Multiple Linear Regression - Estimated Regression Equation |
Q4 [t] = + 0.865045701430835 + 0.145400006160318Q1[t] + 0.252561146567979Q2[t] + 0.220272402114639Q3[t] -0.0776944496009527M1[t] -0.135576717001389M2[t] + 0.0716598829398656M3[t] + 0.0976981103730005M4[t] + 0.278051810260123M5[t] + 0.0567419658771181M6[t] + 0.133278071817606M7[t] + 0.0873192329729293M8[t] + 0.12122700224052M9[t] + 0.207612182563193M10[t] + 0.230802626594899M11[t] + 0.00207493155891959t + 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) | 0.865045701430835 | 0.261534 | 3.3076 | 0.0012 | 6e-04 |
Q1 | 0.145400006160318 | 0.067585 | 2.1514 | 0.03319 | 0.016595 |
Q2 | 0.252561146567979 | 0.076826 | 3.2874 | 0.001282 | 0.000641 |
Q3 | 0.220272402114639 | 0.072113 | 3.0546 | 0.002706 | 0.001353 |
M1 | -0.0776944496009527 | 0.258216 | -0.3009 | 0.763951 | 0.381976 |
M2 | -0.135576717001389 | 0.259051 | -0.5234 | 0.601564 | 0.300782 |
M3 | 0.0716598829398656 | 0.256919 | 0.2789 | 0.780724 | 0.390362 |
M4 | 0.0976981103730005 | 0.259071 | 0.3771 | 0.706672 | 0.353336 |
M5 | 0.278051810260123 | 0.255952 | 1.0863 | 0.279221 | 0.139611 |
M6 | 0.0567419658771181 | 0.255813 | 0.2218 | 0.82479 | 0.412395 |
M7 | 0.133278071817606 | 0.25755 | 0.5175 | 0.605646 | 0.302823 |
M8 | 0.0873192329729293 | 0.265127 | 0.3293 | 0.742391 | 0.371196 |
M9 | 0.12122700224052 | 0.259243 | 0.4676 | 0.640794 | 0.320397 |
M10 | 0.207612182563193 | 0.261986 | 0.7925 | 0.429456 | 0.214728 |
M11 | 0.230802626594899 | 0.256484 | 0.8999 | 0.369756 | 0.184878 |
t | 0.00207493155891959 | 0.001186 | 1.75 | 0.082333 | 0.041166 |
Multiple Linear Regression - Regression Statistics | |
Multiple R | 0.701482221157589 |
R-squared | 0.492077306600185 |
Adjusted R-squared | 0.436868318187161 |
F-TEST (value) | 8.91299262574619 |
F-TEST (DF numerator) | 15 |
F-TEST (DF denominator) | 138 |
p-value | 3.71924713249427e-14 |
Multiple Linear Regression - Residual Statistics | |
Residual Standard Deviation | 0.646445212137204 |
Sum Squared Residuals | 57.6690148967258 |
Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
1 | 3 | 3.0420880006459 | -0.042088000645902 |
2 | 2 | 1.97008595723316 | 0.0299140427668448 |
3 | 4 | 2.68451978186929 | 1.31548021813071 |
4 | 1 | 2.23979939217872 | -1.23979939217872 |
5 | 2 | 2.86277282785404 | -0.862772827854045 |
6 | 2 | 1.91814321977936 | 0.0818567802206368 |
7 | 3 | 3.63118251969294 | -0.631182519692938 |
8 | 2 | 2.74879265544961 | -0.748792655449606 |
9 | 2 | 3.47788130707337 | -1.47788130707337 |
10 | 2 | 1.85704076058648 | 0.142959239413523 |
11 | 4 | 3.59160679454559 | 0.408393205454409 |
12 | 3 | 2.59924553850636 | 0.400754461493641 |
13 | 4 | 3.28725958146758 | 0.712740418532421 |
14 | 2 | 2.79090744139678 | -0.790907441396783 |
15 | 3 | 1.80633551471207 | 1.19366448528793 |
16 | 3 | 3.02833213188901 | -0.0283321318890123 |
17 | 3 | 2.78051086615342 | 0.219489133846581 |
18 | 4 | 3.21179825262561 | 0.788201747374392 |
