Multiple Linear Regression - Estimated Regression Equation |
PS[t] = + 15.4323237613405 + 0.364294694129429CM[t] -0.321728388550003D[t] + 0.142655035713217PE[t] -0.0849617358950159PC[t] + 1.18753715676232M1[t] + 0.582940513559847M2[t] + 1.4142918417762M3[t] + 1.37572882776538M4[t] + 1.13169308310493M5[t] + 1.21435808901099M6[t] + 1.63067391786142M7[t] + 2.61302398862814M8[t] + 2.20955916043914M9[t] + 1.17050255859489M10[t] + 0.130689993576573M11[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) | 15.4323237613405 | 2.046627 | 7.5404 | 0 | 0 |
CM | 0.364294694129429 | 0.064801 | 5.6217 | 0 | 0 |
D | -0.321728388550003 | 0.126426 | -2.5448 | 0.011995 | 0.005997 |
PE | 0.142655035713217 | 0.116233 | 1.2273 | 0.221719 | 0.110859 |
PC | -0.0849617358950159 | 0.148896 | -0.5706 | 0.569159 | 0.28458 |
M1 | 1.18753715676232 | 1.467547 | 0.8092 | 0.419745 | 0.209873 |
M2 | 0.582940513559847 | 1.492804 | 0.3905 | 0.696748 | 0.348374 |
M3 | 1.4142918417762 | 1.47771 | 0.9571 | 0.34014 | 0.17007 |
M4 | 1.37572882776538 | 1.510899 | 0.9105 | 0.364072 | 0.182036 |
M5 | 1.13169308310493 | 1.518284 | 0.7454 | 0.457268 | 0.228634 |
M6 | 1.21435808901099 | 1.52834 | 0.7946 | 0.428186 | 0.214093 |
M7 | 1.63067391786142 | 1.532172 | 1.0643 | 0.288992 | 0.144496 |
M8 | 2.61302398862814 | 1.511423 | 1.7289 | 0.085994 | 0.042997 |
M9 | 2.20955916043914 | 1.498284 | 1.4747 | 0.142484 | 0.071242 |
M10 | 1.17050255859489 | 1.495098 | 0.7829 | 0.434984 | 0.217492 |
M11 | 0.130689993576573 | 1.544946 | 0.0846 | 0.932704 | 0.466352 |
Multiple Linear Regression - Regression Statistics | |
Multiple R | 0.516397323766253 |
R-squared | 0.266666195992948 |
Adjusted R-squared | 0.189743069698502 |
F-TEST (value) | 3.46665832291065 |
F-TEST (DF numerator) | 15 |
F-TEST (DF denominator) | 143 |
p-value | 4.76876238936219e-05 |
Multiple Linear Regression - Residual Statistics | |
Residual Standard Deviation | 3.79586465897246 |
Sum Squared Residuals | 2060.42815682077 |
Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
1 | 24 | 21.4084006996143 | 2.59159930038574 |
2 | 25 | 21.9025107169184 | 3.0974892830816 |
3 | 30 | 22.8546967919815 | 7.1453032080185 |
4 | 19 | 20.2514728908076 | -1.25147289080757 |
5 | 22 | 21.4946990358786 | 0.505300964121442 |
6 | 22 | 20.3752413482158 | 1.62475865178422 |
7 | 25 | 22.3609661255558 | 2.63903387444424 |
8 | 23 | 20.9696768799896 | 2.03032312001035 |
9 | 17 | 20.1686614766028 | -3.16866147660277 |
10 | 21 | 20.5166071590923 | 0.483392840907681 |
11 | 19 | 20.7369523379887 | -1.73695233798871 |
12 | 19 | 23.9332871350846 | -4.93328713508462 |
13 | 15 | 23.1443998085749 | -8.14439980857486 |
14 | 16 | 19.458684576602 | -3.45868457660204 |
15 | 23 | 19.6615352466933 | 3.33846475330668 |
16 | 27 | 21.6926539565772 | 5.30734604342283 |
17 | 22 | 21.8378896225772 | 0.162110377422807 |
18 | 14 | 20.4267866595781 | -6.42678665957812 |
19 | 22 | 23.60546790925 | -1.60546790925002 |
20 | 23 | 26.3248423405604 | -3.32484234056038 |
