Multiple Linear Regression - Estimated Regression Equation |
Yt[t] = + 1.04779067010842 -0.0580797728659307X1[t] -0.0287868899563356X2[t] + 0.139832767583328X3[t] -0.0610909867704954X4[t] + 0.291585366512453X5[t] + 0.217252184272917X6[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) | 1.04779067010842 | 0.454059 | 2.3076 | 0.02237 | 0.011185 |
X1 | -0.0580797728659307 | 0.077633 | -0.7481 | 0.455539 | 0.227769 |
X2 | -0.0287868899563356 | 0.085238 | -0.3377 | 0.736038 | 0.368019 |
X3 | 0.139832767583328 | 0.085354 | 1.6383 | 0.103435 | 0.051718 |
X4 | -0.0610909867704954 | 0.082531 | -0.7402 | 0.460312 | 0.230156 |
X5 | 0.291585366512453 | 0.06371 | 4.5768 | 1e-05 | 5e-06 |
X6 | 0.217252184272917 | 0.074892 | 2.9009 | 0.004274 | 0.002137 |
Multiple Linear Regression - Regression Statistics | |
Multiple R | 0.447149626952174 |
R-squared | 0.199942788883469 |
Adjusted R-squared | 0.168361583181500 |
F-TEST (value) | 6.33106888857657 |
F-TEST (DF numerator) | 6 |
F-TEST (DF denominator) | 152 |
p-value | 5.77565851023198e-06 |
Multiple Linear Regression - Residual Statistics | |
Residual Standard Deviation | 0.86648628101019 |
Sum Squared Residuals | 114.121368227188 |
Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
1 | 4 | 2.04468335305416 | 1.95531664694584 |
2 | 2 | 2.94822634254786 | -0.948226342547861 |
3 | 3 | 2.23565386832205 | 0.764346131677947 |
4 | 2 | 2.20889441202053 | -0.208894412020534 |
5 | 2 | 2.36454961656970 | -0.364549616569695 |
6 | 2 | 1.92411520874901 | 0.0758847912509917 |
7 | 1 | 1.9689527861459 | -0.968952786145898 |
8 | 1 | 2.52114178647989 | -1.52114178647989 |
9 | 1 | 2.54552007786293 | -1.54552007786293 |
10 | 2 | 2.28631382871012 | -0.286313828710122 |
11 | 2 | 2.09405723041192 | -0.0940572304119174 |
12 | 2 | 2.48744030499700 | -0.487440304996997 |
13 | 2 | 2.68535284544626 | -0.685352845446256 |
14 | 2 | 1.74509716056511 | 0.254902839434894 |
15 | 1 | 2.40064866272022 | -1.40064866272022 |
16 | 3 | 2.20245837979242 | 0.79754162020758 |
17 | 2 | 1.58088610159874 | 0.419113898401262 |
18 | 2 | 1.99113623479436 | 0.0088637652056422 |
19 | 2 | 2.08972365238411 | -0.0897236523841077 |
20 | 2 | 2.55372362577259 | -0.553723625772588 |
21 | 3 | 2.36064701094966 | 0.639352989050342 |
22 | 4 | 2.77398702395007 | 1.22601297604993 |
23 | 2 | 1.89754207463139 | 0.102457925368610 |
24 | 2 | 2.57481296077252 | -0.574812960772523 |
25 | 2 | 1.90477556492535 | 0.095224435074649 |
26 | 1 | 2.24889606379109 | -1.24889606379109 |
27 | 2 | 2.30998705056159 | -0.309987050561589 |
28 | 2 | 2.44240000566706 | -0.442400005667056 |
29 | 2 | 2.74140518465737 | -0.74140518465737 |
30 | 2 | 1.87548268201576 | 0.124517317984244 |
31 | 4 | 2.57488798131801 | 1.42511201868199 |
32 | 2 | 2.75905597869971 | -0.759055978699708 |
33 | 4 | 2.44799146106841 | 1.55200853893159 |
34 | 3 | 2.58230779379587 | 0.417692206204128 |
35 | 1 | 1.95731069727864 | -0.95731069727864 |
36 | 4 | 2.92245066649609 | 1.07754933350391 |
37 | 3 | 3.04162142613252 | -0.0416214261325159 |
38 | 2 | 1.64498830227380 | 0.355011697726202 |
