Multiple Linear Regression - Estimated Regression Equation |
PS[t] = + 22.1825037707391 + 1.49646268763916M1[t] -0.494038641097464M2[t] + 1.37260288730877M3[t] + 0.462472168354522M4[t] -0.220336852689793M5[t] + 0.404546433958199M6[t] + 1.3371220282985M7[t] + 1.96200531494649M8[t] + 1.66381167851756M9[t] + 1.1348488113194M10[t] -0.471037132801838M11[t] -0.00949867126337714t + 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) | 22.1825037707391 | 1.338124 | 16.5773 | 0 | 0 |
M1 | 1.49646268763916 | 1.646464 | 0.9089 | 0.364904 | 0.182452 |
M2 | -0.494038641097464 | 1.646315 | -0.3001 | 0.764537 | 0.382269 |
M3 | 1.37260288730877 | 1.646198 | 0.8338 | 0.405755 | 0.202877 |
M4 | 0.462472168354522 | 1.677297 | 0.2757 | 0.783149 | 0.391575 |
M5 | -0.220336852689793 | 1.677053 | -0.1314 | 0.895653 | 0.447826 |
M6 | 0.404546433958199 | 1.676841 | 0.2413 | 0.809696 | 0.404848 |
M7 | 1.3371220282985 | 1.676662 | 0.7975 | 0.426461 | 0.213231 |
M8 | 1.96200531494649 | 1.676515 | 1.1703 | 0.243792 | 0.121896 |
M9 | 1.66381167851756 | 1.676401 | 0.9925 | 0.3226 | 0.1613 |
M10 | 1.1348488113194 | 1.676319 | 0.677 | 0.499485 | 0.249742 |
M11 | -0.471037132801838 | 1.676271 | -0.281 | 0.779106 | 0.389553 |
t | -0.00949867126337714 | 0.007393 | -1.2848 | 0.200894 | 0.100447 |
Multiple Linear Regression - Regression Statistics | |
Multiple R | 0.225715608925364 |
R-squared | 0.050947536112548 |
Adjusted R-squared | -0.0270567759877907 |
F-TEST (value) | 0.653137432287245 |
F-TEST (DF numerator) | 12 |
F-TEST (DF denominator) | 146 |
p-value | 0.793449743611323 |
Multiple Linear Regression - Residual Statistics | |
Residual Standard Deviation | 4.27362654504094 |
Sum Squared Residuals | 2666.52704158586 |
Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
1 | 24 | 23.6694677871149 | 0.33053221288513 |
2 | 25 | 21.6694677871148 | 3.33053221288515 |
3 | 30 | 23.5266106442577 | 6.4733893557423 |
4 | 19 | 22.6069812540401 | -3.60698125404008 |
5 | 22 | 21.9146735617324 | 0.0853264382676138 |
6 | 22 | 22.530058177117 | -0.530058177116999 |
7 | 25 | 23.4531351001939 | 1.54686489980608 |
8 | 23 | 24.0685197155785 | -1.06851971557854 |
9 | 17 | 23.7608274078862 | -6.76082740788623 |
10 | 21 | 23.2223658694247 | -2.22236586942469 |
11 | 19 | 21.6069812540401 | -2.60698125404008 |
12 | 19 | 22.0685197155785 | -3.06851971557854 |
13 | 15 | 23.5554837319543 | -8.55548373195432 |
14 | 16 | 21.5554837319543 | -5.55548373195432 |
15 | 23 | 23.4126265890972 | -0.412626589097177 |
16 | 27 | 22.4929971988796 | 4.50700280112045 |
17 | 22 | 21.8006895065719 | 0.199310493428141 |
18 | 14 | 22.4160741219565 | -8.41607412195648 |
19 | 22 | 23.3391510450334 | -1.33915104503340 |
20 | 23 | 23.954535660418 | -0.954535660418013 |
21 | 23 | 23.6468433527257 | -0.646843352725706 |
22 | 21 | 23.1083818142642 | -2.10838181426417 |
23 | 19 | 21.4929971988796 | -2.49299719887955 |
24 | 18 | 21.954535660418 | -3.95453566041801 |
25 | 20 | 23.4414996767938 | -3.44149967679379 |
26 | 23 | 21.4414996767938 | 1.55850032320621 |
