Multiple Linear Regression - Estimated Regression Equation |
Spaar[t] = + 50.6298826025243 + 0.224827909425653Alg_E[t] + 0.85574414100791M1[t] + 0.479212425823561M2[t] -1.78112277147162M3[t] -0.431389132537066M4[t] + 0.271033806029273M5[t] + 2.11538884570027M6[t] + 0.824847139715868M7[t] -1.74790201229214M8[t] -1.58340930016167M9[t] -0.766227288399419M10[t] -0.207113175532512M11[t] -0.11952713024534t + 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) | 50.6298826025243 | 2.228464 | 22.7196 | 0 | 0 |
Alg_E | 0.224827909425653 | 0.03841 | 5.8534 | 0 | 0 |
M1 | 0.85574414100791 | 1.648074 | 0.5192 | 0.604666 | 0.302333 |
M2 | 0.479212425823561 | 1.695835 | 0.2826 | 0.778043 | 0.389022 |
M3 | -1.78112277147162 | 1.691833 | -1.0528 | 0.294815 | 0.147407 |
M4 | -0.431389132537066 | 1.687817 | -0.2556 | 0.798758 | 0.399379 |
M5 | 0.271033806029273 | 1.685106 | 0.1608 | 0.872522 | 0.436261 |
M6 | 2.11538884570027 | 1.684915 | 1.2555 | 0.212037 | 0.106018 |
M7 | 0.824847139715868 | 1.684764 | 0.4896 | 0.625425 | 0.312712 |
M8 | -1.74790201229214 | 1.684281 | -1.0378 | 0.301715 | 0.150858 |
M9 | -1.58340930016167 | 1.684061 | -0.9402 | 0.349216 | 0.174608 |
M10 | -0.766227288399419 | 1.684891 | -0.4548 | 0.650201 | 0.3251 |
M11 | -0.207113175532512 | 1.683906 | -0.123 | 0.902341 | 0.451171 |
t | -0.11952713024534 | 0.011623 | -10.2841 | 0 | 0 |
Multiple Linear Regression - Regression Statistics | |
Multiple R | 0.857292104916475 |
R-squared | 0.73494975315212 |
Adjusted R-squared | 0.702747386712659 |
F-TEST (value) | 22.8228492006564 |
F-TEST (DF numerator) | 13 |
F-TEST (DF denominator) | 107 |
p-value | 0 |
Multiple Linear Regression - Residual Statistics | |
Residual Standard Deviation | 3.76483670875441 |
Sum Squared Residuals | 1516.61751246357 |
Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
1 | 62 | 58.7854206243334 | 3.21457937566656 |
2 | 64 | 59.6383292354577 | 4.36167076454234 |
3 | 62 | 58.607434364471 | 3.39256563552894 |
4 | 64 | 60.062468782586 | 3.93753121741406 |
5 | 64 | 60.4205366814813 | 3.57946331851871 |
6 | 69 | 62.145364590907 | 6.85463540909306 |
7 | 69 | 61.6346073923798 | 7.36539260762019 |
8 | 65 | 59.1671590195521 | 5.83284098044788 |
9 | 56 | 60.1114362391399 | -4.11143623913986 |
10 | 58 | 61.933230667785 | -3.93323066778503 |
11 | 53 | 62.1479897409809 | -9.14798974098094 |
12 | 62 | 61.7859199674168 | 0.214080032583189 |
13 | 55 | 60.7235137027742 | -5.72351370277416 |
14 | 60 | 60.6771106761958 | -0.677110676195773 |
15 | 59 | 58.7469041675066 | 0.253095832493444 |
16 | 58 | 60.2019385856214 | -2.20193858562142 |
17 | 53 | 61.2344902127937 | -8.23449021279373 |
18 | 57 | 60.2613832091115 | -3.26138320911155 |
19 | 57 | 58.6264864634562 | -1.62648646345616 |
20 | 53 | 55.0348985435002 | -2.0348985435002 |
21 | 54 | 55.7543478536623 | -1.75434785366229 |
22 | 53 | 56.4520027351792 | -3.4520027351792 |
23 | 57 | 56.4419338989495 | 0.55806610105054 |
24 | 57 | 55.4053803971084 | 1.59461960289163 |
25 | 55 | 54.5678020418914 | 0.43219795810863 |
26 | 49 | 51.3738082833538 | -2.37380828335385 |
27 | 50 | 48.7691180463877 | 1.23088195361233 |
28 | 49 | 53.821399015313 | -4.82139901531298 |
29 | 54 | 56.6525739178905 | -2.65257391789051 |
30 | 58 | 58.8270576461675 | -0.827057646167467 |
31 | 58 | 58.0914725382147 | -0.0914725382146861 |
32 | 52 | 54.4998846182587 | -2.49988461825873 |
33 | 56 | 55.2193339284208 | 0.780666071579181 |
34 | 52 | 55.9169888099377 | -3.91698880993773 |
