Multiple Linear Regression - Estimated Regression Equation |
Concernovermistakes[t] = + 23.2383107088989 + 1.26328736622854M1[t] -2.74211735976439M2[t] -1.31895065718594M3[t] -3.5721468074409M4[t] -3.8083207642031M5[t] -4.42911010558068M6[t] -3.12682252388133M7[t] -2.43991955756661M8[t] -1.44532428355956M9[t] -0.989190548014066M10[t] -2.68690296631471M11[t] + 0.00540472599296133t + 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) | 23.2383107088989 | 1.786634 | 13.0068 | 0 | 0 |
M1 | 1.26328736622854 | 2.198322 | 0.5747 | 0.566406 | 0.283203 |
M2 | -2.74211735976439 | 2.198123 | -1.2475 | 0.214218 | 0.107109 |
M3 | -1.31895065718594 | 2.197968 | -0.6001 | 0.549385 | 0.274692 |
M4 | -3.5721468074409 | 2.23949 | -1.5951 | 0.112859 | 0.056429 |
M5 | -3.8083207642031 | 2.239164 | -1.7008 | 0.091114 | 0.045557 |
M6 | -4.42911010558068 | 2.238881 | -1.9783 | 0.04978 | 0.02489 |
M7 | -3.12682252388133 | 2.238642 | -1.3967 | 0.164608 | 0.082304 |
M8 | -2.43991955756661 | 2.238446 | -1.09 | 0.277506 | 0.138753 |
M9 | -1.44532428355956 | 2.238294 | -0.6457 | 0.51947 | 0.259735 |
M10 | -0.989190548014066 | 2.238185 | -0.442 | 0.659171 | 0.329586 |
M11 | -2.68690296631471 | 2.238119 | -1.2005 | 0.231882 | 0.115941 |
t | 0.00540472599296133 | 0.009871 | 0.5475 | 0.584849 | 0.292424 |
Multiple Linear Regression - Regression Statistics | |
Multiple R | 0.285229909227530 |
R-squared | 0.0813561011179448 |
Adjusted R-squared | 0.0058511231276388 |
F-TEST (value) | 1.07749321016146 |
F-TEST (DF numerator) | 12 |
F-TEST (DF denominator) | 146 |
p-value | 0.383217157247471 |
Multiple Linear Regression - Residual Statistics | |
Residual Standard Deviation | 5.70605193364234 |
Sum Squared Residuals | 4753.61818573583 |
Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
1 | 24 | 24.5070028011206 | -0.507002801120587 |
2 | 25 | 20.5070028011204 | 4.49299719887957 |
3 | 17 | 21.9355742296919 | -4.93557422969188 |
4 | 18 | 19.6877828054298 | -1.68778280542985 |
5 | 18 | 19.4570135746607 | -1.45701357466066 |
6 | 16 | 18.841628959276 | -2.84162895927602 |
7 | 20 | 20.1493212669683 | -0.149321266968339 |
8 | 16 | 20.841628959276 | -4.84162895927602 |
9 | 18 | 21.841628959276 | -3.84162895927600 |
10 | 17 | 22.3031674208145 | -5.30316742081448 |
11 | 23 | 20.6108597285068 | 2.38914027149322 |
12 | 30 | 23.3031674208145 | 6.6968325791855 |
13 | 23 | 24.5718595130360 | -1.57185951303597 |
14 | 18 | 20.571859513036 | -2.57185951303599 |
15 | 15 | 22.0004309416074 | -7.00043094160741 |
16 | 12 | 19.7526395173454 | -7.7526395173454 |
17 | 21 | 19.5218702865762 | 1.47812971342383 |
18 | 15 | 18.9064856711916 | -3.90648567119155 |
19 | 20 | 20.2141779788839 | -0.21417797888386 |
20 | 31 | 20.9064856711916 | 10.0935143288084 |
21 | 27 | 21.9064856711916 | 5.09351432880845 |
22 | 34 | 22.36802413273 | 11.6319758672700 |
23 | 21 | 20.6757164404223 | 0.324283559577679 |
24 | 31 | 23.36802413273 | 7.63197586727 |
25 | 19 | 24.6367162249515 | -5.63671622495151 |
26 | 16 | 20.6367162249515 | -4.63671622495152 |
