Multiple Linear Regression - Estimated Regression Equation |
pe_b[t] = -3.3167593452465 + 3.35943414633357Br[t] + 0.00693286009409913org[t] -0.000531295134700565cm[t] + 0.00396717664181525cm_b[t] + 0.0574140713295431d[t] -0.0630114852430697d_b[t] + 0.973189821980576pe[t] -0.623529846461795pc[t] + 0.644309517450024pc_b[t] -0.223550340334766ps[t] + 0.221838290372535ps_b[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) | -3.3167593452465 | 0.848095 | -3.9108 | 0.00014 | 7e-05 |
Br | 3.35943414633357 | 0.849246 | 3.9558 | 0.000118 | 5.9e-05 |
org | 0.00693286009409913 | 0.0107 | 0.6479 | 0.518052 | 0.259026 |
cm | -0.000531295134700565 | 0.037055 | -0.0143 | 0.98858 | 0.49429 |
cm_b | 0.00396717664181525 | 0.037931 | 0.1046 | 0.916844 | 0.458422 |
d | 0.0574140713295431 | 0.054643 | 1.0507 | 0.295117 | 0.147559 |
d_b | -0.0630114852430697 | 0.056719 | -1.1109 | 0.268411 | 0.134206 |
pe | 0.973189821980576 | 0.013625 | 71.4281 | 0 | 0 |
pc | -0.623529846461795 | 0.082019 | -7.6023 | 0 | 0 |
pc_b | 0.644309517450024 | 0.082886 | 7.7734 | 0 | 0 |
ps | -0.223550340334766 | 0.032932 | -6.7883 | 0 | 0 |
ps_b | 0.221838290372535 | 0.034668 | 6.3989 | 0 | 0 |
Multiple Linear Regression - Regression Statistics | |
Multiple R | 0.996336455957132 |
R-squared | 0.992686333469218 |
Adjusted R-squared | 0.992139052300248 |
F-TEST (value) | 1813.85070372019 |
F-TEST (DF numerator) | 11 |
F-TEST (DF denominator) | 147 |
p-value | 0 |
Multiple Linear Regression - Residual Statistics | |
Residual Standard Deviation | 0.452791176290144 |
Sum Squared Residuals | 30.1379178509532 |
Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
1 | 11 | 11.1403814194666 | -0.140381419466573 |
2 | 7 | 7.1622209405945 | -0.162220940594507 |
3 | 0 | 2.04149255972577 | -2.04149255972577 |
4 | 10 | 10.0624141218463 | -0.0624141218462946 |
5 | 12 | 12.0190955021867 | -0.0190955021866933 |
6 | 0 | -0.154604960207914 | 0.154604960207914 |
7 | 11 | 10.9741452711300 | 0.0258547288699511 |
8 | 11 | 11.0759546876537 | -0.0759546876537369 |
9 | 12 | 11.9621156789955 | 0.0378843210045264 |
10 | 13 | 12.9738070694699 | 0.0261929305300589 |
11 | 14 | 14.0568069474377 | -0.0568069474376607 |
12 | 16 | 15.9496786733211 | 0.0503213266789092 |
13 | 11 | 11.1166476887478 | -0.116647688747833 |
14 | 10 | 10.0120873909802 | -0.0120873909801950 |
15 | 11 | 11.0171126532760 | -0.0171126532760307 |
16 | 15 | 14.8903764708344 | 0.109623529165571 |
17 | 9 | 9.11116912694688 | -0.111169126946882 |
18 | 11 | 10.9799847437357 | 0.0200152562643023 |
19 | 17 | 16.8850213335978 | 0.114978666402161 |
20 | 17 | 16.9429067403092 | 0.057093259690768 |
21 | 11 | 11.0498003866014 | -0.0498003866014301 |
22 | 18 | 17.9186334789086 | 0.0813665210914399 |
23 | 14 | 14.0723059307835 | -0.0723059307834722 |
24 | 10 | 10.0975978035740 | -0.097597803573965 |
25 | 11 | 11.0775894897558 | -0.077589489755777 |
26 | 15 | 14.9647454556225 | 0.0352545443775432 |
27 | 15 | 14.9071284548482 | 0.0928715451517605 |
28 | 13 | 13.0367960051323 | -0.0367960051322751 |
29 | 16 | 15.9443082426759 | 0.0556917573241361 |
