Multiple Linear Regression - Estimated Regression Equation |
y[t] = + 0.653455385234217 + 0.0261778726526484x1[t] + 0.228695811251476x2[t] + 0.164523727475987x3[t] + 0.101091007906319x4[t] + 0.197018661004521x5[t] + 0.0540437767073316x6[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) | 0.653455385234217 | 0.412787 | 1.583 | 0.115592 | 0.057796 |
x1 | 0.0261778726526484 | 0.061873 | 0.4231 | 0.672858 | 0.336429 |
x2 | 0.228695811251476 | 0.072759 | 3.1432 | 0.002027 | 0.001014 |
x3 | 0.164523727475987 | 0.065636 | 2.5066 | 0.013293 | 0.006647 |
x4 | 0.101091007906319 | 0.081426 | 1.2415 | 0.216425 | 0.108212 |
x5 | 0.197018661004521 | 0.073942 | 2.6645 | 0.008584 | 0.004292 |
x6 | 0.0540437767073316 | 0.062317 | 0.8672 | 0.387244 | 0.193622 |
Multiple Linear Regression - Regression Statistics | |
Multiple R | 0.55649571399397 |
R-squared | 0.309687479693659 |
Adjusted R-squared | 0.281122823680983 |
F-TEST (value) | 10.8416316848426 |
F-TEST (DF numerator) | 6 |
F-TEST (DF denominator) | 145 |
p-value | 5.9757754300449e-10 |
Multiple Linear Regression - Residual Statistics | |
Residual Standard Deviation | 0.643938914498158 |
Sum Squared Residuals | 60.1253122127345 |
Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
1 | 4 | 3.96835462447888 | 0.0316453755211221 |
2 | 4 | 3.63856780532104 | 0.361432194678961 |
3 | 5 | 4.06394635479085 | 0.936053645209152 |
4 | 3 | 3.03752181388844 | -0.0375218138884397 |
5 | 2 | 2.83533979807580 | -0.835339798075795 |
6 | 5 | 3.54345793550441 | 1.45654206449559 |
7 | 4 | 3.21917039394092 | 0.780829606059077 |
8 | 2 | 3.4032113713474 | -1.40321137134740 |
9 | 4 | 3.65393788627307 | 0.346062113726933 |
10 | 4 | 2.44130247606675 | 1.55869752393325 |
11 | 4 | 3.25608931807175 | 0.743910681928247 |
12 | 2 | 2.74880108783993 | -0.74880108783993 |
13 | 5 | 3.74490058711123 | 1.25509941288877 |
14 | 3 | 3.01665245534209 | -0.0166524553420947 |
15 | 4 | 3.71348094057471 | 0.286519059425295 |
16 | 4 | 3.68180379032775 | 0.31819620967225 |
17 | 3 | 2.94193008357642 | 0.0580699164235791 |
18 | 4 | 3.73965881322735 | 0.260341186772646 |
19 | 2 | 2.61677229389248 | -0.616772293892475 |
20 | 4 | 3.58621206001574 | 0.413787939984263 |
21 | 3 | 3.20204554136442 | -0.202045541364422 |
22 | 3 | 3.2881023911049 | -0.288102391104897 |
23 | 4 | 3.2822671907244 | 0.717732809275598 |
24 | 4 | 3.51096300197588 | 0.489036998024122 |
25 | 4 | 3.73965881322735 | 0.260341186772646 |
26 | 4 | 3.32965034470958 | 0.670349655290422 |
27 | 5 | 3.73965881322735 | 1.26034118677265 |
28 | 3 | 3.1819155470239 | -0.181915547023902 |
29 | 1 | 3.73965881322735 | -2.73965881322735 |
30 | 4 | 3.49028440691754 | 0.509715593082464 |
31 | 4 | 3.68730306792206 | 0.312696932077943 |
32 | 3 | 3.1819155470239 | -0.181915547023902 |
33 | 3 | 3.49028440691754 | -0.490284406917536 |
34 | 4 | 3.86692769378632 | 0.133072306213678 |
35 | 4 | 3.73965881322735 | 0.260341186772646 |
36 | 4 | 3.79370258993469 | 0.206297410065314 |