27 | 20 | 22.0652876535229 | -2.06528765352294 |
28 | 21 | 19.8174962292609 | 1.18250377073907 |
29 | 22 | 19.5867269984917 | 2.4132730015083 |
30 | 17 | 18.9713423831071 | -1.97134238310709 |
31 | 24 | 20.2790346907994 | 3.72096530920060 |
32 | 25 | 20.9713423831071 | 4.02865761689292 |
33 | 26 | 21.9713423831071 | 4.02865761689291 |
34 | 25 | 22.4328808446455 | 2.56711915535445 |
35 | 17 | 20.7405731523379 | -3.74057315233786 |
36 | 32 | 23.4328808446455 | 8.56711915535446 |
37 | 33 | 24.7015729368670 | 8.29842706313296 |
38 | 13 | 20.7015729368671 | -7.70157293686706 |
39 | 32 | 22.1301443654385 | 9.86985563456152 |
40 | 25 | 19.8823529411765 | 5.11764705882353 |
41 | 29 | 19.6515837104072 | 9.34841628959276 |
42 | 22 | 19.0361990950226 | 2.96380090497738 |
43 | 18 | 20.3438914027149 | -2.34389140271493 |
44 | 17 | 21.0361990950226 | -4.03619909502262 |
45 | 20 | 22.0361990950226 | -2.03619909502262 |
46 | 15 | 22.4977375565611 | -7.49773755656108 |
47 | 20 | 20.8054298642534 | -0.805429864253393 |
48 | 33 | 23.4977375565611 | 9.50226244343892 |
49 | 29 | 24.7664296487826 | 4.23357035121742 |
50 | 23 | 20.7664296487826 | 2.23357035121740 |
51 | 26 | 22.195001077354 | 3.80499892264598 |
52 | 18 | 19.947209653092 | -1.94720965309201 |
53 | 20 | 19.7164404223228 | 0.283559577677226 |
54 | 11 | 19.1010558069382 | -8.10105580693816 |
55 | 28 | 20.4087481146305 | 7.59125188536953 |
56 | 26 | 21.1010558069382 | 4.89894419306184 |
57 | 22 | 22.1010558069382 | -0.101055806938159 |
58 | 17 | 22.5625942684766 | -5.56259426847662 |
59 | 12 | 20.8702865761689 | -8.87028657616893 |
60 | 14 | 23.5625942684766 | -9.56259426847661 |
61 | 17 | 24.8312863606981 | -7.83128636069812 |
62 | 21 | 20.8312863606981 | 0.168713639301869 |
63 | 19 | 22.2598577892695 | -3.25985778926955 |
64 | 18 | 20.0120663650075 | -2.01206636500754 |
65 | 10 | 19.7812971342383 | -9.7812971342383 |
66 | 29 | 19.1659125188537 | 9.8340874811463 |
67 | 31 | 20.473604826546 | 10.526395173454 |
68 | 19 | 21.1659125188537 | -2.16591251885369 |
69 | 9 | 22.1659125188537 | -13.1659125188537 |
70 | 20 | 22.6274509803922 | -2.62745098039216 |
71 | 28 | 20.9351432880845 | 7.06485671191554 |
72 | 19 | 23.6274509803921 | -4.62745098039214 |
73 | 30 | 24.8961430726137 | 5.10385692738635 |
74 | 29 | 20.8961430726137 | 8.10385692738634 |
75 | 26 | 22.3247145011851 | 3.67528549881491 |
76 | 23 | 20.0769230769231 | 2.92307692307692 |
77 | 13 | 19.8461538461538 | -6.84615384615385 |
78 | 21 | 19.2307692307692 | 1.76923076923077 |
79 | 19 | 20.5384615384615 | -1.53846153846154 |
80 | 28 | 21.2307692307692 | 6.76923076923077 |
81 | 23 | 22.2307692307692 | 0.769230769230769 |
82 | 18 | 22.6923076923077 | -4.69230769230769 |
83 | 21 | 21 | -1.1518563880486e-15 |
84 | 20 | 23.6923076923077 | -3.69230769230768 |
85 | 23 | 24.9609997845292 | -1.96099978452919 |
86 | 21 | 20.9609997845292 | 0.0390002154707971 |
87 | 21 | 22.3895712131006 | -1.38957121310062 |
88 | 15 | 20.1417797888386 | -5.14177978883861 |