39 | 4 | 3.15545026718935 | 0.844549732810647 |
40 | 2 | 2.60157241707404 | -0.601572417074042 |
41 | 3 | 2.28120016060525 | 0.718799839394746 |
42 | 3 | 2.15382585305917 | 0.846174146940832 |
43 | 2 | 1.93356245488169 | 0.0664375451183134 |
44 | 1 | 2.41662432961528 | -1.41662432961528 |
45 | 2 | 2.13456122978100 | -0.134561229780997 |
46 | 1 | 2.04027475448087 | -1.04027475448087 |
47 | 2 | 2.33647144149967 | -0.336471441499671 |
48 | 4 | 3.16106992824748 | 0.838930071752519 |
49 | 2 | 2.30998705056159 | -0.309987050561589 |
50 | 2 | 2.27327435517413 | -0.273274355174133 |
51 | 2 | 2.40548458834655 | -0.405484588346548 |
52 | 2 | 2.67590559931358 | -0.675905599313578 |
53 | 2 | 2.42614659629345 | -0.42614659629345 |
54 | 1 | 1.73696863320093 | -0.736968633200934 |
55 | 2 | 2.86658464946888 | -0.866584649468876 |
56 | 3 | 2.92245066649609 | 0.0775493335039101 |
57 | 2 | 2.42614659629345 | -0.42614659629345 |
58 | 2 | 2.46173964949071 | -0.461739649490714 |
59 | 1 | 2.04328596838543 | -1.04328596838543 |
60 | 1 | 1.45050058014809 | -0.450500580148088 |
61 | 2 | 1.94961314232224 | 0.0503868576777594 |
62 | 2 | 2.07207285834177 | -0.0720728583417701 |
63 | 1 | 1.96594157224133 | -0.965941572241334 |
64 | 2 | 1.98863101384305 | 0.0113689861569474 |
65 | 1 | 1.71939650505882 | -0.719396505058822 |
66 | 4 | 3.05794985605161 | 0.942050143948391 |
67 | 4 | 2.95123755645243 | 1.04876244354757 |
68 | 1 | 2.39763744881565 | -1.39763744881565 |
69 | 1 | 1.75170060187298 | -0.751700601872982 |
70 | 3 | 2.71773196280590 | 0.282268037194097 |
71 | 4 | 1.82251657725469 | 2.17748342274531 |
72 | 2 | 2.06906164443721 | -0.0690616444372054 |
73 | 4 | 2.71261829470103 | 1.28738170529897 |
74 | 4 | 2.49536611042812 | 1.50463388957188 |
75 | 3 | 2.92546188040065 | 0.0745381195993453 |
76 | 4 | 2.42614659629345 | 1.57385340370655 |
77 | 2 | 1.71939650505882 | 0.280603494941178 |
78 | 2 | 2.20378074391567 | -0.203780743915665 |
79 | 2 | 1.90477556492535 | 0.095224435074649 |
80 | 2 | 2.95424877035699 | -0.95424877035699 |
81 | 2 | 1.76634018201075 | 0.233659817989246 |
82 | 2 | 1.96234934483802 | 0.0376506551619778 |
83 | 2 | 1.73263870052786 | 0.267361299472137 |
84 | 1 | 2.08081503494288 | -1.08081503494288 |
85 | 3 | 2.49607117995969 | 0.50392882004031 |
86 | 3 | 1.73564991443243 | 1.26435008556757 |
87 | 2 | 2.28631382871012 | -0.286313828710122 |
88 | 4 | 2.02703255901183 | 1.97296744098817 |
89 | 4 | 3.17282331875315 | 0.827176681246849 |
90 | 2 | 1.99465344165218 | 0.00534655834781807 |
91 | 2 | 2.45865341504066 | -0.458653415040662 |
92 | 1 | 2.02703255901183 | -1.02703255901183 |
93 | 1 | 1.88059635012062 | -0.880596350120624 |
94 | 1 | 2.62293949455252 | -1.62293949455252 |
95 | 2 | 2.49235489652355 | -0.492354896523553 |
96 | 2 | 3.18102686666281 | -1.18102686666281 |
97 | 3 | 3.13282166698259 | -0.132821666982592 |
98 | 4 | 3.02997933726526 | 0.970020662734741 |
99 | 2 | 2.15382585305917 | -0.153825853059168 |
100 | 2 | 1.99465344165218 | 0.00534655834781807 |
101 | 4 | 2.44981981814492 | 1.55018018185508 |
