Multiple Linear Regression - Estimated Regression Equation |
Y[t] = + 611.409334928083 -0.270247144144274X[t] -5.79884393448892M1[t] -9.67956344989054M2[t] -16.3712953588341M3[t] -23.567174859071M4[t] -33.0244073542023M5[t] -27.9999130256084M6[t] + 19.0253656640922M7[t] + 31.9597633501936M8[t] + 29.2273517585181M9[t] + 14.9727760992730M10[t] -2.22756473669992M11[t] -0.686870792856947t + 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) | 611.409334928083 | 102.132788 | 5.9864 | 0 | 0 |
X | -0.270247144144274 | 1.082846 | -0.2496 | 0.803801 | 0.4019 |
M1 | -5.79884393448892 | 20.755812 | -0.2794 | 0.780944 | 0.390472 |
M2 | -9.67956344989054 | 20.877896 | -0.4636 | 0.64465 | 0.322325 |
M3 | -16.3712953588341 | 24.895068 | -0.6576 | 0.513389 | 0.256694 |
M4 | -23.567174859071 | 21.906802 | -1.0758 | 0.286475 | 0.143237 |
M5 | -33.0244073542023 | 21.247907 | -1.5542 | 0.125567 | 0.062783 |
M6 | -27.9999130256084 | 25.684772 | -1.0901 | 0.280161 | 0.140081 |
M7 | 19.0253656640922 | 23.395589 | 0.8132 | 0.419427 | 0.209714 |
M8 | 31.9597633501936 | 20.484405 | 1.5602 | 0.124153 | 0.062077 |
M9 | 29.2273517585181 | 25.763968 | 1.1344 | 0.261282 | 0.130641 |
M10 | 14.9727760992730 | 25.801105 | 0.5803 | 0.56395 | 0.281975 |
M11 | -2.22756473669992 | 21.717199 | -0.1026 | 0.918657 | 0.459328 |
t | -0.686870792856947 | 0.263334 | -2.6084 | 0.011551 | 0.005775 |
Multiple Linear Regression - Regression Statistics | |
Multiple R | 0.62323044184832 |
R-squared | 0.388416183646452 |
Adjusted R-squared | 0.251337052394795 |
F-TEST (value) | 2.83351798410056 |
F-TEST (DF numerator) | 13 |
F-TEST (DF denominator) | 58 |
p-value | 0.00330494121873914 |
Multiple Linear Regression - Residual Statistics | |
Residual Standard Deviation | 35.3937833758541 |
Sum Squared Residuals | 72657.7542960995 |
Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
1 | 519 | 578.601548361082 | -59.6015483610821 |
2 | 517 | 574.142056910484 | -57.1420569104838 |
3 | 510 | 564.493378197871 | -54.4933781978713 |
4 | 509 | 557.340295193967 | -48.340295193967 |
5 | 501 | 548.439328769043 | -47.4393287690425 |
6 | 507 | 551.047370582256 | -44.0473705822561 |
7 | 569 | 602.007004643967 | -33.0070046439668 |
8 | 580 | 613.57891367685 | -33.5789136768505 |
9 | 578 | 604.781713123847 | -26.7817131238471 |
10 | 565 | 589.326797097871 | -24.3267970978708 |
11 | 547 | 574.979823057331 | -27.979823057331 |
12 | 555 | 576.979937146219 | -21.9799371462193 |
13 | 562 | 570.980667278333 | -8.9806672783331 |
14 | 561 | 565.8996073962 | -4.89960739620039 |
15 | 555 | 554.278124531335 | 0.721875468665248 |
16 | 544 | 549.043796250855 | -5.0437962508548 |
17 | 537 | 540.38605225566 | -3.38605225566009 |
18 | 543 | 540.940215773377 | 2.05978422662282 |
19 | 594 | 593.764555129683 | 0.235444870316577 |
20 | 611 | 603.471758867972 | 7.52824113202827 |
21 | 613 | 595.377200889743 | 17.6227991102567 |
22 | 611 | 581.462693585389 | 29.5373064146106 |
23 | 594 | 565.305063679083 | 28.694936320917 |
24 | 595 | 567.467326054458 | 27.5326739455422 |
25 | 591 | 562.873341336122 | 28.1266586638781 |
26 | 589 | 557.954429740476 | 31.0455702595243 |
27 | 584 | 548.197652170206 | 35.8023478297944 |
28 | 573 | 540.828371450986 | 32.1716285490141 |
29 | 567 | 531.954429740476 | 35.0455702595243 |
30 | 569 | 532.022148398733 | 36.9778516012669 |
31 | 621 | 587.278712052338 | 33.7212879476622 |
32 | 629 | 595.526581212247 | 33.4734187877529 |
33 | 628 | 587.37797380519 | 40.6220261948102 |
34 | 612 | 574.409331505341 | 37.5906684946591 |
35 | 595 | 555.738403158493 | 39.2615968415073 |
36 | 597 | 559.035703539273 | 37.9642964607266 |
37 | 593 | 553.441804387604 | 39.5581956123963 |
38 | 590 | 548.4147939343 | 41.5852060657001 |
39 | 580 | 537.036533499164 | 42.9634665008359 |
40 | 574 | 533.153440939406 | 40.8465590605945 |
41 | 573 | 520.52306392529 | 52.4769360747101 |
42 | 573 | 523.590525883549 | 49.4094741164512 |
43 | 620 | 577.820150389405 | 42.1798496105948 |
44 | 626 | 585.986945406071 | 40.0130545939288 |
45 | 620 | 578.703128860276 | 41.2968711397244 |
46 | 588 | 563.302262263128 | 24.6977377368718 |
47 | 566 | 546.387940353218 | 19.6120596467822 |
48 | 557 | 550.874328168233 | 6.12567183176662 |
