Multiple Linear Regression - Estimated Regression Equation |
Y_t[t] = + 0.0158598705609177 -0.00379664026461638X_1t[t] + 0.261788999309723X_2t[t] + 0.00183128940147963X_3t[t] -0.00295797398314777X_4t[t] -0.256111822739559X_5t[t] + 0.00494102191102556X_6t[t] -0.0142133503663819X_7t[t] + 0.0044653395713538X_8t[t] -0.00943433115097334X_9t[t] + 0.238885433628411X_10t[t] -0.00145084519409485X_11t[t] + 0.240612892049589X_12t[t] -0.00281276409301581t + 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) | 0.0158598705609177 | 1.301586 | 0.0122 | 0.990331 | 0.495165 |
X_1t | -0.00379664026461638 | 0.011363 | -0.3341 | 0.739804 | 0.369902 |
X_2t | 0.261788999309723 | 0.016405 | 15.9581 | 0 | 0 |
X_3t | 0.00183128940147963 | 0.008882 | 0.2062 | 0.837555 | 0.418778 |
X_4t | -0.00295797398314777 | 0.010088 | -0.2932 | 0.770669 | 0.385335 |
X_5t | -0.256111822739559 | 0.007685 | -33.326 | 0 | 0 |
X_6t | 0.00494102191102556 | 0.01422 | 0.3475 | 0.729817 | 0.364909 |
X_7t | -0.0142133503663819 | 0.021581 | -0.6586 | 0.513424 | 0.256712 |
X_8t | 0.0044653395713538 | 0.034842 | 0.1282 | 0.898582 | 0.449291 |
X_9t | -0.00943433115097334 | 0.042162 | -0.2238 | 0.823933 | 0.411966 |
X_10t | 0.238885433628411 | 0.043385 | 5.5061 | 2e-06 | 1e-06 |
X_11t | -0.00145084519409485 | 0.012426 | -0.1168 | 0.907563 | 0.453781 |
X_12t | 0.240612892049589 | 0.02312 | 10.4071 | 0 | 0 |
t | -0.00281276409301581 | 0.005994 | -0.4692 | 0.641112 | 0.320556 |
Multiple Linear Regression - Regression Statistics | |
Multiple R | 0.999231404290997 |
R-squared | 0.998463399321359 |
Adjusted R-squared | 0.99802914260783 |
F-TEST (value) | 2299.24689294314 |
F-TEST (DF numerator) | 13 |
F-TEST (DF denominator) | 46 |
p-value | 0 |
Multiple Linear Regression - Residual Statistics | |
Residual Standard Deviation | 0.327670177865718 |
Sum Squared Residuals | 4.93891629127737 |
Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
1 | -8 | -8.03988935699106 | 0.0398893569910646 |
2 | -1 | -1.32979162207042 | 0.329791622070422 |
3 | 1 | 0.873638055575799 | 0.126361944424201 |
4 | -1 | -0.625305071065087 | -0.374694928934913 |
5 | 2 | 1.81045927746166 | 0.189540722538337 |
6 | 2 | 1.87993884416918 | 0.120061155830816 |
7 | 1 | 1.40863085304116 | -0.408630853041161 |
8 | -1 | -0.825335710734478 | -0.174664289265522 |
9 | -2 | -2.46794465210392 | 0.467944652103924 |
10 | -2 | -1.8471005870932 | -0.152899412906797 |
11 | -1 | -0.867030357816808 | -0.132969642183192 |
12 | -8 | -7.59424444948332 | -0.405755550516685 |
13 | -4 | -3.98561340897042 | -0.0143865910295777 |
14 | -6 | -6.17961055752408 | 0.179610557524075 |
15 | -3 | -3.37623242865594 | 0.376232428655942 |
16 | -3 | -3.0126443942703 | 0.0126443942703029 |
17 | -7 | -7.01809888257546 | 0.0180988825754639 |
18 | -9 | -8.74978413442691 | -0.250215865573086 |
19 | -11 | -10.9826120383344 | -0.0173879616656237 |
20 | -13 | -13.0597010744391 | 0.0597010744391171 |
21 | -11 | -11.1736337256083 | 0.173633725608333 |
22 | -9 | -8.56714548396922 | -0.43285451603078 |
23 | -17 | -17.1116256255954 | 0.111625625595428 |
24 | -22 | -21.7081700540606 | -0.291829945939378 |
25 | -25 | -24.6344503989929 | -0.365549601007146 |
26 | -20 | -20.4859726415844 | 0.485972641584382 |
27 | -24 | -24.2491153725968 | 0.249115372596771 |
28 | -24 | -24.2179617107419 | 0.217961710741883 |
29 | -22 | -21.4998538501846 | -0.50014614981541 |
30 | -19 | -19.5685429137242 | 0.568542913724238 |
31 | -18 | -17.6658486368572 | -0.334151363142822 |
