Multiple Linear Regression - Estimated Regression Equation |
PS[t] = + 7.05980418777325 -0.625089264853433M[t] + 0.296179087537003CM[t] + 0.070642119661626CM_M[t] -0.283469161339915D[t] -0.193290505489402D_M[t] + 0.260800182428789PE[t] -0.27410715866219PE_M[t] -0.0177004220449542PC[t] + 0.114293878489504PC_M[t] + 0.392234889899682O[t] + 0.135450774613635O_M[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) | 7.05980418777325 | 2.88598 | 2.4462 | 0.015658 | 0.007829 |
M | -0.625089264853433 | 5.017803 | -0.1246 | 0.901037 | 0.450518 |
CM | 0.296179087537003 | 0.077759 | 3.8089 | 0.000207 | 0.000104 |
CM_M | 0.070642119661626 | 0.118583 | 0.5957 | 0.552312 | 0.276156 |
D | -0.283469161339915 | 0.155718 | -1.8204 | 0.070804 | 0.035402 |
D_M | -0.193290505489402 | 0.239269 | -0.8078 | 0.420535 | 0.210268 |
PE | 0.260800182428789 | 0.136399 | 1.912 | 0.057885 | 0.028943 |
PE_M | -0.27410715866219 | 0.22474 | -1.2197 | 0.224614 | 0.112307 |
PC | -0.0177004220449542 | 0.161925 | -0.1093 | 0.913109 | 0.456554 |
PC_M | 0.114293878489504 | 0.282815 | 0.4041 | 0.686726 | 0.343363 |
O | 0.392234889899682 | 0.094006 | 4.1725 | 5.2e-05 | 2.6e-05 |
O_M | 0.135450774613635 | 0.166314 | 0.8144 | 0.416763 | 0.208381 |
Multiple Linear Regression - Regression Statistics | |
Multiple R | 0.624684363935184 |
R-squared | 0.390230554545106 |
Adjusted R-squared | 0.342994893277473 |
F-TEST (value) | 8.2613547492031 |
F-TEST (DF numerator) | 11 |
F-TEST (DF denominator) | 142 |
p-value | 4.33513225317483e-11 |
Multiple Linear Regression - Residual Statistics | |
Residual Standard Deviation | 3.45563605556431 |
Sum Squared Residuals | 1695.68171788928 |
Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
1 | 24 | 23.2963605761899 | 0.703639423810088 |
2 | 25 | 22.0515209697938 | 2.94847903020616 |
3 | 30 | 24.4919056802846 | 5.50809431971537 |
4 | 19 | 20.092828823572 | -1.09282882357201 |
5 | 22 | 20.5460357715548 | 1.45396422844518 |
6 | 22 | 23.3444890168877 | -1.34448901688771 |
7 | 25 | 22.7525668911431 | 2.24743310885693 |
8 | 23 | 19.5915388657417 | 3.40846113425826 |
9 | 17 | 19.4903879946245 | -2.49038799462446 |
10 | 21 | 22.0490595659149 | -1.04905956591486 |
11 | 19 | 22.3110067780938 | -3.31100677809376 |
12 | 19 | 23.5995735944097 | -4.59957359440972 |
13 | 15 | 22.9251352744651 | -7.92513527446513 |
14 | 16 | 17.3393196237838 | -1.33931962378381 |
15 | 23 | 18.9281322280587 | 4.07186777194127 |
16 | 27 | 23.8914985306362 | 3.10850146936385 |
17 | 22 | 20.7609382154392 | 1.23906178456077 |
18 | 14 | 15.0815545834135 | -1.08155458341351 |
19 | 22 | 23.0714532797215 | -1.0714532797215 |
20 | 23 | 24.3563838994501 | -1.35638389945009 |
21 | 23 | 21.751033027379 | 1.24896697262098 |
22 | 19 | 22.386372329303 | -3.38637232930304 |
23 | 18 | 23.9079851834956 | -5.90798518349556 |
24 | 20 | 23.5615310439331 | -3.56153104393315 |
25 | 23 | 22.6972525932656 | 0.302747406734413 |
