Multiple Linear Regression - Estimated Regression Equation |
Y[t] = + 34.2655743166752 -0.165157690441535X[t] -0.169194606178226M1[t] -0.0910606501698221M2[t] + 0.00598734433123115M3[t] + 0.0204107229500253M4[t] + 0.0301358968138449M5[t] + 0.119936519488922M6[t] + 0.209080988193435M7[t] + 0.233451803331717M8[t] + 0.217166464499433M9[t] + 0.128935549086204M10[t] + 0.0860589923985128M11[t] + 0.0656817483422296t + 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) | 34.2655743166752 | 30.273129 | 1.1319 | 0.262343 | 0.131171 |
X | -0.165157690441535 | 0.155704 | -1.0607 | 0.293215 | 0.146607 |
M1 | -0.169194606178226 | 0.400678 | -0.4223 | 0.674389 | 0.337194 |
M2 | -0.0910606501698221 | 0.400246 | -0.2275 | 0.820826 | 0.410413 |
M3 | 0.00598734433123115 | 0.399872 | 0.015 | 0.988105 | 0.494052 |
M4 | 0.0204107229500253 | 0.40165 | 0.0508 | 0.959646 | 0.479823 |
M5 | 0.0301358968138449 | 0.4026 | 0.0749 | 0.940589 | 0.470295 |
M6 | 0.119936519488922 | 0.40274 | 0.2978 | 0.766919 | 0.383459 |
M7 | 0.209080988193435 | 0.40456 | 0.5168 | 0.607253 | 0.303627 |
M8 | 0.233451803331717 | 0.402817 | 0.5795 | 0.564464 | 0.282232 |
M9 | 0.217166464499433 | 0.402734 | 0.5392 | 0.591792 | 0.295896 |
M10 | 0.128935549086204 | 0.399511 | 0.3227 | 0.748058 | 0.374029 |
M11 | 0.0860589923985128 | 0.398957 | 0.2157 | 0.82997 | 0.414985 |
t | 0.0656817483422296 | 0.062038 | 1.0587 | 0.294108 | 0.147054 |
Multiple Linear Regression - Regression Statistics | |
Multiple R | 0.205311131411143 |
R-squared | 0.0421526606813234 |
Adjusted R-squared | -0.172537260200449 |
F-TEST (value) | 0.196342056991751 |
F-TEST (DF numerator) | 13 |
F-TEST (DF denominator) | 58 |
p-value | 0.998747705775358 |
Multiple Linear Regression - Residual Statistics | |
Residual Standard Deviation | 0.689831138014099 |
Sum Squared Residuals | 27.6002859404819 |
Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
1 | 1.79 | 1.97282759178389 | -0.182827591783894 |
2 | 1.95 | 2.01754868186965 | -0.0675486818696511 |
3 | 2.26 | 2.09769957949216 | 0.162300420507844 |
4 | 2.04 | 2.14477316836487 | -0.104773168364875 |
5 | 2.16 | 2.22018009057092 | -0.0601800905709236 |
6 | 2.75 | 2.37566246158823 | 0.374337538411769 |
7 | 2.79 | 2.53048867863497 | 0.259511321365028 |
8 | 2.88 | 2.48841508976225 | 0.391584910237746 |
9 | 3.36 | 2.42220111596313 | 0.937798884036872 |
10 | 2.97 | 2.35010464175966 | 0.619895358240335 |
11 | 3.1 | 2.33987829532590 | 0.760121704674103 |
12 | 2.49 | 2.26995374413715 | 0.220046255862848 |
13 | 2.2 | 2.14992511725700 | 0.0500748827429965 |
14 | 2.25 | 2.14509890021025 | 0.104901099789747 |
15 | 2.09 | 2.22524979783277 | -0.135249797832769 |
16 | 2.79 | 2.09064992721979 | 0.699350072780206 |
17 | 3.14 | 2.01741492802847 | 1.12258507197153 |
18 | 2.93 | 2.05728691573669 | 0.872713084263306 |
19 | 2.65 | 2.11301851851852 | 0.536981481481484 |