37 | 3 | 3.39517453710091 | -0.395174537100912 |
38 | 4 | 3.68730306792206 | 0.312696932077943 |
39 | 3 | 3.32026140184724 | -0.320261401847241 |
40 | 4 | 3.49491343639139 | 0.505086563608614 |
41 | 3 | 3.27702541684053 | -0.277025416840526 |
42 | 4 | 3.46704753233670 | 0.532952467663297 |
43 | 3 | 2.52634391838858 | 0.47365608161142 |
44 | 2 | 2.66027342166970 | -0.660273421669704 |
45 | 3 | 3.84074982113367 | -0.840749821133673 |
46 | 4 | 3.46465513498271 | 0.53534486501729 |
47 | 4 | 4.03776848213819 | -0.0377684821381942 |
48 | 3 | 3.68730306792206 | -0.687303067922057 |
49 | 3 | 3.3519385520942 | -0.351938552094197 |
50 | 4 | 3.74134684462939 | 0.258653155370612 |
51 | 4 | 3.63325929121473 | 0.366740708785275 |
52 | 3 | 3.04133306008071 | -0.0413330600807061 |
53 | 2 | 2.78869600829644 | -0.788696008296438 |
54 | 4 | 3.73965881322735 | 0.260341186772646 |
55 | 4 | 3.40837472615552 | 0.591625273844479 |
56 | 3 | 3.10550514385619 | -0.105505143856194 |
57 | 2 | 2.58536028641603 | -0.585360286416033 |
58 | 4 | 3.73965881322735 | 0.260341186772646 |
59 | 3 | 3.73965881322735 | -0.739658813227354 |
60 | 3 | 3.52109130904403 | -0.521091309044034 |
61 | 4 | 3.46704753233670 | 0.532952467663297 |
62 | 3 | 2.76801741323810 | 0.231982586761904 |
63 | 4 | 3.79370258993469 | 0.206297410065314 |
64 | 3 | 3.41061135827538 | -0.410611358275378 |
65 | 4 | 3.76752471728204 | 0.232475282717963 |
66 | 4 | 4.43098802086566 | -0.430988020865658 |
67 | 4 | 3.46873556373874 | 0.531264436261263 |
68 | 3 | 3.04302109148274 | -0.0430210914827404 |
69 | 3 | 2.63443147180324 | 0.365568528196756 |
70 | 3 | 3.68561503652002 | -0.685615036520023 |
71 | 4 | 2.6797906716002 | 1.32020932839980 |
72 | 3 | 2.55951833654957 | 0.440481663450427 |
73 | 2 | 2.45278289175076 | -0.452782891750756 |
74 | 4 | 3.84243785253571 | 0.157562147464292 |
75 | 4 | 3.90587057210538 | 0.0941294278946235 |
76 | 4 | 4.06394635479084 | -0.063946354790843 |
77 | 3 | 2.5121351825644 | 0.487864817435603 |
78 | 5 | 4.10120120170786 | 0.898798798292137 |
79 | 3 | 3.30421183626275 | -0.304211836262749 |
80 | 2 | 2.94193008357642 | -0.941930083576421 |
81 | 3 | 3.31394434097136 | -0.313944340971357 |
82 | 3 | 3.34643927449989 | -0.34643927449989 |
83 | 4 | 3.35656758156805 | 0.643432418431954 |
84 | 4 | 3.14942061349537 | 0.85057938650463 |
85 | 3 | 3.40456347996325 | -0.404563479963249 |
86 | 2 | 2.28825916427477 | -0.288259164274768 |
87 | 4 | 3.45765858947437 | 0.542341410525634 |
88 | 4 | 3.07932727120355 | 0.920672728796455 |
89 | 3 | 2.72539417264141 | 0.274605827358593 |
90 | 4 | 3.46873556373874 | 0.531264436261263 |
91 | 3 | 3.1819155470239 | -0.181915547023902 |
92 | 2 | 3.05431074367875 | -1.05431074367875 |
93 | 3 | 3.46241850286285 | -0.462418502862853 |
94 | 3 | 3.09537683678804 | -0.0953768367880378 |
95 | 3 | 2.82513307193188 | 0.174866928068119 |
96 | 4 | 3.28776646831871 | 0.712233531681291 |
97 | 4 | 3.71729218676698 | 0.282707813233022 |