26 | 25 | 23.6516010482085 | 1.34839895179145 |
27 | 19 | 23.2079296379135 | -4.20792963791352 |
28 | 24 | 23.0071442518986 | 0.992855748101375 |
29 | 22 | 21.8492285308403 | 0.15077146915972 |
30 | 26 | 23.753608683351 | 2.24639131664902 |
31 | 29 | 23.308428880684 | 5.69157111931603 |
32 | 32 | 25.0080995678018 | 6.99190043219816 |
33 | 25 | 22.0548582146212 | 2.94514178537879 |
34 | 29 | 24.7244641139198 | 4.27553588608019 |
35 | 28 | 25.3643409972118 | 2.63565900278825 |
36 | 17 | 15.5076041339478 | 1.49239586605216 |
37 | 28 | 26.2470708498501 | 1.75292915014988 |
38 | 29 | 22.5373698650511 | 6.46263013494893 |
39 | 26 | 26.9548735237134 | -0.954873523713413 |
40 | 25 | 23.5378228848192 | 1.46217711518078 |
41 | 14 | 17.8136992889837 | -3.81369928898374 |
42 | 25 | 22.6493295001716 | 2.3506704998284 |
43 | 26 | 21.7799905716279 | 4.22000942837209 |
44 | 20 | 20.0344295547694 | -0.0344295547693637 |
45 | 18 | 21.9026533709004 | -3.90265337090037 |
46 | 32 | 24.9894333257504 | 7.01056667424956 |
47 | 25 | 24.8237073934257 | 0.176292606574296 |
48 | 25 | 22.4499877772336 | 2.55001222276644 |
49 | 23 | 21.3282065337459 | 1.67179346625409 |
50 | 21 | 22.0241795361065 | -1.02417953610648 |
51 | 20 | 24.1192700550911 | -4.11927005509109 |
52 | 15 | 16.3867168274286 | -1.38671682742862 |
53 | 30 | 25.0578463794026 | 4.9421536205974 |
54 | 24 | 25.438171986193 | -1.43817198619304 |
55 | 26 | 24.3193933402654 | 1.68060665973459 |
56 | 24 | 20.8589458013546 | 3.14105419864537 |
57 | 22 | 22.5676753400154 | -0.567675340015414 |
58 | 14 | 16.4788312268021 | -2.4788312268021 |
59 | 24 | 22.2816374498657 | 1.71836255013428 |
60 | 24 | 22.4413896017506 | 1.55861039824945 |
61 | 24 | 23.7954534317768 | 0.204546568223215 |
62 | 24 | 20.2669622301674 | 3.73303776983263 |
63 | 19 | 17.8086911540746 | 1.19130884592543 |
64 | 31 | 28.0219480280792 | 2.97805197192078 |
65 | 22 | 27.2829218727514 | -5.28292187275137 |
66 | 27 | 20.7946367735318 | 6.20536322646824 |
67 | 19 | 17.1768627080926 | 1.82313729190742 |
68 | 25 | 22.3982960416233 | 2.60170395837666 |
69 | 20 | 24.7199321607138 | -4.7199321607138 |
70 | 21 | 21.3806855541542 | -0.380685554154177 |
71 | 27 | 27.3447604372431 | -0.344760437243079 |
72 | 23 | 24.918061415164 | -1.918061415164 |
73 | 25 | 25.8209104633302 | -0.820910463330248 |
74 | 20 | 22.2621630884043 | -2.26216308840432 |
75 | 22 | 22.7834712031622 | -0.783471203162157 |
76 | 23 | 23.6257640178505 | -0.625764017850549 |
77 | 25 | 24.1480252811678 | 0.851974718832198 |
78 | 25 | 23.7070951207816 | 1.29290487921837 |
79 | 17 | 23.6155185631486 | -6.61551856314859 |
80 | 19 | 20.6256858519544 | -1.62568585195438 |
81 | 25 | 24.1250687037974 | 0.874931296202566 |
82 | 19 | 22.8209917670929 | -3.82099176709295 |
83 | 20 | 22.0213024626656 | -2.02130246266558 |
84 | 26 | 22.6388106667354 | 3.36118933326456 |
85 | 23 | 21.2182668316308 | 1.7817331683692 |
86 | 27 | 24.5053532907546 | 2.49464670924538 |