21 | 23 | 23.4564636048144 | -0.456463604814387 |
22 | 21 | 25.4744032515286 | -4.47440325152863 |
23 | 19 | 21.2103147680349 | -2.21031476803485 |
24 | 18 | 22.9681183096248 | -4.96811830962476 |
25 | 20 | 20.8919593381972 | -0.891959338197159 |
26 | 23 | 20.6453221852143 | 2.35467781478574 |
27 | 25 | 22.8670091090834 | 2.13299089091662 |
28 | 19 | 22.6525455100905 | -3.65254551009051 |
29 | 24 | 23.2007695666991 | 0.79923043330086 |
30 | 22 | 21.2888812025034 | 0.711118797496557 |
31 | 25 | 23.362911358857 | 1.63708864114299 |
32 | 26 | 23.2134637549219 | 2.78653624507807 |
33 | 29 | 25.7175146584576 | 3.28248534154245 |
34 | 32 | 24.2534948420646 | 7.74650515793545 |
35 | 25 | 20.5209480422368 | 4.47905195776315 |
36 | 29 | 22.716224662731 | 6.28377533726899 |
37 | 28 | 25.8766984563728 | 2.12330154362723 |
38 | 17 | 16.8904928308664 | 0.109507169133642 |
39 | 28 | 26.1915549647561 | 1.80844503524392 |
40 | 29 | 23.171807557035 | 5.82819244296497 |
41 | 26 | 24.3425388183865 | 1.65746118161345 |
42 | 25 | 22.9981245011788 | 2.00187549882124 |
43 | 14 | 21.8631499365697 | -7.8631499365697 |
44 | 25 | 23.2004739451553 | 1.79952605484474 |
45 | 26 | 22.4573493888402 | 3.5426506111598 |
46 | 20 | 19.096017574962 | 0.903982425037993 |
47 | 18 | 19.4922633388405 | -1.49226333884045 |
48 | 32 | 23.7239761339604 | 8.27602386603956 |
49 | 25 | 24.9992897037547 | 0.00071029624532456 |
50 | 25 | 21.7202482560367 | 3.27975174396329 |
51 | 23 | 21.5440516686678 | 1.45594833133221 |
52 | 21 | 21.501968127884 | -0.501968127884017 |
53 | 20 | 21.6647933829324 | -1.66479338293243 |
54 | 15 | 19.2396364251744 | -4.23963642517439 |
55 | 30 | 26.4139081456428 | 3.58609185435724 |
56 | 24 | 24.3667072875822 | -0.3667072875822 |
57 | 26 | 23.4712488485255 | 2.52875115147451 |
58 | 24 | 21.7094090963506 | 2.29059090364944 |
59 | 22 | 18.3411896710326 | 3.65881032896738 |
60 | 14 | 16.8813452280141 | -2.88134522801411 |
61 | 24 | 20.8645200268565 | 3.13547997314349 |
62 | 24 | 21.79291401502 | 2.20708598497998 |
63 | 24 | 21.3099124776957 | 2.6900875223043 |
64 | 24 | 19.5594726949361 | 4.44052730506388 |
65 | 19 | 18.13407661361 | 0.86592338639004 |
66 | 31 | 24.5313023479987 | 6.46869765200126 |
67 | 22 | 26.6718175944994 | -4.67181759449943 |
68 | 27 | 23.2462130185894 | 3.75378698141058 |
69 | 19 | 17.6548460595565 | 1.34515394044351 |
70 | 25 | 21.2392194341592 | 3.76078056584084 |
71 | 20 | 24.3065663594345 | -4.30656635943452 |
72 | 21 | 20.1475306230034 | 0.85246937699657 |
73 | 27 | 26.0283161576787 | 0.971683842321257 |
74 | 23 | 23.3870961243964 | -0.387096124396441 |
75 | 25 | 25.05277727386 | -0.0527772738599558 |
76 | 20 | 23.0017132099812 | -3.00171320998116 |
77 | 21 | 18.1403954773297 | 2.85960452267035 |
78 | 22 | 21.6686446413993 | 0.33135535860068 |
79 | 23 | 20.870712675033 | 2.12928732496696 |
80 | 25 | 26.0513319604443 | -1.05133196044432 |
81 | 25 | 22.5213615523781 | 2.47863844762191 |
82 | 17 | 22.1192719886503 | -5.11927198865032 |
