Multiple Linear Regression - Estimated Regression Equation |
Y[t] = + 103.708251028807 + 7.79209876543207X[t] -1.25631687242790M1[t] -0.0279835390946507M2[t] + 0.108683127572014M3[t] + 0.140349794238680M4[t] + 0.138683127572013M5[t] + 0.143683127572011M6[t] + 0.413683127572011M7[t] -0.314999999999997M8[t] -0.151666666666663M9[t] -0.0999999999999963M10[t] -0.0416666666666662M11[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) | 103.708251028807 | 2.171404 | 47.7609 | 0 | 0 |
X | 7.79209876543207 | 1.265432 | 6.1577 | 0 | 0 |
M1 | -1.25631687242790 | 2.692659 | -0.4666 | 0.642525 | 0.321263 |
M2 | -0.0279835390946507 | 2.692659 | -0.0104 | 0.991743 | 0.495872 |
M3 | 0.108683127572014 | 2.692659 | 0.0404 | 0.96794 | 0.48397 |
M4 | 0.140349794238680 | 2.692659 | 0.0521 | 0.958607 | 0.479303 |
M5 | 0.138683127572013 | 2.692659 | 0.0515 | 0.959098 | 0.479549 |
M6 | 0.143683127572011 | 2.692659 | 0.0534 | 0.957625 | 0.478812 |
M7 | 0.413683127572011 | 2.692659 | 0.1536 | 0.878423 | 0.439211 |
M8 | -0.314999999999997 | 2.684387 | -0.1173 | 0.906985 | 0.453493 |
M9 | -0.151666666666663 | 2.684387 | -0.0565 | 0.955135 | 0.477567 |
M10 | -0.0999999999999963 | 2.684387 | -0.0373 | 0.970409 | 0.485205 |
M11 | -0.0416666666666662 | 2.684387 | -0.0155 | 0.987668 | 0.493834 |
Multiple Linear Regression - Regression Statistics | |
Multiple R | 0.633977059741042 |
R-squared | 0.401926912277897 |
Adjusted R-squared | 0.280284928334419 |
F-TEST (value) | 3.30417919247892 |
F-TEST (DF numerator) | 12 |
F-TEST (DF denominator) | 59 |
p-value | 0.00106190316840671 |
Multiple Linear Regression - Residual Statistics | |
Residual Standard Deviation | 4.64949479158511 |
Sum Squared Residuals | 1275.45030720165 |
Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
1 | 103.52 | 102.451934156378 | 1.06806584362184 |
2 | 103.5 | 103.680267489712 | -0.180267489711939 |
3 | 103.52 | 103.816934156379 | -0.296934156378628 |
4 | 103.53 | 103.848600823045 | -0.318600823045288 |
5 | 103.53 | 103.846934156379 | -0.316934156378624 |
6 | 103.53 | 103.851934156379 | -0.321934156378616 |
7 | 103.52 | 104.121934156379 | -0.601934156378624 |
8 | 103.54 | 103.393251028807 | 0.146748971193395 |
9 | 103.59 | 103.55658436214 | 0.0334156378600592 |
10 | 103.59 | 103.608251028807 | -0.0182510288066077 |
11 | 103.59 | 103.66658436214 | -0.0765843621399387 |
12 | 103.59 | 103.708251028807 | -0.118251028806605 |
13 | 103.63 | 102.451934156379 | 1.17806584362129 |
14 | 103.74 | 103.680267489712 | 0.0597325102880376 |
15 | 103.7 | 103.816934156379 | -0.116934156378618 |
16 | 103.72 | 103.848600823045 | -0.128600823045290 |
17 | 103.81 | 103.846934156379 | -0.0369341563786187 |
18 | 103.8 | 103.851934156379 | -0.0519341563786220 |
19 | 104.22 | 104.121934156379 | 0.0980658436213797 |
20 | 106.91 | 111.185349794239 | -4.27534979423868 |