87 | 17 | 20.2345906264913 | -3.23459062649129 |
88 | 17 | 22.5483369070821 | -5.54833690708213 |
89 | 17 | 19.5594726829038 | -2.55947268290383 |
90 | 22 | 22.3915505023439 | -0.391550502343912 |
91 | 21 | 24.1805516259676 | -3.18055162596756 |
92 | 32 | 28.869170191878 | 3.13082980812197 |
93 | 21 | 24.0532027303745 | -3.05320273037451 |
94 | 21 | 24.6828295359995 | -3.68282953599951 |
95 | 18 | 20.7113502933206 | -2.71135029332061 |
96 | 18 | 21.4423144034967 | -3.44231440349674 |
97 | 23 | 23.0091627916008 | -0.00916279160077999 |
98 | 19 | 20.1009913417402 | -1.10099134174018 |
99 | 20 | 21.4861209705464 | -1.48612097054643 |
100 | 21 | 22.4874405664953 | -1.48744056649528 |
101 | 20 | 24.3194094496421 | -4.31940944964213 |
102 | 17 | 19.1595363624267 | -2.15953636242665 |
103 | 18 | 20.1639037335988 | -2.16390373359879 |
104 | 19 | 20.713801336222 | -1.71380133622203 |
105 | 22 | 22.4499438992702 | -0.449943899270173 |
106 | 15 | 17.4973160883322 | -2.49731608833222 |
107 | 14 | 19.1005411779597 | -5.10054117795971 |
108 | 18 | 26.4591005600035 | -8.45910056000355 |
109 | 24 | 21.8203614645123 | 2.17963853548773 |
110 | 35 | 23.6476890163372 | 11.3523109836628 |
111 | 29 | 18.9377002921953 | 10.0622997078047 |
112 | 21 | 22.2464539165878 | -1.24645391658783 |
113 | 20 | 17.9121446884937 | 2.08785531150626 |
114 | 22 | 22.2648021800946 | -0.264802180094649 |
115 | 13 | 15.666614386354 | -2.66661438635403 |
116 | 26 | 22.914804118222 | 3.08519588177802 |
117 | 17 | 17.3696081117779 | -0.369608111777926 |
118 | 25 | 20.516136674431 | 4.48386332556899 |
119 | 20 | 20.499208019904 | -0.499208019904032 |
120 | 19 | 17.630964521185 | 1.369035478815 |
121 | 21 | 21.2100820711648 | -0.210082071164784 |
122 | 22 | 21.1855747038094 | 0.814425296190587 |
123 | 24 | 22.790530931523 | 1.20946906847698 |
124 | 21 | 23.2463420430303 | -2.24634204303034 |
125 | 26 | 25.3982166955846 | 0.601783304415367 |
126 | 24 | 20.7135090861223 | 3.28649091387771 |
127 | 16 | 20.4723786369852 | -4.47237863698522 |
128 | 23 | 22.4362562648342 | 0.563743735165762 |
129 | 18 | 20.8287187190179 | -2.82871871901795 |
130 | 16 | 22.1201978263597 | -6.12019782635974 |
131 | 26 | 22.0830703003735 | 3.91692969962649 |
132 | 19 | 19.5740261208898 | -0.574026120889791 |
133 | 21 | 17.3195499692259 | 3.68045003077414 |
134 | 21 | 22.2110311335162 | -1.21103113351623 |
135 | 22 | 18.6736650672247 | 3.32633493277529 |
136 | 23 | 19.6557948571746 | 3.34420514282541 |
137 | 29 | 24.9077129715797 | 4.09228702842034 |
138 | 21 | 20.0270788662912 | 0.97292113370882 |
139 | 21 | 20.0408396685598 | 0.959160331440173 |
140 | 23 | 22.4625319652193 | 0.537468034780665 |
141 | 27 | 23.289727976947 | 3.71027202305298 |
142 | 25 | 25.4168956603399 | -0.416895660339886 |
143 | 21 | 21.0217603368497 | -0.0217603368497115 |
144 | 10 | 17.3167990957428 | -7.31679909574281 |
145 | 20 | 22.6268869544151 | -2.62688695441514 |