30 | 13 | 12.9486444561583 | 0.051355543841663 |
31 | 9 | 9.11079993555021 | -0.110799935550211 |
32 | 18 | 18.0107800908509 | -0.0107800908509158 |
33 | 18 | 17.7668933506039 | 0.233106649396147 |
34 | 12 | 12.0260639917023 | -0.0260639917023221 |
35 | 17 | 16.8847408869704 | 0.115259113029564 |
36 | 9 | 9.07705572399475 | -0.0770557239947482 |
37 | 9 | 9.08245928465533 | -0.0824592846553304 |
38 | 12 | 11.9033769294834 | 0.0966230705165576 |
39 | 0 | 1.28338009720315 | -1.28338009720315 |
40 | 12 | 11.9949447657467 | 0.00505523425328857 |
41 | 18 | 17.9526375793416 | 0.0473624206583547 |
42 | 14 | 13.9962165487525 | 0.0037834512475189 |
43 | 15 | 14.9065211488228 | 0.0934788511772117 |
44 | 16 | 15.8422981012251 | 0.157701898774856 |
45 | 10 | 10.0684963629520 | -0.0684963629519611 |
46 | 11 | 11.0374499695315 | -0.0374499695314946 |
47 | 14 | 14.0010545969886 | -0.00105459698856436 |
48 | 9 | 9.07268456325402 | -0.0726845632540236 |
49 | 12 | 12.0475109904394 | -0.0475109904393759 |
50 | 17 | 16.8358097644690 | 0.164190235530967 |
51 | 5 | 5.11852838463848 | -0.118528384638484 |
52 | 12 | 12.0290947677177 | -0.0290947677176641 |
53 | 12 | 12.059812607157 | -0.0598126071569941 |
54 | 6 | 6.05438764209266 | -0.0543876420926603 |
55 | 24 | 23.9535450222915 | 0.0464549777084812 |
56 | 12 | 12.0637203147043 | -0.0637203147042778 |
57 | 12 | 12.0494792103037 | -0.049479210303739 |
58 | 14 | 13.9170747320339 | 0.082925267966122 |
59 | 7 | 7.0966259030604 | -0.0966259030603979 |
60 | 13 | 12.9114780491714 | 0.0885219508285541 |
61 | 12 | 12.0482352674062 | -0.0482352674061845 |
62 | 13 | 12.9602993284429 | 0.0397006715570933 |
63 | 0 | 1.45097540024459 | -1.45097540024459 |
64 | 8 | 8.12958934524279 | -0.129589345242790 |
65 | 11 | 10.9569727066323 | 0.04302729336768 |
66 | 9 | 9.09826281850474 | -0.0982628185047413 |
67 | 11 | 11.1044567692809 | -0.104456769280875 |
68 | 13 | 12.9746495911497 | 0.0253504088503282 |
69 | 10 | 9.99820015258048 | 0.00179984741952341 |
70 | 0 | -2.39441819924024 | 2.39441819924024 |
71 | 12 | 12.0361176554881 | -0.0361176554881409 |
72 | 9 | 9.08524865220072 | -0.0852486522007223 |
73 | 15 | 15.0142679031478 | -0.0142679031478093 |
74 | 18 | 17.9244259656443 | 0.0755740343556527 |
75 | 15 | 14.9346766039850 | 0.0653233960149735 |
76 | 12 | 12.0215902310196 | -0.0215902310196441 |
77 | 13 | 12.9224916307127 | 0.0775083692873257 |
78 | 14 | 13.9880574354856 | 0.0119425645144205 |
79 | 10 | 10.1005989640691 | -0.100598964069080 |
80 | 13 | 12.9631753149288 | 0.0368246850712469 |
81 | 13 | 13.046986650076 | -0.0469866500760132 |
82 | 0 | -0.885090382846324 | 0.885090382846324 |
83 | 13 | 12.9853583722153 | 0.0146416277847314 |
84 | 16 | 15.9690343746953 | 0.030965625304742 |
85 | 0 | -1.91758203501526 | 1.91758203501526 |
86 | 16 | 15.9018992513083 | 0.0981007486917389 |
87 | 11 | 10.9897159135691 | 0.0102840864309359 |
88 | 9 | 9.102470788233 | -0.102470788232993 |
89 | 16 | 16.0399606349383 | -0.0399606349383254 |
90 | 0 | 0.906089975309023 | -0.906089975309023 |
