Multiple Linear Regression - Estimated Regression Equation |
Y[t] = -14.1035350383858 + 3.01913453757866X[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) | -14.1035350383858 | 3.263874 | -4.3211 | 5e-05 | 2.5e-05 |
X | 3.01913453757866 | 0.408932 | 7.383 | 0 | 0 |
Multiple Linear Regression - Regression Statistics | |
Multiple R | 0.661656111589322 |
R-squared | 0.437788810003502 |
Adjusted R-squared | 0.429757221574981 |
F-TEST (value) | 54.5083720237515 |
F-TEST (DF numerator) | 1 |
F-TEST (DF denominator) | 70 |
p-value | 2.49030684962293e-10 |
Multiple Linear Regression - Residual Statistics | |
Residual Standard Deviation | 2.40192550633485 |
Sum Squared Residuals | 403.847229658734 |
Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
1 | 11 | 10.9552816235170 | 0.0447183764829767 |
2 | 8 | 10.6533681697591 | -2.65336816975913 |
3 | 6 | 10.0495412622434 | -4.04954126224341 |
4 | 10 | 9.74762780848554 | 0.252372191514458 |
5 | 11 | 8.84188744721194 | 2.15811255278806 |
6 | 10 | 8.84188744721194 | 1.15811255278806 |
7 | 9 | 10.955281623517 | -1.95528162351700 |
8 | 8 | 11.2571950772749 | -3.25719507727487 |
9 | 11 | 11.2571950772749 | -0.257195077274869 |
10 | 10 | 11.2571950772749 | -1.25719507727487 |
11 | 12 | 11.2571950772749 | 0.74280492272513 |
12 | 13 | 11.8610219847906 | 1.13897801520940 |
13 | 13 | 12.7667623460642 | 0.233237653935804 |
14 | 13 | 12.4648488923063 | 0.535151107693668 |
15 | 13 | 10.955281623517 | 2.04471837648299 |
16 | 13 | 8.53997399345408 | 4.46002600654592 |
17 | 12 | 7.63423363218048 | 4.36576636781952 |
18 | 13 | 8.23806053969622 | 4.76193946030378 |
19 | 12 | 12.4648488923063 | -0.464848892306332 |
20 | 13 | 13.9744161610957 | -0.974416161095659 |
21 | 12 | 13.9744161610957 | -1.97441616109566 |
22 | 14 | 12.1629354385485 | 1.83706456145154 |
23 | 11 | 10.6533681697591 | 0.346631830240865 |
24 | 12 | 10.955281623517 | 1.04471837648300 |
25 | 13 | 11.5591085310327 | 1.44089146896727 |
26 | 13 | 11.8610219847906 | 1.13897801520940 |
27 | 12 | 11.5591085310327 | 0.440891468967266 |
28 | 10 | 10.6533681697591 | -0.653368169759135 |
29 | 9 | 10.3514547160013 | -1.35145471600127 |
30 | 10 | 9.74762780848554 | 0.252372191514458 |
31 | 10 | 11.8610219847906 | -1.86102198479060 |
32 | 9 | 12.1629354385485 | -3.16293543854846 |
33 | 7 | 12.1629354385485 | -5.16293543854846 |
34 | 11 | 11.5591085310327 | -0.559108531032734 |
35 | 11 | 11.2571950772749 | -0.257195077274869 |
36 | 12 | 11.5591085310327 | 0.440891468967266 |
37 | 13 | 12.1629354385485 | 0.837064561451538 |
38 | 13 | 12.1629354385485 | 0.837064561451538 |
39 | 12 | 11.8610219847906 | 0.138978015209402 |
40 | 12 | 11.5591085310327 | 0.440891468967266 |
41 | 10 | 10.955281623517 | -0.955281623517005 |
42 | 12 | 10.0495412622434 | 1.95045873775659 |
43 | 12 | 10.6533681697591 | 1.34663183024086 |
44 | 12 | 10.3514547160013 | 1.64854528399873 |
45 | 10 | 10.3514547160013 | -0.351454716001271 |