27 | 25 | 23.2986425339367 | 1.70135746606335 |
28 | 19 | 22.3790131437190 | -3.37901314371903 |
29 | 24 | 21.6867054514113 | 2.31329454858867 |
30 | 22 | 22.3020900667959 | -0.302090066795949 |
31 | 25 | 23.2251669898729 | 1.77483301012713 |
32 | 26 | 23.8405516052575 | 2.15944839474251 |
33 | 29 | 23.5328592975652 | 5.46714070243482 |
34 | 32 | 22.9943977591036 | 9.00560224089636 |
35 | 25 | 21.3790131437190 | 3.62098685628097 |
36 | 29 | 21.8405516052575 | 7.15944839474251 |
37 | 28 | 23.3275156216333 | 4.67248437836674 |
38 | 17 | 21.3275156216333 | -4.32751562163327 |
39 | 28 | 23.1846584787761 | 4.81534152122387 |
40 | 29 | 22.2650290885585 | 6.7349709114415 |
41 | 26 | 21.5727213962508 | 4.42727860374919 |
42 | 25 | 22.1881060116354 | 2.81189398836458 |
43 | 14 | 23.1111829347123 | -9.11118293471235 |
44 | 25 | 23.7265675500970 | 1.27343244990304 |
45 | 26 | 23.4188752424047 | 2.58112475759535 |
46 | 20 | 22.8804137039431 | -2.88041370394312 |
47 | 18 | 21.2650290885585 | -3.2650290885585 |
48 | 32 | 21.7265675500970 | 10.2734324499030 |
49 | 25 | 23.2135315664727 | 1.78646843352726 |
50 | 25 | 21.2135315664727 | 3.78646843352726 |
51 | 23 | 23.0706744236156 | -0.0706744236156003 |
52 | 21 | 22.1510450333980 | -1.15104503339797 |
53 | 20 | 21.4587373410903 | -1.45873734109028 |
54 | 15 | 22.0741219564749 | -7.0741219564749 |
55 | 30 | 22.9971988795518 | 7.00280112044818 |
56 | 24 | 23.6125834949364 | 0.387416505063564 |
57 | 26 | 23.3048911872441 | 2.69510881275587 |
58 | 24 | 22.7664296487826 | 1.23357035121741 |
59 | 22 | 21.1510450333980 | 0.848954966602025 |
60 | 14 | 21.6125834949364 | -7.61258349493644 |
61 | 24 | 23.0995475113122 | 0.900452488687784 |
62 | 24 | 21.0995475113122 | 2.90045248868778 |
63 | 24 | 22.9566903684551 | 1.04330963154493 |
64 | 24 | 22.0370609782374 | 1.96293902176255 |
65 | 19 | 21.3447532859298 | -2.34475328592976 |
66 | 31 | 21.9601379013144 | 9.03986209868563 |
67 | 22 | 22.8832148243913 | -0.883214824391294 |
68 | 27 | 23.4985994397759 | 3.50140056022409 |
69 | 19 | 23.1909071320836 | -4.19090713208361 |
70 | 25 | 22.6524455936221 | 2.34755440637794 |
71 | 20 | 21.0370609782374 | -1.03706097823745 |
72 | 21 | 21.4985994397759 | -0.49859943977591 |
73 | 27 | 22.9855634561517 | 4.01443654384831 |
74 | 23 | 20.9855634561517 | 2.01443654384831 |
75 | 25 | 22.8427063132945 | 2.15729368670545 |
76 | 20 | 21.9230769230769 | -1.92307692307692 |
77 | 21 | 21.2307692307692 | -0.230769230769231 |
78 | 22 | 21.8461538461538 | 0.153846153846154 |
79 | 23 | 22.7692307692308 | 0.230769230769231 |
80 | 25 | 23.3846153846154 | 1.61538461538462 |
81 | 25 | 23.0769230769231 | 1.92307692307692 |
82 | 17 | 22.5384615384615 | -5.53846153846154 |
83 | 19 | 20.9230769230769 | -1.92307692307692 |
84 | 25 | 21.3846153846154 | 3.61538461538462 |
85 | 19 | 22.8715794009912 | -3.87157940099116 |
86 | 20 | 20.8715794009912 | -0.871579400991166 |
87 | 26 | 22.7287222581340 | 3.27127774186598 |
88 | 23 | 21.8090928679164 | 1.19090713208360 |