146 | 26 | 22.337767595239 | 3.662232404761 |
147 | 24 | 24.262148957464 | -0.26214895746405 |
148 | 29 | 31.924161423221 | -2.92416142322096 |
149 | 19 | 19.2763403620576 | -0.276340362057584 |
150 | 24 | 22.6958211237593 | 1.30417887624075 |
151 | 19 | 21.0647587510409 | -2.06475875104092 |
152 | 24 | 23.3219002501796 | 0.67809974982041 |
153 | 22 | 22.2548111099437 | -0.254811109943715 |
154 | 17 | 24.2225438314031 | -7.22254383140306 |
Goldfeld-Quandt test for Heteroskedasticity | |||
p-values | Alternative Hypothesis | ||
breakpoint index | greater | 2-sided | less |
15 | 0.971140216261243 | 0.0577195674775142 | 0.0288597837387571 |
16 | 0.940991784782653 | 0.118016430434693 | 0.0590082152173467 |
17 | 0.896452661139316 | 0.207094677721368 | 0.103547338860684 |
18 | 0.832860848873107 | 0.334278302253786 | 0.167139151126893 |
19 | 0.821460230990964 | 0.357079538018073 | 0.178539769009036 |
20 | 0.807845205704287 | 0.384309588591425 | 0.192154794295713 |
21 | 0.790356195849519 | 0.419287608300962 | 0.209643804150481 |
22 | 0.743912489475258 | 0.512175021049483 | 0.256087510524741 |
23 | 0.692254225976114 | 0.615491548047773 | 0.307745774023886 |
24 | 0.713619459499475 | 0.572761081001049 | 0.286380540500525 |
25 | 0.638217574462226 | 0.723564851075547 | 0.361782425537774 |
26 | 0.561282620156937 | 0.877434759686126 | 0.438717379843063 |
27 | 0.510914653155239 | 0.978170693689521 | 0.489085346844761 |
28 | 0.482254100413728 | 0.964508200827455 | 0.517745899586272 |
29 | 0.414570754773301 | 0.829141509546602 | 0.585429245226699 |
30 | 0.425954283129319 | 0.851908566258638 | 0.574045716870681 |
31 | 0.517701203376458 | 0.964597593247084 | 0.482298796623542 |
32 | 0.658302905035247 | 0.683394189929506 | 0.341697094964753 |
33 | 0.620775651353814 | 0.758448697292372 | 0.379224348646186 |
34 | 0.690362588758182 | 0.619274822483635 | 0.309637411241818 |
35 | 0.730989118760846 | 0.538021762478308 | 0.269010881239154 |
36 | 0.69128590027984 | 0.617428199440318 | 0.308714099720159 |
37 | 0.639582217967185 | 0.72083556406563 | 0.360417782032815 |
38 | 0.739851119595555 | 0.520297760808891 | 0.260148880404445 |
39 | 0.688124900018619 | 0.623750199962762 | 0.311875099981381 |
40 | 0.63650071956591 | 0.72699856086818 | 0.36349928043409 |
41 | 0.629218214333736 | 0.741563571332528 | 0.370781785666264 |
42 | 0.59101454242873 | 0.81797091514254 | 0.40898545757127 |
43 | 0.603718026732879 | 0.792563946534243 | 0.396281973267121 |
44 | 0.548941923012575 | 0.90211615397485 | 0.451058076987425 |
45 | 0.558571591862487 | 0.882856816275026 | 0.441428408137513 |
46 | 0.647102219136567 | 0.705795561726867 | 0.352897780863433 |
47 | 0.597148802832046 | 0.805702394335908 | 0.402851197167954 |
48 | 0.566626669407023 | 0.866746661185954 | 0.433373330592977 |
49 | 0.57325543203634 | 0.85348913592732 | 0.42674456796366 |
50 | 0.52557761703835 | 0.9488447659233 | 0.47442238296165 |
51 | 0.563381815346443 | 0.873236369307114 | 0.436618184653557 |