35 | 59 | 55.232436245431 | 3.76756375456897 |
36 | 53 | 54.19588274359 | -1.19588274358994 |
37 | 52 | 55.1569276637782 | -3.15692766377816 |
38 | 53 | 55.1105246371998 | -2.11052463719978 |
39 | 51 | 52.9554902190849 | -1.95549021908491 |
40 | 50 | 52.6119013617946 | -2.61190136179455 |
41 | 56 | 51.3961738947103 | 4.60382610528967 |
42 | 52 | 52.446518075859 | -0.446518075859024 |
43 | 46 | 49.0129980547984 | -3.01299805479841 |
44 | 48 | 50.1427962327812 | -2.14279623278116 |
45 | 46 | 51.7615571806459 | -5.76155718064586 |
46 | 48 | 51.3350725150345 | -3.33507251503451 |
47 | 48 | 51.1001757693791 | -3.10017576937912 |
48 | 49 | 51.6374176335176 | -2.63741763351759 |
49 | 53 | 54.1722579196854 | -1.17225791968539 |
50 | 48 | 51.2030920705735 | -3.20309207057352 |
51 | 51 | 51.7459925655665 | -0.74599256556648 |
52 | 48 | 52.9761990742557 | -4.9761990742557 |
53 | 50 | 54.4584065202793 | -4.45840652027931 |
54 | 55 | 56.8577181579819 | -1.85771815798191 |
55 | 52 | 54.9979935029009 | -2.99799350290087 |
56 | 53 | 51.6312334923706 | 1.36876650762943 |
57 | 52 | 50.7768874365531 | 1.22311256344691 |
58 | 55 | 53.2731655934752 | 1.72683440652478 |
59 | 53 | 51.6893013912659 | 1.31069860873409 |
60 | 53 | 52.6761990742557 | 0.323800925744307 |
61 | 56 | 53.1875881755926 | 2.81241182440739 |
62 | 54 | 51.1177339641834 | 2.88226603581665 |
63 | 52 | 48.9626995460685 | 3.03730045393152 |
64 | 55 | 50.642561873609 | 4.357438126391 |
65 | 54 | 51.22545768193 | 2.77454231807000 |
66 | 59 | 53.399941410207 | 5.60005858979304 |
67 | 56 | 52.8891842116798 | 3.11081578832017 |
68 | 56 | 48.6231125634469 | 7.37688743655308 |
69 | 51 | 46.4197990510755 | 4.58020094892448 |
70 | 53 | 46.8926260231668 | 6.10737397683322 |
71 | 52 | 46.882557186937 | 5.11744281306296 |
72 | 51 | 48.0942827793525 | 2.90571722064753 |
73 | 46 | 46.5822206958585 | -0.582220695858516 |
74 | 49 | 49.0089246729623 | -0.00892467296231159 |
75 | 46 | 46.6290623454218 | -0.62906234542179 |
76 | 55 | 48.7585804918136 | 6.24141950818638 |
77 | 57 | 50.0159600284116 | 6.98403997158843 |
78 | 53 | 51.5159600284116 | 1.48403997158843 |
79 | 52 | 49.4314074639049 | 2.56859253609512 |
80 | 53 | 46.7391311816515 | 6.26086881834847 |
81 | 50 | 46.7840967635367 | 3.21590323646334 |
82 | 54 | 48.3810632827562 | 5.61893671724382 |
83 | 53 | 49.4951339936547 | 3.50486600634529 |
84 | 50 | 48.4585804918136 | 1.54141950818638 |
85 | 51 | 49.6444533214275 | 1.35554667857251 |
86 | 52 | 50.4973619325517 | 1.50263806744828 |
87 | 47 | 47.8926716955855 | -0.892671695585544 |
88 | 51 | 47.0994270194439 | 3.90057298055612 |
89 | 49 | 49.0312902843188 | -0.0312902843187983 |
90 | 53 | 50.9809461031701 | 2.01905389682990 |
91 | 52 | 48.8963935386634 | 3.10360646133659 |
92 | 45 | 47.7779126223896 | -2.77791262238963 |
93 | 53 | 47.3732223854235 | 5.62677761457654 |
94 | 51 | 48.295705176366 | 2.70429482363398 |
95 | 48 | 48.0608084307106 | -0.0608084307106281 |
96 | 48 | 45.9001153817413 | 2.09988461825873 |
97 | 48 | 46.6363323925038 | 1.36366760749616 |
98 | 48 | 46.3651014564998 | 1.63489854350020 |
99 | 40 | 41.0624763064258 | -1.06247630642579 |
100 | 43 | 43.6416502716689 | -0.641650271668926 |
101 | 40 | 43.7748902611386 | -3.77489026113862 |
102 | 39 | 46.3990298082669 | -7.39902980826689 |
103 | 39 | 45.4386167908885 | -6.43861679088845 |
104 | 36 | 41.6222009615068 | -5.62220096150684 |
105 | 41 | 40.3181990868381 | 0.681800913161947 |
106 | 39 | 39.8917144212267 | -0.8917144212267 |