89 | 27 | 21.1167851756087 | 5.8832148243913 |
90 | 17 | 21.7321697909933 | -4.73216979099332 |
91 | 17 | 22.6552467140702 | -5.65524671407025 |
92 | 19 | 23.2706313294549 | -4.27063132945486 |
93 | 17 | 22.9629390217626 | -5.96293902176255 |
94 | 22 | 22.424477483301 | -0.424477483301013 |
95 | 21 | 20.8090928679164 | 0.190907132083602 |
96 | 32 | 21.2706313294549 | 10.7293686705451 |
97 | 21 | 22.7575953458306 | -1.75759534583064 |
98 | 21 | 20.7575953458306 | 0.242404654169360 |
99 | 18 | 22.6147382029735 | -4.6147382029735 |
100 | 18 | 21.6951088127559 | -3.69510881275587 |
101 | 23 | 21.0028011204482 | 1.99719887955182 |
102 | 19 | 21.6181857358328 | -2.61818573583280 |
103 | 20 | 22.5412626589097 | -2.54126265890972 |
104 | 21 | 23.1566472742943 | -2.15664727429433 |
105 | 20 | 22.8489549666020 | -2.84895496660203 |
106 | 17 | 22.3104934281405 | -5.31049342814049 |
107 | 18 | 20.6951088127559 | -2.69510881275587 |
108 | 19 | 21.1566472742943 | -2.15664727429433 |
109 | 22 | 22.6436112906701 | -0.643611290670113 |
110 | 15 | 20.6436112906701 | -5.64361129067011 |
111 | 14 | 22.5007541478130 | -8.50075414781297 |
112 | 18 | 21.5811247575953 | -3.58112475759535 |
113 | 24 | 20.8888170652877 | 3.11118293471235 |
114 | 35 | 21.5042016806723 | 13.4957983193277 |
115 | 29 | 22.4272786037492 | 6.5727213962508 |
116 | 21 | 23.0426632191338 | -2.04266321913381 |
117 | 25 | 22.7349709114415 | 2.2650290885585 |
118 | 20 | 22.1965093729800 | -2.19650937297996 |
119 | 22 | 20.5811247575953 | 1.41887524240465 |
120 | 13 | 21.0426632191338 | -8.0426632191338 |
121 | 26 | 22.5296272355096 | 3.47037276449041 |
122 | 17 | 20.5296272355096 | -3.52962723550959 |
123 | 25 | 22.3867700926524 | 2.61322990734755 |
124 | 20 | 21.4671407024348 | -1.46714070243482 |
125 | 19 | 20.7748330101271 | -1.77483301012713 |
126 | 21 | 21.3902176255117 | -0.390217625511743 |
127 | 22 | 22.3132945485887 | -0.313294548588666 |
128 | 24 | 22.9286791639733 | 1.07132083602672 |
129 | 21 | 22.6209868562810 | -1.62098685628097 |
130 | 26 | 22.0825253178194 | 3.91747468218057 |
131 | 24 | 20.4671407024348 | 3.53285929756518 |
132 | 16 | 20.9286791639733 | -4.92867916397328 |
133 | 23 | 22.4156431803491 | 0.584356819650939 |
134 | 18 | 20.4156431803491 | -2.41564318034906 |
135 | 16 | 22.2727860374919 | -6.27278603749192 |
136 | 26 | 21.3531566472743 | 4.6468433527257 |
137 | 19 | 20.6608489549666 | -1.66084895496660 |
138 | 21 | 21.2762335703512 | -0.276233570351217 |
139 | 21 | 22.1993104934281 | -1.19931049342814 |
140 | 22 | 22.8146951088128 | -0.814695108812756 |
141 | 23 | 22.5070028011204 | 0.492997198879551 |
142 | 29 | 21.9685412626589 | 7.03145873734109 |
143 | 21 | 20.3531566472743 | 0.646843352725705 |
144 | 21 | 20.8146951088128 | 0.185304891187244 |
145 | 23 | 22.3016591251885 | 0.698340874811464 |
146 | 27 | 20.3016591251885 | 6.69834087481146 |
147 | 25 | 22.1588019823314 | 2.84119801766861 |
148 | 21 | 21.2391725921138 | -0.239172592113768 |
149 | 10 | 20.5468648998061 | -10.5468648998061 |