46 | 13 | 10.0495412622434 | 2.95045873775659 |
47 | 13 | 9.74762780848554 | 3.25237219151446 |
48 | 11 | 9.74762780848554 | 1.25237219151446 |
49 | 13 | 10.0495412622434 | 2.95045873775659 |
50 | 12 | 10.0495412622434 | 1.95045873775659 |
51 | 11 | 9.74762780848554 | 1.25237219151446 |
52 | 12 | 10.0495412622434 | 1.95045873775659 |
53 | 12 | 9.14380090096981 | 2.85619909903019 |
54 | 11 | 7.63423363218048 | 3.36576636781952 |
55 | 10 | 8.53997399345408 | 1.46002600654592 |
56 | 9 | 7.93614708593835 | 1.06385291406165 |
57 | 10 | 7.03040672466475 | 2.96959327533525 |
58 | 9 | 7.03040672466475 | 1.96959327533525 |
59 | 6 | 7.03040672466475 | -1.03040672466475 |
60 | 7 | 7.63423363218048 | -0.634233632180484 |
61 | 5 | 7.93614708593835 | -2.93614708593835 |
62 | 8 | 7.33232017842262 | 0.667679821577383 |
63 | 5 | 6.42657981714902 | -1.42657981714902 |
64 | 5 | 5.21892600211756 | -0.218926002117562 |
65 | 5 | 4.31318564084396 | 0.686814359156037 |
66 | 1 | 5.52083945587543 | -4.52083945587543 |
67 | 3 | 9.14380090096981 | -6.14380090096981 |
68 | 5 | 9.74762780848554 | -4.74762780848554 |
69 | 7 | 8.53997399345408 | -1.53997399345408 |
70 | 2 | 6.72849327090689 | -4.72849327090689 |
71 | 3 | 5.82275290963329 | -2.82275290963329 |
72 | 2 | 6.72849327090689 | -4.72849327090689 |
Goldfeld-Quandt test for Heteroskedasticity | |||
p-values | Alternative Hypothesis | ||
breakpoint index | greater | 2-sided | less |
5 | 0.61789313795859 | 0.764213724082821 | 0.382106862041410 |
6 | 0.450570539210524 | 0.901141078421048 | 0.549429460789476 |
7 | 0.310967187487238 | 0.621934374974477 | 0.689032812512762 |
8 | 0.215235882245318 | 0.430471764490637 | 0.784764117754682 |
9 | 0.221019534933623 | 0.442039069867245 | 0.778980465066377 |
10 | 0.153897824244827 | 0.307795648489654 | 0.846102175755173 |
11 | 0.178055047254458 | 0.356110094508917 | 0.821944952745542 |
12 | 0.221735708718971 | 0.443471417437942 | 0.778264291281029 |
13 | 0.18717283393969 | 0.37434566787938 | 0.81282716606031 |
14 | 0.147813373899723 | 0.295626747799446 | 0.852186626100277 |
15 | 0.157698468801577 | 0.315396937603153 | 0.842301531198423 |
16 | 0.288837349004974 | 0.577674698009949 | 0.711162650995026 |
17 | 0.320140497225507 | 0.640280994451014 | 0.679859502774493 |
18 | 0.385966057401436 | 0.771932114802872 | 0.614033942598564 |
19 | 0.320763465299878 | 0.641526930599755 | 0.679236534700122 |
20 | 0.279995886158283 | 0.559991772316565 | 0.720004113841717 |
21 | 0.234909266929152 | 0.469818533858304 | 0.765090733070848 |
22 | 0.240279255242336 | 0.480558510484672 | 0.759720744757664 |
23 | 0.184539996359595 | 0.36907999271919 | 0.815460003640405 |
24 | 0.143403529286958 | 0.286807058573917 | 0.856596470713042 |
25 | 0.121054542101003 | 0.242109084202006 | 0.878945457898997 |
26 | 0.0980262826131491 | 0.196052565226298 | 0.90197371738685 |
27 | 0.0704226849202957 | 0.140845369840591 | 0.929577315079704 |