102 | 2 | 2.07207285834177 | -0.0720728583417701 |
103 | 3 | 2.22955641996744 | 0.770443580032564 |
104 | 2 | 2.50047977853299 | -0.500479778532987 |
105 | 2 | 2.33927993347118 | -0.339279933471184 |
106 | 4 | 2.47622554318277 | 1.52377445681723 |
107 | 2 | 2.73398537217951 | -0.733985372179509 |
108 | 3 | 2.32888154282695 | 0.671118457173055 |
109 | 2 | 2.29365862064250 | -0.293658620642496 |
110 | 2 | 1.82302257020795 | 0.176977429792047 |
111 | 2 | 1.47285143787631 | 0.52714856212369 |
112 | 4 | 2.33647144149967 | 1.66352855850033 |
113 | 3 | 2.02050413824944 | 0.97949586175056 |
114 | 1 | 3.19216296257681 | -2.19216296257681 |
115 | 1 | 2.16854045374243 | -1.16854045374243 |
116 | 1 | 2.2119056259251 | -1.2119056259251 |
117 | 2 | 2.07597546396181 | -0.0759754639618074 |
118 | 2 | 2.2002598917031 | -0.200259891703102 |
119 | 3 | 2.75765859403098 | 0.242341405969024 |
120 | 1 | 2.46677829705010 | -1.46677829705010 |
121 | 3 | 1.99773967610223 | 1.00226032389777 |
122 | 1 | 1.67076397832557 | -0.67076397832557 |
123 | 2 | 2.31943429669427 | -0.319434296694267 |
124 | 1 | 1.67126997127883 | -0.671269971278829 |
125 | 2 | 1.79071847339379 | 0.209281526606207 |
126 | 2 | 1.90426957197209 | 0.0957304280279084 |
127 | 3 | 2.23124526974876 | 0.768754730251244 |
128 | 2 | 2.36806682342752 | -0.368066823427520 |
129 | 2 | 2.22823405584419 | -0.228234055844191 |
130 | 4 | 2.89014656968193 | 1.10985343031807 |
131 | 2 | 2.84452525685324 | -0.844525256853242 |
132 | 3 | 1.64197708836923 | 1.35802291163077 |
133 | 2 | 1.87856891646581 | 0.121431083534192 |
134 | 1 | 1.72240771896339 | -0.722407718963387 |
135 | 2 | 2.57481296077252 | -0.574812960772523 |
136 | 3 | 2.30998705056159 | 0.690012949438411 |
137 | 1 | 2.38943390090599 | -1.38943390090599 |
138 | 2 | 1.74005851300572 | 0.259941486994276 |
139 | 2 | 2.35173839350843 | -0.351738393508427 |
140 | 3 | 2.13537760095098 | 0.864622399049017 |
141 | 3 | 2.72745695141712 | 0.27254304858288 |
142 | 3 | 3.28898286448501 | -0.288982864485013 |
143 | 4 | 3.0545439508322 | 0.945456049167802 |
144 | 4 | 2.20448581344724 | 1.79551418655276 |
145 | 2 | 2.04410233955542 | -0.04410233955542 |
146 | 3 | 2.65965218993997 | 0.340347810060027 |
147 | 3 | 2.47118689562339 | 0.528813104376608 |
148 | 2 | 2.49997378557973 | -0.499973785579727 |
149 | 1 | 1.57296029616762 | -0.572960296167617 |
150 | 2 | 2.15514821718241 | -0.155148217182413 |
151 | 2 | 2.69145029380087 | -0.691450293800873 |
152 | 4 | 2.89315778358649 | 1.10684221641351 |
153 | 4 | 3.60291908872569 | 0.397080911274312 |
154 | 2 | 1.7932236943451 | 0.206776305654901 |
155 | 3 | 2.44169493613548 | 0.558305063864516 |
156 | 2 | 2.15081463915460 | -0.150814639154603 |
157 | 4 | 2.51673318790659 | 1.48326681209341 |
158 | 2 | 2.58965258572825 | -0.589652585728246 |
159 | 4 | 2.64492386662266 | 1.35507613337734 |
Goldfeld-Quandt test for Heteroskedasticity | |||
p-values | Alternative Hypothesis | ||
breakpoint index | greater | 2-sided | less |
10 | 0.700904353137251 | 0.598191293725498 | 0.299095646862749 |
