Multiple Linear Regression - Estimated Regression Equation |
best[t] = + 1.22151640213814 + 0.231803248360643standards[t] + 0.0583245373239288performance[t] + 0.467278936963013excellence[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) | 1.22151640213814 | 0.284986 | 4.2862 | 3.2e-05 | 1.6e-05 |
standards | 0.231803248360643 | 0.088029 | 2.6333 | 0.009314 | 0.004657 |
performance | 0.0583245373239288 | 0.109204 | 0.5341 | 0.594046 | 0.297023 |
excellence | 0.467278936963013 | 0.102773 | 4.5467 | 1.1e-05 | 5e-06 |
Multiple Linear Regression - Regression Statistics | |
Multiple R | 0.536873098061071 |
R-squared | 0.288232723421692 |
Adjusted R-squared | 0.274456582584693 |
F-TEST (value) | 20.9226028415423 |
F-TEST (DF numerator) | 3 |
F-TEST (DF denominator) | 155 |
p-value | 1.95858884666222e-11 |
Multiple Linear Regression - Residual Statistics | |
Residual Standard Deviation | 0.963925850954448 |
Sum Squared Residuals | 144.018722151430 |
Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
1 | 4 | 2.67800531010939 | 1.32199468989061 |
2 | 1 | 2.21072637314639 | -1.21072637314639 |
3 | 5 | 4.13449421808062 | 0.86550578191938 |
4 | 3 | 2.67800531010939 | 0.321994689890611 |
5 | 3 | 2.96813309579396 | 0.0318669042060444 |
6 | 3 | 3.14161180683067 | -0.141611806830668 |
7 | 2 | 3.02645763311788 | -1.02645763311788 |
8 | 3 | 2.90980855847003 | 0.0901914415299734 |
9 | 4 | 2.44252962150701 | 1.55747037849299 |
10 | 4 | 3.61256318403541 | 0.387436815964589 |
11 | 4 | 3.1999363441546 | 0.800063655845403 |
12 | 2 | 3.78386435576547 | -1.78386435576547 |
13 | 2 | 2.96813309579396 | -0.968133095793956 |
14 | 2 | 2.90980855847003 | -0.909808558470027 |
15 | 4 | 2.67433286986766 | 1.32566713013234 |
16 | 4 | 3.72553981844154 | 0.274460181558461 |
17 | 3 | 2.50085415883094 | 0.499145841169057 |
18 | 2 | 2.96813309579396 | -0.968133095793956 |
19 | 5 | 3.96101550704391 | 1.03898449295609 |
20 | 4 | 4.19281875540455 | -0.192818755404552 |
21 | 3 | 3.1452842470724 | -0.145284247072398 |
22 | 4 | 3.43173959251524 | 0.568260407484761 |
23 | 3 | 3.66721528111761 | -0.66721528111761 |
24 | 2 | 2.73632984743331 | -0.736329847433314 |
25 | 2 | 2.96813309579396 | -0.968133095793956 |
26 | 3 | 3.72553981844154 | -0.725539818441539 |
27 | 4 | 3.66721528111761 | 0.33278471888239 |
28 | 4 | 2.96813309579396 | 1.03186690420604 |
29 | 5 | 4.13449421808062 | 0.865505781919377 |
30 | 4 | 3.1999363441546 | 0.800063655845403 |
31 | 3 | 2.50452659907267 | 0.495473400927328 |
32 | 4 | 3.72553981844154 | 0.274460181558461 |
33 | 4 | 4.83357640340428 | -0.833576403404278 |
34 | 4 | 2.73632984743331 | 1.26367015256669 |
35 | 5 | 3.66721528111761 | 1.33278471888239 |
36 | 2 | 2.50085415883094 | -0.500854158830943 |
37 | 2 | 2.73632984743331 | -0.736329847433314 |
38 | 4 | 3.14161180683067 | 0.858388193169332 |
39 | 5 | 4.36629746644127 | 0.633702533558735 |
40 | 3 | 3.14161180683067 | -0.141611806830668 |
41 | 5 | 4.13449421808062 | 0.865505781919377 |
42 | 2 | 3.66721528111761 | -1.66721528111761 |
43 | 4 | 2.96813309579396 | 1.03186690420604 |