91 | 14 | 13.9818225940170 | 0.0181774059829752 |
92 | 8 | 8.09310284134055 | -0.0931028413405518 |
93 | 0 | -0.693546120787273 | 0.693546120787273 |
94 | 15 | 14.8858075134592 | 0.114192486540761 |
95 | 11 | 11.1216987495030 | -0.121698749502958 |
96 | 21 | 20.9050240657784 | 0.094975934221612 |
97 | 14 | 14.0086715049589 | -0.00867150495894964 |
98 | 18 | 17.9459588441959 | 0.0540411558041064 |
99 | 12 | 11.9960885478409 | 0.00391145215905488 |
100 | 13 | 12.9809025512294 | 0.0190974487706307 |
101 | 15 | 14.9775828890511 | 0.0224171109488623 |
102 | 12 | 11.9710481286891 | 0.0289518713109204 |
103 | 19 | 18.8361037957818 | 0.163896204218179 |
104 | 15 | 14.9819552693612 | 0.0180447306388206 |
105 | 11 | 11.1230329761142 | -0.123032976114214 |
106 | 0 | 1.36483120019741 | -1.36483120019741 |
107 | 10 | 10.0344466404312 | -0.0344466404311514 |
108 | 13 | 13.0054875797950 | -0.00548757979495669 |
109 | 15 | 14.9845567173617 | 0.0154432826382789 |
110 | 0 | 2.20743937802792 | -2.20743937802792 |
111 | 12 | 11.9740531523725 | 0.0259468476274913 |
112 | 16 | 16.0500651184642 | -0.0500651184642499 |
113 | 9 | 9.1549017829124 | -0.154901782912404 |
114 | 0 | 0.0240419701462767 | -0.0240419701462767 |
115 | 8 | 8.16391454114465 | -0.163914541144647 |
116 | 13 | 12.9386712276328 | 0.0613287723671505 |
117 | 17 | 16.8390952000783 | 0.160904799921677 |
118 | 9 | 9.02038299995704 | -0.0203829999570453 |
119 | 15 | 14.9637959556676 | 0.0362040443324395 |
120 | 8 | 7.98632866969238 | 0.0136713303076233 |
121 | 7 | 7.08420087261372 | -0.0842008726137225 |
122 | 12 | 11.9347620619701 | 0.065237938029946 |
123 | 0 | -1.21585580952926 | 1.21585580952926 |
124 | 6 | 6.15233117330626 | -0.152331173306261 |
125 | 8 | 8.06777709728402 | -0.0677770972840157 |
126 | 17 | 16.8837879527136 | 0.116212047286379 |
127 | 0 | -0.379356212778565 | 0.379356212778565 |
128 | 11 | 11.0603114512258 | -0.0603114512257693 |
129 | 14 | 14.0045223889417 | -0.00452238894171759 |
130 | 11 | 11.0778287090591 | -0.0778287090591191 |
131 | 13 | 13.0204389904130 | -0.0204389904130452 |
132 | 12 | 12.0099846742323 | -0.00998467423229209 |
133 | 11 | 11.0005716715290 | -0.000571671529022328 |
134 | 9 | 9.02333555851491 | -0.0233355585149103 |
135 | 12 | 12.0354323880425 | -0.0354323880425376 |
136 | 20 | 19.8388441119422 | 0.161155888057811 |
137 | 12 | 11.9408384296352 | 0.0591615703648346 |
138 | 13 | 12.9300105579108 | 0.0699894420892005 |
139 | 12 | 12.0520359711123 | -0.052035971112305 |
140 | 12 | 12.0602392022240 | -0.0602392022240392 |
141 | 9 | 9.07079578041646 | -0.0707957804164556 |
142 | 0 | -0.61161742588035 | 0.61161742588035 |
143 | 24 | 23.852296861501 | 0.147703138499008 |
144 | 7 | 7.07752980589028 | -0.0775298058902813 |
145 | 17 | 16.9280110593398 | 0.0719889406601921 |
146 | 11 | 11.0026861031708 | -0.0026861031708185 |
147 | 17 | 16.9189775078818 | 0.0810224921181561 |
148 | 0 | -1.02617943456896 | 1.02617943456896 |
149 | 12 | 11.9855737642411 | 0.0144262357588853 |
150 | 14 | 14.0103553031831 | -0.0103553031830943 |