11 | 0.548350795765601 | 0.903298408468797 | 0.451649204234399 |
12 | 0.667445216461547 | 0.665109567076905 | 0.332554783538453 |
13 | 0.688269018828925 | 0.623461962342151 | 0.311730981171075 |
14 | 0.585004296314544 | 0.829991407370911 | 0.414995703685456 |
15 | 0.594330712308339 | 0.811338575383322 | 0.405669287691661 |
16 | 0.66370282946078 | 0.67259434107844 | 0.33629717053922 |
17 | 0.576746172409873 | 0.846507655180253 | 0.423253827590127 |
18 | 0.487244031173466 | 0.974488062346931 | 0.512755968826534 |
19 | 0.398345465161099 | 0.796690930322198 | 0.601654534838901 |
20 | 0.346589093351314 | 0.693178186702628 | 0.653410906648686 |
21 | 0.395543028554495 | 0.79108605710899 | 0.604456971445505 |
22 | 0.669866825308829 | 0.660266349382342 | 0.330133174691171 |
23 | 0.61373906568817 | 0.772521868623659 | 0.386260934311830 |
24 | 0.549929681138955 | 0.90014063772209 | 0.450070318861045 |
25 | 0.476960381831964 | 0.953920763663929 | 0.523039618168036 |
26 | 0.56570907024076 | 0.86858185951848 | 0.43429092975924 |
27 | 0.5030889767728 | 0.9938220464544 | 0.4969110232272 |
28 | 0.438700434274991 | 0.877400868549983 | 0.561299565725009 |
29 | 0.385658676637406 | 0.771317353274812 | 0.614341323362594 |
30 | 0.324213713924165 | 0.64842742784833 | 0.675786286075835 |
31 | 0.443566249546796 | 0.887132499093591 | 0.556433750453204 |
32 | 0.393298773982683 | 0.786597547965367 | 0.606701226017317 |
33 | 0.534859419251352 | 0.930281161497296 | 0.465140580748648 |
34 | 0.480035185873147 | 0.960070371746293 | 0.519964814126853 |
35 | 0.543774131214557 | 0.912451737570886 | 0.456225868785443 |
36 | 0.621550300027261 | 0.756899399945477 | 0.378449699972739 |
37 | 0.564776482669887 | 0.870447034660227 | 0.435223517330113 |
38 | 0.513854975886206 | 0.972290048227588 | 0.486145024113794 |
39 | 0.552240168114169 | 0.895519663771662 | 0.447759831885831 |
40 | 0.523258797318652 | 0.953482405362695 | 0.476741202681348 |
41 | 0.49527895475044 | 0.99055790950088 | 0.50472104524956 |
42 | 0.481909062676729 | 0.963818125353459 | 0.518090937323271 |
43 | 0.428559670900642 | 0.857119341801283 | 0.571440329099358 |
44 | 0.516374714643145 | 0.96725057071371 | 0.483625285356855 |
45 | 0.471561401221563 | 0.943122802443126 | 0.528438598778437 |
46 | 0.50370356102363 | 0.99259287795274 | 0.49629643897637 |
47 | 0.460559211136162 | 0.921118422272324 | 0.539440788863838 |
48 | 0.462195543510216 | 0.924391087020432 | 0.537804456489784 |
49 | 0.419980363937573 | 0.839960727875146 | 0.580019636062427 |
50 | 0.376786596214604 | 0.753573192429208 | 0.623213403785396 |
51 | 0.349075484956314 | 0.698150969912628 | 0.650924515043686 |
52 | 0.322254380440027 | 0.644508760880054 | 0.677745619559973 |
53 | 0.28788766830764 | 0.57577533661528 | 0.71211233169236 |
54 | 0.270352532163572 | 0.540705064327144 | 0.729647467836428 |
55 | 0.253402291881909 | 0.506804583763819 | 0.746597708118091 |
56 | 0.215847150245017 | 0.431694300490033 | 0.784152849754983 |
57 | 0.187245595743058 | 0.374491191486115 | 0.812754404256942 |
58 | 0.169521699764976 | 0.339043399529953 | 0.830478300235024 |
