Multiple Linear Regression - Estimated Regression Equation |
Concernovermistakes[t] = + 23.2383107088989 + 1.26328736622854M1[t] -2.74211735976442M2[t] -1.31895065718595M3[t] -3.57214680744093M4[t] -3.80832076420312M5[t] -4.42911010558069M6[t] -3.12682252388135M7[t] -2.43991955756662M8[t] -1.44532428355958M9[t] -0.989190548014078M10[t] -2.68690296631473M11[t] + 0.00540472599296128t + 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 | -2.74211735976442 | 2.198123 | -1.2475 | 0.214218 | 0.107109 |
M3 | -1.31895065718595 | 2.197968 | -0.6001 | 0.549385 | 0.274692 |
M4 | -3.57214680744093 | 2.23949 | -1.5951 | 0.112859 | 0.056429 |
M5 | -3.80832076420312 | 2.239164 | -1.7008 | 0.091114 | 0.045557 |
M6 | -4.42911010558069 | 2.238881 | -1.9783 | 0.04978 | 0.02489 |
M7 | -3.12682252388135 | 2.238642 | -1.3967 | 0.164608 | 0.082304 |
M8 | -2.43991955756662 | 2.238446 | -1.09 | 0.277506 | 0.138753 |
M9 | -1.44532428355958 | 2.238294 | -0.6457 | 0.51947 | 0.259735 |
M10 | -0.989190548014078 | 2.238185 | -0.442 | 0.659171 | 0.329586 |
M11 | -2.68690296631473 | 2.238119 | -1.2005 | 0.231882 | 0.115941 |
t | 0.00540472599296128 | 0.009871 | 0.5475 | 0.584849 | 0.292424 |
Multiple Linear Regression - Regression Statistics | |
Multiple R | 0.28522990922753 |
R-squared | 0.081356101117945 |
Adjusted R-squared | 0.00585112312763891 |
F-TEST (value) | 1.07749321016146 |
F-TEST (DF numerator) | 12 |
F-TEST (DF denominator) | 146 |
p-value | 0.383217157247469 |
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 | 24.5070028011204 | -0.507002801120426 |
2 | 25 | 20.5070028011204 | 4.49299719887955 |
3 | 17 | 21.9355742296919 | -4.93557422969187 |
4 | 18 | 19.6877828054299 | -1.68778280542987 |
5 | 18 | 19.4570135746606 | -1.45701357466063 |
6 | 16 | 18.841628959276 | -2.84162895927602 |
7 | 20 | 20.1493212669683 | -0.149321266968327 |
8 | 16 | 20.841628959276 | -4.84162895927602 |
9 | 18 | 21.841628959276 | -3.84162895927602 |
10 | 17 | 22.3031674208145 | -5.30316742081448 |
11 | 23 | 20.6108597285068 | 2.38914027149321 |
12 | 30 | 23.3031674208145 | 6.69683257918552 |
13 | 23 | 24.571859513036 | -1.57185951303598 |
14 | 18 | 20.571859513036 | -2.57185951303598 |
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 | -0.214177978883861 |
20 | 31 | 20.9064856711916 | 10.0935143288084 |
21 | 27 | 21.9064856711916 | 5.09351432880845 |
22 | 34 | 22.36802413273 | 11.63197586727 |
23 | 21 | 20.6757164404223 | 0.324283559577677 |
24 | 31 | 23.36802413273 | 7.63197586726998 |
25 | 19 | 24.6367162249515 | -5.63671622495152 |
26 | 16 | 20.6367162249515 | -4.63671622495152 |
27 | 20 | 22.0652876535229 | -2.06528765352295 |
28 | 21 | 19.8174962292609 | 1.18250377073906 |
29 | 22 | 19.5867269984917 | 2.4132730015083 |
30 | 17 | 18.9713423831071 | -1.97134238310709 |
31 | 24 | 20.2790346907994 | 3.7209653092006 |
32 | 25 | 20.9713423831071 | 4.02865761689291 |
33 | 26 | 21.9713423831071 | 4.02865761689291 |
34 | 25 | 22.4328808446456 | 2.56711915535445 |
35 | 17 | 20.7405731523379 | -3.74057315233786 |
36 | 32 | 23.4328808446456 | 8.56711915535445 |
37 | 33 | 24.7015729368671 | 8.29842706313294 |