44 | 4 | 4.13449421808062 | -0.134494218080623 |
45 | 2 | 2.73632984743331 | -0.736329847433314 |
46 | 2 | 2.79465438475724 | -0.794654384757243 |
47 | 4 | 3.1999363441546 | 0.800063655845403 |
48 | 2 | 2.73632984743331 | -0.736329847433314 |
49 | 2 | 3.1999363441546 | -1.19993634415460 |
50 | 4 | 3.78386435576547 | 0.216135644234532 |
51 | 1 | 1.97892312478573 | -0.97892312478573 |
52 | 2 | 3.1999363441546 | -1.19993634415460 |
53 | 4 | 2.73632984743331 | 1.26367015256669 |
54 | 1 | 1.97892312478573 | -0.97892312478573 |
55 | 5 | 4.77674676701542 | 0.223253232984577 |
56 | 4 | 2.96813309579396 | 1.03186690420604 |
57 | 4 | 2.73632984743331 | 1.26367015256669 |
58 | 4 | 3.1999363441546 | 0.800063655845403 |
59 | 1 | 2.44252962150701 | -1.44252962150701 |
60 | 4 | 2.73632984743331 | 1.26367015256669 |
61 | 4 | 2.73632984743331 | 1.26367015256669 |
62 | 4 | 2.96813309579396 | 1.03186690420604 |
63 | 4 | 3.67088772135934 | 0.32911227864066 |
64 | 2 | 2.50452659907267 | -0.504526599072672 |
65 | 4 | 2.44252962150701 | 1.55747037849299 |
66 | 3 | 2.67800531010939 | 0.321994689890615 |
67 | 2 | 2.96813309579396 | -0.968133095793956 |
68 | 4 | 2.96813309579396 | 1.03186690420604 |
69 | 4 | 2.44252962150701 | 1.55747037849299 |
70 | 3 | 2.73632984743331 | 0.263670152566686 |
71 | 3 | 2.96813309579396 | 0.0318669042060444 |
72 | 2 | 2.67800531010939 | -0.678005310109385 |
73 | 4 | 3.72553981844154 | 0.274460181558461 |
74 | 4 | 3.72553981844154 | 0.274460181558461 |
75 | 4 | 3.25826088147853 | 0.741739118521474 |
76 | 4 | 2.73632984743331 | 1.26367015256669 |
77 | 4 | 3.43541203275697 | 0.564587967243031 |
78 | 4 | 3.1999363441546 | 0.800063655845403 |
79 | 2 | 2.90980855847003 | -0.909808558470027 |
80 | 2 | 3.31658541880245 | -1.31658541880245 |
81 | 4 | 2.79465438475724 | 1.20534561524276 |
82 | 2 | 2.96813309579396 | -0.968133095793956 |
83 | 4 | 2.50085415883094 | 1.49914584116906 |
84 | 5 | 3.66721528111761 | 1.33278471888239 |
85 | 2 | 2.67800531010939 | -0.678005310109385 |
86 | 4 | 4.13449421808062 | -0.134494218080623 |
87 | 2 | 2.79465438475724 | -0.794654384757243 |
88 | 4 | 2.21072637314637 | 1.78927362685363 |
89 | 4 | 4.13449421808062 | -0.134494218080623 |
90 | 2 | 3.43541203275697 | -1.43541203275697 |
91 | 4 | 3.1999363441546 | 0.800063655845403 |
92 | 1 | 3.1452842470724 | -2.1452842470724 |
93 | 2 | 2.67800531010939 | -0.678005310109385 |
94 | 5 | 3.43541203275697 | 1.56458796724303 |
95 | 2 | 2.96813309579396 | -0.968133095793956 |
96 | 5 | 4.95022547805214 | 0.049774521947864 |
97 | 4 | 3.20360878439633 | 0.796391215603673 |
98 | 4 | 4.01934004436784 | -0.0193400443678395 |
99 | 2 | 3.14161180683067 | -1.14161180683067 |
100 | 2 | 3.02645763311788 | -1.02645763311788 |
101 | 4 | 3.1999363441546 | 0.800063655845403 |
102 | 2 | 3.43541203275697 | -1.43541203275697 |
103 | 4 | 4.01934004436784 | -0.0193400443678395 |
104 | 4 | 3.26193332172026 | 0.738066678279744 |
105 | 2 | 2.96813309579396 | -0.968133095793956 |
106 | 4 | 2.67800531010939 | 1.32199468989062 |
107 | 2 | 3.37708749543304 | -1.37708749543304 |