59 | 0.186477945823723 | 0.372955891647447 | 0.813522054176277 |
60 | 0.162252971459717 | 0.324505942919434 | 0.837747028540283 |
61 | 0.134890154153717 | 0.269780308307434 | 0.865109845846283 |
62 | 0.109940580570197 | 0.219881161140395 | 0.890059419429802 |
63 | 0.120875622040767 | 0.241751244081534 | 0.879124377959233 |
64 | 0.103379707843613 | 0.206759415687226 | 0.896620292156387 |
65 | 0.0971741391927675 | 0.194348278385535 | 0.902825860807232 |
66 | 0.0994954733427339 | 0.198990946685468 | 0.900504526657266 |
67 | 0.11397334390406 | 0.22794668780812 | 0.88602665609594 |
68 | 0.158435016239479 | 0.316870032478959 | 0.84156498376052 |
69 | 0.149947192679534 | 0.299894385359068 | 0.850052807320466 |
70 | 0.126425361688258 | 0.252850723376517 | 0.873574638311742 |
71 | 0.333232369521831 | 0.666464739043663 | 0.666767630478169 |
72 | 0.291779487020370 | 0.583558974040741 | 0.70822051297963 |
73 | 0.348190123983725 | 0.69638024796745 | 0.651809876016275 |
74 | 0.440251960874322 | 0.880503921748644 | 0.559748039125678 |
75 | 0.396833755112435 | 0.79366751022487 | 0.603166244887565 |
76 | 0.500840841701973 | 0.998318316596055 | 0.499159158298027 |
77 | 0.460329204757866 | 0.920658409515732 | 0.539670795242134 |
78 | 0.417004553205477 | 0.834009106410953 | 0.582995446794523 |
79 | 0.375067258496455 | 0.750134516992909 | 0.624932741503545 |
80 | 0.385502369054811 | 0.771004738109623 | 0.614497630945189 |
81 | 0.348027712196838 | 0.696055424393676 | 0.651972287803162 |
82 | 0.307448641242394 | 0.614897282484788 | 0.692551358757606 |
83 | 0.274378493888456 | 0.548756987776912 | 0.725621506111544 |
84 | 0.298553312626462 | 0.597106625252924 | 0.701446687373538 |
85 | 0.273876843368789 | 0.547753686737579 | 0.726123156631211 |
86 | 0.313849094650876 | 0.627698189301751 | 0.686150905349124 |
87 | 0.277286796513138 | 0.554573593026276 | 0.722713203486862 |
88 | 0.473455739939637 | 0.946911479879275 | 0.526544260060363 |
89 | 0.474866008080998 | 0.949732016161997 | 0.525133991919002 |
90 | 0.427712355759074 | 0.855424711518148 | 0.572287644240926 |
91 | 0.396632427699677 | 0.793264855399353 | 0.603367572300323 |
92 | 0.40618591285616 | 0.81237182571232 | 0.59381408714384 |
93 | 0.409472425742448 | 0.818944851484897 | 0.590527574257552 |
94 | 0.5224723565063 | 0.9550552869874 | 0.4775276434937 |
95 | 0.496974482780911 | 0.993948965561822 | 0.503025517219089 |
96 | 0.559149694627852 | 0.881700610744296 | 0.440850305372148 |
97 | 0.511364817004308 | 0.977270365991383 | 0.488635182995692 |
98 | 0.516966113664924 | 0.966067772670152 | 0.483033886335076 |
99 | 0.469249094362215 | 0.93849818872443 | 0.530750905637785 |
100 | 0.420935059836616 | 0.841870119673233 | 0.579064940163384 |
101 | 0.532434795040296 | 0.935130409919408 | 0.467565204959704 |
102 | 0.483695641195002 | 0.967391282390004 | 0.516304358804998 |
103 | 0.465497664227504 | 0.930995328455009 | 0.534502335772496 |
104 | 0.433382017380138 | 0.866764034760276 | 0.566617982619862 |
105 | 0.390957364085224 | 0.781914728170449 | 0.609042635914776 |