20 | 2.67 | 2.20307108199903 | 0.466928918000972 |
21 | 2.26 | 2.16988864628821 | 0.0901113537117932 |
22 | 2.35 | 2.13082371017305 | 0.219176289826946 |
23 | 2.13 | 2.12059736373928 | 0.00940263626071736 |
24 | 2.18 | 2.06718858159469 | 0.112811418405306 |
25 | 2.9 | 1.91412841662624 | 0.985871583373764 |
26 | 2.63 | 2.00839681384441 | 0.621603186155589 |
27 | 2.67 | 2.07203194242277 | 0.597968057577227 |
28 | 1.81 | 2.02001091703057 | -0.210010917030567 |
29 | 1.33 | 2.02935476306 | -0.699354763060001 |
30 | 0.88 | 2.151805595989 | -1.27180559598900 |
31 | 1.28 | 2.19102142972667 | -0.911021429726667 |
32 | 1.26 | 2.24804245511887 | -0.988042455118874 |
33 | 1.26 | 2.21486001940805 | -0.954860019408051 |
34 | 1.29 | 2.1757950832929 | -0.8857950832929 |
35 | 1.1 | 2.13253719877082 | -1.03253719877082 |
36 | 1.37 | 2.09564418567039 | -0.725644185670386 |
37 | 1.21 | 1.89303671356947 | -0.68303671356947 |
38 | 1.74 | 2.02033664887595 | -0.280336648875946 |
39 | 1.76 | 2.16655062267508 | -0.406550622675076 |
40 | 1.48 | 2.23013998059195 | -0.750139980591947 |
41 | 1.04 | 2.17342075044477 | -1.13342075044477 |
42 | 1.62 | 2.22980850719715 | -0.609808507197153 |
43 | 1.49 | 2.33508741711144 | -0.845087417111437 |
44 | 1.79 | 2.37559267345949 | -0.585592673459486 |
45 | 1.8 | 2.39195754488113 | -0.591957544881127 |
46 | 1.58 | 2.33637683972182 | -0.756376839721818 |
47 | 1.86 | 2.27660318615559 | -0.416603186155588 |
48 | 1.74 | 2.17364709687854 | -0.433647096878537 |
49 | 1.59 | 2.02058693191008 | -0.430586931910083 |
50 | 1.26 | 2.11485532912825 | -0.854855329128254 |
51 | 1.13 | 2.22803776483907 | -1.09803776483907 |
52 | 1.92 | 2.22556404657933 | -0.30556404657933 |
53 | 2.61 | 2.26793943069707 | 0.342060569302926 |
54 | 2.26 | 2.274779880317 | -0.0147798803169983 |
55 | 2.41 | 2.34702725214297 | 0.0629727478570277 |
56 | 2.26 | 2.35450097040272 | -0.094500970402717 |
57 | 2.03 | 2.35435007278020 | -0.324350072780205 |
58 | 2.86 | 2.28225359857674 | 0.577746401423257 |
59 | 2.55 | 2.23899571405467 | 0.311004285945334 |
60 | 2.27 | 2.18558693191008 | 0.0844130680899229 |
61 | 2.26 | 1.99949522885331 | 0.260504771146687 |
62 | 2.57 | 2.09376362607148 | 0.476236373928516 |
63 | 3.07 | 2.19043029273815 | 0.879569707261848 |
64 | 2.76 | 2.08886196021349 | 0.671138039786513 |
65 | 2.51 | 2.08169003719877 | 0.428309962801231 |
66 | 2.87 | 2.22065663917192 | 0.649343360828077 |
67 | 3.14 | 2.24335670386543 | 0.896643296134566 |
68 | 3.11 | 2.30037772925764 | 0.809622270742358 |
69 | 3.16 | 2.31674260067928 | 0.843257399320717 |
70 | 2.47 | 2.24464612647582 | 0.225353873524180 |
71 | 2.57 | 2.20138824195374 | 0.368611758046257 |
72 | 2.89 | 2.14797945980916 | 0.742020540190845 |
Goldfeld-Quandt test for Heteroskedasticity | |||
p-values | Alternative Hypothesis | ||
breakpoint index | greater | 2-sided | less |