150 | 20 | 21.1622495151907 | -1.16224951519069 |
151 | 26 | 22.0853264382676 | 3.91467356173239 |
152 | 24 | 22.7007110536522 | 1.29928894634777 |
153 | 29 | 22.3930187459599 | 6.60698125404008 |
154 | 19 | 21.8545572074984 | -2.85455720749838 |
155 | 24 | 20.2391725921138 | 3.76082740788623 |
156 | 19 | 20.7007110536522 | -1.70071105365223 |
157 | 24 | 22.187675070028 | 1.81232492997199 |
158 | 22 | 20.187675070028 | 1.81232492997199 |
159 | 17 | 22.0448179271709 | -5.04481792717087 |
Goldfeld-Quandt test for Heteroskedasticity | |||
p-values | Alternative Hypothesis | ||
breakpoint index | greater | 2-sided | less |
16 | 0.857561527870773 | 0.284876944258453 | 0.142438472129227 |
17 | 0.784920266399044 | 0.430159467201911 | 0.215079733600956 |
18 | 0.735866948983079 | 0.528266102033842 | 0.264133051016921 |
19 | 0.627746100330746 | 0.744507799338508 | 0.372253899669254 |
20 | 0.553153828752255 | 0.89369234249549 | 0.446846171247745 |
21 | 0.651311085741764 | 0.697377828516472 | 0.348688914258236 |
22 | 0.568812239020549 | 0.862375521958902 | 0.431187760979451 |
23 | 0.486340975020941 | 0.972681950041883 | 0.513659024979059 |
24 | 0.405173916564293 | 0.810347833128586 | 0.594826083435707 |
25 | 0.357057556523215 | 0.71411511304643 | 0.642942443476785 |
26 | 0.330547183177384 | 0.661094366354769 | 0.669452816822616 |
27 | 0.257241710953765 | 0.51448342190753 | 0.742758289046235 |
28 | 0.213599169978848 | 0.427198339957696 | 0.786400830021152 |
29 | 0.185040352268515 | 0.37008070453703 | 0.814959647731485 |
30 | 0.186145247972273 | 0.372290495944547 | 0.813854752027727 |
31 | 0.147060046476078 | 0.294120092952156 | 0.852939953523922 |
32 | 0.125118155914185 | 0.250236311828369 | 0.874881844085815 |
33 | 0.221202138955183 | 0.442404277910367 | 0.778797861044817 |
34 | 0.403651186035953 | 0.807302372071906 | 0.596348813964047 |
35 | 0.386607873841484 | 0.773215747682969 | 0.613392126158516 |
36 | 0.495600167867139 | 0.991200335734278 | 0.504399832132861 |
37 | 0.496893253151023 | 0.993786506302047 | 0.503106746848977 |
38 | 0.558915512080048 | 0.882168975839903 | 0.441084487919952 |
39 | 0.514985752615892 | 0.970028494768215 | 0.485014247384108 |
40 | 0.523153048620603 | 0.953693902758794 | 0.476846951379397 |
41 | 0.477741876907737 | 0.955483753815474 | 0.522258123092263 |
42 | 0.433384729075087 | 0.866769458150174 | 0.566615270924913 |
43 | 0.722908665868471 | 0.554182668263058 | 0.277091334131529 |
44 | 0.67536107182686 | 0.649277856346281 | 0.324638928173140 |
45 | 0.626593044843034 | 0.746813910313933 | 0.373406955156966 |
46 | 0.649257628192567 | 0.701484743614866 | 0.350742371807433 |
47 | 0.641914240090821 | 0.716171519818358 | 0.358085759909179 |
48 | 0.764367200211826 | 0.471265599576347 | 0.235632799788174 |
49 | 0.721307146733176 | 0.557385706533648 | 0.278692853266824 |
50 | 0.689122512186745 | 0.62175497562651 | 0.310877487813255 |
51 | 0.694052376569756 | 0.611895246860487 | 0.305947623430244 |
52 | 0.676880061945791 | 0.646239876108418 | 0.323119938054209 |