108 | 4 | 2.73632984743331 | 1.26367015256669 |
109 | 4 | 3.25826088147853 | 0.741739118521474 |
110 | 4 | 2.73632984743331 | 1.26367015256669 |
111 | 3 | 3.14161180683067 | -0.141611806830668 |
112 | 3 | 3.66721528111761 | -0.66721528111761 |
113 | 2 | 2.50452659907267 | -0.504526599072672 |
114 | 5 | 4.36629746644127 | 0.633702533558735 |
115 | 3 | 2.21072637314637 | 0.789273626853628 |
116 | 4 | 2.96813309579396 | 1.03186690420604 |
117 | 3 | 4.19281875540455 | -1.19281875540455 |
118 | 2 | 2.50452659907267 | -0.504526599072672 |
119 | 4 | 3.43173959251524 | 0.568260407484761 |
120 | 2 | 2.44252962150701 | -0.442529621507014 |
121 | 1 | 2.44252962150701 | -1.44252962150701 |
122 | 2 | 3.43541203275697 | -1.43541203275697 |
123 | 4 | 3.43541203275697 | 0.564587967243031 |
124 | 1 | 2.21072637314637 | -1.21072637314637 |
125 | 1 | 2.2690509104703 | -1.2690509104703 |
126 | 4 | 3.72553981844154 | 0.274460181558461 |
127 | 3 | 2.67433286986766 | 0.325667130132345 |
128 | 2 | 2.96813309579396 | -0.968133095793956 |
129 | 3 | 3.43541203275697 | -0.435412032756969 |
130 | 2 | 2.96813309579396 | -0.968133095793956 |
131 | 3 | 3.1999363441546 | -0.199936344154597 |
132 | 4 | 2.96813309579396 | 1.03186690420604 |
133 | 2 | 3.14161180683067 | -1.14161180683067 |
134 | 1 | 3.14161180683067 | -2.14161180683067 |
135 | 4 | 2.73632984743331 | 1.26367015256669 |
136 | 4 | 4.25114329272848 | -0.251143292728481 |
137 | 4 | 2.73632984743331 | 1.26367015256669 |
138 | 3 | 3.1999363441546 | -0.199936344154597 |
139 | 2 | 3.43541203275697 | -1.43541203275697 |
140 | 2 | 2.96813309579396 | -0.968133095793956 |
141 | 2 | 2.73632984743331 | -0.736329847433314 |
142 | 5 | 3.67088772135934 | 1.32911227864066 |
143 | 5 | 4.54127107841305 | 0.458728921586948 |
144 | 2 | 2.21072637314637 | -0.210726373146372 |
145 | 3 | 3.78386435576547 | -0.783864355765468 |
146 | 2 | 2.96813309579396 | -0.968133095793956 |
147 | 4 | 3.96101550704391 | 0.0389844929560892 |
148 | 2 | 2.96813309579396 | -0.968133095793956 |
149 | 2 | 2.50085415883094 | -0.500854158830943 |
150 | 4 | 3.1999363441546 | 0.800063655845403 |
151 | 2 | 3.14161180683067 | -1.14161180683067 |
152 | 5 | 3.66721528111761 | 1.33278471888239 |
153 | 5 | 4.77674676701542 | 0.223253232984577 |
154 | 4 | 3.1999363441546 | 0.800063655845403 |
155 | 4 | 4.42462200376519 | -0.424622003765194 |
156 | 4 | 2.96813309579396 | 1.03186690420604 |
157 | 2 | 2.96813309579396 | -0.968133095793956 |
158 | 4 | 3.66721528111761 | 0.33278471888239 |
159 | 3 | 4.25114329272848 | -1.25114329272848 |
Goldfeld-Quandt test for Heteroskedasticity | |||
p-values | Alternative Hypothesis | ||
breakpoint index | greater | 2-sided | less |
7 | 0.348705772283607 | 0.697411544567213 | 0.651294227716393 |
8 | 0.196926117674761 | 0.393852235349521 | 0.80307388232524 |
9 | 0.649090344972348 | 0.701819310055305 | 0.350909655027653 |
10 | 0.563581108480416 | 0.872837783039167 | 0.436418891519584 |
11 | 0.495547822651428 | 0.991095645302857 | 0.504452177348572 |
12 | 0.460498102535905 | 0.92099620507181 | 0.539501897464095 |