89 | 28 | 19.9110105580694 | 8.08898944193062 |
90 | 19 | 19.2956259426848 | -0.295625942684766 |
91 | 26 | 20.6033182503771 | 5.39668174962293 |
92 | 10 | 21.2956259426848 | -11.2956259426848 |
93 | 16 | 22.2956259426848 | -6.29562594268477 |
94 | 22 | 22.7571644042232 | -0.757164404223229 |
95 | 19 | 21.0648567119155 | -2.06485671191554 |
96 | 31 | 23.7571644042232 | 7.24283559577678 |
97 | 31 | 25.0258564964447 | 5.97414350355528 |
98 | 29 | 21.0258564964447 | 7.97414350355526 |
99 | 19 | 22.4544279250162 | -3.45442792501616 |
100 | 22 | 20.2066365007542 | 1.79336349924585 |
101 | 23 | 19.9758672699849 | 3.02413273001508 |
102 | 15 | 19.3604826546003 | -4.3604826546003 |
103 | 20 | 20.6681749622926 | -0.668174962292612 |
104 | 18 | 21.3604826546003 | -3.3604826546003 |
105 | 23 | 22.3604826546003 | 0.639517345399697 |
106 | 25 | 22.8220211161388 | 2.17797888386124 |
107 | 21 | 21.1297134238311 | -0.129713423831073 |
108 | 24 | 23.8220211161388 | 0.177978883861245 |
109 | 25 | 25.0907132083603 | -0.090713208360257 |
110 | 17 | 21.0907132083603 | -4.09071320836027 |
111 | 13 | 22.5192846369317 | -9.5192846369317 |
112 | 28 | 20.2714932126697 | 7.72850678733031 |
113 | 21 | 20.0407239819005 | 0.959276018099546 |
114 | 25 | 19.4253393665158 | 5.57466063348416 |
115 | 9 | 20.7330316742081 | -11.7330316742081 |
116 | 16 | 21.4253393665158 | -5.42533936651584 |
117 | 19 | 22.4253393665158 | -3.42533936651584 |
118 | 17 | 22.8868778280543 | -5.8868778280543 |
119 | 25 | 21.1945701357466 | 3.80542986425339 |
120 | 20 | 23.8868778280543 | -3.88687782805429 |
121 | 29 | 25.1555699202758 | 3.84443007972420 |
122 | 14 | 21.1555699202758 | -7.15556992027581 |
123 | 22 | 22.5841413488472 | -0.584141348847231 |
124 | 15 | 20.3363499245852 | -5.33634992458522 |
125 | 19 | 20.105580693816 | -1.10558069381599 |
126 | 20 | 19.4901960784314 | 0.509803921568626 |
127 | 15 | 20.7978883861237 | -5.79788838612368 |
128 | 20 | 21.4901960784314 | -1.49019607843137 |
129 | 18 | 22.4901960784314 | -4.49019607843137 |
130 | 33 | 22.9517345399698 | 10.0482654600302 |
131 | 22 | 21.2594268476621 | 0.740573152337855 |
132 | 16 | 23.9517345399698 | -7.95173453996983 |
133 | 17 | 25.2204266321913 | -8.22042663219133 |
134 | 16 | 21.2204266321913 | -5.22042663219135 |
135 | 21 | 22.6489980607628 | -1.64899806076277 |
136 | 26 | 20.4012066365008 | 5.59879336349924 |
137 | 18 | 20.1704374057315 | -2.17043740573152 |
138 | 18 | 19.5550527903469 | -1.55505279034691 |
139 | 17 | 20.8627450980392 | -3.86274509803922 |
140 | 22 | 21.5550527903469 | 0.44494720965309 |
141 | 30 | 22.5550527903469 | 7.4449472096531 |
142 | 30 | 23.0165912518854 | 6.98340874811463 |
143 | 24 | 21.3242835595777 | 2.67571644042232 |
144 | 21 | 24.0165912518854 | -3.01659125188536 |
145 | 21 | 25.2852833441069 | -4.28528334410686 |
146 | 29 | 21.2852833441069 | 7.71471665589312 |
147 | 31 | 22.7138547726783 | 8.2861452273217 |
148 | 20 | 20.4660633484163 | -0.466063348416294 |
149 | 16 | 20.2352941176471 | -4.23529411764706 |