83 | 19 | 20.5272832461467 | -1.5272832461467 |
84 | 25 | 21.5772537479903 | 3.42274625200966 |
85 | 19 | 21.2108730496103 | -2.21087304961026 |
86 | 20 | 21.8141889977146 | -1.81418899771465 |
87 | 26 | 22.423917007705 | 3.57608299229505 |
88 | 23 | 18.3724769956061 | 4.62752300439394 |
89 | 27 | 23.9965438863506 | 3.00345611364937 |
90 | 17 | 21.4681254306041 | -4.46812543060407 |
91 | 17 | 23.3479388996919 | -6.3479388996919 |
92 | 19 | 20.7111226188485 | -1.71112261884852 |
93 | 17 | 20.7906723957443 | -3.79067239574431 |
94 | 22 | 23.0300808256109 | -1.03008082561092 |
95 | 21 | 20.3086454803214 | 0.69135451967861 |
96 | 32 | 25.4843903130901 | 6.5156096869099 |
97 | 21 | 23.9978570962449 | -2.99785709624493 |
98 | 21 | 23.9455911656014 | -2.94559116560143 |
99 | 18 | 21.9897875719193 | -3.98978757191928 |
100 | 18 | 22.7800735515649 | -4.78007355156495 |
101 | 23 | 23.0157191006703 | -0.0157191006703341 |
102 | 19 | 21.0610935556314 | -2.06109355563137 |
103 | 20 | 23.3141643844414 | -3.3141643844414 |
104 | 21 | 23.3190333126464 | -2.3190333126464 |
105 | 20 | 22.2360514809517 | -2.23605148095166 |
106 | 17 | 22.3503929468413 | -5.35039294684134 |
107 | 18 | 21.4711934291021 | -3.47119342910208 |
108 | 19 | 22.2847390288184 | -3.2847390288184 |
109 | 22 | 22.4282772724915 | -0.428277272491546 |
110 | 15 | 18.9061666485891 | -3.90616664858907 |
111 | 14 | 20.1257477956927 | -6.12574779569271 |
112 | 18 | 25.6974166570011 | -7.69741665700112 |
113 | 24 | 21.9896945393372 | 2.01030546066284 |
114 | 35 | 25.1351620317299 | 9.8648379682701 |
115 | 29 | 18.6179407859273 | 10.3820592140727 |
116 | 21 | 22.7299425324362 | -1.72994253243619 |
117 | 25 | 24.3785534989033 | 0.6214465010967 |
118 | 20 | 20.0309487521345 | -0.0309487521344678 |
119 | 22 | 21.5413535810958 | 0.458646418904167 |
120 | 13 | 19.9805987120047 | -6.98059871200469 |
121 | 26 | 24.3041330802187 | 1.69586691978135 |
122 | 17 | 18.6935059959558 | -1.69350599595577 |
123 | 25 | 21.4194928394039 | 3.58050716059607 |
124 | 20 | 20.0448056915565 | -0.0448056915564629 |
125 | 19 | 17.5975563963451 | 1.40244360365489 |
126 | 21 | 22.1390051788546 | -1.13900517885456 |
127 | 22 | 21.0402943962954 | 0.959705603704602 |
128 | 24 | 22.6817408641924 | 1.31825913580759 |
129 | 21 | 22.2144184075392 | -1.21441840753919 |
130 | 26 | 25.0098652921917 | 0.990134707808268 |
131 | 24 | 20.9584211211411 | 3.04157887885891 |
132 | 16 | 19.3976499118598 | -3.39764991185978 |
133 | 23 | 21.0617119347234 | 1.93828806527665 |
134 | 18 | 20.21420065041 | -2.21420065041004 |
135 | 16 | 22.3116868357331 | -6.31168683573312 |
136 | 26 | 24.1007289406351 | 1.89927105936486 |
137 | 19 | 20.1409423008136 | -1.14094230081359 |
138 | 21 | 20.4331055232978 | 0.566894476702186 |
139 | 21 | 21.6293851765056 | -0.629385176505612 |
140 | 22 | 22.4847198315894 | -0.484719831589402 |
141 | 23 | 24.5857660043262 | -1.58576600432624 |
142 | 29 | 24.9611346579663 | 4.03886534203371 |
143 | 21 | 21.5263751135402 | -0.526375113540181 |