19 | 2 | 2.12881457639347 | -0.128814576393467 |
20 | 2 | 2.48289182183601 | -0.482891821836005 |
21 | 2 | 2.15320211438756 | -0.153202114387559 |
22 | 3 | 3.33867945109402 | -0.338679451094022 |
23 | 4 | 3.36394482668465 | 0.636055173315352 |
24 | 2 | 2.00591116237046 | -0.0059111623704582 |
25 | 3 | 3.31215876017461 | -0.312158760174614 |
26 | 4 | 3.40175143049341 | 0.598248569506586 |
27 | 3 | 3.46566295583327 | -0.465662955833271 |
28 | 3 | 3.27350371271069 | -0.273503712710687 |
29 | 3 | 3.45593234415673 | -0.455932344156728 |
30 | 2 | 2.22050272376141 | -0.220502723761412 |
31 | 2 | 2.29911376126082 | -0.299113761260819 |
32 | 4 | 3.05115215943166 | 0.948847840568345 |
33 | 3 | 3.27511851791946 | -0.275118517919465 |
34 | 3 | 2.15940026456853 | 0.840599735431475 |
35 | 2 | 2.99088285266339 | -0.990882852663387 |
36 | 4 | 3.41267745692368 | 0.587322543076318 |
37 | 3 | 2.27827957980944 | 0.721720420190565 |
38 | 2 | 2.04478349335426 | -0.0447834933542608 |
39 | 3 | 3.27028973242567 | -0.270289732425667 |
40 | 4 | 3.51867529353236 | 0.481324706467639 |
41 | 4 | 3.08287037013547 | 0.917129629864532 |
42 | 2 | 1.62716834762551 | 0.372831652374489 |
43 | 1 | 2.54428534208249 | -1.54428534208249 |
44 | 2 | 2.57092904500273 | -0.570929045002733 |
45 | 3 | 2.09583933139397 | 0.904160668606032 |
46 | 3 | 3.27536654680111 | -0.275366546801114 |
47 | 4 | 3.41374318409872 | 0.586256815901282 |
48 | 2 | 1.83543711766989 | 0.164562882330111 |
49 | 3 | 2.71143481829241 | 0.288565181707591 |
50 | 4 | 3.30614978174717 | 0.693850218252833 |
51 | 2 | 1.66076064871854 | 0.339239351281465 |
52 | 2 | 3.79613561880737 | -1.79613561880737 |
53 | 3 | 3.07548080438916 | -0.0754808043891635 |
54 | 2 | 2.37746222158314 | -0.377462221583143 |
55 | 4 | 3.14917920987981 | 0.850820790120193 |
56 | 3 | 3.32122291896036 | -0.321222918960364 |
57 | 3 | 2.88437207110426 | 0.115627928895743 |
58 | 4 | 3.66593813378311 | 0.334061866216893 |
59 | 4 | 2.45473639968786 | 1.54526360031214 |
60 | 4 | 3.20991466776977 | 0.790085332230226 |
61 | 2 | 2.15038918660985 | -0.150389186609848 |
62 | 4 | 3.3310489604542 | 0.668951039545798 |
63 | 4 | 4.15859404679731 | -0.158594046797312 |
64 | 4 | 3.17051249821814 | 0.829487501781865 |
65 | 2 | 2.04160162402398 | -0.0416016240239844 |
66 | 3 | 3.05883382088577 | -0.0588338208857702 |
67 | 3 | 3.61027840706780 | -0.610278407067795 |
68 | 2 | 2.10965498798153 | -0.109654987981528 |
69 | 4 | 2.98414364576561 | 1.01585635423439 |
70 | 1 | 1.83613664796134 | -0.836136647961335 |
71 | 3 | 3.46354154151279 | -0.463541541512788 |
72 | 3 | 2.98225269990883 | 0.0177473000911697 |
73 | 2 | 2.7186495242055 | -0.718649524205497 |
74 | 2 | 3.35594813916124 | -1.35594813916124 |
75 | 3 | 2.94702611581848 | 0.0529738841815237 |
76 | 3 | 3.59337282965347 | -0.593372829653466 |
77 | 3 | 3.63040145493919 | -0.63040145493919 |
78 | 3 | 3.15860539554713 | -0.158605395547127 |
79 | 3 | 2.17843807397432 | 0.82156192602568 |