151 | 11 | 11.0723252375672 | -0.072325237567246 |
152 | 16 | 15.9118948234297 | 0.0881051765702638 |
153 | 21 | 20.8455141976425 | 0.154485802357494 |
154 | 14 | 13.8678883745261 | 0.132111625473910 |
155 | 20 | 19.8813210434275 | 0.118678956572498 |
156 | 13 | 12.9399148858568 | 0.0600851141431682 |
157 | 11 | 11.0571405413539 | -0.0571405413539098 |
158 | 15 | 14.9659996758598 | 0.0340003241402262 |
159 | 19 | 18.9922622111579 | 0.0077377888421377 |
Goldfeld-Quandt test for Heteroskedasticity | |||
p-values | Alternative Hypothesis | ||
breakpoint index | greater | 2-sided | less |
15 | 7.12352139600324e-40 | 1.42470427920065e-39 | 1 |
16 | 8.62983344447803e-54 | 1.72596668889561e-53 | 1 |
17 | 4.36699623746823e-68 | 8.73399247493646e-68 | 1 |
18 | 6.18005865344976e-82 | 1.23601173068995e-81 | 1 |
19 | 7.80798434956018e-93 | 1.56159686991204e-92 | 1 |
20 | 1.20551027143727e-107 | 2.41102054287453e-107 | 1 |
21 | 3.77957387486951e-125 | 7.55914774973902e-125 | 1 |
22 | 2.22125472940736e-132 | 4.44250945881471e-132 | 1 |
23 | 6.50921349735127e-151 | 1.30184269947025e-150 | 1 |
24 | 3.35171382141838e-157 | 6.70342764283675e-157 | 1 |
25 | 3.95511321780597e-173 | 7.91022643561194e-173 | 1 |
26 | 3.00649926631648e-187 | 6.01299853263297e-187 | 1 |
27 | 1.11092214173037e-204 | 2.22184428346074e-204 | 1 |
28 | 5.33479796323646e-218 | 1.06695959264729e-217 | 1 |
29 | 7.61007223513885e-231 | 1.52201444702777e-230 | 1 |
30 | 4.35196393477539e-240 | 8.70392786955077e-240 | 1 |
31 | 3.12009680586135e-257 | 6.2401936117227e-257 | 1 |
32 | 9.86845602833614e-261 | 1.97369120566723e-260 | 1 |
33 | 7.55669658911429e-275 | 1.51133931782286e-274 | 1 |
34 | 5.16232513458644e-292 | 1.03246502691729e-291 | 1 |
35 | 1.60824534574185e-309 | 3.21649069148371e-309 | 1 |
36 | 1.87744945419674e-322 | 3.75489890839347e-322 | 1 |
37 | 0 | 0 | 1 |
38 | 0 | 0 | 1 |
39 | 0 | 0 | 1 |
40 | 0 | 0 | 1 |
41 | 0 | 0 | 1 |
42 | 0 | 0 | 1 |
43 | 0 | 0 | 1 |
44 | 0 | 0 | 1 |
45 | 0 | 0 | 1 |
46 | 0 | 0 | 1 |
47 | 0 | 0 | 1 |
48 | 0 | 0 | 1 |
49 | 0 | 0 | 1 |
50 | 0 | 0 | 1 |
51 | 0 | 0 | 1 |
52 | 0 | 0 | 1 |
53 | 0 | 0 | 1 |
54 | 0 | 0 | 1 |
55 | 0 | 0 | 1 |
56 | 0 | 0 | 1 |
57 | 0 | 0 | 1 |
58 | 0 | 0 | 1 |
59 | 0 | 0 | 1 |
60 | 0 | 0 | 1 |
61 | 0 | 0 | 1 |
62 | 0 | 0 | 1 |
63 | 0 | 0 | 1 |
64 | 0 | 0 | 1 |
65 | 0 | 0 | 1 |
66 | 0 | 0 | 1 |
67 | 0 | 0 | 1 |
68 | 0 | 0 | 1 |
69 | 0 | 0 | 1 |
70 | 0 | 0 | 1 |
71 | 0 | 0 | 1 |
72 | 0 | 0 | 1 |
73 | 0 | 0 | 1 |
74 | 0 | 0 | 1 |
75 | 0 | 0 | 1 |
76 | 0 | 0 | 1 |
77 | 0 | 0 | 1 |
78 | 0 | 0 | 1 |
79 | 0 | 0 | 1 |
80 | 0 | 0 | 1 |
81 | 0 | 0 | 1 |
82 | 0.0178970316975103 | 0.0357940633950206 | 0.98210296830249 |
83 | 0.0131453380655995 | 0.0262906761311991 | 0.9868546619344 |
84 | 0.00953322389459974 | 0.0190664477891995 | 0.9904667761054 |
85 | 0.540559517454388 | 0.918880965091224 | 0.459440482545612 |
86 | 0.493889169844935 | 0.98777833968987 | 0.506110830155065 |
87 | 0.445017748978533 | 0.890035497957067 | 0.554982251021467 |
88 | 0.397592896147290 | 0.795185792294579 | 0.60240710385271 |