38 | 13 | 20.7015729368671 | -7.70157293686705 |
39 | 32 | 22.1301443654385 | 9.86985563456151 |
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 | -4.03619909502263 |
45 | 20 | 22.0361990950226 | -2.03619909502262 |
46 | 15 | 22.4977375565611 | -7.49773755656109 |
47 | 20 | 20.8054298642534 | -0.805429864253394 |
48 | 33 | 23.4977375565611 | 9.50226244343891 |
49 | 29 | 24.7664296487826 | 4.23357035121741 |
50 | 23 | 20.7664296487826 | 2.23357035121741 |
51 | 26 | 22.195001077354 | 3.80499892264598 |
52 | 18 | 19.947209653092 | -1.94720965309201 |
53 | 20 | 19.7164404223228 | 0.283559577677225 |
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 | -9.56259426847662 |
61 | 17 | 24.8312863606981 | -7.83128636069813 |
62 | 21 | 20.8312863606981 | 0.168713639301874 |
63 | 19 | 22.2598577892696 | -3.25985778926955 |
64 | 18 | 20.0120663650075 | -2.01206636500754 |
65 | 10 | 19.7812971342383 | -9.78129713423831 |
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 | 23.6274509803922 | -4.62745098039216 |
73 | 30 | 24.8961430726137 | 5.10385692738634 |
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 | 0.76923076923077 |
82 | 18 | 22.6923076923077 | -4.69230769230769 |
83 | 21 | 21 | 3.2564351063781e-16 |
84 | 20 | 23.6923076923077 | -3.69230769230769 |
85 | 23 | 24.9609997845292 | -1.9609997845292 |
86 | 21 | 20.9609997845292 | 0.0390002154708037 |
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 | -0.757164404223228 |
95 | 19 | 21.0648567119155 | -2.06485671191554 |
96 | 31 | 23.7571644042232 | 7.24283559577677 |
97 | 31 | 25.0258564964447 | 5.97414350355527 |
98 | 29 | 21.0258564964447 | 7.97414350355527 |
99 | 19 | 22.4544279250162 | -3.45442792501616 |
100 | 22 | 20.2066365007541 | 1.79336349924585 |
101 | 23 | 19.9758672699849 | 3.02413273001508 |
102 | 15 | 19.3604826546003 | -4.3604826546003 |
103 | 20 | 20.6681749622926 | -0.668174962292609 |
104 | 18 | 21.3604826546003 | -3.3604826546003 |
105 | 23 | 22.3604826546003 | 0.639517345399699 |
106 | 25 | 22.8220211161388 | 2.17797888386124 |
107 | 21 | 21.1297134238311 | -0.129713423831071 |
108 | 24 | 23.8220211161388 | 0.177978883861235 |
109 | 25 | 25.0907132083603 | -0.0907132083602677 |
110 | 17 | 21.0907132083603 | -4.09071320836027 |
111 | 13 | 22.5192846369317 | -9.5192846369317 |
112 | 28 | 20.2714932126697 | 7.72850678733032 |
113 | 21 | 20.0407239819005 | 0.959276018099547 |
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 | -3.8868778280543 |
121 | 29 | 25.1555699202758 | 3.8444300797242 |
122 | 14 | 21.1555699202758 | -7.1555699202758 |
123 | 22 | 22.5841413488472 | -0.58414134884723 |
124 | 15 | 20.3363499245852 | -5.33634992458522 |
125 | 19 | 20.105580693816 | -1.10558069381599 |
126 | 20 | 19.4901960784314 | 0.509803921568628 |
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 | 0.740573152337858 |
132 | 16 | 23.9517345399698 | -7.95173453996983 |
133 | 17 | 25.2204266321913 | -8.22042663219134 |
134 | 16 | 21.2204266321913 | -5.22042663219134 |
135 | 21 | 22.6489980607628 | -1.64899806076277 |
136 | 26 | 20.4012066365008 | 5.59879336349925 |