53 | 0.66869170198945 | 0.6626165960211 | 0.33130829801055 |
54 | 0.745702542225365 | 0.508594915549271 | 0.254297457774635 |
55 | 0.790577591691547 | 0.418844816616907 | 0.209422408308453 |
56 | 0.75506251972096 | 0.489874960558081 | 0.244937480279040 |
57 | 0.720303463782255 | 0.55939307243549 | 0.279696536217745 |
58 | 0.678882459520566 | 0.642235080958867 | 0.321117540479434 |
59 | 0.631474502288448 | 0.737050995423104 | 0.368525497711552 |
60 | 0.78652785899584 | 0.426944282008319 | 0.213472141004160 |
61 | 0.747656962430718 | 0.504686075138565 | 0.252343037569282 |
62 | 0.715524298262629 | 0.568951403474743 | 0.284475701737371 |
63 | 0.68910374924923 | 0.62179250150154 | 0.31089625075077 |
64 | 0.650260476212035 | 0.69947904757593 | 0.349739523787965 |
65 | 0.634773661022367 | 0.730452677955266 | 0.365226338977633 |
66 | 0.766933274310082 | 0.466133451379835 | 0.233066725689918 |
67 | 0.733849491086004 | 0.532301017827992 | 0.266150508913996 |
68 | 0.713126155364934 | 0.573747689270133 | 0.286873844635066 |
69 | 0.725277066828842 | 0.549445866342316 | 0.274722933171158 |
70 | 0.694273198785619 | 0.611453602428761 | 0.305726801214381 |
71 | 0.653938336764123 | 0.692123326471754 | 0.346061663235877 |
72 | 0.613805351918812 | 0.772389296162376 | 0.386194648081188 |
73 | 0.598442047337542 | 0.803115905324917 | 0.401557952662458 |
74 | 0.561373138245197 | 0.877253723509606 | 0.438626861754803 |
75 | 0.54637304916599 | 0.90725390166802 | 0.45362695083401 |
76 | 0.519115805232321 | 0.961768389535359 | 0.480884194767679 |
77 | 0.476774945282825 | 0.95354989056565 | 0.523225054717175 |
78 | 0.428264233839888 | 0.856528467679775 | 0.571735766160112 |
79 | 0.382555893073689 | 0.765111786147378 | 0.617444106926311 |
80 | 0.351192850876367 | 0.702385701752735 | 0.648807149123633 |
81 | 0.317568105330253 | 0.635136210660505 | 0.682431894669747 |
82 | 0.352300520283008 | 0.704601040566016 | 0.647699479716992 |
83 | 0.316083124969443 | 0.632166249938886 | 0.683916875030557 |
84 | 0.309511119219198 | 0.619022238438395 | 0.690488880780802 |
85 | 0.301690522108698 | 0.603381044217396 | 0.698309477891302 |
86 | 0.265499783342194 | 0.530999566684388 | 0.734500216657806 |
87 | 0.282209750377815 | 0.56441950075563 | 0.717790249622185 |
88 | 0.252461032666094 | 0.504922065332189 | 0.747538967333906 |
89 | 0.315571661495704 | 0.631143322991408 | 0.684428338504296 |
90 | 0.322708226595779 | 0.645416453191559 | 0.67729177340422 |
91 | 0.350735937577211 | 0.701471875154422 | 0.649264062422789 |
92 | 0.344141068774635 | 0.688282137549271 | 0.655858931225365 |
93 | 0.378455367832385 | 0.75691073566477 | 0.621544632167615 |
94 | 0.332265718486539 | 0.664531436973078 | 0.667734281513461 |
95 | 0.288478142132923 | 0.576956284265846 | 0.711521857867077 |
96 | 0.651660630352625 | 0.696678739294751 | 0.348339369647375 |
97 | 0.608400286675239 | 0.783199426649523 | 0.391599713324761 |
98 | 0.56966134750561 | 0.86067730498878 | 0.43033865249439 |
99 | 0.567671188183679 | 0.864657623632642 | 0.432328811816321 |