13 | 0.418658897868757 | 0.837317795737515 | 0.581341102131243 |
14 | 0.51855254582394 | 0.96289490835212 | 0.48144745417606 |
15 | 0.486034437932817 | 0.972068875865634 | 0.513965562067183 |
16 | 0.450172255035902 | 0.900344510071803 | 0.549827744964098 |
17 | 0.428511631942873 | 0.857023263885745 | 0.571488368057127 |
18 | 0.402747700093628 | 0.805495400187256 | 0.597252299906372 |
19 | 0.516693141578095 | 0.96661371684381 | 0.483306858421905 |
20 | 0.443959681809271 | 0.887919363618542 | 0.556040318190729 |
21 | 0.385710220492061 | 0.771420440984122 | 0.614289779507939 |
22 | 0.319204145781872 | 0.638408291563745 | 0.680795854218128 |
23 | 0.32474124201608 | 0.64948248403216 | 0.67525875798392 |
24 | 0.271240687987990 | 0.542481375975981 | 0.72875931201201 |
25 | 0.255361068854513 | 0.510722137709027 | 0.744638931145487 |
26 | 0.215430613630148 | 0.430861227260296 | 0.784569386369852 |
27 | 0.170193005941472 | 0.340386011882943 | 0.829806994058528 |
28 | 0.205833480669213 | 0.411666961338426 | 0.794166519330787 |
29 | 0.175246591380767 | 0.350493182761533 | 0.824753408619233 |
30 | 0.156603356831314 | 0.313206713662628 | 0.843396643168686 |
31 | 0.174195360454385 | 0.34839072090877 | 0.825804639545615 |
32 | 0.146119857525579 | 0.292239715051159 | 0.85388014247442 |
33 | 0.182747410996591 | 0.365494821993182 | 0.817252589003409 |
34 | 0.227706476999612 | 0.455412953999225 | 0.772293523000388 |
35 | 0.260384794811586 | 0.520769589623172 | 0.739615205188414 |
36 | 0.228456985043727 | 0.456913970087455 | 0.771543014956273 |
37 | 0.207734032365106 | 0.415468064730211 | 0.792265967634894 |
38 | 0.180456979785985 | 0.360913959571970 | 0.819543020214015 |
39 | 0.152500220353588 | 0.305000440707176 | 0.847499779646412 |
40 | 0.135356002620245 | 0.270712005240489 | 0.864643997379755 |
41 | 0.123694373734863 | 0.247388747469726 | 0.876305626265137 |
42 | 0.216588212089664 | 0.433176424179328 | 0.783411787910336 |
43 | 0.225825225214339 | 0.451650450428679 | 0.77417477478566 |
44 | 0.191388927874139 | 0.382777855748279 | 0.80861107212586 |
45 | 0.174118073807088 | 0.348236147614176 | 0.825881926192912 |
46 | 0.152198019059945 | 0.304396038119891 | 0.847801980940055 |
47 | 0.140945971578895 | 0.281891943157790 | 0.859054028421105 |
48 | 0.126043494477298 | 0.252086988954595 | 0.873956505522702 |
49 | 0.150195546811567 | 0.300391093623135 | 0.849804453188433 |
50 | 0.138416525556095 | 0.276833051112189 | 0.861583474443905 |
51 | 0.139641469679819 | 0.279282939359637 | 0.860358530320181 |
52 | 0.162163707968603 | 0.324327415937206 | 0.837836292031397 |
53 | 0.200538516362102 | 0.401077032724203 | 0.799461483637898 |
54 | 0.201318713863104 | 0.402637427726209 | 0.798681286136896 |
55 | 0.179446009136708 | 0.358892018273416 | 0.820553990863292 |
56 | 0.188492702114846 | 0.376985404229692 | 0.811507297885154 |
57 | 0.222159809915979 | 0.444319619831958 | 0.777840190084021 |
58 | 0.209746683820366 | 0.419493367640731 | 0.790253316179634 |
59 | 0.262953677341465 | 0.52590735468293 | 0.737046322658535 |