52 | 0.519718527597729 | 0.960562944804542 | 0.480281472402271 |
53 | 0.674603680741398 | 0.650792638517205 | 0.325396319258602 |
54 | 0.634456078336714 | 0.731087843326572 | 0.365543921663286 |
55 | 0.593558676481876 | 0.812882647036247 | 0.406441323518124 |
56 | 0.574172595906738 | 0.851654808186523 | 0.425827404093262 |
57 | 0.523429074062279 | 0.953141851875442 | 0.476570925937721 |
58 | 0.485557635868885 | 0.97111527173777 | 0.514442364131115 |
59 | 0.44598320042983 | 0.89196640085966 | 0.55401679957017 |
60 | 0.40700760475867 | 0.81401520951734 | 0.59299239524133 |
61 | 0.359196722690647 | 0.718393445381294 | 0.640803277309353 |
62 | 0.369403337001482 | 0.738806674002964 | 0.630596662998518 |
63 | 0.326134104412136 | 0.652268208824272 | 0.673865895587864 |
64 | 0.366243426962338 | 0.732486853924677 | 0.633756573037662 |
65 | 0.435502339729128 | 0.871004679458257 | 0.564497660270872 |
66 | 0.545699377564336 | 0.908601244871328 | 0.454300622435664 |
67 | 0.497496013290682 | 0.994992026581364 | 0.502503986709318 |
68 | 0.478545699559379 | 0.957091399118759 | 0.521454300440621 |
69 | 0.548179263668204 | 0.903641472663593 | 0.451820736331796 |
70 | 0.49932848358501 | 0.99865696717002 | 0.50067151641499 |
71 | 0.453344672586434 | 0.906689345172869 | 0.546655327413566 |
72 | 0.419304424984347 | 0.838608849968693 | 0.580695575015653 |
73 | 0.383263959015615 | 0.76652791803123 | 0.616736040984385 |
74 | 0.355922472209099 | 0.711844944418198 | 0.644077527790901 |
75 | 0.312382967271722 | 0.624765934543445 | 0.687617032728278 |
76 | 0.274569070330402 | 0.549138140660805 | 0.725430929669598 |
77 | 0.237461167618929 | 0.474922335237858 | 0.762538832381071 |
78 | 0.207742054432064 | 0.415484108864127 | 0.792257945567936 |
79 | 0.321939016482694 | 0.643878032965387 | 0.678060983517306 |
80 | 0.29363788239093 | 0.58727576478186 | 0.70636211760907 |
81 | 0.255133149625803 | 0.510266299251606 | 0.744866850374197 |
82 | 0.254141859415932 | 0.508283718831864 | 0.745858140584068 |
83 | 0.229426734388909 | 0.458853468777819 | 0.770573265611091 |
84 | 0.228598545190489 | 0.457197090380979 | 0.77140145480951 |
85 | 0.203055443291978 | 0.406110886583956 | 0.796944556708022 |
86 | 0.187336753961978 | 0.374673507923956 | 0.812663246038022 |
87 | 0.180319448691667 | 0.360638897383333 | 0.819680551308333 |
88 | 0.220392958107721 | 0.440785916215443 | 0.779607041892279 |
89 | 0.198239747733655 | 0.39647949546731 | 0.801760252266345 |
90 | 0.169617410516135 | 0.33923482103227 | 0.830382589483865 |
91 | 0.156831488741058 | 0.313662977482116 | 0.843168511258942 |
92 | 0.156574667749615 | 0.313149335499231 | 0.843425332250385 |
93 | 0.145239513388168 | 0.290479026776335 | 0.854760486611832 |
94 | 0.145781080273111 | 0.291562160546222 | 0.85421891972689 |
95 | 0.130551341089482 | 0.261102682178963 | 0.869448658910518 |
96 | 0.125990005985334 | 0.251980011970668 | 0.874009994014666 |