150 | 22 | 19.6199095022624 | 2.38009049773755 |
151 | 20 | 20.9276018099548 | -0.927601809954756 |
152 | 28 | 21.6199095022624 | 6.38009049773756 |
153 | 38 | 22.6199095022624 | 15.3800904977376 |
154 | 22 | 23.0814479638009 | -1.08144796380091 |
155 | 20 | 21.3891402714932 | -1.38914027149322 |
156 | 17 | 24.0814479638009 | -7.0814479638009 |
157 | 28 | 25.3501400560224 | 2.6498599439776 |
158 | 22 | 21.3501400560224 | 0.649859943977581 |
159 | 31 | 22.7787114845938 | 8.22128851540616 |
Goldfeld-Quandt test for Heteroskedasticity | |||
p-values | Alternative Hypothesis | ||
breakpoint index | greater | 2-sided | less |
16 | 0.0565687891798083 | 0.113137578359617 | 0.943431210820192 |
17 | 0.0839659028663624 | 0.167931805732725 | 0.916034097133638 |
18 | 0.0367537036556018 | 0.0735074073112037 | 0.963246296344398 |
19 | 0.0166035069260113 | 0.0332070138520226 | 0.983396493073989 |
20 | 0.31258535125928 | 0.62517070251856 | 0.68741464874072 |
21 | 0.328614862613942 | 0.657229725227883 | 0.671385137386058 |
22 | 0.583569550402658 | 0.832860899194683 | 0.416430449597342 |
23 | 0.512577557448716 | 0.974844885102568 | 0.487422442551284 |
24 | 0.435076853934405 | 0.87015370786881 | 0.564923146065595 |
25 | 0.435693232606444 | 0.871386465212888 | 0.564306767393556 |
26 | 0.42543745092194 | 0.85087490184388 | 0.57456254907806 |
27 | 0.363228603103468 | 0.726457206206935 | 0.636771396896532 |
28 | 0.319845446939040 | 0.639690893878081 | 0.68015455306096 |
29 | 0.253411545645171 | 0.506823091290343 | 0.746588454354829 |
30 | 0.196227070850857 | 0.392454141701713 | 0.803772929149143 |
31 | 0.153547415235307 | 0.307094830470614 | 0.846452584764693 |
32 | 0.115456325044678 | 0.230912650089357 | 0.884543674955321 |
33 | 0.0863857570120045 | 0.172771514024009 | 0.913614242987995 |
34 | 0.0647520070783626 | 0.129504014156725 | 0.935247992921637 |
35 | 0.0655339780689108 | 0.131067956137822 | 0.934466021931089 |
36 | 0.0534670586357996 | 0.106934117271599 | 0.9465329413642 |
37 | 0.0793797507878676 | 0.158759501575735 | 0.920620249212132 |
38 | 0.115445697507034 | 0.230891395014069 | 0.884554302492966 |
39 | 0.225973925175037 | 0.451947850350074 | 0.774026074824963 |
40 | 0.207548412350879 | 0.415096824701757 | 0.792451587649121 |
41 | 0.215755276609695 | 0.431510553219391 | 0.784244723390304 |
42 | 0.178869710283796 | 0.357739420567593 | 0.821130289716204 |
43 | 0.182556945663054 | 0.365113891326109 | 0.817443054336946 |
44 | 0.233346704975982 | 0.466693409951964 | 0.766653295024018 |
45 | 0.224537952917625 | 0.44907590583525 | 0.775462047082375 |
46 | 0.332734110762307 | 0.665468221524614 | 0.667265889237693 |
47 | 0.285886216736989 | 0.571772433473977 | 0.714113783263011 |
48 | 0.298810296496208 | 0.597620592992415 | 0.701189703503792 |
49 | 0.266059945706883 | 0.532119891413765 | 0.733940054293117 |
50 | 0.22970326848285 | 0.4594065369657 | 0.77029673151715 |
51 | 0.201173352803007 | 0.402346705606013 | 0.798826647196993 |
52 | 0.173860716098747 | 0.347721432197493 | 0.826139283901253 |