100 | 0.53996346597397 | 0.92007306805206 | 0.46003653402603 |
101 | 0.550691501197217 | 0.898616997605567 | 0.449308498802783 |
102 | 0.524788409132754 | 0.950423181734492 | 0.475211590867246 |
103 | 0.492650394052451 | 0.985300788104902 | 0.507349605947549 |
104 | 0.44613812168672 | 0.89227624337344 | 0.55386187831328 |
105 | 0.417550760440048 | 0.835101520880097 | 0.582449239559952 |
106 | 0.440459424210382 | 0.880918848420765 | 0.559540575789618 |
107 | 0.420504733467427 | 0.841009466934854 | 0.579495266532573 |
108 | 0.387811339661995 | 0.775622679323991 | 0.612188660338004 |
109 | 0.340786556553087 | 0.681573113106174 | 0.659213443446913 |
110 | 0.368362360389485 | 0.73672472077897 | 0.631637639610515 |
111 | 0.469882570329389 | 0.939765140658777 | 0.530117429670611 |
112 | 0.462843009347271 | 0.925686018694542 | 0.537156990652729 |
113 | 0.51045038803378 | 0.97909922393244 | 0.48954961196622 |
114 | 0.909994177145815 | 0.18001164570837 | 0.090005822854185 |
115 | 0.938695525460202 | 0.122608949079597 | 0.0613044745397984 |
116 | 0.92071186960197 | 0.158576260796061 | 0.0792881303980306 |
117 | 0.90019516912682 | 0.199609661746359 | 0.0998048308731796 |
118 | 0.890139596381939 | 0.219720807236123 | 0.109860403618061 |
119 | 0.859675238545357 | 0.280649522909286 | 0.140324761454643 |
120 | 0.888599243081435 | 0.222801513837130 | 0.111400756918565 |
121 | 0.871133448304773 | 0.257733103390453 | 0.128866551695227 |
122 | 0.877846057668334 | 0.244307884663332 | 0.122153942331666 |
123 | 0.89102498260371 | 0.217950034792579 | 0.108975017396289 |
124 | 0.870616211455658 | 0.258767577088684 | 0.129383788544342 |
125 | 0.866917231461237 | 0.266165537077526 | 0.133082768538763 |
126 | 0.825856082186513 | 0.348287835626975 | 0.174143917813487 |
127 | 0.777010085881579 | 0.445979828236842 | 0.222989914118421 |
128 | 0.723491029894036 | 0.553017940211928 | 0.276508970105964 |
129 | 0.709200392783668 | 0.581599214432664 | 0.290799607216332 |
130 | 0.661550117107276 | 0.676899765785448 | 0.338449882892724 |
131 | 0.604337739692248 | 0.791324520615504 | 0.395662260307752 |
132 | 0.572312887643971 | 0.855374224712058 | 0.427687112356029 |
133 | 0.490223062464867 | 0.980446124929733 | 0.509776937535134 |
134 | 0.549840382869446 | 0.900319234261108 | 0.450159617130554 |
135 | 0.630512195258164 | 0.738975609483671 | 0.369487804741836 |
136 | 0.573036155908666 | 0.853927688182667 | 0.426963844091334 |
137 | 0.633648539453804 | 0.732702921092392 | 0.366351460546196 |
138 | 0.53005850277725 | 0.9398829944455 | 0.46994149722275 |
139 | 0.533598593400618 | 0.932802813198765 | 0.466401406599383 |
140 | 0.460687174511608 | 0.921374349023216 | 0.539312825488392 |
141 | 0.609505988426515 | 0.780988023146969 | 0.390494011573485 |
142 | 0.707128975341159 | 0.585742049317682 | 0.292871024658841 |
143 | 0.743540867351822 | 0.512918265296355 | 0.256459132648178 |
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 | 0 | 0 | OK |
10% type I error level | 0 | 0 | OK |