Multiple Linear Regression - Estimated Regression Equation |
Y[t] = + 663.747235364029 -0.849955888088473X[t] -0.514576813656158t + 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) | 663.747235364029 | 55.060133 | 12.055 | 0 | 0 |
X | -0.849955888088473 | 0.549176 | -1.5477 | 0.126271 | 0.063135 |
t | -0.514576813656158 | 0.234269 | -2.1965 | 0.031417 | 0.015709 |
Multiple Linear Regression - Regression Statistics | |
Multiple R | 0.373029972736068 |
R-squared | 0.139151360559472 |
Adjusted R-squared | 0.114199226082935 |
F-TEST (value) | 5.57673174975546 |
F-TEST (DF numerator) | 2 |
F-TEST (DF denominator) | 69 |
p-value | 0.00568819544894872 |
Multiple Linear Regression - Residual Statistics | |
Residual Standard Deviation | 38.499212515376 |
Sum Squared Residuals | 102271.066136982 |
Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
1 | 519 | 580.446955050553 | -61.4469550505531 |
2 | 517 | 580.272360592135 | -63.272360592135 |
3 | 510 | 572.618154318536 | -62.6181543185356 |
4 | 509 | 574.398458402718 | -65.3984584027184 |
5 | 501 | 577.793678674269 | -76.7936786742692 |
6 | 507 | 571.839384176847 | -64.8393841768468 |
7 | 569 | 585.859053049503 | -16.8590530495035 |
8 | 580 | 583.219586515626 | -3.21958651562619 |
9 | 578 | 565.790887529009 | 12.2091124709906 |
10 | 565 | 563.661394527985 | 1.33860547201484 |
11 | 547 | 574.281239848288 | -27.281239848288 |
12 | 555 | 575.211588044382 | -20.2115880443822 |
13 | 562 | 576.226931829285 | -14.2269318292854 |
14 | 561 | 574.097438828261 | -13.0974388282611 |
15 | 555 | 560.238554571616 | -5.2385545716159 |
16 | 544 | 568.053545461227 | -24.0535454612268 |
17 | 537 | 572.213726032057 | -35.2137260320572 |
18 | 543 | 559.799766785162 | -16.7997667851624 |
19 | 594 | 579.684131285630 | 14.3158687143704 |
20 | 611 | 571.179969123942 | 39.8200308760582 |
21 | 613 | 555.961155446355 | 57.0388445536449 |
22 | 611 | 558.676411007435 | 52.3235889925649 |
23 | 594 | 563.601551877545 | 30.3984481224548 |
24 | 595 | 565.041873606493 | 29.9581263935075 |
25 | 591 | 570.476988009456 | 20.5230119905443 |
26 | 589 | 568.857468541285 | 20.1425314587155 |
27 | 584 | 560.86327991245 | 23.1367200875502 |
28 | 573 | 561.963619286162 | 11.0363807138383 |
29 | 567 | 565.443835146521 | 1.55616485347860 |
30 | 569 | 551.499955301067 | 17.5000446989326 |
31 | 621 | 579.033922794331 | 41.9660772056692 |
32 | 629 | 565.939998836965 | 63.0600011630347 |
33 | 628 | 550.551193981761 | 77.4488060182392 |
34 | 612 | 556.241295151151 | 55.7587048488495 |
35 | 595 | 553.261846262038 | 41.7381537379622 |
36 | 597 | 558.271982720957 | 38.7280172790433 |
37 | 593 | 560.562260337992 | 32.4377396620075 |
38 | 590 | 558.602758514586 | 31.3972414854141 |
39 | 580 | 545.50883455722 | 34.4911654427796 |
40 | 574 | 557.573604887274 | 16.4263951127264 |
41 | 573 | 549.239433903203 | 23.7605660967965 |
42 | 573 | 544.730064415532 | 28.2699355844685 |
43 | 620 | 569.034199534059 | 50.9658004659412 |
44 | 626 | 555.685288810267 | 70.3147111897333 |
45 | 620 | 543.016342796945 | 76.9836572030546 |
46 | 588 | 541.056840973539 | 46.9431590264612 |
47 | 566 | 543.602105357001 | 22.3978946429988 |
48 | 557 | 552.352047723509 | 4.64795227649065 |
49 | 561 | 548.437647357499 | 12.5623526425007 |
50 | 549 | 548.518039665505 | 0.481960334494919 |
51 | 532 | 536.529058362654 | -4.52905836265454 |
52 | 526 | 546.808921327722 | -20.808921327722 |
53 | 511 | 543.574485672183 | -32.5744856721827 |
54 | 499 | 536.345257342628 | -37.3452573426276 |
55 | 555 | 556.824590964757 | -1.82459096475674 |
56 | 565 | 546.365530260465 | 18.6344697395346 |
57 | 542 | 538.796319575675 | 3.20368042432503 |
58 | 527 | 529.867179469943 | -2.86717946994292 |
59 | 510 | 537.087201237892 | -27.0872012378919 |
60 | 514 | 547.877037735812 | -33.8770377358124 |
61 | 517 | 538.26793291961 | -21.2679329196096 |
62 | 508 | 535.968448740968 | -27.9684487409676 |
63 | 493 | 538.003739591577 | -45.0037395915769 |
64 | 490 | 531.114493617257 | -41.1144936172572 |
65 | 469 | 537.569555085926 | -68.5695550859265 |
66 | 478 | 531.275278233269 | -53.2752782332687 |
67 | 528 | 547.674823592573 | -19.6748235925732 |
68 | 534 | 543.930414404181 | -9.93041440418084 |
69 | 518 | 528.966587493021 | -10.9665874930206 |
70 | 506 | 529.386962156262 | -23.3869621562618 |
71 | 502 | 542.726666318448 | -40.7266663184478 |
72 | 516 | 546.546864534043 | -30.5468645340428 |