80 | 2 | 1.95686541607491 | 0.0431345839250939 |
81 | 2 | 2.17053686751507 | -0.170536867515074 |
82 | 3 | 3.24290294251456 | -0.242902942514559 |
83 | 3 | 3.37532945851284 | -0.375329458512845 |
84 | 2 | 2.67971833609357 | -0.679718336093565 |
85 | 2 | 1.58195398918098 | 0.418046010819017 |
86 | 3 | 2.76261376302534 | 0.237386236974663 |
87 | 2 | 2.35369173968258 | -0.353691739682576 |
88 | 3 | 2.74747730694959 | 0.252522693050413 |
89 | 3 | 3.54813949323856 | -0.548139493238565 |
90 | 2 | 2.49039862345691 | -0.490398623456905 |
91 | 3 | 2.56900966095631 | 0.430990339043687 |
92 | 3 | 3.14335930851349 | -0.143359308513491 |
93 | 4 | 3.65217555802262 | 0.347824441977381 |
94 | 4 | 3.74063566990421 | 0.259364330095788 |
95 | 3 | 2.96997874003824 | 0.0300212599617556 |
96 | 2 | 2.30070624077299 | -0.300706240772987 |
97 | 1 | 1.60685316788802 | -0.606853167888018 |
98 | 2 | 2.02387938072912 | -0.0238793807291185 |
99 | 3 | 3.36249688150750 | -0.362496881507503 |
100 | 3 | 2.87953762606428 | 0.120462373935717 |
101 | 5 | 3.82559981851358 | 1.17440018148642 |
102 | 4 | 3.46096489952918 | 0.539035100470824 |
103 | 5 | 3.61010354723458 | 1.38989645276542 |
104 | 2 | 2.82237407220085 | -0.822374072200847 |
105 | 1 | 0.781628885493354 | 0.218371114506646 |
106 | 3 | 2.84513312683664 | 0.154866873163363 |
107 | 3 | 2.30951138259791 | 0.690488617402086 |
108 | 4 | 4.64794705416629 | -0.647947054166285 |
109 | 2 | 2.26470617580247 | -0.264706175802468 |
110 | 2 | 1.94685125598526 | 0.0531487440147399 |
111 | 3 | 2.30834807879893 | 0.691651921201068 |
112 | 4 | 4.46863188137442 | -0.468631881374425 |
113 | 2 | 2.15843053571391 | -0.158430535713911 |
114 | 3 | 2.98448042664534 | 0.0155195733546601 |
115 | 3 | 2.19315766592756 | 0.80684233407244 |
116 | 4 | 3.41117390311605 | 0.588826096883946 |
117 | 4 | 4.55396691763241 | -0.553966917632411 |
118 | 2 | 2.81569940290891 | -0.815699402908907 |
119 | 3 | 4.18901055514463 | -1.18901055514463 |
120 | 2 | 1.89311863498796 | 0.106881365012041 |
121 | 3 | 2.45554485398938 | 0.544455146010622 |
122 | 4 | 4.64866167791832 | -0.64866167791832 |
123 | 2 | 1.44040839791363 | 0.559591602086372 |
124 | 4 | 3.65512577381301 | 0.344874226186990 |
125 | 4 | 4.0217350006894 | -0.0217350006893962 |
126 | 2 | 2.51450189848833 | -0.514501898488332 |
127 | 3 | 3.69089039331721 | -0.690890393317214 |
128 | 3 | 2.63580599061817 | 0.364194009381829 |
129 | 3 | 1.96063254149651 | 1.03936745850349 |
130 | 3 | 2.40005377738666 | 0.599946222613336 |
131 | 4 | 3.96134858728369 | 0.0386514127163119 |
132 | 3 | 3.29978425885206 | -0.299784258852059 |
133 | 2 | 1.64193807573884 | 0.358061924261162 |
134 | 3 | 3.21692201551397 | -0.216922015513970 |
135 | 3 | 2.48140161350277 | 0.518598386497229 |
136 | 3 | 2.64773620806671 | 0.352263791933295 |
137 | 4 | 4.20822889312798 | -0.208228893127981 |
138 | 3 | 2.61427347314969 | 0.385726526850311 |
139 | 4 | 3.24295602334163 | 0.757043976658369 |