144 | 21 | 18.8303630803259 | 2.16963691967413 |
145 | 23 | 21.5781369559503 | 1.42186304404974 |
146 | 27 | 22.491591165329 | 4.508408834671 |
147 | 25 | 26.9046756082485 | -1.90467560824849 |
148 | 21 | 22.1728642163247 | -1.17286421632468 |
149 | 10 | 20.4443812590697 | -10.4443812590697 |
150 | 20 | 23.2348911538338 | -3.23489115383375 |
151 | 26 | 22.9013426117307 | 3.09865738826931 |
152 | 24 | 24.7007316530439 | -0.700731653043916 |
153 | 29 | 30.3470926233603 | -1.34709262336033 |
154 | 19 | 23.2091541784477 | -4.20915417844771 |
155 | 24 | 21.0584935110847 | 2.94150648891528 |
156 | 19 | 20.0745231134925 | -1.07452311349246 |
157 | 24 | 23.205426419712 | 0.794573580287986 |
158 | 22 | 21.1374866713458 | 0.862513328654194 |
159 | 17 | 24.3431548085598 | -7.34315480855979 |
Goldfeld-Quandt test for Heteroskedasticity | |||
p-values | Alternative Hypothesis | ||
breakpoint index | greater | 2-sided | less |
19 | 0.608608438383602 | 0.782783123232795 | 0.391391561616398 |
20 | 0.95934633517793 | 0.08130732964414 | 0.04065366482207 |
21 | 0.946385770088966 | 0.107228459822069 | 0.0536142299110343 |
22 | 0.914331835385903 | 0.171336329228195 | 0.0856681646140974 |
23 | 0.865323332375598 | 0.269353335248805 | 0.134676667624402 |
24 | 0.821406039795468 | 0.357187920409063 | 0.178593960204532 |
25 | 0.750097172192068 | 0.499805655615865 | 0.249902827807932 |
26 | 0.697155990382783 | 0.605688019234435 | 0.302844009617217 |
27 | 0.656418216644454 | 0.687163566711092 | 0.343581783355546 |
28 | 0.622696906864119 | 0.754606186271762 | 0.377303093135881 |
29 | 0.541877742132009 | 0.916244515735981 | 0.458122257867991 |
30 | 0.481020670707198 | 0.962041341414395 | 0.518979329292802 |
31 | 0.417653022865185 | 0.835306045730369 | 0.582346977134815 |
32 | 0.422132157568433 | 0.844264315136866 | 0.577867842431567 |
33 | 0.416922054809742 | 0.833844109619484 | 0.583077945190258 |
34 | 0.593028032550688 | 0.813943934898624 | 0.406971967449312 |
35 | 0.58569258102303 | 0.828614837953941 | 0.41430741897697 |
36 | 0.750827369987106 | 0.498345260025788 | 0.249172630012894 |
37 | 0.697547742023785 | 0.60490451595243 | 0.302452257976215 |
38 | 0.655638208292424 | 0.688723583415152 | 0.344361791707576 |
39 | 0.60675013403792 | 0.786499731924161 | 0.393249865962081 |
40 | 0.656625280309514 | 0.686749439380971 | 0.343374719690486 |
41 | 0.609593922562435 | 0.78081215487513 | 0.390406077437565 |
42 | 0.600041122326102 | 0.799917755347796 | 0.399958877673898 |
43 | 0.675821309567245 | 0.64835738086551 | 0.324178690432755 |
44 | 0.672355216880823 | 0.655289566238353 | 0.327644783119177 |
45 | 0.66129623133333 | 0.67740753733334 | 0.33870376866667 |
46 | 0.606582840439208 | 0.786834319121584 | 0.393417159560792 |
47 | 0.561371956046201 | 0.877256087907597 | 0.438628043953799 |
48 | 0.68690285340554 | 0.62619429318892 | 0.31309714659446 |
49 | 0.634500073007418 | 0.730999853985164 | 0.365499926992582 |
50 | 0.615328223892246 | 0.769343552215507 | 0.384671776107754 |