49 | 561 | 543.30762486431 | 17.6923751356896 |
50 | 549 | 538.929207556953 | 10.0707924430472 |
51 | 532 | 527.902268409205 | 4.09773159079539 |
52 | 526 | 523.451656846743 | 2.54834315325695 |
53 | 511 | 512.442762697493 | -1.44276269749314 |
54 | 499 | 514.64543379449 | -15.6454337944903 |
55 | 555 | 567.658946151698 | -12.6589461516976 |
56 | 565 | 576.744581458454 | -11.744581458454 |
57 | 542 | 571.082247777524 | -29.0822477775240 |
58 | 527 | 553.465354598394 | -26.4653545983937 |
59 | 510 | 538.037391981277 | -28.0373919812767 |
60 | 514 | 543.172372942239 | -29.1723729422386 |
61 | 517 | 533.795013772549 | -16.7950137725489 |
62 | 508 | 528.659904461587 | -20.6599044615874 |
63 | 493 | 522.09204319222 | -29.0920431922197 |
64 | 490 | 512.182439318044 | -22.1824393180438 |
65 | 469 | 504.254362612039 | -35.2543626120386 |
66 | 478 | 506.754305567595 | -28.7543055675945 |
67 | 528 | 558.470631632909 | -30.4706316329092 |
68 | 534 | 569.691219378405 | -35.6912193784055 |
69 | 518 | 561.67773554342 | -43.6777355434203 |
70 | 506 | 547.033560949877 | -41.0335609498770 |
71 | 502 | 533.551377770599 | -31.5513777705988 |
72 | 516 | 536.470332149578 | -20.4703321495776 |
Goldfeld-Quandt test for Heteroskedasticity | |||
p-values | Alternative Hypothesis | ||
breakpoint index | greater | 2-sided | less |
17 | 0.00644778127808402 | 0.0128955625561680 | 0.993552218721916 |
18 | 0.00225279661393863 | 0.00450559322787726 | 0.997747203386061 |
19 | 0.0054425898603343 | 0.0108851797206686 | 0.994557410139666 |
20 | 0.00322354028482769 | 0.00644708056965537 | 0.996776459715172 |
21 | 0.00123466300703667 | 0.00246932601407334 | 0.998765336992963 |
22 | 0.000743526827240503 | 0.00148705365448101 | 0.99925647317276 |
23 | 0.000598897642356057 | 0.00119779528471211 | 0.999401102357644 |
24 | 0.000274135801131366 | 0.000548271602262733 | 0.999725864198869 |
25 | 0.000204154207093493 | 0.000408308414186985 | 0.999795845792907 |
26 | 0.000129175832117017 | 0.000258351664234033 | 0.999870824167883 |
27 | 5.47284121447155e-05 | 0.000109456824289431 | 0.999945271587855 |
28 | 5.94250176119117e-05 | 0.000118850035223823 | 0.999940574982388 |
29 | 4.82197329504265e-05 | 9.64394659008531e-05 | 0.99995178026705 |
30 | 8.12224824216973e-05 | 0.000162444964843395 | 0.999918777517578 |
31 | 0.000154868672867804 | 0.000309737345735607 | 0.999845131327132 |
32 | 0.00147085936930335 | 0.00294171873860670 | 0.998529140630697 |
33 | 0.00346453978311962 | 0.00692907956623924 | 0.99653546021688 |
34 | 0.0126404112874278 | 0.0252808225748555 | 0.987359588712572 |
35 | 0.0412199339851324 | 0.0824398679702648 | 0.958780066014868 |
36 | 0.0715712124309706 | 0.143142424861941 | 0.92842878756903 |
37 | 0.121654221938479 | 0.243308443876959 | 0.87834577806152 |
38 | 0.150450693562218 | 0.300901387124436 | 0.849549306437782 |
39 | 0.167958104097917 | 0.335916208195835 | 0.832041895902083 |
40 | 0.189403232147621 | 0.378806464295242 | 0.810596767852379 |
41 | 0.207690248243707 | 0.415380496487415 | 0.792309751756293 |
42 | 0.253628827267871 | 0.507257654535741 | 0.746371172732129 |
43 | 0.274459732322652 | 0.548919464645304 | 0.725540267677348 |
44 | 0.353350784173529 | 0.706701568347057 | 0.646649215826471 |
45 | 0.782750234149327 | 0.434499531701347 | 0.217249765850673 |
46 | 0.932521835768292 | 0.134956328463416 | 0.0674781642317078 |
47 | 0.981572207588882 | 0.0368555848222359 | 0.0184277924111179 |
48 | 0.989122348504822 | 0.0217553029903568 | 0.0108776514951784 |
49 | 0.987857342742398 | 0.0242853145152030 | 0.0121426572576015 |
50 | 0.98448859363279 | 0.0310228127344214 | 0.0155114063672107 |
51 | 0.993144810698055 | 0.0137103786038904 | 0.00685518930194521 |
52 | 0.987270368096989 | 0.0254592638060227 | 0.0127296319030113 |
53 | 0.99063247342898 | 0.0187350531420395 | 0.00936752657101974 |
54 | 0.97717447274714 | 0.0456510545057187 | 0.0228255272528593 |
55 | 0.93686765234524 | 0.126264695309522 | 0.0631323476547608 |
Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
Description | # significant tests | % significant tests | OK/NOK |
1% type I error level | 15 | 0.384615384615385 | NOK |
5% type I error level | 26 | 0.666666666666667 | NOK |
10% type I error level | 27 | 0.692307692307692 | NOK |