140 | 4 | 3.75177227285076 | 0.248227727149241 |
141 | 4 | 4.58767123816437 | -0.587671238164373 |
142 | 3 | 3.64522535820834 | -0.645225358208338 |
143 | 3 | 3.79826410832942 | -0.798264108329423 |
144 | 2 | 1.47008344371941 | 0.529916556280588 |
145 | 3 | 3.65064254687464 | -0.650642546874641 |
146 | 1 | 1.47818763321775 | -0.478187633217751 |
147 | 2 | 1.52249549978104 | 0.477504500218962 |
148 | 4 | 3.92519653334172 | 0.074803466658281 |
149 | 4 | 4.0877280656747 | -0.0877280656746981 |
150 | 3 | 3.16633910317411 | -0.166339103174106 |
151 | 3 | 2.48812760416331 | 0.511872395836695 |
152 | 4 | 4.68560434803224 | -0.685604348032241 |
153 | 2 | 2.67012453691537 | -0.670124536915373 |
154 | 4 | 3.7160021466288 | 0.283997853371202 |
155 | 3 | NA | NA |
156 | 3 | NA | NA |
Goldfeld-Quandt test for Heteroskedasticity | |||
p-values | Alternative Hypothesis | ||
breakpoint index | greater | 2-sided | less |
19 | 0.661928744714834 | 0.676142510570332 | 0.338071255285166 |
20 | 0.531888007174701 | 0.936223985650599 | 0.468111992825299 |
21 | 0.55676172694791 | 0.88647654610418 | 0.44323827305209 |
22 | 0.471386535495319 | 0.942773070990638 | 0.528613464504681 |
23 | 0.368247978311205 | 0.73649595662241 | 0.631752021688795 |
24 | 0.393728139493427 | 0.787456278986854 | 0.606271860506573 |
25 | 0.45879327737091 | 0.91758655474182 | 0.54120672262909 |
26 | 0.470658478855072 | 0.941316957710144 | 0.529341521144928 |
27 | 0.76873701282131 | 0.462525974357379 | 0.231262987178690 |
28 | 0.716415823839952 | 0.567168352320096 | 0.283584176160048 |
29 | 0.660266595049818 | 0.679466809900364 | 0.339733404950182 |
30 | 0.668565124515494 | 0.662869750969012 | 0.331434875484506 |
31 | 0.600314166185512 | 0.799371667628975 | 0.399685833814488 |
32 | 0.722068360545392 | 0.555863278909216 | 0.277931639454608 |
33 | 0.683101873368574 | 0.633796253262852 | 0.316898126631426 |
34 | 0.648397163236929 | 0.703205673526142 | 0.351602836763071 |
35 | 0.800736429511335 | 0.398527140977329 | 0.199263570488665 |
36 | 0.761438656415732 | 0.477122687168536 | 0.238561343584268 |
37 | 0.723490808002726 | 0.553018383994548 | 0.276509191997274 |
38 | 0.666312052510807 | 0.667375894978387 | 0.333687947489193 |
39 | 0.725891679798901 | 0.548216640402198 | 0.274108320201099 |
40 | 0.75769064676132 | 0.484618706477359 | 0.242309353238680 |
41 | 0.790561036977505 | 0.418877926044991 | 0.209438963022495 |
42 | 0.751555624260349 | 0.496888751479302 | 0.248444375739651 |
43 | 0.876668304487178 | 0.246663391025645 | 0.123331695512822 |
44 | 0.864593003680123 | 0.270813992639755 | 0.135406996319877 |
45 | 0.893481353494578 | 0.213037293010843 | 0.106518646505422 |
46 | 0.879246036966696 | 0.241507926066608 | 0.120753963033304 |
47 | 0.858180332733436 | 0.283639334533127 | 0.141819667266564 |
48 | 0.844824083324463 | 0.310351833351073 | 0.155175916675537 |
49 | 0.810878092498214 | 0.378243815003572 | 0.189121907501786 |
50 | 0.809118298274472 | 0.381763403451056 | 0.190881701725528 |