98 | 4 | 2.96253025955900 | 1.03746974044100 |
99 | 3 | 3.05431074367875 | -0.0543107436787454 |
100 | 4 | 3.73266226771901 | 0.26733773228099 |
101 | 4 | 3.12324274084272 | 0.87675725915728 |
102 | 3 | 2.55918241376338 | 0.440817586236615 |
103 | 4 | 3.78839407582838 | 0.211605924171624 |
104 | 3 | 3.70409199771237 | -0.704091997712368 |
105 | 4 | 3.59750171221174 | 0.402498287788257 |
106 | 4 | 4.06563438619288 | -0.0656343861928771 |
107 | 3 | 3.54895721309872 | -0.548957213098717 |
108 | 3 | 3.49028440691754 | -0.490284406917536 |
109 | 3 | 3.46873556373874 | -0.468735563738737 |
110 | 3 | 3.41469178703141 | -0.414691787031405 |
111 | 3 | 3.01549111021425 | -0.0154911102142459 |
112 | 2 | 2.55918241376338 | -0.559182413763385 |
113 | 4 | 3.54827772846626 | 0.451722271533743 |
114 | 2 | 2.74015150918341 | -0.740151509183413 |
115 | 3 | 3.1819155470239 | -0.181915547023902 |
116 | 3 | 3.3519385520942 | -0.351938552094197 |
117 | 3 | 3.12324274084272 | -0.123242740842721 |
118 | 4 | 3.77215374675589 | 0.227846253244113 |
119 | 4 | 3.16512661723359 | 0.83487338276641 |
120 | 3 | 2.93254114071408 | 0.067458859285916 |
121 | 4 | 3.65943716386737 | 0.340562836132626 |
122 | 3 | 3.02846879381229 | -0.0284687938122853 |
123 | 3 | 3.54895721309872 | -0.548957213098717 |
124 | 3 | 3.44753028240621 | -0.447530282406210 |
125 | 4 | 3.70648439506636 | 0.293515604933639 |
126 | 2 | 3.04451835939678 | -1.04451835939678 |
127 | 4 | 3.50157405911354 | 0.498425940886459 |
128 | 3 | 3.46873556373874 | -0.468735563738737 |
129 | 3 | 3.01052615795421 | -0.0105261579542077 |
130 | 4 | 3.75536481696558 | 0.244635183034425 |
131 | 4 | 3.21917039394092 | 0.780829606059078 |
132 | 4 | 3.65943716386737 | 0.340562836132626 |
133 | 3 | 3.23727643409322 | -0.237276434093219 |
134 | 2 | 2.21402551365356 | -0.214025513653557 |
135 | 4 | 3.73965881322735 | 0.260341186772646 |
136 | 2 | 3.63157125981269 | -1.63157125981269 |
137 | 3 | 3.32026140184724 | -0.320261401847241 |
138 | 4 | 3.62218231695035 | 0.377817683049646 |
139 | 3 | 3.211356065151 | -0.211356065151001 |
140 | 3 | 3.01134394123578 | -0.0113439412357851 |
141 | 3 | 3.35656758156805 | -0.356567581568046 |
142 | 3 | 3.54264015222283 | -0.542640152222834 |
143 | 4 | 3.73965881322735 | 0.260341186772646 |
144 | 3 | 3.68730306792206 | -0.687303067922057 |
145 | 3 | 3.56813854024302 | -0.568138540243022 |
146 | 2 | 2.98584555321560 | -0.985845553215596 |
147 | 2 | 3.73965881322735 | -1.73965881322735 |
148 | 3 | 3.09074780731419 | -0.090747807314188 |
149 | 4 | 3.63325929121473 | 0.366740708785275 |
150 | 3 | 3.26621762513991 | -0.26621762513991 |
151 | 4 | 3.5768231171534 | 0.423176882846600 |
152 | 3 | 4.45716589351831 | -1.45716589351831 |
Goldfeld-Quandt test for Heteroskedasticity | |||
p-values | Alternative Hypothesis | ||
breakpoint index | greater | 2-sided | less |
10 | 0.827499504489573 | 0.345000991020855 | 0.172500495510427 |
11 | 0.733948042078901 | 0.532103915842198 | 0.266051957921099 |