107 | 40 | 39.6568176755713 | 0.343182324428691 |
108 | 39 | 41.992682815115 | -2.99268281511501 |
109 | 46 | 43.1785556447289 | 2.82144435527112 |
110 | 40 | 42.0080130710222 | -2.00801307102224 |
111 | 37 | 39.6281507434817 | -2.62815074348171 |
112 | 37 | 40.1838735238940 | -3.18387352389397 |
113 | 44 | 42.7902205170458 | 1.20977948295416 |
114 | 41 | 43.1660809699176 | -2.16608096991758 |
115 | 40 | 41.9808400431135 | -1.98084004311349 |
116 | 36 | 41.7616707645423 | -5.76167076454233 |
117 | 38 | 42.4811200747044 | -4.48112007470442 |
118 | 43 | 43.6284307750726 | -0.628430775072634 |
119 | 42 | 44.2928456671198 | -2.29284566711985 |
120 | 45 | 46.8535387160892 | -1.85353871608921 |
121 | 46 | 47.3649278174261 | -1.36492781742612 |
Goldfeld-Quandt test for Heteroskedasticity | |||
p-values | Alternative Hypothesis | ||
breakpoint index | greater | 2-sided | less |
17 | 0.325234881047865 | 0.650469762095729 | 0.674765118952135 |
18 | 0.322521920833765 | 0.645043841667531 | 0.677478079166235 |
19 | 0.195657895024613 | 0.391315790049225 | 0.804342104975387 |
20 | 0.113710167967367 | 0.227420335934734 | 0.886289832032633 |
21 | 0.397790152341236 | 0.795580304682471 | 0.602209847658764 |
22 | 0.358468691135862 | 0.716937382271725 | 0.641531308864138 |
23 | 0.652876302691013 | 0.694247394617973 | 0.347123697308987 |
24 | 0.562158998972255 | 0.87568200205549 | 0.437841001027745 |
25 | 0.555503486212317 | 0.888993027575365 | 0.444496513787683 |
26 | 0.612790180223478 | 0.774419639553044 | 0.387209819776522 |
27 | 0.551892349250934 | 0.896215301498131 | 0.448107650749066 |
28 | 0.516677823621695 | 0.96664435275661 | 0.483322176378305 |
29 | 0.53580038550908 | 0.92839922898184 | 0.46419961449092 |
30 | 0.507570857514545 | 0.98485828497091 | 0.492429142485455 |
31 | 0.465079388310612 | 0.930158776621224 | 0.534920611689388 |
32 | 0.399965404430136 | 0.799930808860272 | 0.600034595569864 |
33 | 0.553131811461384 | 0.893736377077232 | 0.446868188538616 |
34 | 0.55993039139897 | 0.880139217202061 | 0.440069608601031 |
35 | 0.769204357222667 | 0.461591285554665 | 0.230795642777333 |
36 | 0.715547788304659 | 0.568904423390683 | 0.284452211695341 |
37 | 0.688307191774671 | 0.623385616450657 | 0.311692808225329 |
38 | 0.650071206187309 | 0.699857587625382 | 0.349928793812691 |
39 | 0.59539431196973 | 0.80921137606054 | 0.40460568803027 |
40 | 0.5547641428917 | 0.8904717142166 | 0.4452358571083 |
41 | 0.64258147389741 | 0.71483705220518 | 0.35741852610259 |
42 | 0.58565512702801 | 0.82868974594398 | 0.41434487297199 |
43 | 0.612535914273895 | 0.77492817145221 | 0.387464085726105 |
44 | 0.561570623483743 | 0.876858753032513 | 0.438429376516257 |
45 | 0.610486680249302 | 0.779026639501396 | 0.389513319750698 |
46 | 0.632477276397816 | 0.735045447204368 | 0.367522723602184 |
47 | 0.630720903487861 | 0.738558193024277 | 0.369279096512139 |
48 | 0.613497705151923 | 0.773004589696153 | 0.386502294848077 |
49 | 0.646126220866446 | 0.707747558267108 | 0.353873779133554 |
50 | 0.655351757096599 | 0.689296485806802 | 0.344648242903401 |
51 | 0.629124621509907 | 0.741750756980185 | 0.370875378490093 |
52 | 0.74715698533434 | 0.505686029331318 | 0.252843014665659 |
53 | 0.839824378826056 | 0.320351242347889 | 0.160175621173944 |
54 | 0.854138110491453 | 0.291723779017094 | 0.145861889508547 |
55 | 0.892828500252739 | 0.214342999494522 | 0.107171499747261 |
56 | 0.901779483247096 | 0.196441033505808 | 0.0982205167529041 |