51 | 0.789447397747515 | 0.421105204504971 | 0.210552602252485 |
52 | 0.936473344532813 | 0.127053310934374 | 0.0635266554671868 |
53 | 0.918038401826802 | 0.163923196346396 | 0.081961598173198 |
54 | 0.90559428027429 | 0.188811439451421 | 0.0944057197257105 |
55 | 0.949886942571512 | 0.100226114856977 | 0.0501130574284885 |
56 | 0.939610632398013 | 0.120778735203974 | 0.0603893676019871 |
57 | 0.922402712139681 | 0.155194575720638 | 0.0775972878603188 |
58 | 0.904300231511105 | 0.19139953697779 | 0.095699768488895 |
59 | 0.960409689995648 | 0.0791806200087036 | 0.0395903100043518 |
60 | 0.96452776554655 | 0.0709444689068982 | 0.0354722344534491 |
61 | 0.96084488690336 | 0.0783102261932812 | 0.0391551130966406 |
62 | 0.960403011064763 | 0.0791939778704733 | 0.0395969889352367 |
63 | 0.953633670726624 | 0.0927326585467526 | 0.0463663292733763 |
64 | 0.968867627024477 | 0.0622647459510459 | 0.0311323729755230 |
65 | 0.960702335295448 | 0.0785953294091046 | 0.0392976647045523 |
66 | 0.949764368529425 | 0.10047126294115 | 0.050235631470575 |
67 | 0.950247356557502 | 0.0995052868849962 | 0.0497526434424981 |
68 | 0.93695164406825 | 0.126096711863499 | 0.0630483559317495 |
69 | 0.957180952282703 | 0.0856380954345948 | 0.0428190477172974 |
70 | 0.970361108131088 | 0.0592777837378244 | 0.0296388918689122 |
71 | 0.97052354583492 | 0.0589529083301594 | 0.0294764541650797 |
72 | 0.963637649234399 | 0.0727247015312022 | 0.0363623507656011 |
73 | 0.968868131006179 | 0.0622637379876423 | 0.0311318689938212 |
74 | 0.99087907117093 | 0.0182418576581396 | 0.00912092882906981 |
75 | 0.988294224697656 | 0.0234115506046872 | 0.0117057753023436 |
76 | 0.991102914792074 | 0.0177941704158515 | 0.00889708520792575 |
77 | 0.99201826529669 | 0.0159634694066209 | 0.00798173470331045 |
78 | 0.988905640701226 | 0.0221887185975475 | 0.0110943592987738 |
79 | 0.99079068687266 | 0.0184186262546813 | 0.00920931312734064 |
80 | 0.987126827971741 | 0.0257463440565171 | 0.0128731720282586 |
81 | 0.982822037800577 | 0.0343559243988455 | 0.0171779621994227 |
82 | 0.979031544582582 | 0.0419369108348368 | 0.0209684554174184 |
83 | 0.975451839452904 | 0.0490963210941923 | 0.0245481605470961 |
84 | 0.976368102156104 | 0.0472637956877925 | 0.0236318978438962 |
85 | 0.974565330565851 | 0.050869338868298 | 0.025434669434149 |
86 | 0.96623015344489 | 0.0675396931102219 | 0.0337698465551110 |
87 | 0.959147067900253 | 0.0817058641994931 | 0.0408529320997466 |
88 | 0.951289612501369 | 0.0974207749972625 | 0.0487103874986313 |
89 | 0.959151659023119 | 0.0816966819537622 | 0.0408483409768811 |
90 | 0.956460006698845 | 0.0870799866023102 | 0.0435399933011551 |
91 | 0.948532050766015 | 0.10293589846797 | 0.051467949233985 |
92 | 0.94460791429422 | 0.110784171411560 | 0.0553920857057798 |
93 | 0.930540269364754 | 0.138919461270492 | 0.0694597306352459 |
94 | 0.913848043896709 | 0.172303912206582 | 0.0861519561032911 |