137 | 18 | 20.1704374057315 | -2.17043740573152 |
138 | 18 | 19.5550527903469 | -1.55505279034691 |
139 | 17 | 20.8627450980392 | -3.86274509803922 |
140 | 22 | 21.5550527903469 | 0.444947209653092 |
141 | 30 | 22.5550527903469 | 7.4449472096531 |
142 | 30 | 23.0165912518854 | 6.98340874811463 |
143 | 24 | 21.3242835595777 | 2.67571644042232 |
144 | 21 | 24.0165912518854 | -3.01659125188537 |
145 | 21 | 25.2852833441069 | -4.28528334410687 |
146 | 29 | 21.2852833441069 | 7.71471665589313 |
147 | 31 | 22.7138547726783 | 8.2861452273217 |
148 | 20 | 20.4660633484163 | -0.466063348416289 |
149 | 16 | 20.2352941176471 | -4.23529411764706 |
150 | 22 | 19.6199095022624 | 2.38009049773756 |
151 | 20 | 20.9276018099548 | -0.92760180995475 |
152 | 28 | 21.6199095022624 | 6.38009049773756 |
153 | 38 | 22.6199095022624 | 15.3800904977376 |
154 | 22 | 23.0814479638009 | -1.08144796380091 |
155 | 20 | 21.3891402714932 | -1.38914027149321 |
156 | 17 | 24.0814479638009 | -7.0814479638009 |
157 | 28 | 25.3501400560224 | 2.64985994397759 |
158 | 22 | 21.3501400560224 | 0.649859943977591 |
159 | 31 | 22.7787114845938 | 8.22128851540616 |
Goldfeld-Quandt test for Heteroskedasticity | |||
p-values | Alternative Hypothesis | ||
breakpoint index | greater | 2-sided | less |
16 | 0.056568789179808 | 0.113137578359616 | 0.943431210820192 |
17 | 0.0839659028663623 | 0.167931805732725 | 0.916034097133638 |
18 | 0.0367537036556019 | 0.0735074073112038 | 0.963246296344398 |
19 | 0.0166035069260112 | 0.0332070138520223 | 0.98339649307399 |
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 | 0.870153707868811 | 0.564923146065595 |
25 | 0.435693232606443 | 0.871386465212886 | 0.564306767393557 |
26 | 0.425437450921941 | 0.850874901843881 | 0.574562549078059 |
27 | 0.363228603103467 | 0.726457206206933 | 0.636771396896533 |
28 | 0.319845446939039 | 0.639690893878079 | 0.680154553060961 |
29 | 0.253411545645171 | 0.506823091290341 | 0.746588454354829 |
30 | 0.196227070850856 | 0.392454141701712 | 0.803772929149144 |
31 | 0.153547415235308 | 0.307094830470616 | 0.846452584764692 |
32 | 0.115456325044678 | 0.230912650089357 | 0.884543674955322 |
33 | 0.0863857570120044 | 0.172771514024009 | 0.913614242987996 |
34 | 0.0647520070783623 | 0.129504014156725 | 0.935247992921638 |
35 | 0.0655339780689105 | 0.131067956137821 | 0.93446602193109 |
36 | 0.0534670586357991 | 0.106934117271598 | 0.9465329413642 |
37 | 0.0793797507878682 | 0.158759501575736 | 0.920620249212132 |
38 | 0.115445697507034 | 0.230891395014068 | 0.884554302492966 |
39 | 0.225973925175037 | 0.451947850350073 | 0.774026074824963 |
40 | 0.207548412350879 | 0.415096824701758 | 0.792451587649121 |
41 | 0.215755276609696 | 0.431510553219392 | 0.784244723390304 |
42 | 0.178869710283797 | 0.357739420567593 | 0.821130289716203 |
43 | 0.182556945663055 | 0.365113891326109 | 0.817443054336945 |
44 | 0.233346704975981 | 0.466693409951962 | 0.766653295024019 |
45 | 0.224537952917625 | 0.44907590583525 | 0.775462047082375 |
46 | 0.332734110762306 | 0.665468221524613 | 0.667265889237694 |
47 | 0.285886216736991 | 0.571772433473983 | 0.714113783263009 |