53 | 0.157677134722782 | 0.315354269445563 | 0.842322865277218 |
54 | 0.192400741225735 | 0.38480148245147 | 0.807599258774265 |
55 | 0.20754962209104 | 0.41509924418208 | 0.79245037790896 |
56 | 0.189733430561107 | 0.379466861122213 | 0.810266569438893 |
57 | 0.161245958520749 | 0.322491917041499 | 0.83875404147925 |
58 | 0.170744408642889 | 0.341488817285779 | 0.82925559135711 |
59 | 0.224232022908898 | 0.448464045817796 | 0.775767977091102 |
60 | 0.46091207395646 | 0.92182414791292 | 0.53908792604354 |
61 | 0.501430525086617 | 0.997138949826766 | 0.498569474913383 |
62 | 0.4538151879924 | 0.9076303759848 | 0.5461848120076 |
63 | 0.415228804260661 | 0.830457608521322 | 0.584771195739339 |
64 | 0.369670555266206 | 0.739341110532411 | 0.630329444733794 |
65 | 0.466484551961428 | 0.932969103922857 | 0.533515448038572 |
66 | 0.595442078767857 | 0.809115842464287 | 0.404557921232143 |
67 | 0.701696464980854 | 0.596607070038292 | 0.298303535019146 |
68 | 0.668245847554227 | 0.663508304891546 | 0.331754152445773 |
69 | 0.818361916953823 | 0.363276166092354 | 0.181638083046177 |
70 | 0.789107217391002 | 0.421785565217997 | 0.210892782608998 |
71 | 0.81822726417456 | 0.363545471650881 | 0.181772735825440 |
72 | 0.8177122578938 | 0.364575484212398 | 0.182287742106199 |
73 | 0.816466604484336 | 0.367066791031328 | 0.183533395515664 |
74 | 0.854593666932024 | 0.290812666135951 | 0.145406333067976 |
75 | 0.841138396973498 | 0.317723206053004 | 0.158861603026502 |
76 | 0.820418529201479 | 0.359162941597042 | 0.179581470798521 |
77 | 0.8278918057246 | 0.3442163885508 | 0.1721081942754 |
78 | 0.799732914680829 | 0.400534170638342 | 0.200267085319171 |
79 | 0.776735951533299 | 0.446528096933403 | 0.223264048466701 |
80 | 0.809604318584409 | 0.380791362831182 | 0.190395681415591 |
81 | 0.776737766908299 | 0.446524466183403 | 0.223262233091701 |
82 | 0.759394593497527 | 0.481210813004947 | 0.240605406502473 |
83 | 0.719765970018004 | 0.560468059963993 | 0.280234029981996 |
84 | 0.699178699007767 | 0.601642601984466 | 0.300821300992233 |
85 | 0.65720917941888 | 0.68558164116224 | 0.34279082058112 |
86 | 0.612166380446944 | 0.775667239106111 | 0.387833619553056 |
87 | 0.564656826145423 | 0.870686347709153 | 0.435343173854577 |
88 | 0.549409316810711 | 0.901181366378577 | 0.450590683189288 |
89 | 0.615610673546239 | 0.768778652907522 | 0.384389326453761 |
90 | 0.567380589084137 | 0.865238821831726 | 0.432619410915863 |
91 | 0.624603686566704 | 0.750792626866592 | 0.375396313433296 |
92 | 0.717846302869109 | 0.564307394261782 | 0.282153697130891 |
93 | 0.728548220779603 | 0.542903558440794 | 0.271451779220397 |
94 | 0.688873795220087 | 0.622252409559826 | 0.311126204779913 |
95 | 0.646687012053426 | 0.706625975893149 | 0.353312987946574 |
96 | 0.743103518763444 | 0.513792962473111 | 0.256896481236556 |
97 | 0.77789152730727 | 0.444216945385459 | 0.222108472692729 |
98 | 0.858532536170661 | 0.282934927658677 | 0.141467463829339 |
99 | 0.832100571438638 | 0.335798857122723 | 0.167899428561361 |