95 | 0.901032932302957 | 0.197934135394087 | 0.0989670676970435 |
96 | 0.880977469413442 | 0.238045061173116 | 0.119022530586558 |
97 | 0.87262350882535 | 0.254752982349300 | 0.127376491174650 |
98 | 0.842781256593949 | 0.314437486812103 | 0.157218743406051 |
99 | 0.816032938837112 | 0.367934122325776 | 0.183967061162888 |
100 | 0.787961521824953 | 0.424076956350095 | 0.212038478175047 |
101 | 0.833313412717427 | 0.333373174565147 | 0.166686587282573 |
102 | 0.81999263593724 | 0.360014728125519 | 0.180007364062760 |
103 | 0.895365343743458 | 0.209269312513084 | 0.104634656256542 |
104 | 0.91388095929191 | 0.172238081416180 | 0.0861190407080898 |
105 | 0.890915216274405 | 0.218169567451191 | 0.109084783725595 |
106 | 0.866452816915675 | 0.267094366168650 | 0.133547183084325 |
107 | 0.898239669249282 | 0.203520661501436 | 0.101760330750718 |
108 | 0.906794964882848 | 0.186410070234304 | 0.0932050351171518 |
109 | 0.901513108049871 | 0.196973783900257 | 0.0984868919501287 |
110 | 0.87325556258433 | 0.253488874831339 | 0.126744437415670 |
111 | 0.85435959584641 | 0.29128080830718 | 0.14564040415359 |
112 | 0.85002704427733 | 0.299945911445339 | 0.149972955722669 |
113 | 0.813173249558997 | 0.373653500882007 | 0.186826750441003 |
114 | 0.767690325151492 | 0.464619349697015 | 0.232309674848508 |
115 | 0.74462049934664 | 0.510759001306719 | 0.255379500653360 |
116 | 0.793396962889083 | 0.413206074221834 | 0.206603037110917 |
117 | 0.79763937086761 | 0.404721258264779 | 0.202360629132389 |
118 | 0.787574576622231 | 0.424850846755538 | 0.212425423377769 |
119 | 0.831459740335892 | 0.337080519328215 | 0.168540259664108 |
120 | 0.780246734604794 | 0.439506530790413 | 0.219753265395206 |
121 | 0.774618620876481 | 0.450762758247038 | 0.225381379123519 |
122 | 0.729892569962016 | 0.540214860075968 | 0.270107430037984 |
123 | 0.669975567033452 | 0.660048865933097 | 0.330024432966548 |
124 | 0.595258421811809 | 0.809483156376382 | 0.404741578188191 |
125 | 0.514682216078486 | 0.970635567843028 | 0.485317783921514 |
126 | 0.580732728740025 | 0.83853454251995 | 0.419267271259975 |
127 | 0.802273688108276 | 0.395452623783447 | 0.197726311891723 |
128 | 0.730535539966569 | 0.538928920066862 | 0.269464460033431 |
129 | 0.891109099166985 | 0.21778180166603 | 0.108890900833015 |
130 | 0.959663826723787 | 0.0806723465524269 | 0.0403361732762134 |
131 | 0.929500961835798 | 0.140998076328404 | 0.0704990381642022 |
132 | 0.919460385136665 | 0.161079229726670 | 0.0805396148633351 |
133 | 0.90667942847662 | 0.186641143046758 | 0.0933205715233792 |
134 | 0.842107591376955 | 0.315784817246089 | 0.157892408623045 |
135 | 0.752511058952942 | 0.494977882094116 | 0.247488941047058 |
136 | 0.55657683537395 | 0.886846329252099 | 0.443423164626049 |
137 | 0.5918122316753 | 0.8163755366494 | 0.4081877683247 |
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 | 11 | 0.092436974789916 | NOK |
10% type I error level | 31 | 0.260504201680672 | NOK |