21 | 107.06 | 111.348683127572 | -4.28868312757201 |
22 | 107.17 | 111.400349794239 | -4.23034979423868 |
23 | 107.25 | 111.458683127572 | -4.20868312757201 |
24 | 107.28 | 111.500349794239 | -4.22034979423868 |
25 | 107.24 | 110.244032921811 | -3.00403292181079 |
26 | 107.23 | 111.472366255144 | -4.24236625514402 |
27 | 107.34 | 111.609032921811 | -4.26903292181069 |
28 | 107.34 | 111.640699588477 | -4.30069958847735 |
29 | 107.3 | 111.639032921811 | -4.33903292181069 |
30 | 107.24 | 111.644032921811 | -4.40403292181069 |
31 | 107.3 | 111.914032921811 | -4.61403292181069 |
32 | 107.32 | 111.185349794239 | -3.86534979423869 |
33 | 107.28 | 111.348683127572 | -4.06868312757201 |
34 | 107.33 | 111.400349794239 | -4.07034979423868 |
35 | 107.33 | 111.458683127572 | -4.12868312757201 |
36 | 107.33 | 111.500349794239 | -4.17034979423868 |
37 | 107.28 | 110.244032921811 | -2.96403292181078 |
38 | 107.28 | 111.472366255144 | -4.19236625514402 |
39 | 107.29 | 111.609032921811 | -4.31903292181069 |
40 | 107.29 | 111.640699588477 | -4.35069958847735 |
41 | 107.23 | 111.639032921811 | -4.40903292181069 |
42 | 107.24 | 111.644032921811 | -4.40403292181069 |
43 | 107.24 | 111.914032921811 | -4.67403292181069 |
44 | 107.2 | 111.185349794239 | -3.98534979423868 |
45 | 107.23 | 111.348683127572 | -4.11868312757201 |
46 | 107.2 | 111.400349794239 | -4.20034979423868 |
47 | 107.21 | 111.458683127572 | -4.24868312757202 |
48 | 107.24 | 111.500349794239 | -4.26034979423868 |
49 | 107.21 | 110.244032921811 | -3.03403292181079 |
50 | 113.89 | 111.472366255144 | 2.41763374485597 |
51 | 114.05 | 111.609032921811 | 2.44096707818931 |
52 | 114.05 | 111.640699588477 | 2.40930041152264 |
53 | 114.05 | 111.639032921811 | 2.41096707818931 |
54 | 114.05 | 111.644032921811 | 2.40596707818931 |
55 | 115.12 | 111.914032921811 | 3.20596707818931 |
56 | 115.68 | 111.185349794239 | 4.49465020576133 |
57 | 116.05 | 111.348683127572 | 4.70131687242798 |
58 | 116.18 | 111.400349794239 | 4.77965020576133 |
59 | 116.35 | 111.458683127572 | 4.89131687242798 |
60 | 116.44 | 111.500349794239 | 4.93965020576132 |
61 | 117 | 110.244032921811 | 6.75596707818922 |
62 | 117.61 | 111.472366255144 | 6.13763374485597 |
63 | 118.17 | 111.609032921811 | 6.56096707818931 |
64 | 118.33 | 111.640699588477 | 6.68930041152264 |
65 | 118.33 | 111.639032921811 | 6.69096707818931 |
66 | 118.42 | 111.644032921811 | 6.77596707818931 |
67 | 118.5 | 111.914032921811 | 6.58596707818931 |
68 | 118.67 | 111.185349794239 | 7.48465020576132 |
69 | 119.09 | 111.348683127572 | 7.74131687242799 |
70 | 119.14 | 111.400349794239 | 7.73965020576132 |
71 | 119.23 | 111.458683127572 | 7.771316872428 |
72 | 119.33 | 111.500349794239 | 7.82965020576132 |
Goldfeld-Quandt test for Heteroskedasticity | |||
p-values | Alternative Hypothesis | ||