106 | 0.489795424361867 | 0.979590848723734 | 0.510204575638133 |
107 | 0.480893360444426 | 0.961786720888851 | 0.519106639555574 |
108 | 0.467082574176083 | 0.934165148352166 | 0.532917425823917 |
109 | 0.420600749068694 | 0.841201498137389 | 0.579399250931306 |
110 | 0.373125817822229 | 0.746251635644458 | 0.626874182177771 |
111 | 0.337616840037471 | 0.675233680074941 | 0.66238315996253 |
112 | 0.403152179080101 | 0.806304358160202 | 0.596847820919899 |
113 | 0.420981651008435 | 0.841963302016871 | 0.579018348991565 |
114 | 0.745491473368884 | 0.509017053262232 | 0.254508526631116 |
115 | 0.850539899779238 | 0.298920200441524 | 0.149460100220762 |
116 | 0.871406280353181 | 0.257187439293638 | 0.128593719646819 |
117 | 0.839307220261477 | 0.321385559477047 | 0.160692779738523 |
118 | 0.828087258813845 | 0.34382548237231 | 0.171912741186155 |
119 | 0.79399735412459 | 0.412005291750819 | 0.206002645875409 |
120 | 0.857594479821773 | 0.284811040356454 | 0.142405520178227 |
121 | 0.899187669433472 | 0.201624661133057 | 0.100812330566529 |
122 | 0.879466361075454 | 0.241067277849093 | 0.120533638924546 |
123 | 0.846770103291865 | 0.306459793416269 | 0.153229896708135 |
124 | 0.845276084500333 | 0.309447830999333 | 0.154723915499667 |
125 | 0.812700360685052 | 0.374599278629896 | 0.187299639314948 |
126 | 0.767786842693416 | 0.464426314613167 | 0.232213157306584 |
127 | 0.771572166544629 | 0.456855666910742 | 0.228427833455371 |
128 | 0.732678572162316 | 0.534642855675368 | 0.267321427837684 |
129 | 0.687443777390876 | 0.625112445218248 | 0.312556222609124 |
130 | 0.654356379107007 | 0.691287241785987 | 0.345643620892993 |
131 | 0.688222636096606 | 0.623554727806789 | 0.311777363903394 |
132 | 0.772589920763949 | 0.454820158472102 | 0.227410079236051 |
133 | 0.718705809592374 | 0.562588380815251 | 0.281294190407626 |
134 | 0.681991904371887 | 0.636016191256225 | 0.318008095628113 |
135 | 0.72200618420021 | 0.55598763159958 | 0.27799381579979 |
136 | 0.695885606557144 | 0.608228786885712 | 0.304114393442856 |
137 | 0.831329044727345 | 0.337341910545309 | 0.168670955272655 |
138 | 0.77459856569307 | 0.450802868613861 | 0.225401434306930 |
139 | 0.709727986404954 | 0.580544027190093 | 0.290272013595046 |
140 | 0.926166352368753 | 0.147667295262494 | 0.073833647631247 |
141 | 0.911574832342628 | 0.176850335314745 | 0.0884251676573723 |
142 | 0.904570826855883 | 0.190858346288234 | 0.095429173144117 |
143 | 0.96971113538641 | 0.0605777292271805 | 0.0302888646135902 |
144 | 0.989255806471385 | 0.0214883870572300 | 0.0107441935286150 |
145 | 0.97844685165793 | 0.0431062966841401 | 0.0215531483420700 |
146 | 0.952890043832138 | 0.0942199123357246 | 0.0471099561678623 |
147 | 0.957094496860412 | 0.0858110062791766 | 0.0429055031395883 |
148 | 0.922152775304786 | 0.155694449390428 | 0.0778472246952139 |
149 | 0.978178742314237 | 0.0436425153715268 | 0.0218212576857634 |
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 | 3 | 0.0214285714285714 | OK |
10% type I error level | 6 | 0.0428571428571429 | OK |