Multiple Linear Regression - Estimated Regression Equation |
WLH[t] = + 12.3068296466899 + 4.33014916145824X[t] + 1.01868507239736`Y(t-1)`[t] -0.148970908506937`Y(t-2)`[t] + 4.26344451199578M1[t] + 4.33777525395675M2[t] + 2.85371517838113M3[t] + 0.970842279890648M4[t] + 2.74283742150709M5[t] -1.39068521698368M6[t] + 6.24100022216994M7[t] + 35.1906468259991M8[t] + 9.74545135874112M9[t] + 5.14442295711167M10[t] -1.95298550853488M11[t] -0.129219519629923t + 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) | 12.3068296466899 | 8.19304 | 1.5021 | 0.140551 | 0.070276 |
X | 4.33014916145824 | 1.340706 | 3.2298 | 0.002408 | 0.001204 |
`Y(t-1)` | 1.01868507239736 | 0.144455 | 7.0519 | 0 | 0 |
`Y(t-2)` | -0.148970908506937 | 0.14104 | -1.0562 | 0.296899 | 0.148449 |
M1 | 4.26344451199578 | 1.681337 | 2.5357 | 0.01503 | 0.007515 |
M2 | 4.33777525395675 | 2.028613 | 2.1383 | 0.038355 | 0.019177 |
M3 | 2.85371517838113 | 2.144412 | 1.3308 | 0.190445 | 0.095223 |
M4 | 0.970842279890648 | 2.08789 | 0.465 | 0.644342 | 0.322171 |
M5 | 2.74283742150709 | 2.052061 | 1.3366 | 0.188541 | 0.09427 |
M6 | -1.39068521698368 | 2.245373 | -0.6194 | 0.539027 | 0.269514 |
M7 | 6.24100022216994 | 2.184915 | 2.8564 | 0.006635 | 0.003317 |
M8 | 35.1906468259991 | 2.704291 | 13.0129 | 0 | 0 |
M9 | 9.74545135874112 | 6.079908 | 1.6029 | 0.116453 | 0.058227 |
M10 | 5.14442295711167 | 2.814623 | 1.8277 | 0.074697 | 0.037349 |
M11 | -1.95298550853488 | 2.059561 | -0.9483 | 0.348425 | 0.174213 |
t | -0.129219519629923 | 0.051414 | -2.5133 | 0.015884 | 0.007942 |
Multiple Linear Regression - Regression Statistics | |
Multiple R | 0.993002779799179 |
R-squared | 0.986054520688897 |
Adjusted R-squared | 0.981073992363503 |
F-TEST (value) | 197.98191201149 |
F-TEST (DF numerator) | 15 |
F-TEST (DF denominator) | 42 |
p-value | 0 |
Multiple Linear Regression - Residual Statistics | |
Residual Standard Deviation | 2.38810920845841 |
Sum Squared Residuals | 239.528754844003 |
Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
1 | 135 | 135.841614334755 | -0.841614334755449 |
2 | 130 | 133.201694352566 | -3.20169435256636 |
3 | 127 | 127.090873029402 | -0.0908730294017102 |
4 | 122 | 122.767579936624 | -0.767579936623912 |
5 | 117 | 119.763842922144 | -2.76384292214445 |
6 | 112 | 111.152529944572 | 0.847470055428355 |
7 | 113 | 114.306425044643 | -1.30642504464321 |
8 | 149 | 144.890391743775 | 4.10960825622543 |
9 | 157 | 155.839668454685 | 1.16033154531534 |
10 | 157 | 153.895948406354 | 3.10405159364556 |
11 | 147 | 145.477553153022 | 1.52244684697752 |
12 | 137 | 137.114468417954 | -0.114468417953803 |
13 | 132 | 132.551551771415 | -0.551551771415443 |
14 | 125 | 128.892946716829 | -3.89294671682906 |
15 | 123 | 120.893726157377 | 2.10627384262333 |
16 | 117 | 117.88705995401 | -0.887059954010097 |
17 | 114 | 113.715666958626 | 0.284333041373675 |
18 | 111 | 107.290695034355 | 3.70930496564482 |
19 | 112 | 112.184018462208 | -0.184018462207592 |
20 | 144 | 142.470043344325 | 1.52995665567495 |
21 | 150 | 149.344579765646 | 0.655420234354274 |
22 | 149 | 145.959373206549 | 3.04062679345147 |
23 | 134 | 136.820234697833 | -2.82023469783308 |
24 | 123 | 123.512695509285 | -0.512695509284553 |
25 | 116 | 118.675948332883 | -2.6759483328835 |