12 | 0.63740793968802 | 0.725184120623962 | 0.362592060311981 |
13 | 0.585202766433549 | 0.829594467132903 | 0.414797233566451 |
14 | 0.800708957861648 | 0.398582084276705 | 0.199291042138352 |
15 | 0.727720058252465 | 0.544559883495069 | 0.272279941747535 |
16 | 0.648864460814805 | 0.70227107837039 | 0.351135539185195 |
17 | 0.555492287646862 | 0.889015424706277 | 0.444507712353138 |
18 | 0.512612472697588 | 0.974775054604824 | 0.487387527302412 |
19 | 0.432826958004582 | 0.865653916009163 | 0.567173041995418 |
20 | 0.413126767184344 | 0.826253534368688 | 0.586873232815656 |
21 | 0.386370506897769 | 0.772741013795538 | 0.613629493102231 |
22 | 0.331315906611843 | 0.662631813223686 | 0.668684093388157 |
23 | 0.293553651999874 | 0.587107303999748 | 0.706446348000126 |
24 | 0.252983640319836 | 0.505967280639672 | 0.747016359680164 |
25 | 0.213621141023804 | 0.427242282047607 | 0.786378858976196 |
26 | 0.299332201576741 | 0.598664403153482 | 0.700667798423259 |
27 | 0.350261740544991 | 0.700523481089981 | 0.64973825945501 |
28 | 0.446103675660155 | 0.89220735132031 | 0.553896324339845 |
29 | 0.9992604280613 | 0.00147914387739965 | 0.000739571938699827 |
30 | 0.998885020227328 | 0.00222995954534459 | 0.00111497977267230 |
31 | 0.998270662649638 | 0.00345867470072382 | 0.00172933735036191 |
32 | 0.997707017058046 | 0.00458596588390891 | 0.00229298294195445 |
33 | 0.997775698857804 | 0.00444860228439215 | 0.00222430114219608 |
34 | 0.996686180142432 | 0.00662763971513504 | 0.00331381985756752 |
35 | 0.99516025754758 | 0.00967948490483908 | 0.00483974245241954 |
36 | 0.993832563658303 | 0.0123348726833944 | 0.00616743634169719 |
37 | 0.993255636987188 | 0.0134887260256234 | 0.00674436301281172 |
38 | 0.990877464411527 | 0.0182450711769455 | 0.00912253558847276 |
39 | 0.988931446250827 | 0.0221371074983455 | 0.0110685537491727 |
40 | 0.990979833941727 | 0.0180403321165466 | 0.00902016605827328 |
41 | 0.987948245095376 | 0.0241035098092473 | 0.0120517549046237 |
42 | 0.99024479417113 | 0.0195104116577411 | 0.00975520582887057 |
43 | 0.989500326715926 | 0.0209993465681472 | 0.0104996732840736 |
44 | 0.992654166511312 | 0.0146916669773752 | 0.0073458334886876 |
45 | 0.99494634947856 | 0.0101073010428807 | 0.00505365052144033 |
46 | 0.993917355801222 | 0.0121652883975552 | 0.00608264419877758 |
47 | 0.99176227978467 | 0.0164754404306582 | 0.0082377202153291 |
48 | 0.992290122809025 | 0.0154197543819509 | 0.00770987719097547 |
49 | 0.99010219351347 | 0.0197956129730591 | 0.00989780648652953 |
50 | 0.986693872831584 | 0.0266122543368315 | 0.0133061271684158 |
51 | 0.983897160846946 | 0.0322056783061085 | 0.0161028391530542 |
52 | 0.978193428881253 | 0.0436131422374941 | 0.0218065711187471 |
53 | 0.980571200815026 | 0.0388575983699486 | 0.0194287991849743 |
54 | 0.975039226979904 | 0.049921546040192 | 0.024960773020096 |
55 | 0.974266397877726 | 0.0514672042445475 | 0.0257336021222737 |
56 | 0.966869909259656 | 0.0662601814806887 | 0.0331300907403443 |