48 | 0.298810296496208 | 0.597620592992416 | 0.701189703503792 |
49 | 0.266059945706882 | 0.532119891413765 | 0.733940054293118 |
50 | 0.22970326848285 | 0.4594065369657 | 0.77029673151715 |
51 | 0.201173352803008 | 0.402346705606015 | 0.798826647196992 |
52 | 0.173860716098747 | 0.347721432197494 | 0.826139283901253 |
53 | 0.157677134722783 | 0.315354269445566 | 0.842322865277217 |
54 | 0.192400741225735 | 0.38480148245147 | 0.807599258774265 |
55 | 0.207549622091039 | 0.415099244182078 | 0.792450377908961 |
56 | 0.189733430561107 | 0.379466861122213 | 0.810266569438894 |
57 | 0.161245958520749 | 0.322491917041498 | 0.838754041479251 |
58 | 0.170744408642889 | 0.341488817285779 | 0.82925559135711 |
59 | 0.224232022908898 | 0.448464045817795 | 0.775767977091102 |
60 | 0.460912073956459 | 0.921824147912918 | 0.539087926043541 |
61 | 0.501430525086617 | 0.997138949826766 | 0.498569474913383 |
62 | 0.4538151879924 | 0.9076303759848 | 0.5461848120076 |
63 | 0.415228804260661 | 0.830457608521322 | 0.584771195739339 |
64 | 0.369670555266206 | 0.739341110532412 | 0.630329444733794 |
65 | 0.466484551961429 | 0.932969103922858 | 0.533515448038571 |
66 | 0.595442078767856 | 0.809115842464288 | 0.404557921232144 |
67 | 0.701696464980854 | 0.596607070038292 | 0.298303535019146 |
68 | 0.668245847554226 | 0.663508304891548 | 0.331754152445774 |
69 | 0.818361916953824 | 0.363276166092352 | 0.181638083046176 |
70 | 0.789107217391001 | 0.421785565217998 | 0.210892782608999 |
71 | 0.81822726417456 | 0.363545471650881 | 0.181772735825441 |
72 | 0.817712257893803 | 0.364575484212394 | 0.182287742106197 |
73 | 0.816466604484336 | 0.367066791031329 | 0.183533395515664 |
74 | 0.854593666932024 | 0.290812666135952 | 0.145406333067976 |
75 | 0.841138396973497 | 0.317723206053005 | 0.158861603026503 |
76 | 0.820418529201478 | 0.359162941597044 | 0.179581470798522 |
77 | 0.8278918057246 | 0.3442163885508 | 0.1721081942754 |
78 | 0.79973291468083 | 0.400534170638339 | 0.200267085319169 |
79 | 0.776735951533297 | 0.446528096933406 | 0.223264048466703 |
80 | 0.80960431858441 | 0.380791362831182 | 0.190395681415591 |
81 | 0.776737766908298 | 0.446524466183405 | 0.223262233091702 |
82 | 0.759394593497528 | 0.481210813004945 | 0.240605406502472 |
83 | 0.719765970018004 | 0.560468059963992 | 0.280234029981996 |
84 | 0.699178699007766 | 0.601642601984468 | 0.300821300992234 |
85 | 0.65720917941888 | 0.685581641162241 | 0.34279082058112 |
86 | 0.612166380446944 | 0.775667239106111 | 0.387833619553056 |
87 | 0.564656826145422 | 0.870686347709156 | 0.435343173854578 |
88 | 0.549409316810712 | 0.901181366378577 | 0.450590683189288 |
89 | 0.615610673546239 | 0.768778652907523 | 0.384389326453761 |
90 | 0.567380589084139 | 0.865238821831722 | 0.432619410915861 |
91 | 0.624603686566703 | 0.750792626866594 | 0.375396313433297 |
92 | 0.717846302869108 | 0.564307394261784 | 0.282153697130892 |
93 | 0.728548220779603 | 0.542903558440795 | 0.271451779220397 |
94 | 0.688873795220088 | 0.622252409559824 | 0.311126204779912 |
95 | 0.646687012053425 | 0.70662597589315 | 0.353312987946575 |