26 | 117 | 113.128944042009 | 3.87105595799067 |
27 | 111 | 113.577145878750 | -2.57714587874970 |
28 | 105 | 105.303972117738 | -0.303972117738187 |
29 | 102 | 101.728462756382 | 0.271537243617835 |
30 | 95 | 95.303490832111 | -0.303490832111012 |
31 | 93 | 96.122073970374 | -3.12207397037399 |
32 | 124 | 123.947927269327 | 0.0520727306728794 |
33 | 130 | 130.250691343771 | -0.250691343771236 |
34 | 124 | 127.014455693181 | -3.01445569318098 |
35 | 115 | 112.781891822479 | 2.21810817752128 |
36 | 106 | 106.331317610849 | -0.331317610849049 |
37 | 105 | 102.638115128201 | 2.36188487179890 |
38 | 105 | 102.905279454697 | 2.09472054530279 |
39 | 101 | 101.440970767999 | -0.440970767998598 |
40 | 95 | 95.3541380602887 | -0.354138060288751 |
41 | 93 | 91.4806868819188 | 1.51931311808115 |
42 | 84 | 86.074400030045 | -2.07440003004506 |
43 | 87 | 84.7066421150064 | 2.29335788499362 |
44 | 116 | 117.923862592960 | -1.92386259296019 |
45 | 120 | 121.444401980075 | -1.44440198007489 |
46 | 117 | 120.798887163162 | -3.79888716316202 |
47 | 109 | 109.920320326666 | -0.92032032666572 |
48 | 105 | 104.041518461913 | 0.958481538087397 |
49 | 107 | 105.292770432745 | 1.70722956725549 |
50 | 109 | 107.871135433898 | 1.12886456610197 |
51 | 109 | 107.997284166473 | 1.00271583352667 |
52 | 108 | 105.687249931339 | 2.31275006866095 |
53 | 107 | 106.311340480928 | 0.688659519071789 |
54 | 99 | 101.178884158917 | -2.1788841589171 |
55 | 103 | 100.680840407769 | 2.31915959223117 |
56 | 131 | 134.767775049613 | -3.76777504961307 |
57 | 137 | 137.120658455823 | -0.120658455823482 |
58 | 135 | 134.331335530754 | 0.668664469245966 |
Goldfeld-Quandt test for Heteroskedasticity | |||
p-values | Alternative Hypothesis | ||
breakpoint index | greater | 2-sided | less |
19 | 0.192830144016746 | 0.385660288033493 | 0.807169855983254 |
20 | 0.140575807283262 | 0.281151614566524 | 0.859424192716738 |
21 | 0.0717162680200237 | 0.143432536040047 | 0.928283731979976 |
22 | 0.208851234881068 | 0.417702469762136 | 0.791148765118932 |
23 | 0.56289031844168 | 0.874219363116639 | 0.437109681558319 |
24 | 0.44876986491339 | 0.89753972982678 | 0.55123013508661 |
25 | 0.522263631712589 | 0.955472736574822 | 0.477736368287411 |
26 | 0.88698099453639 | 0.226038010927219 | 0.113019005463609 |
27 | 0.89323302101032 | 0.213533957979360 | 0.106766978989680 |
28 | 0.851454436864561 | 0.297091126270877 | 0.148545563135439 |
29 | 0.78467827937304 | 0.43064344125392 | 0.21532172062696 |
30 | 0.786274831309862 | 0.427450337380276 | 0.213725168690138 |
31 | 0.90647890631879 | 0.187042187362419 | 0.0935210936812095 |
32 | 0.94554094713492 | 0.108918105730161 | 0.0544590528650805 |
33 | 0.961534900300635 | 0.0769301993987293 | 0.0384650996993647 |
34 | 0.947738548192084 | 0.104522903615831 | 0.0522614518079157 |
35 | 0.980671718877877 | 0.0386565622442467 | 0.0193282811221234 |
36 | 0.958885198074412 | 0.0822296038511756 | 0.0411148019255878 |
37 | 0.942068180125394 | 0.115863639749213 | 0.0579318198746063 |
38 | 0.963863995520063 | 0.0722720089598748 | 0.0361360044799374 |
39 | 0.988721775714146 | 0.0225564485717079 | 0.0112782242858540 |
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 | 0.0952380952380952 | NOK |
10% type I error level | 5 | 0.238095238095238 | NOK |