97 | 0.101236371063763 | 0.202472742127527 | 0.898763628936237 |
98 | 0.0813290582887364 | 0.162658116577473 | 0.918670941711264 |
99 | 0.065668787685082 | 0.131337575370164 | 0.934331212314918 |
100 | 0.0520129731833612 | 0.104025946366722 | 0.947987026816639 |
101 | 0.0598440165236808 | 0.119688033047362 | 0.94015598347632 |
102 | 0.0494982087569201 | 0.0989964175138403 | 0.95050179124308 |
103 | 0.0427158648611557 | 0.0854317297223113 | 0.957284135138844 |
104 | 0.0364716822328041 | 0.0729433644656083 | 0.963528317767196 |
105 | 0.027206795665499 | 0.054413591330998 | 0.9727932043345 |
106 | 0.0230951931816015 | 0.0461903863632029 | 0.976904806818399 |
107 | 0.0292251626577491 | 0.0584503253154983 | 0.97077483734225 |
108 | 0.128028114095878 | 0.256056228191755 | 0.871971885904122 |
109 | 0.129923949723467 | 0.259847899446935 | 0.870076050276533 |
110 | 0.599291445658965 | 0.80141710868207 | 0.400708554341035 |
111 | 0.883248466929744 | 0.233503066140512 | 0.116751533070256 |
112 | 0.854287106411135 | 0.29142578717773 | 0.145712893588865 |
113 | 0.913368899643712 | 0.173262200712576 | 0.0866311003562878 |
114 | 0.889572288043413 | 0.220855423913174 | 0.110427711956587 |
115 | 0.865249738163321 | 0.269500523673358 | 0.134750261836679 |
116 | 0.842605279181801 | 0.314789441636398 | 0.157394720818199 |
117 | 0.800342220082195 | 0.39931555983561 | 0.199657779917805 |
118 | 0.818937357586229 | 0.362125284827542 | 0.181062642413771 |
119 | 0.774151552292186 | 0.451696895415628 | 0.225848447707814 |
120 | 0.727337472072414 | 0.545325055855172 | 0.272662527927586 |
121 | 0.66704572179679 | 0.665908556406421 | 0.332954278203211 |
122 | 0.621859015922598 | 0.756281968154804 | 0.378140984077402 |
123 | 0.565519320452085 | 0.868961359095831 | 0.434480679547915 |
124 | 0.501332199145718 | 0.997335601708565 | 0.498667800854282 |
125 | 0.438203446546686 | 0.876406893093372 | 0.561796553453314 |
126 | 0.41716359084699 | 0.83432718169398 | 0.58283640915301 |
127 | 0.421726837149128 | 0.843453674298256 | 0.578273162850872 |
128 | 0.346024432501256 | 0.692048865002511 | 0.653975567498744 |
129 | 0.309994553022863 | 0.619989106045727 | 0.690005446977137 |
130 | 0.260890441305358 | 0.521780882610716 | 0.739109558694642 |
131 | 0.204484520214074 | 0.408969040428148 | 0.795515479785926 |
132 | 0.150780454098876 | 0.301560908197753 | 0.849219545901124 |
133 | 0.141081219639182 | 0.282162439278363 | 0.858918780360818 |
134 | 0.0979067442508138 | 0.195813488501628 | 0.902093255749186 |
135 | 0.0718708334502956 | 0.143741666900591 | 0.928129166549704 |
136 | 0.0509469894092621 | 0.101893978818524 | 0.949053010590738 |
137 | 0.056307138070233 | 0.112614276140466 | 0.943692861929767 |
138 | 0.092552016220124 | 0.185104032440248 | 0.907447983779876 |
139 | 0.0460123624513617 | 0.0920247249027233 | 0.953987637548638 |
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 | 1 | 0.008 | OK |
10% type I error level | 8 | 0.064 | OK |