Multiple Linear Regression - Estimated Regression Equation |
Y[t] = + 21.5714285714286 -3.18506493506494X[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) | 21.5714285714286 | 0.320466 | 67.3127 | 0 | 0 |
X | -3.18506493506494 | 0.409941 | -7.7696 | 0 | 0 |
Multiple Linear Regression - Regression Statistics | |
Multiple R | 0.680478106956758 |
R-squared | 0.463050454047453 |
Adjusted R-squared | 0.455379746248131 |
F-TEST (value) | 60.3660660999726 |
F-TEST (DF numerator) | 1 |
F-TEST (DF denominator) | 70 |
p-value | 4.85240736480819e-11 |
Multiple Linear Regression - Residual Statistics | |
Residual Standard Deviation | 1.69574661617556 |
Sum Squared Residuals | 201.288961038961 |
Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
1 | 22 | 21.5714285714285 | 0.428571428571511 |
2 | 22 | 21.5714285714286 | 0.428571428571439 |
3 | 20 | 21.5714285714286 | -1.57142857142857 |
4 | 21 | 21.5714285714286 | -0.571428571428575 |
5 | 20 | 21.5714285714286 | -1.57142857142857 |
6 | 21 | 21.5714285714286 | -0.571428571428575 |
7 | 21 | 21.5714285714286 | -0.571428571428575 |
8 | 21 | 21.5714285714286 | -0.571428571428575 |
9 | 19 | 21.5714285714286 | -2.57142857142858 |
10 | 21 | 21.5714285714286 | -0.571428571428575 |
11 | 21 | 21.5714285714286 | -0.571428571428575 |
12 | 22 | 21.5714285714286 | 0.428571428571425 |
13 | 19 | 21.5714285714286 | -2.57142857142858 |
14 | 24 | 21.5714285714286 | 2.42857142857142 |
15 | 22 | 21.5714285714286 | 0.428571428571425 |
16 | 22 | 21.5714285714286 | 0.428571428571425 |
17 | 22 | 21.5714285714286 | 0.428571428571425 |
18 | 24 | 21.5714285714286 | 2.42857142857142 |
19 | 22 | 21.5714285714286 | 0.428571428571425 |
20 | 23 | 21.5714285714286 | 1.42857142857143 |
21 | 24 | 21.5714285714286 | 2.42857142857142 |
22 | 21 | 21.5714285714286 | -0.571428571428575 |
23 | 20 | 21.5714285714286 | -1.57142857142857 |
24 | 22 | 21.5714285714286 | 0.428571428571425 |
25 | 23 | 21.5714285714286 | 1.42857142857143 |
26 | 23 | 21.5714285714286 | 1.42857142857143 |
27 | 22 | 21.5714285714286 | 0.428571428571425 |
28 | 20 | 21.5714285714286 | -1.57142857142857 |
29 | 21 | 18.3863636363636 | 2.61363636363636 |
30 | 21 | 18.3863636363636 | 2.61363636363636 |
31 | 20 | 18.3863636363636 | 1.61363636363636 |
32 | 20 | 18.3863636363636 | 1.61363636363636 |
33 | 17 | 18.3863636363636 | -1.38636363636364 |
34 | 18 | 18.3863636363636 | -0.386363636363637 |
35 | 19 | 18.3863636363636 | 0.613636363636363 |
36 | 19 | 18.3863636363636 | 0.613636363636363 |
37 | 20 | 18.3863636363636 | 1.61363636363636 |
38 | 21 | 18.3863636363636 | 2.61363636363636 |
39 | 20 | 18.3863636363636 | 1.61363636363636 |
40 | 21 | 18.3863636363636 | 2.61363636363636 |
41 | 19 | 18.3863636363636 | 0.613636363636363 |
42 | 22 | 18.3863636363636 | 3.61363636363636 |
43 | 20 | 18.3863636363636 | 1.61363636363636 |
44 | 18 | 18.3863636363636 | -0.386363636363637 |