57 | 0.964178178855292 | 0.0716436422894156 | 0.0358218211447078 |
58 | 0.955356479932238 | 0.089287040135524 | 0.044643520067762 |
59 | 0.959668855875318 | 0.0806622882493636 | 0.0403311441246818 |
60 | 0.954935542850706 | 0.090128914298587 | 0.0450644571492935 |
61 | 0.95171993485195 | 0.0965601302960993 | 0.0482800651480496 |
62 | 0.941866230652898 | 0.116267538694204 | 0.0581337693471018 |
63 | 0.928557111130621 | 0.142885777738757 | 0.0714428888693786 |
64 | 0.917569845026846 | 0.164860309946308 | 0.0824301549731538 |
65 | 0.901128028938075 | 0.197743942123850 | 0.0988719710619248 |
66 | 0.89317776855981 | 0.213644462880378 | 0.106822231440189 |
67 | 0.884994671234071 | 0.230010657531858 | 0.115005328765929 |
68 | 0.860199641307763 | 0.279600717384475 | 0.139800358692237 |
69 | 0.842483493540261 | 0.315033012919478 | 0.157516506459739 |
70 | 0.843781677591291 | 0.312436644817417 | 0.156218322408709 |
71 | 0.916004392730153 | 0.167991214539693 | 0.0839956072698466 |
72 | 0.906147400733441 | 0.187705198533118 | 0.093852599266559 |
73 | 0.898557583344475 | 0.202884833311050 | 0.101442416655525 |
74 | 0.878158864612354 | 0.243682270775291 | 0.121841135387646 |
75 | 0.856315340425334 | 0.287369319149333 | 0.143684659574666 |
76 | 0.828322648048068 | 0.343354703903864 | 0.171677351951932 |
77 | 0.813621731888202 | 0.372756536223597 | 0.186378268111798 |
78 | 0.86113034282475 | 0.277739314350500 | 0.138869657175250 |
79 | 0.840711737499146 | 0.318576525001708 | 0.159288262500854 |
80 | 0.872559814747873 | 0.254880370504255 | 0.127440185252127 |
81 | 0.852887134198 | 0.294225731604001 | 0.147112865802001 |
82 | 0.830308656560613 | 0.339382686878775 | 0.169691343439387 |
83 | 0.830140607735088 | 0.339718784529824 | 0.169859392264912 |
84 | 0.858789000117917 | 0.282421999764167 | 0.141210999882083 |
85 | 0.839921460440978 | 0.320157079118044 | 0.160078539559022 |
86 | 0.826399083196087 | 0.347201833607827 | 0.173600916803913 |
87 | 0.816491601091038 | 0.367016797817925 | 0.183508398908962 |
88 | 0.839721975875816 | 0.320556048248369 | 0.160278024124184 |
89 | 0.813309903178064 | 0.373380193643872 | 0.186690096821936 |
90 | 0.801944379576226 | 0.396111240847549 | 0.198055620423774 |
91 | 0.767725784991793 | 0.464548430016414 | 0.232274215008207 |
92 | 0.823846770152669 | 0.352306459694662 | 0.176153229847331 |
93 | 0.80520618537565 | 0.389587629248699 | 0.194793814624349 |
94 | 0.769396438355509 | 0.461207123288982 | 0.230603561644491 |
95 | 0.733925892275498 | 0.532148215449004 | 0.266074107724502 |
96 | 0.761080576099965 | 0.477838847800071 | 0.238919423900035 |
97 | 0.7426426686632 | 0.5147146626736 | 0.2573573313368 |
98 | 0.825195902232604 | 0.349608195534792 | 0.174804097767396 |
99 | 0.790242131518271 | 0.419515736963458 | 0.209757868481729 |
100 | 0.772871569327724 | 0.454256861344552 | 0.227128430672276 |
101 | 0.827371909175064 | 0.345256181649873 | 0.172628090824936 |