100 | 0.803394102850334 | 0.393211794299332 | 0.196605897149666 |
101 | 0.804957325277445 | 0.39008534944511 | 0.195042674722555 |
102 | 0.781316860859402 | 0.437366278281197 | 0.218683139140598 |
103 | 0.790753304761872 | 0.418493390476255 | 0.209246695238128 |
104 | 0.754971664587716 | 0.490056670824568 | 0.245028335412284 |
105 | 0.713501113889501 | 0.572997772220997 | 0.286498886110499 |
106 | 0.67788122084635 | 0.6442375583073 | 0.32211877915365 |
107 | 0.629941156629434 | 0.740117686741132 | 0.370058843370566 |
108 | 0.663893842211742 | 0.672212315576517 | 0.336106157788258 |
109 | 0.641855196504106 | 0.716289606991788 | 0.358144803495894 |
110 | 0.599503164137837 | 0.800993671724326 | 0.400496835862163 |
111 | 0.668697455287973 | 0.662605089424054 | 0.331302544712027 |
112 | 0.760017912926561 | 0.479964174146879 | 0.239982087073439 |
113 | 0.759934984600914 | 0.480130030798172 | 0.240065015399086 |
114 | 0.80404853143598 | 0.391902937128039 | 0.195951468564020 |
115 | 0.826303859184972 | 0.347392281630056 | 0.173696140815028 |
116 | 0.801428005131353 | 0.397143989737294 | 0.198571994868647 |
117 | 0.792212355641932 | 0.415575288716137 | 0.207787644358068 |
118 | 0.816642245741585 | 0.36671550851683 | 0.183357754258415 |
119 | 0.814852602495942 | 0.370294795008116 | 0.185147397504058 |
120 | 0.808800081930461 | 0.382399836139077 | 0.191199918069539 |
121 | 0.888995987968798 | 0.222008024062404 | 0.111004012031202 |
122 | 0.873817526299002 | 0.252364947401996 | 0.126182473700998 |
123 | 0.837310408783627 | 0.325379182432747 | 0.162689591216373 |
124 | 0.820125949520516 | 0.359748100958969 | 0.179874050479484 |
125 | 0.799589858739027 | 0.400820282521945 | 0.200410141260973 |
126 | 0.760569280852472 | 0.478861438295056 | 0.239430719147528 |
127 | 0.709224136555239 | 0.581551726889522 | 0.290775863444761 |
128 | 0.646384436557423 | 0.707231126885154 | 0.353615563442577 |
129 | 0.820331020648015 | 0.35933795870397 | 0.179668979351985 |
130 | 0.897881396170347 | 0.204237207659306 | 0.102118603829653 |
131 | 0.86918115967249 | 0.26163768065502 | 0.13081884032751 |
132 | 0.829994296186691 | 0.340011407626618 | 0.170005703813309 |
133 | 0.804924521151705 | 0.39015095769659 | 0.195075478848295 |
134 | 0.820482741905018 | 0.359034516189964 | 0.179517258094982 |
135 | 0.888396403449321 | 0.223207193101357 | 0.111603596550678 |
136 | 0.880485176598369 | 0.239029646803262 | 0.119514823401631 |
137 | 0.826884324275871 | 0.346231351448258 | 0.173115675724129 |
138 | 0.769350671028098 | 0.461298657943804 | 0.230649328971902 |
139 | 0.690621719115386 | 0.618756561769228 | 0.309378280884614 |
140 | 0.67009773942681 | 0.65980452114638 | 0.32990226057319 |
141 | 0.78793192286437 | 0.42413615427126 | 0.21206807713563 |
142 | 0.761735649786674 | 0.476528700426651 | 0.238264350213326 |
143 | 0.626515308756556 | 0.746969382486888 | 0.373484691243444 |
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 | 1 | 0.0078125 | OK |
10% type I error level | 2 | 0.015625 | OK |