96 | 0.743103518763444 | 0.513792962473111 | 0.256896481236556 |
97 | 0.77789152730727 | 0.444216945385459 | 0.22210847269273 |
98 | 0.858532536170661 | 0.282934927658678 | 0.141467463829339 |
99 | 0.832100571438637 | 0.335798857122725 | 0.167899428561363 |
100 | 0.803394102850335 | 0.393211794299331 | 0.196605897149665 |
101 | 0.804957325277446 | 0.390085349445108 | 0.195042674722554 |
102 | 0.781316860859401 | 0.437366278281198 | 0.218683139140599 |
103 | 0.790753304761872 | 0.418493390476256 | 0.209246695238128 |
104 | 0.754971664587716 | 0.490056670824568 | 0.245028335412284 |
105 | 0.713501113889501 | 0.572997772220998 | 0.286498886110499 |
106 | 0.677881220846351 | 0.644237558307298 | 0.322118779153649 |
107 | 0.629941156629433 | 0.740117686741134 | 0.370058843370567 |
108 | 0.663893842211742 | 0.672212315576515 | 0.336106157788258 |
109 | 0.641855196504105 | 0.716289606991789 | 0.358144803495895 |
110 | 0.599503164137837 | 0.800993671724326 | 0.400496835862163 |
111 | 0.668697455287973 | 0.662605089424055 | 0.331302544712027 |
112 | 0.760017912926561 | 0.479964174146879 | 0.239982087073439 |
113 | 0.759934984600913 | 0.480130030798173 | 0.240065015399087 |
114 | 0.80404853143598 | 0.391902937128039 | 0.195951468564019 |
115 | 0.826303859184972 | 0.347392281630057 | 0.173696140815028 |
116 | 0.801428005131352 | 0.397143989737296 | 0.198571994868648 |
117 | 0.792212355641931 | 0.415575288716138 | 0.207787644358069 |
118 | 0.816642245741584 | 0.366715508516833 | 0.183357754258416 |
119 | 0.814852602495942 | 0.370294795008116 | 0.185147397504058 |
120 | 0.80880008193046 | 0.382399836139079 | 0.191199918069539 |
121 | 0.888995987968798 | 0.222008024062404 | 0.111004012031202 |
122 | 0.873817526299002 | 0.252364947401995 | 0.126182473700997 |
123 | 0.837310408783627 | 0.325379182432746 | 0.162689591216373 |
124 | 0.820125949520516 | 0.359748100958968 | 0.179874050479484 |
125 | 0.799589858739028 | 0.400820282521944 | 0.200410141260972 |
126 | 0.760569280852471 | 0.478861438295057 | 0.239430719147529 |
127 | 0.709224136555241 | 0.581551726889519 | 0.290775863444759 |
128 | 0.646384436557422 | 0.707231126885156 | 0.353615563442578 |
129 | 0.820331020648016 | 0.359337958703969 | 0.179668979351984 |
130 | 0.897881396170347 | 0.204237207659306 | 0.102118603829653 |
131 | 0.86918115967249 | 0.261637680655019 | 0.13081884032751 |
132 | 0.829994296186691 | 0.340011407626618 | 0.170005703813309 |
133 | 0.804924521151704 | 0.390150957696592 | 0.195075478848296 |
134 | 0.820482741905018 | 0.359034516189964 | 0.179517258094982 |
135 | 0.888396403449321 | 0.223207193101357 | 0.111603596550679 |
136 | 0.880485176598369 | 0.239029646803262 | 0.119514823401631 |
137 | 0.826884324275871 | 0.346231351448258 | 0.173115675724129 |
138 | 0.769350671028098 | 0.461298657943805 | 0.230649328971902 |
139 | 0.690621719115386 | 0.618756561769228 | 0.309378280884614 |
140 | 0.67009773942681 | 0.65980452114638 | 0.32990226057319 |
141 | 0.78793192286437 | 0.424136154271261 | 0.21206807713563 |
142 | 0.761735649786674 | 0.476528700426653 | 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 |