45 | 16 | 18.3863636363636 | -2.38636363636364 |
46 | 17 | 18.3863636363636 | -1.38636363636364 |
47 | 18 | 18.3863636363636 | -0.386363636363637 |
48 | 19 | 18.3863636363636 | 0.613636363636363 |
49 | 18 | 18.3863636363636 | -0.386363636363637 |
50 | 20 | 18.3863636363636 | 1.61363636363636 |
51 | 21 | 18.3863636363636 | 2.61363636363636 |
52 | 18 | 18.3863636363636 | -0.386363636363637 |
53 | 19 | 18.3863636363636 | 0.613636363636363 |
54 | 19 | 18.3863636363636 | 0.613636363636363 |
55 | 19 | 18.3863636363636 | 0.613636363636363 |
56 | 21 | 18.3863636363636 | 2.61363636363636 |
57 | 19 | 18.3863636363636 | 0.613636363636363 |
58 | 19 | 18.3863636363636 | 0.613636363636363 |
59 | 17 | 18.3863636363636 | -1.38636363636364 |
60 | 16 | 18.3863636363636 | -2.38636363636364 |
61 | 16 | 18.3863636363636 | -2.38636363636364 |
62 | 17 | 18.3863636363636 | -1.38636363636364 |
63 | 16 | 18.3863636363636 | -2.38636363636364 |
64 | 15 | 18.3863636363636 | -3.38636363636364 |
65 | 16 | 18.3863636363636 | -2.38636363636364 |
66 | 16 | 18.3863636363636 | -2.38636363636364 |
67 | 16 | 18.3863636363636 | -2.38636363636364 |
68 | 18 | 18.3863636363636 | -0.386363636363637 |
69 | 19 | 18.3863636363636 | 0.613636363636363 |
70 | 16 | 18.3863636363636 | -2.38636363636364 |
71 | 16 | 18.3863636363636 | -2.38636363636364 |
72 | 16 | 18.3863636363636 | -2.38636363636364 |
Goldfeld-Quandt test for Heteroskedasticity | |||
p-values | Alternative Hypothesis | ||
breakpoint index | greater | 2-sided | less |
5 | 0.277476792983213 | 0.554953585966426 | 0.722523207016787 |
6 | 0.142201363355241 | 0.284402726710483 | 0.857798636644759 |
7 | 0.066559588035858 | 0.133119176071716 | 0.933440411964142 |
8 | 0.0287925079534631 | 0.0575850159069261 | 0.971207492046537 |
9 | 0.0755786837960871 | 0.151157367592174 | 0.924421316203913 |
10 | 0.0402566834339167 | 0.0805133668678333 | 0.959743316566083 |
11 | 0.0204192747150891 | 0.0408385494301782 | 0.97958072528491 |
12 | 0.0171998160001288 | 0.0343996320002576 | 0.982800183999871 |
13 | 0.0366614930150881 | 0.0733229860301762 | 0.963338506984912 |
14 | 0.169890235134315 | 0.339780470268630 | 0.830109764865685 |
15 | 0.133101588991073 | 0.266203177982146 | 0.866898411008927 |
16 | 0.101307015786341 | 0.202614031572682 | 0.898692984213659 |
17 | 0.0749425116538495 | 0.149885023307699 | 0.92505748834615 |
18 | 0.150956792388904 | 0.301913584777808 | 0.849043207611096 |
19 | 0.111965168280726 | 0.223930336561452 | 0.888034831719274 |
20 | 0.108009288037406 | 0.216018576074812 | 0.891990711962594 |
21 | 0.164056766056922 | 0.328113532113844 | 0.835943233943078 |
22 | 0.124439557540613 | 0.248879115081227 | 0.875560442459387 |
23 | 0.122046495628497 | 0.244092991256994 | 0.877953504371503 |
24 | 0.0895288970714947 | 0.179057794142989 | 0.910471102928505 |
25 | 0.081930430607418 | 0.163860861214836 | 0.918069569392582 |