60 | 0.296995263970196 | 0.593990527940393 | 0.703004736029804 |
61 | 0.328566393896580 | 0.657132787793159 | 0.67143360610342 |
62 | 0.333840925837394 | 0.667681851674787 | 0.666159074162606 |
63 | 0.296959393841308 | 0.593918787682617 | 0.703040606158692 |
64 | 0.267914185352451 | 0.535828370704902 | 0.732085814647549 |
65 | 0.327736007503593 | 0.655472015007185 | 0.672263992496407 |
66 | 0.290495008101899 | 0.580990016203799 | 0.7095049918981 |
67 | 0.292650692468213 | 0.585301384936427 | 0.707349307531786 |
68 | 0.297630790775706 | 0.595261581551412 | 0.702369209224294 |
69 | 0.358864118834767 | 0.717728237669534 | 0.641135881165233 |
70 | 0.319195731848384 | 0.638391463696767 | 0.680804268151616 |
71 | 0.278965482800249 | 0.557930965600498 | 0.721034517199751 |
72 | 0.264501862442975 | 0.529003724885951 | 0.735498137557025 |
73 | 0.230918716016209 | 0.461837432032418 | 0.769081283983791 |
74 | 0.199862300436688 | 0.399724600873377 | 0.800137699563312 |
75 | 0.187060595360049 | 0.374121190720098 | 0.812939404639951 |
76 | 0.210798844001545 | 0.42159768800309 | 0.789201155998455 |
77 | 0.189999602716159 | 0.379999205432317 | 0.810000397283841 |
78 | 0.180272345667962 | 0.360544691335925 | 0.819727654332038 |
79 | 0.181549720305771 | 0.363099440611542 | 0.81845027969423 |
80 | 0.21093193560702 | 0.42186387121404 | 0.78906806439298 |
81 | 0.231368952933079 | 0.462737905866158 | 0.768631047066921 |
82 | 0.232760139203398 | 0.465520278406796 | 0.767239860796602 |
83 | 0.284378567596510 | 0.568757135193019 | 0.71562143240349 |
84 | 0.325903640542349 | 0.651807281084698 | 0.674096359457651 |
85 | 0.306112539447341 | 0.612225078894682 | 0.693887460552659 |
86 | 0.270407787277440 | 0.540815574554881 | 0.72959221272256 |
87 | 0.259989735597835 | 0.51997947119567 | 0.740010264402165 |
88 | 0.366827299543004 | 0.733654599086008 | 0.633172700456996 |
89 | 0.327736948427311 | 0.655473896854622 | 0.672263051572689 |
90 | 0.373887649114284 | 0.747775298228568 | 0.626112350885716 |
91 | 0.366465984010432 | 0.732931968020864 | 0.633534015989568 |
92 | 0.536615143614498 | 0.926769712771004 | 0.463384856385502 |
93 | 0.51112357704594 | 0.97775284590812 | 0.48887642295406 |
94 | 0.596723236578608 | 0.806553526842783 | 0.403276763421392 |
95 | 0.592996790894391 | 0.814006418211218 | 0.407003209105609 |
96 | 0.547071094629374 | 0.905857810741252 | 0.452928905370626 |
97 | 0.536010579309808 | 0.927978841380383 | 0.463989420690192 |
98 | 0.48931844579632 | 0.97863689159264 | 0.51068155420368 |
99 | 0.49811380485273 | 0.99622760970546 | 0.50188619514727 |
100 | 0.504141464163961 | 0.991717071672078 | 0.495858535836039 |
101 | 0.500236509943281 | 0.999526980113438 | 0.499763490056719 |
102 | 0.548313604430781 | 0.903372791138437 | 0.451686395569218 |
103 | 0.501493791646521 | 0.997012416706957 | 0.498506208353479 |
104 | 0.478291272835013 | 0.956582545670027 | 0.521708727164987 |
105 | 0.472058648936499 | 0.944117297872997 | 0.527941351063501 |
106 | 0.532616150985185 | 0.93476769802963 | 0.467383849014815 |
107 | 0.562676239339327 | 0.874647521321345 | 0.437323760660673 |