32 | -17 | -17.3531866531479 | 0.353186653147879 |
33 | -11 | -11.0111483486613 | 0.0111483486612728 |
34 | -11 | -11.062362330699 | 0.0623623306989769 |
35 | -12 | -11.4020175170614 | -0.597982482938564 |
36 | -10 | -9.75796208803816 | -0.242037911961839 |
37 | -15 | -15.152481654661 | 0.152481654661005 |
38 | -15 | -15.0702237895864 | 0.0702237895864136 |
39 | -15 | -15.1703810063484 | 0.170381006348365 |
40 | -13 | -12.6445832816141 | -0.355416718385877 |
41 | -8 | -7.99904388567119 | -0.000956114328810113 |
42 | -13 | -12.934487800119 | -0.0655121998809817 |
43 | -9 | -9.44733426832891 | 0.447334268328908 |
44 | -7 | -6.71439947042818 | -0.285600529571817 |
45 | -4 | -4.07142417924703 | 0.0714241792470257 |
46 | -4 | -4.05192169573835 | 0.0519216957383477 |
47 | -2 | -2.55565638889264 | 0.555656388892641 |
48 | 0 | -0.196079684820423 | 0.196079684820423 |
49 | -2 | -1.74447618632881 | -0.255523813671191 |
50 | -3 | -3.06347242847346 | 0.063472428473457 |
51 | 1 | 1.21336278591619 | -0.213362785916191 |
52 | -2 | -2.48767533802754 | 0.487675338027538 |
53 | -1 | -1.13705545480072 | 0.137055454800717 |
54 | 1 | 0.923290110169084 | 0.0767098898309164 |
55 | -3 | -2.47380333946715 | -0.526196660532852 |
56 | -4 | -4.27483859382454 | 0.274838593824541 |
57 | -9 | -8.80938154340936 | -0.19061845659064 |
58 | -9 | -8.72348554830976 | -0.276514451690237 |
59 | -7 | -6.7965330941959 | -0.203466905804097 |
60 | -14 | -14.1606452159621 | 0.160645215962066 |
Goldfeld-Quandt test for Heteroskedasticity | |||
p-values | Alternative Hypothesis | ||
breakpoint index | greater | 2-sided | less |
17 | 0.681901367076115 | 0.63619726584777 | 0.318098632923885 |
18 | 0.522199405422576 | 0.955601189154847 | 0.477800594577424 |
19 | 0.558707006430138 | 0.882585987139724 | 0.441292993569862 |
20 | 0.459677982515802 | 0.919355965031605 | 0.540322017484198 |
21 | 0.355130123169635 | 0.71026024633927 | 0.644869876830365 |
22 | 0.290302160590421 | 0.580604321180842 | 0.709697839409579 |
23 | 0.247836383633751 | 0.495672767267502 | 0.752163616366249 |
24 | 0.186189542705978 | 0.372379085411957 | 0.813810457294022 |
25 | 0.248485399406257 | 0.496970798812515 | 0.751514600593743 |
26 | 0.247697905340102 | 0.495395810680204 | 0.752302094659898 |
27 | 0.190730281438267 | 0.381460562876535 | 0.809269718561733 |
28 | 0.142646075808273 | 0.285292151616545 | 0.857353924191727 |
29 | 0.434507470164971 | 0.869014940329942 | 0.565492529835029 |
30 | 0.483023525965021 | 0.966047051930043 | 0.516976474034979 |
31 | 0.756986817000512 | 0.486026365998976 | 0.243013182999488 |
32 | 0.677186564244985 | 0.64562687151003 | 0.322813435755015 |
33 | 0.626181154674775 | 0.74763769065045 | 0.373818845325225 |
34 | 0.590960218072599 | 0.818079563854803 | 0.409039781927401 |
35 | 0.575509033260455 | 0.84898193347909 | 0.424490966739545 |
36 | 0.507587773898279 | 0.984824452203441 | 0.492412226101721 |
37 | 0.666461105941355 | 0.667077788117289 | 0.333538894058645 |
38 | 0.584763894067215 | 0.83047221186557 | 0.415236105932785 |
39 | 0.884502488457235 | 0.23099502308553 | 0.115497511542765 |
40 | 0.972963365516659 | 0.0540732689666816 | 0.0270366344833408 |
41 | 0.979209760755066 | 0.0415804784898675 | 0.0207902392449338 |
42 | 0.959482936697656 | 0.0810341266046873 | 0.0405170633023436 |
43 | 0.990711248736035 | 0.0185775025279303 | 0.00928875126396515 |
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 | 2 | 0.0740740740740741 | NOK |
10% type I error level | 4 | 0.148148148148148 | NOK |