17 | 0.0475668647276972 | 0.0951337294553944 | 0.952433135272303 |
18 | 0.0917543847318008 | 0.183508769463602 | 0.9082456152682 |
19 | 0.0913075949779908 | 0.182615189955982 | 0.90869240502201 |
20 | 0.0738785601296186 | 0.147757120259237 | 0.926121439870381 |
21 | 0.222683004298351 | 0.445366008596703 | 0.777316995701649 |
22 | 0.211915560868156 | 0.423831121736311 | 0.788084439131844 |
23 | 0.259345628220498 | 0.518691256440995 | 0.740654371779502 |
24 | 0.215421838900496 | 0.430843677800993 | 0.784578161099504 |
25 | 0.49161697354269 | 0.98323394708538 | 0.50838302645731 |
26 | 0.657537511677119 | 0.684924976645761 | 0.342462488322881 |
27 | 0.854740835009741 | 0.290518329980517 | 0.145259164990259 |
28 | 0.92884086945715 | 0.142318261085700 | 0.0711591305428499 |
29 | 0.984367796144413 | 0.0312644077111749 | 0.0156322038555874 |
30 | 0.998486974433686 | 0.00302605113262815 | 0.00151302556631408 |
31 | 0.998758119194305 | 0.00248376161139078 | 0.00124188080569539 |
32 | 0.99884619626418 | 0.00230760747164020 | 0.00115380373582010 |
33 | 0.998746459044235 | 0.002507081911531 | 0.0012535409557655 |
34 | 0.998170340408367 | 0.0036593191832652 | 0.0018296595916326 |
35 | 0.997594707726219 | 0.00481058454756239 | 0.00240529227378119 |
36 | 0.995582505015682 | 0.00883498996863683 | 0.00441749498431842 |
37 | 0.991812803555085 | 0.0163743928898297 | 0.00818719644491483 |
38 | 0.99287315830626 | 0.0142536833874802 | 0.00712684169374009 |
39 | 0.994708570059998 | 0.0105828598800037 | 0.00529142994000184 |
40 | 0.990114337423484 | 0.0197713251530311 | 0.00988566257651555 |
41 | 0.98628505111947 | 0.0274298977610586 | 0.0137149488805293 |
42 | 0.97712043573048 | 0.0457591285390394 | 0.0228795642695197 |
43 | 0.963967233047536 | 0.0720655339049281 | 0.0360327669524640 |
44 | 0.941961297772421 | 0.116077404455157 | 0.0580387022275786 |
45 | 0.911680739535312 | 0.176638520929375 | 0.0883192604646876 |
46 | 0.86581665732663 | 0.268366685346742 | 0.134183342673371 |
47 | 0.823412271722587 | 0.353175456554826 | 0.176587728277413 |
48 | 0.781670167023096 | 0.436659665953807 | 0.218329832976904 |
49 | 0.704421262954735 | 0.59115747409053 | 0.295578737045265 |
50 | 0.636820999421488 | 0.726358001157025 | 0.363179000578512 |
51 | 0.837330690471809 | 0.325338619056383 | 0.162669309528191 |
52 | 0.806364651472857 | 0.387270697054287 | 0.193635348527143 |
53 | 0.814676981703064 | 0.370646036593872 | 0.185323018296936 |
54 | 0.706042757504804 | 0.587914484990392 | 0.293957242495196 |
55 | 0.596362558545417 | 0.807274882909166 | 0.403637441454583 |
Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
Description | # significant tests | % significant tests | OK/NOK |
1% type I error level | 7 | 0.179487179487179 | NOK |
5% type I error level | 14 | 0.358974358974359 | NOK |
10% type I error level | 16 | 0.41025641025641 | NOK |