57 | 0.939667482887394 | 0.120665034225213 | 0.0603325171126064 |
58 | 0.976278555727244 | 0.047442888545513 | 0.0237214442727565 |
59 | 0.984183443420348 | 0.0316331131593049 | 0.0158165565796525 |
60 | 0.988347182523573 | 0.0233056349528534 | 0.0116528174764267 |
61 | 0.99168395119863 | 0.0166320976027419 | 0.00831604880137097 |
62 | 0.991546486859949 | 0.0169070262801024 | 0.0084535131400512 |
63 | 0.989213155645487 | 0.0215736887090264 | 0.0107868443545132 |
64 | 0.991747084685636 | 0.0165058306287283 | 0.00825291531436416 |
65 | 0.99204080733085 | 0.015918385338301 | 0.0079591926691505 |
66 | 0.992470332404372 | 0.0150593351912565 | 0.00752966759562824 |
67 | 0.99010753555239 | 0.0197849288952201 | 0.00989246444761007 |
68 | 0.995029595452334 | 0.00994080909533178 | 0.00497040454766589 |
69 | 0.994369016535492 | 0.0112619669290158 | 0.00563098346450792 |
70 | 0.994697527885314 | 0.0106049442293726 | 0.00530247211468631 |
71 | 0.993487050577588 | 0.0130258988448237 | 0.00651294942241186 |
72 | 0.990275846072576 | 0.0194483078548474 | 0.0097241539274237 |
73 | 0.993148073662142 | 0.0137038526757163 | 0.00685192633785813 |
74 | 0.9935367811999 | 0.0129264376001995 | 0.00646321880009973 |
75 | 0.992941808885715 | 0.0141163822285694 | 0.00705819111428468 |
76 | 0.9923859255612 | 0.0152281488776015 | 0.00761407443880074 |
77 | 0.993889316045119 | 0.0122213679097628 | 0.00611068395488138 |
78 | 0.990334272744525 | 0.0193314545109498 | 0.0096657272554749 |
79 | 0.985020704996184 | 0.0299585900076322 | 0.0149792950038161 |
80 | 0.996004313161733 | 0.00799137367653452 | 0.00399568683826726 |
81 | 0.99369172500906 | 0.0126165499818787 | 0.00630827499093935 |
82 | 0.992040093688891 | 0.0159198126222174 | 0.00795990631110871 |
83 | 0.987607177341122 | 0.024785645317756 | 0.012392822658878 |
84 | 0.980721762349027 | 0.0385564753019467 | 0.0192782376509734 |
85 | 0.977409162445373 | 0.0451816751092544 | 0.0225908375546272 |
86 | 0.966967672191184 | 0.0660646556176317 | 0.0330323278088158 |
87 | 0.959579153393047 | 0.0808416932139068 | 0.0404208466069534 |
88 | 0.948969045570097 | 0.102061908859807 | 0.0510309544299035 |
89 | 0.93270913822412 | 0.134581723551761 | 0.0672908617758806 |
90 | 0.926214052827828 | 0.147571894344343 | 0.0737859471721716 |
91 | 0.936693985254029 | 0.126612029491943 | 0.0633060147459715 |
92 | 0.917662178859019 | 0.164675642281963 | 0.0823378211409813 |
93 | 0.955798075304036 | 0.0884038493919276 | 0.0442019246959638 |
94 | 0.947002560762715 | 0.105994878474570 | 0.0529974392372848 |
95 | 0.919031187795338 | 0.161937624409325 | 0.0809688122046623 |
96 | 0.923611357331691 | 0.152777285336618 | 0.0763886426683088 |
97 | 0.880141638459926 | 0.239716723080149 | 0.119858361540074 |
98 | 0.909521090287238 | 0.180957819425524 | 0.090478909712762 |
99 | 0.88440653945586 | 0.231186921088279 | 0.115593460544140 |
100 | 0.9464241909892 | 0.107151618021600 | 0.0535758090108002 |
101 | 0.93095633987471 | 0.138087320250579 | 0.0690436601252893 |
102 | 0.901347431648554 | 0.197305136702893 | 0.0986525683514464 |
103 | 0.886921610836934 | 0.226156778326131 | 0.113078389163066 |
104 | 0.887589796320515 | 0.224820407358970 | 0.112410203679485 |
Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
Description | # significant tests | % significant tests | OK/NOK |
1% type I error level | 2 | 0.0227272727272727 | NOK |
5% type I error level | 28 | 0.318181818181818 | NOK |
10% type I error level | 31 | 0.352272727272727 | NOK |