breakpoint index | greater | 2-sided | less |
16 | 3.05761553116227e-05 | 6.11523106232454e-05 | 0.999969423844688 |
17 | 1.67616289768937e-06 | 3.35232579537874e-06 | 0.999998323837102 |
18 | 8.65071151287355e-08 | 1.73014230257471e-07 | 0.999999913492885 |
19 | 4.42190766381789e-08 | 8.84381532763578e-08 | 0.999999955780923 |
20 | 1.86561742461450e-09 | 3.73123484922901e-09 | 0.999999998134383 |
21 | 7.64247020955035e-11 | 1.52849404191007e-10 | 0.999999999923575 |
22 | 3.20560846422532e-12 | 6.41121692845065e-12 | 0.999999999996794 |
23 | 1.38580969181783e-13 | 2.77161938363566e-13 | 0.999999999999861 |
24 | 5.80915115406661e-15 | 1.16183023081332e-14 | 0.999999999999994 |
25 | 2.0791217265765e-16 | 4.158243453153e-16 | 1 |
26 | 7.24435287739447e-18 | 1.44887057547889e-17 | 1 |
27 | 2.98616000440021e-19 | 5.97232000880043e-19 | 1 |
28 | 1.13290598184980e-20 | 2.26581196369959e-20 | 1 |
29 | 3.78662500913844e-22 | 7.57325001827689e-22 | 1 |
30 | 1.28099039044866e-23 | 2.56198078089732e-23 | 1 |
31 | 6.44130023183776e-25 | 1.28826004636755e-24 | 1 |
32 | 6.58627463579632e-26 | 1.31725492715926e-25 | 1 |
33 | 3.28257033663368e-27 | 6.56514067326736e-27 | 1 |
34 | 1.63406811258701e-28 | 3.26813622517401e-28 | 1 |
35 | 7.45162305307745e-30 | 1.49032461061549e-29 | 1 |
36 | 3.39437538610767e-31 | 6.78875077221533e-31 | 1 |
37 | 1.12001750893996e-32 | 2.24003501787992e-32 | 1 |
38 | 5.89001857616625e-34 | 1.17800371523325e-33 | 1 |
39 | 3.52863098029060e-35 | 7.05726196058119e-35 | 1 |
40 | 2.37896549793899e-36 | 4.75793099587798e-36 | 1 |
41 | 2.0455254055737e-37 | 4.0910508111474e-37 | 1 |
42 | 1.94376099665675e-38 | 3.88752199331351e-38 | 1 |
43 | 5.48634687005665e-39 | 1.09726937401133e-38 | 1 |
44 | 1.44965644724045e-39 | 2.89931289448091e-39 | 1 |
45 | 7.67810623754994e-40 | 1.53562124750999e-39 | 1 |
46 | 1.06083314804767e-39 | 2.12166629609535e-39 | 1 |
47 | 7.66757483720664e-39 | 1.53351496744133e-38 | 1 |
48 | 1.27426931324897e-36 | 2.54853862649794e-36 | 1 |
49 | 4.81602224676094e-34 | 9.63204449352188e-34 | 1 |
50 | 4.11740315149802e-06 | 8.23480630299603e-06 | 0.999995882596848 |
51 | 0.00252444260048059 | 0.00504888520096118 | 0.99747555739952 |
52 | 0.0328437147600731 | 0.0656874295201463 | 0.967156285239927 |
53 | 0.120597706973997 | 0.241195413947995 | 0.879402293026003 |
54 | 0.264549251456340 | 0.529098502912681 | 0.73545074854366 |
55 | 0.369243025913480 | 0.738486051826961 | 0.63075697408652 |
56 | 0.425177000433599 | 0.850354000867198 | 0.574822999566401 |
Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
Description | # significant tests | % significant tests | OK/NOK |
1% type I error level | 36 | 0.878048780487805 | NOK |
5% type I error level | 36 | 0.878048780487805 | NOK |
10% type I error level | 37 | 0.902439024390244 | NOK |