89 | 0.351458175500237 | 0.702916351000475 | 0.648541824499763 |
90 | 0.905504626857977 | 0.188990746284046 | 0.094495373142023 |
91 | 0.882736917047842 | 0.234526165904317 | 0.117263082952158 |
92 | 0.857051872116807 | 0.285896255766386 | 0.142948127883193 |
93 | 0.941137035655827 | 0.117725928688346 | 0.058862964344173 |
94 | 0.925398074265002 | 0.149203851469996 | 0.0746019257349978 |
95 | 0.907034819000273 | 0.185930361999455 | 0.0929651809997273 |
96 | 0.884436722768212 | 0.231126554463577 | 0.115563277231788 |
97 | 0.857628555343017 | 0.284742889313965 | 0.142371444656983 |
98 | 0.826900411040575 | 0.346199177918851 | 0.173099588959425 |
99 | 0.791834610130874 | 0.416330779738252 | 0.208165389869126 |
100 | 0.752783949604823 | 0.494432100790354 | 0.247216050395177 |
101 | 0.709965422749139 | 0.580069154501723 | 0.290034577250861 |
102 | 0.663818454405041 | 0.672363091189918 | 0.336181545594959 |
103 | 0.618834550811873 | 0.762330898376254 | 0.381165449188127 |
104 | 0.567784835106224 | 0.864430329787551 | 0.432215164893776 |
105 | 0.519901332192476 | 0.960197335615048 | 0.480098667807524 |
106 | 0.800497179265955 | 0.39900564146809 | 0.199502820734045 |
107 | 0.760464874568872 | 0.479070250862257 | 0.239535125431128 |
108 | 0.716340340839929 | 0.567319318320141 | 0.283659659160071 |
109 | 0.668223417119301 | 0.663553165761398 | 0.331776582880699 |
110 | 1 | 0 | 0 |
111 | 1 | 0 | 0 |
112 | 1 | 0 | 0 |
113 | 1 | 0 | 0 |
114 | 1 | 0 | 0 |
115 | 1 | 0 | 0 |
116 | 1 | 0 | 0 |
117 | 1 | 0 | 0 |
118 | 1 | 0 | 0 |
119 | 1 | 0 | 0 |
120 | 1 | 0 | 0 |
121 | 1 | 0 | 0 |
122 | 1 | 0 | 0 |
123 | 1 | 0 | 0 |
124 | 1 | 0 | 0 |
125 | 1 | 4.33221529656821e-306 | 2.16610764828411e-306 |
126 | 1 | 4.98650200395513e-299 | 2.49325100197757e-299 |
127 | 1 | 4.17189273509107e-283 | 2.08594636754554e-283 |
128 | 1 | 2.77015547334519e-268 | 1.38507773667259e-268 |
129 | 1 | 5.9519889100069e-258 | 2.97599445500345e-258 |
130 | 1 | 1.68413000387365e-240 | 8.42065001936827e-241 |
131 | 1 | 7.93575159425184e-230 | 3.96787579712592e-230 |
132 | 1 | 6.43653674824289e-218 | 3.21826837412144e-218 |
133 | 1 | 6.77176507179549e-202 | 3.38588253589775e-202 |
134 | 1 | 1.3952761090742e-188 | 6.976380545371e-189 |
135 | 1 | 1.59156583494553e-174 | 7.95782917472766e-175 |
136 | 1 | 2.55493355510492e-159 | 1.27746677755246e-159 |
137 | 1 | 1.28900734946478e-145 | 6.44503674732391e-146 |
138 | 1 | 8.30721724397876e-131 | 4.15360862198938e-131 |
139 | 1 | 1.26120439086290e-116 | 6.30602195431449e-117 |
140 | 1 | 1.53789655179996e-100 | 7.68948275899981e-101 |
141 | 1 | 3.6270973435417e-87 | 1.81354867177085e-87 |
142 | 1 | 4.79002646071558e-71 | 2.39501323035779e-71 |
143 | 1 | 1.48258031049960e-56 | 7.41290155249802e-57 |
144 | 1 | 9.65070375797895e-44 | 4.82535187898948e-44 |
Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
Description | # significant tests | % significant tests | OK/NOK |
1% type I error level | 102 | 0.784615384615385 | NOK |
5% type I error level | 105 | 0.807692307692308 | NOK |
10% type I error level | 105 | 0.807692307692308 | NOK |