28 | 0.0540327346616327 | 0.108065469323265 | 0.945967265338367 |
29 | 0.0496792088185215 | 0.099358417637043 | 0.950320791181478 |
30 | 0.0352729512731498 | 0.0705459025462995 | 0.96472704872685 |
31 | 0.0299327900445599 | 0.0598655800891197 | 0.97006720995544 |
32 | 0.0398498506050720 | 0.0796997012101439 | 0.960150149394928 |
33 | 0.150255138354333 | 0.300510276708666 | 0.849744861645667 |
34 | 0.119053890410717 | 0.238107780821435 | 0.880946109589283 |
35 | 0.0908751948529564 | 0.181750389705913 | 0.909124805147044 |
36 | 0.0686019371947821 | 0.137203874389564 | 0.931398062805218 |
37 | 0.0557476171420214 | 0.111495234284043 | 0.944252382857979 |
38 | 0.0444122093043038 | 0.0888244186086076 | 0.955587790695696 |
39 | 0.0328186560765056 | 0.0656373121530113 | 0.967181343923494 |
40 | 0.0234107258641535 | 0.0468214517283069 | 0.976589274135847 |
41 | 0.0198034604149054 | 0.0396069208298108 | 0.980196539585095 |
42 | 0.0142292437640672 | 0.0284584875281344 | 0.985770756235933 |
43 | 0.00947057448017115 | 0.0189411489603423 | 0.990529425519829 |
44 | 0.00627670254612176 | 0.0125534050922435 | 0.993723297453878 |
45 | 0.00440451492728646 | 0.00880902985457292 | 0.995595485072714 |
46 | 0.00403797143288951 | 0.00807594286577902 | 0.99596202856711 |
47 | 0.00425131436105576 | 0.00850262872211151 | 0.995748685638944 |
48 | 0.00257526681604992 | 0.00515053363209983 | 0.99742473318395 |
49 | 0.0026183758182234 | 0.0052367516364468 | 0.997381624181777 |
50 | 0.00192057264542117 | 0.00384114529084234 | 0.998079427354579 |
51 | 0.00124395370089391 | 0.00248790740178783 | 0.998756046299106 |
52 | 0.00110398865092869 | 0.00220797730185738 | 0.998896011349071 |
53 | 0.00195155044883513 | 0.00390310089767027 | 0.998048449551165 |
54 | 0.0050514714540065 | 0.010102942908013 | 0.994948528545994 |
55 | 0.00769990974398844 | 0.0153998194879769 | 0.992300090256012 |
56 | 0.0115362550862788 | 0.0230725101725576 | 0.988463744913721 |
57 | 0.0448057751148655 | 0.089611550229731 | 0.955194224885134 |
58 | 0.124852669261030 | 0.249705338522059 | 0.87514733073897 |
59 | 0.149011580503970 | 0.298023161007939 | 0.85098841949603 |
60 | 0.187854296312689 | 0.375708592625378 | 0.812145703687311 |
61 | 0.195763070286652 | 0.391526140573303 | 0.804236929713348 |
62 | 0.387662612885085 | 0.77532522577017 | 0.612337387114915 |
63 | 0.369437666880671 | 0.738875333761342 | 0.630562333119329 |
64 | 0.370461875869145 | 0.740923751738291 | 0.629538124130855 |
65 | 0.607095074410661 | 0.785809851178679 | 0.392904925589339 |
66 | 0.557847988814895 | 0.88430402237021 | 0.442152011185105 |
67 | 0.617965525152922 | 0.764068949694155 | 0.382034474847078 |
Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
Description | # significant tests | % significant tests | OK/NOK |
1% type I error level | 9 | 0.142857142857143 | NOK |
5% type I error level | 17 | 0.26984126984127 | NOK |
10% type I error level | 24 | 0.380952380952381 | NOK |