26 | 0.0766217939026166 | 0.153243587805233 | 0.923378206097383 |
27 | 0.0578325923685681 | 0.115665184737136 | 0.942167407631432 |
28 | 0.0522708413755597 | 0.104541682751119 | 0.94772915862444 |
29 | 0.0464042644194176 | 0.0928085288388352 | 0.953595735580582 |
30 | 0.0424877921066112 | 0.0849755842132223 | 0.95751220789339 |
31 | 0.0354737344910246 | 0.0709474689820491 | 0.964526265508975 |
32 | 0.0286885708994212 | 0.0573771417988423 | 0.971311429100579 |
33 | 0.0581075713001036 | 0.116215142600207 | 0.941892428699896 |
34 | 0.0519085228968702 | 0.103817045793740 | 0.94809147710313 |
35 | 0.037612952732919 | 0.075225905465838 | 0.962387047267081 |
36 | 0.026644715449061 | 0.053289430898122 | 0.97335528455094 |
37 | 0.0219725998853213 | 0.0439451997706426 | 0.978027400114679 |
38 | 0.0292766159353804 | 0.0585532318707608 | 0.97072338406462 |
39 | 0.0250851895059591 | 0.0501703790119183 | 0.974914810494041 |
40 | 0.0355194738198749 | 0.0710389476397498 | 0.964480526180125 |
41 | 0.0273895184099397 | 0.0547790368198794 | 0.97261048159006 |
42 | 0.0918616968917439 | 0.183723393783488 | 0.908138303108256 |
43 | 0.0959181235556707 | 0.191836247111341 | 0.90408187644433 |
44 | 0.0881971422600426 | 0.176394284520085 | 0.911802857739957 |
45 | 0.164355155484949 | 0.328710310969899 | 0.83564484451505 |
46 | 0.169856488917796 | 0.339712977835592 | 0.830143511082204 |
47 | 0.140490665150458 | 0.280981330300917 | 0.859509334849542 |
48 | 0.117785023771229 | 0.235570047542458 | 0.882214976228771 |
49 | 0.0937688537682373 | 0.187537707536475 | 0.906231146231763 |
50 | 0.106768774594108 | 0.213537549188216 | 0.893231225405892 |
51 | 0.223520957077580 | 0.447041914155159 | 0.77647904292242 |
52 | 0.188367145479248 | 0.376734290958496 | 0.811632854520752 |
53 | 0.179460102160319 | 0.358920204320637 | 0.820539897839681 |
54 | 0.176783770327925 | 0.35356754065585 | 0.823216229672075 |
55 | 0.182105894312442 | 0.364211788624883 | 0.817894105687558 |
56 | 0.578678545855752 | 0.842642908288496 | 0.421321454144248 |
57 | 0.69659310819282 | 0.606813783614361 | 0.303406891807181 |
58 | 0.853581963438107 | 0.292836073123785 | 0.146418036561893 |
59 | 0.826660866026335 | 0.346678267947329 | 0.173339133973665 |
60 | 0.805322548037741 | 0.389354903924518 | 0.194677451962259 |
61 | 0.772347944555013 | 0.455304110889975 | 0.227652055444987 |
62 | 0.711661883889078 | 0.576676232221843 | 0.288338116110922 |
63 | 0.649237078851546 | 0.701525842296907 | 0.350762921148454 |
64 | 0.702892119239515 | 0.594215761520971 | 0.297107880760485 |
65 | 0.622037542280022 | 0.755924915439957 | 0.377962457719978 |
66 | 0.526899933387857 | 0.946200133224286 | 0.473100066612143 |
67 | 0.421746462975193 | 0.843492925950386 | 0.578253537024807 |
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 | 3 | 0.0476190476190476 | OK |
10% type I error level | 16 | 0.253968253968254 | NOK |