51 | 0.636646161716862 | 0.726707676566276 | 0.363353838283138 |
52 | 0.586846381024557 | 0.826307237950887 | 0.413153618975443 |
53 | 0.55187244596643 | 0.896255108067141 | 0.448127554033571 |
54 | 0.589529149170756 | 0.820941701658488 | 0.410470850829244 |
55 | 0.676821401432472 | 0.646357197135056 | 0.323178598567528 |
56 | 0.63470801358738 | 0.73058397282524 | 0.36529198641262 |
57 | 0.596419646568122 | 0.807160706863755 | 0.403580353431878 |
58 | 0.556681671808855 | 0.88663665638229 | 0.443318328191145 |
59 | 0.53717567644293 | 0.925648647114141 | 0.46282432355707 |
60 | 0.499697825945402 | 0.999395651890805 | 0.500302174054598 |
61 | 0.49800147973507 | 0.99600295947014 | 0.501998520264929 |
62 | 0.462541750120747 | 0.925083500241493 | 0.537458249879253 |
63 | 0.440134007209294 | 0.880268014418587 | 0.559865992790706 |
64 | 0.470302875299826 | 0.940605750599652 | 0.529697124700174 |
65 | 0.426179543813603 | 0.852359087627205 | 0.573820456186397 |
66 | 0.516180291180141 | 0.967639417639717 | 0.483819708819859 |
67 | 0.560395270686864 | 0.879209458626273 | 0.439604729313136 |
68 | 0.548480462503033 | 0.903039074993935 | 0.451519537496967 |
69 | 0.508971703441287 | 0.982056593117425 | 0.491028296558713 |
70 | 0.50264406016146 | 0.994711879677081 | 0.49735593983854 |
71 | 0.548963457060948 | 0.902073085878104 | 0.451036542939052 |
72 | 0.500292604081047 | 0.999414791837907 | 0.499707395918953 |
73 | 0.45123762374089 | 0.90247524748178 | 0.54876237625911 |
74 | 0.403507695523349 | 0.807015391046698 | 0.596492304476651 |
75 | 0.400447073382302 | 0.800894146764603 | 0.599552926617698 |
76 | 0.393013085788849 | 0.786026171577699 | 0.606986914211151 |
77 | 0.39019227676727 | 0.780384553534541 | 0.60980772323273 |
78 | 0.344284747493176 | 0.688569494986351 | 0.655715252506824 |
79 | 0.320079951974776 | 0.640159903949551 | 0.679920048025224 |
80 | 0.289845559831988 | 0.579691119663977 | 0.710154440168012 |
81 | 0.266092260563939 | 0.532184521127879 | 0.733907739436061 |
82 | 0.316256440885889 | 0.632512881771778 | 0.683743559114111 |
83 | 0.277060993555666 | 0.554121987111332 | 0.722939006444334 |
84 | 0.268075594860185 | 0.536151189720369 | 0.731924405139815 |
85 | 0.240923909643306 | 0.481847819286611 | 0.759076090356694 |
86 | 0.214780938206791 | 0.429561876413583 | 0.785219061793209 |
87 | 0.259589489984524 | 0.519178979969049 | 0.740410510015476 |
88 | 0.306271985878659 | 0.612543971757317 | 0.693728014121341 |
89 | 0.285726905496725 | 0.571453810993451 | 0.714273094503275 |
90 | 0.302898301376723 | 0.605796602753447 | 0.697101698623277 |
91 | 0.412150537496999 | 0.824301074993998 | 0.587849462503001 |
92 | 0.37502210939285 | 0.7500442187857 | 0.62497789060715 |
93 | 0.367417383538672 | 0.734834767077344 | 0.632582616461328 |
94 | 0.326517579364397 | 0.653035158728794 | 0.673482420635603 |
95 | 0.283109647006484 | 0.566219294012967 | 0.716890352993516 |
96 | 0.407235572856445 | 0.81447114571289 | 0.592764427143555 |
97 | 0.405724641482921 | 0.811449282965841 | 0.59427535851708 |