Goldfeld-Quandt test for Heteroskedasticity | |||
p-values | Alternative Hypothesis | ||
breakpoint index | greater | 2-sided | less |
6 | 0.00262702682734828 | 0.00525405365469655 | 0.997372973172652 |
7 | 0.0556412182581413 | 0.111282436516283 | 0.944358781741859 |
8 | 0.0482245034275335 | 0.096449006855067 | 0.951775496572467 |
9 | 0.186898151165504 | 0.373796302331009 | 0.813101848834496 |
10 | 0.114909873128370 | 0.229819746256741 | 0.88509012687163 |
11 | 0.166414815532933 | 0.332829631065866 | 0.833585184467067 |
12 | 0.164213041907403 | 0.328426083814806 | 0.835786958092597 |
13 | 0.141735639979412 | 0.283471279958824 | 0.858264360020588 |
14 | 0.125948428698682 | 0.251896857397364 | 0.874051571301318 |
15 | 0.101705974930458 | 0.203411949860917 | 0.898294025069542 |
16 | 0.152173881966619 | 0.304347763933238 | 0.847826118033381 |
17 | 0.318258061807952 | 0.636516123615905 | 0.681741938192048 |
18 | 0.392569509524155 | 0.78513901904831 | 0.607430490475845 |
19 | 0.375310675524049 | 0.750621351048099 | 0.624689324475951 |
20 | 0.399919282311147 | 0.799838564622295 | 0.600080717688853 |
21 | 0.465162482671965 | 0.93032496534393 | 0.534837517328036 |
22 | 0.427774085105939 | 0.855548170211878 | 0.572225914894061 |
23 | 0.371867061446387 | 0.743734122892774 | 0.628132938553613 |
24 | 0.324599160868691 | 0.649198321737382 | 0.67540083913131 |
25 | 0.32083814848309 | 0.64167629696618 | 0.67916185151691 |
26 | 0.327675545441481 | 0.655351090882962 | 0.672324454558519 |
27 | 0.335168412813119 | 0.670336825626239 | 0.664831587186881 |
28 | 0.44019179724696 | 0.88038359449392 | 0.55980820275304 |
29 | 0.654257448148238 | 0.691485103703524 | 0.345742551851762 |
30 | 0.731182964033614 | 0.537634071932771 | 0.268817035966386 |
31 | 0.700819946842713 | 0.598360106314573 | 0.299180053157287 |
32 | 0.657241435136975 | 0.68551712972605 | 0.342758564863025 |
33 | 0.662764512229439 | 0.674470975541122 | 0.337235487770561 |
34 | 0.599520294155657 | 0.800959411688687 | 0.400479705844343 |
35 | 0.560133731960291 | 0.879732536079418 | 0.439866268039709 |
36 | 0.527593617813417 | 0.944812764373167 | 0.472406382186583 |
37 | 0.521645935122791 | 0.956708129754419 | 0.478354064877209 |
38 | 0.518299888776417 | 0.963400222447166 | 0.481700111223583 |
39 | 0.504525581722579 | 0.990948836554842 | 0.495474418277421 |
40 | 0.586990175295421 | 0.826019649409158 | 0.413009824704579 |
41 | 0.600289286239479 | 0.799421427521042 | 0.399710713760521 |
42 | 0.580658593819696 | 0.838682812360608 | 0.419341406180304 |
43 | 0.514404093522155 | 0.97119181295569 | 0.485595906477845 |
44 | 0.570050442995261 | 0.859899114009477 | 0.429949557004739 |
45 | 0.80586467945089 | 0.388270641098219 | 0.194135320549109 |
46 | 0.890353386961857 | 0.219293226076286 | 0.109646613038143 |
47 | 0.919763374863576 | 0.160473250272847 | 0.0802366251364237 |
48 | 0.936746816367436 | 0.126506367265128 | 0.0632531836325638 |
49 | 0.946309704734166 | 0.107380590531669 | 0.0536902952658345 |
50 | 0.952363542326623 | 0.095272915346753 | 0.0476364576733765 |
51 | 0.95794798808482 | 0.0841040238303585 | 0.0420520119151792 |
52 | 0.965600985591455 | 0.0687980288170908 | 0.0343990144085454 |
53 | 0.977913326752033 | 0.0441733464959343 | 0.0220866732479671 |
54 | 0.986351082810334 | 0.0272978343793315 | 0.0136489171896657 |
55 | 0.979225193774985 | 0.0415496124500301 | 0.0207748062250150 |
56 | 0.984153108364905 | 0.03169378327019 | 0.015846891635095 |
57 | 0.986392342924885 | 0.0272153141502297 | 0.0136076570751149 |
58 | 0.990617017640363 | 0.0187659647192742 | 0.00938298235963712 |
59 | 0.986116847684536 | 0.0277663046309275 | 0.0138831523154637 |
60 | 0.977233154927614 | 0.0455336901447723 | 0.0227668450723862 |
61 | 0.972010254818514 | 0.0559794903629727 | 0.0279897451814864 |
62 | 0.963768339762057 | 0.0724633204758863 | 0.0362316602379432 |
63 | 0.934812500529094 | 0.130374998941812 | 0.0651874994709058 |
64 | 0.883580578786232 | 0.232838842427535 | 0.116419421213768 |
65 | 0.909417448063266 | 0.181165103873468 | 0.0905825519367341 |
66 | 0.982739152389484 | 0.0345216952210322 | 0.0172608476105161 |
Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
Description | # significant tests | % significant tests | OK/NOK |
1% type I error level | 1 | 0.0163934426229508 | NOK |
5% type I error level | 10 | 0.163934426229508 | NOK |
10% type I error level | 16 | 0.262295081967213 | NOK |