102 | 0.830991694037755 | 0.338016611924490 | 0.169008305962245 |
103 | 0.805917786791212 | 0.388164426417576 | 0.194082213208788 |
104 | 0.798934641122255 | 0.402130717755491 | 0.201065358877745 |
105 | 0.789770003678532 | 0.420459992642937 | 0.210229996321468 |
106 | 0.751296915114298 | 0.497406169771405 | 0.248703084885702 |
107 | 0.726374733725267 | 0.547250532549467 | 0.273625266274733 |
108 | 0.696122523847662 | 0.607754952304676 | 0.303877476152338 |
109 | 0.673970054825446 | 0.652059890349109 | 0.326029945174554 |
110 | 0.652592177127913 | 0.694815645744173 | 0.347407822872087 |
111 | 0.599319295513518 | 0.801361408972964 | 0.400680704486482 |
112 | 0.564354809217237 | 0.871290381565527 | 0.435645190782763 |
113 | 0.520715544121783 | 0.958568911756434 | 0.479284455878217 |
114 | 0.560736949441413 | 0.878526101117175 | 0.439263050558587 |
115 | 0.504521495194325 | 0.99095700961135 | 0.495478504805675 |
116 | 0.453918058654678 | 0.907836117309356 | 0.546081941345322 |
117 | 0.396290441920743 | 0.792580883841487 | 0.603709558079257 |
118 | 0.366058755494459 | 0.732117510988919 | 0.63394124450554 |
119 | 0.433633147830666 | 0.867266295661332 | 0.566366852169334 |
120 | 0.376501303051922 | 0.753002606103843 | 0.623498696948078 |
121 | 0.365154093739325 | 0.73030818747865 | 0.634845906260675 |
122 | 0.307999820908394 | 0.615999641816788 | 0.692000179091606 |
123 | 0.276535195812085 | 0.55307039162417 | 0.723464804187915 |
124 | 0.241263979164014 | 0.482527958328028 | 0.758736020835986 |
125 | 0.209179432699067 | 0.418358865398133 | 0.790820567300933 |
126 | 0.268697411976187 | 0.537394823952375 | 0.731302588023813 |
127 | 0.257983887821663 | 0.515967775643326 | 0.742016112178337 |
128 | 0.240166171310017 | 0.480332342620033 | 0.759833828689983 |
129 | 0.188664803184977 | 0.377329606369955 | 0.811335196815023 |
130 | 0.176502073819329 | 0.353004147638657 | 0.823497926180671 |
131 | 0.298690167754151 | 0.597380335508303 | 0.701309832245849 |
132 | 0.371020369744729 | 0.742040739489458 | 0.628979630255271 |
133 | 0.403606202701408 | 0.807212405402817 | 0.596393797298592 |
134 | 0.324625599409749 | 0.649251198819499 | 0.675374400590251 |
135 | 0.518135120232471 | 0.963729759535057 | 0.481864879767529 |
136 | 0.512603795655777 | 0.974792408688447 | 0.487396204344223 |
137 | 0.411539306259827 | 0.823078612519654 | 0.588460693740173 |
138 | 0.367739710708646 | 0.735479421417292 | 0.632260289291354 |
139 | 0.277326738180859 | 0.554653476361718 | 0.722673261819141 |
140 | 0.208180492932124 | 0.416360985864247 | 0.791819507067876 |
141 | 0.143261637909271 | 0.286523275818542 | 0.856738362090729 |
142 | 0.0822831594503916 | 0.164566318900783 | 0.917716840549608 |
Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
Description | # significant tests | % significant tests | OK/NOK |
1% type I error level | 7 | 0.0526315789473684 | NOK |
5% type I error level | 26 | 0.195488721804511 | NOK |
10% type I error level | 33 | 0.248120300751880 | NOK |