0.755979521449573 | 0.622010239275213 |
144 | 0.298009846375371 | 0.596019692750742 | 0.701990153624629 |
145 | 0.355263275293376 | 0.710526550586753 | 0.644736724706624 |
146 | 0.262950876609858 | 0.525901753219716 | 0.737049123390142 |
147 | 0.340573335736029 | 0.681146671472059 | 0.659426664263971 |
148 | 0.234921271540772 | 0.469842543081545 | 0.765078728459228 |
149 | 0.146077973504985 | 0.292155947009969 | 0.853922026495015 |
150 | 0.0919194134704893 | 0.183838826940979 | 0.908080586529511 |
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 | 6 | 0.0422535211267606 | OK |