108 | 0.607690384652446 | 0.784619230695107 | 0.392309615347554 |
109 | 0.599034149372227 | 0.801931701255545 | 0.400965850627773 |
110 | 0.653449254782541 | 0.693101490434917 | 0.346550745217459 |
111 | 0.608051053143108 | 0.783897893713784 | 0.391948946856892 |
112 | 0.576033342615083 | 0.847933314769835 | 0.423966657384918 |
113 | 0.533078132389604 | 0.933843735220792 | 0.466921867610396 |
114 | 0.512724178025575 | 0.97455164394885 | 0.487275821974425 |
115 | 0.522388900885386 | 0.955222198229227 | 0.477611099114614 |
116 | 0.559654541514306 | 0.880690916971388 | 0.440345458485694 |
117 | 0.585070971788785 | 0.82985805642243 | 0.414929028211215 |
118 | 0.538647478862257 | 0.922705042275487 | 0.461352521137743 |
119 | 0.5387376614854 | 0.9225246770292 | 0.4612623385146 |
120 | 0.491828486797651 | 0.983656973595301 | 0.508171513202349 |
121 | 0.509314556472533 | 0.981370887054934 | 0.490685443527467 |
122 | 0.568048112442305 | 0.86390377511539 | 0.431951887557695 |
123 | 0.534353096385198 | 0.931293807229604 | 0.465646903614802 |
124 | 0.537000315144604 | 0.925999369710791 | 0.462999684855396 |
125 | 0.564558268178149 | 0.870883463643701 | 0.435441731821851 |
126 | 0.519027415992378 | 0.961945168015244 | 0.480972584007622 |
127 | 0.51394434533322 | 0.97211130933356 | 0.48605565466678 |
128 | 0.497710903052184 | 0.995421806104369 | 0.502289096947816 |
129 | 0.447817898449712 | 0.895635796899424 | 0.552182101550288 |
130 | 0.434072766998787 | 0.868145533997575 | 0.565927233001213 |
131 | 0.378440535255841 | 0.756881070511682 | 0.621559464744159 |
132 | 0.403964159973086 | 0.807928319946172 | 0.596035840026914 |
133 | 0.374010887043708 | 0.748021774087416 | 0.625989112956292 |
134 | 0.54356951497271 | 0.91286097005458 | 0.45643048502729 |
135 | 0.601392571207093 | 0.797214857585815 | 0.398607428792907 |
136 | 0.534972640829759 | 0.930054718340482 | 0.465027359170241 |
137 | 0.644497052479459 | 0.711005895041083 | 0.355502947520541 |
138 | 0.573818211902909 | 0.852363576194182 | 0.426181788097091 |
139 | 0.678590614944257 | 0.642818770111485 | 0.321409385055743 |
140 | 0.650921574514103 | 0.698156850971793 | 0.349078425485897 |
141 | 0.598046828558513 | 0.803906342882973 | 0.401953171441487 |
142 | 0.627367853705483 | 0.745264292589034 | 0.372632146294517 |
143 | 0.583102457586113 | 0.833795084827774 | 0.416897542413887 |
144 | 0.495282210747915 | 0.99056442149583 | 0.504717789252085 |
145 | 0.421360069250932 | 0.842720138501863 | 0.578639930749068 |
146 | 0.38338826602527 | 0.76677653205054 | 0.61661173397473 |
147 | 0.295301023728632 | 0.590602047457265 | 0.704698976271368 |
148 | 0.269961531288596 | 0.539923062577191 | 0.730038468711405 |
149 | 0.213089315525369 | 0.426178631050738 | 0.786910684474631 |
150 | 0.165155523818429 | 0.330311047636858 | 0.834844476181571 |
151 | 0.255338586963392 | 0.510677173926785 | 0.744661413036608 |
152 | 0.236826484046643 | 0.473652968093285 | 0.763173515953357 |
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 | 0 | 0 | OK |
10% type I error level | 0 | 0 | OK |