98 | 0.389495648219371 | 0.778991296438741 | 0.610504351780629 |
99 | 0.394187094206399 | 0.788374188412798 | 0.6058129057936 |
100 | 0.406878201669573 | 0.813756403339146 | 0.593121798330427 |
101 | 0.370189415239293 | 0.740378830478585 | 0.629810584760708 |
102 | 0.33960019820761 | 0.67920039641522 | 0.66039980179239 |
103 | 0.362611253843539 | 0.725222507687078 | 0.637388746156461 |
104 | 0.324747767764176 | 0.649495535528351 | 0.675252232235824 |
105 | 0.297057687241027 | 0.594115374482054 | 0.702942312758973 |
106 | 0.342609400519543 | 0.685218801039086 | 0.657390599480457 |
107 | 0.342711920399037 | 0.685423840798075 | 0.657288079600963 |
108 | 0.317356514824533 | 0.634713029649066 | 0.682643485175467 |
109 | 0.278276529384782 | 0.556553058769565 | 0.721723470615218 |
110 | 0.280427513151955 | 0.56085502630391 | 0.719572486848045 |
111 | 0.295487955854742 | 0.590975911709484 | 0.704512044145258 |
112 | 0.44033713952287 | 0.88067427904574 | 0.55966286047713 |
113 | 0.447785838380425 | 0.89557167676085 | 0.552214161619575 |
114 | 0.848912948522607 | 0.302174102954786 | 0.151087051477393 |
115 | 0.973413767817784 | 0.0531724643644324 | 0.0265862321822162 |
116 | 0.962352363986002 | 0.0752952720279959 | 0.037647636013998 |
117 | 0.964904683514543 | 0.0701906329709143 | 0.0350953164854572 |
118 | 0.950445699965474 | 0.0991086000690527 | 0.0495543000345263 |
119 | 0.950692614008457 | 0.0986147719830853 | 0.0493073859915426 |
120 | 0.98177993798644 | 0.0364401240271208 | 0.0182200620135604 |
121 | 0.972940938981177 | 0.0541181220376453 | 0.0270590610188226 |
122 | 0.96312094696173 | 0.0737581060765401 | 0.0368790530382701 |
123 | 0.989342927390955 | 0.021314145218091 | 0.0106570726090455 |
124 | 0.982545718635904 | 0.0349085627281916 | 0.0174542813640958 |
125 | 0.977426903714553 | 0.0451461925708941 | 0.0225730962854471 |
126 | 0.964740299145436 | 0.0705194017091277 | 0.0352597008545638 |
127 | 0.952095437105497 | 0.095809125789005 | 0.0479045628945025 |
128 | 0.940856017016032 | 0.118287965967935 | 0.0591439829839676 |
129 | 0.939212304227733 | 0.121575391544535 | 0.0607876957722674 |
130 | 0.914638256735996 | 0.170723486528008 | 0.085361743264004 |
131 | 0.874731281039574 | 0.250537437920852 | 0.125268718960426 |
132 | 0.824944303145245 | 0.35011139370951 | 0.175055696854755 |
133 | 0.781960662863033 | 0.436078674273935 | 0.218039337136967 |
134 | 0.713349765858321 | 0.573300468283358 | 0.286650234141679 |
135 | 0.6378199510814 | 0.724360097837199 | 0.362180048918599 |
136 | 0.54947368894526 | 0.90105262210948 | 0.45052631105474 |
137 | 0.664138690909855 | 0.67172261818029 | 0.335861309090145 |
138 | 0.71445060665474 | 0.57109878669052 | 0.28554939334526 |
139 | 0.58399847012426 | 0.83200305975148 | 0.41600152987574 |
140 | 0.415003606844583 | 0.830007213689165 | 0.584996393155417 |
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 | 4 | 0.0327868852459016 | OK |
10% type I error level | 14 | 0.114754098360656 | NOK |