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Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R ServerBig Analytics Cloud Computing Center


Multiple Linear Regression - Estimated Regression Equation
^QP[t] = + 2.06431 + 3.03212`^M`[t] + 0.778347`^M-1`[t] + 1.13663`^M-2`[t] + 1.17912`^M-3`[t] + 0.70932`^Gf`[t] + 0.11159`^Gf-1`[t] -0.505465`^Gf-2`[t] -0.573649`^Gf-3`[t] + e[t]


Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STAT
H0: parameter = 0
2-tail p-value1-tail p-value
(Intercept)+2.064 0.6345+3.2540e+00 0.0016 0.0007999
`^M`+3.032 0.4917+6.1660e+00 1.894e-08 9.468e-09
`^M-1`+0.7783 0.6573+1.1840e+00 0.2395 0.1197
`^M-2`+1.137 0.6554+1.7340e+00 0.08626 0.04313
`^M-3`+1.179 0.527+2.2370e+00 0.0277 0.01385
`^Gf`+0.7093 0.2403+2.9520e+00 0.004012 0.002006
`^Gf-1`+0.1116 0.2591+4.3070e-01 0.6677 0.3339
`^Gf-2`-0.5055 0.2664-1.8970e+00 0.06097 0.03049
`^Gf-3`-0.5736 0.2407-2.3830e+00 0.01924 0.009619


Multiple Linear Regression - Regression Statistics
Multiple R 0.8849
R-squared 0.7831
Adjusted R-squared 0.7641
F-TEST (value) 41.08
F-TEST (DF numerator)8
F-TEST (DF denominator)91
p-value 0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation 3.979
Sum Squared Residuals 1441


Menu of Residual Diagnostics
DescriptionLink
HistogramCompute
Central TendencyCompute
QQ PlotCompute
Kernel Density PlotCompute
Skewness/Kurtosis TestCompute
Skewness-Kurtosis PlotCompute
Harrell-Davis PlotCompute
Bootstrap Plot -- Central TendencyCompute
Blocked Bootstrap Plot -- Central TendencyCompute
(Partial) Autocorrelation PlotCompute
Spectral AnalysisCompute
Tukey lambda PPCC PlotCompute
Box-Cox Normality PlotCompute
Summary StatisticsCompute


Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolation
Forecast
Residuals
Prediction Error
1 6 6.08-0.07985
2 7.5 2.794 4.706
3 7 3.081 3.919
4 1.4 0.05464 1.345
5-5.4-2.998-2.402
6-3.5 0.1493-3.649
7 1.9-0.927 2.827
8 4.4 0.4786 3.921
9 4.4 2.932 1.468
10 9.5 6.436 3.064
11 17.7 9.63 8.07
12 11.5 13.02-1.516
13 14.1 16.18-2.075
14 7.9 12.14-4.24
15 6.7 7.904-1.204
16 4.2 9.193-4.993
17 2.7 7.156-4.456
18 7.2 8.522-1.322
19 9.7 9.761-0.06114
20 9.2 8.045 1.155
21 6.1 5.724 0.3763
22 3.3 7.342-4.042
23-1 3.529-4.529
24-5.3 2.498-7.798
25-0.6 1.149-1.749
26-0.2-0.3086 0.1086
27 4.4 7.034-2.634
28 8.9 11.97-3.071
29 12.6 12.64-0.04006
30 8 9.65-1.65
31 8.6 9.379-0.7791
32 6.2 6.923-0.7226
33 1.8 5.446-3.646
34 5.6 4.458 1.142
35 5.1 3.155 1.945
36 8.6 4.784 3.816
37 8.1 5.917 2.183
38 2.1 3.053-0.9532
39 7.1 0.8902 6.21
40-5.4-1.649-3.751
41-7.2 2.483-9.683
42 3.9 7.418-3.518
43 13.2 6.732 6.468
44 13.1 9.028 4.072
45 10 9.963 0.03688
46 10 9.5 0.5003
47 5 9.766-4.766
48 5 3.146 1.854
49 5 2.063 2.937
50 4.3 1.616 2.684
51 1.7 5.845-4.145
52-3.2 2.498-5.698
53 3.4 4.427-1.027
54 11 7.416 3.584
55 9 6.469 2.531
56 14.4 8.997 5.403
57 11.6 9.367 2.233
58 8.5 7.158 1.342
59 6.2 2.987 3.213
60 5.4 5.257 0.1432
61 7.7 7.915-0.2152
62 8.7 6.057 2.643
63 11.1 10.67 0.4273
64 10.6 12.95-2.352
65 12.9 10.06 2.837
66 8.7 8.065 0.6353
67 8.8 11.87-3.066
68 6 14.28-8.277
69 20 12.08 7.924
70 12.9 13.88-0.9798
71 14.7 14.84-0.1429
72 20.8 17.66 3.144
73 21.3 16.16 5.139
74 11.5 14.82-3.319
75 10.6 9.064 1.536
76 14.3 7.964 6.336
77 5.8 8.793-2.993
78 7.9 8.026-0.1257
79 17.1 16.47 0.6322
80 17.6 16.8 0.8007
81 17.9 18.84-0.9369
82 26 21.32 4.677
83 17.7 19.93-2.232
84 15.4 21.12-5.72
85 20.9 21.25-0.3515
86 16.2 18.76-2.563
87 17.9 16.53 1.368
88 6.7 14.3-7.603
89 10 12.22-2.215
90 14.3 9.424 4.876
91 17.3 14.73 2.565
92 22.9 21.3 1.596
93 22.8 23.44-0.6394
94 19.6 26.32-6.722
95 17.7 25.96-8.262
96 19.2 21.54-2.338
97 36.6 30.51 6.09
98 29.3 23.31 5.987
99 24.4 22.72 1.683
100 37.4 30.3 7.098


Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
12 0.4252 0.8504 0.5748
13 0.2754 0.5508 0.7246
14 0.3181 0.6362 0.6819
15 0.5846 0.8307 0.4154
16 0.5122 0.9755 0.4878
17 0.4363 0.8725 0.5637
18 0.341 0.682 0.659
19 0.2933 0.5867 0.7067
20 0.2133 0.4266 0.7867
21 0.1517 0.3034 0.8483
22 0.1575 0.3151 0.8425
23 0.2447 0.4894 0.7553
24 0.5122 0.9757 0.4878
25 0.4537 0.9074 0.5463
26 0.3893 0.7785 0.6107
27 0.3853 0.7707 0.6147
28 0.429 0.8579 0.571
29 0.365 0.73 0.635
30 0.3011 0.6022 0.6989
31 0.2404 0.4808 0.7596
32 0.188 0.3759 0.812
33 0.1741 0.3482 0.8259
34 0.1347 0.2694 0.8653
35 0.1097 0.2194 0.8903
36 0.1102 0.2205 0.8898
37 0.08457 0.1691 0.9154
38 0.06235 0.1247 0.9376
39 0.09117 0.1823 0.9088
40 0.0925 0.185 0.9075
41 0.3557 0.7114 0.6443
42 0.3373 0.6746 0.6627
43 0.3918 0.7836 0.6082
44 0.3894 0.7787 0.6106
45 0.3358 0.6716 0.6642
46 0.2817 0.5634 0.7183
47 0.2899 0.5799 0.7101
48 0.2539 0.5078 0.7461
49 0.271 0.5419 0.729
50 0.2522 0.5045 0.7478
51 0.2741 0.5482 0.7259
52 0.3503 0.7005 0.6497
53 0.3114 0.6228 0.6886
54 0.3013 0.6025 0.6987
55 0.2668 0.5337 0.7332
56 0.3017 0.6034 0.6983
57 0.2634 0.5269 0.7366
58 0.2218 0.4437 0.7782
59 0.2247 0.4494 0.7753
60 0.2094 0.4187 0.7906
61 0.17 0.34 0.83
62 0.1517 0.3034 0.8483
63 0.1173 0.2345 0.8827
64 0.1035 0.207 0.8965
65 0.1124 0.2248 0.8876
66 0.08722 0.1744 0.9128
67 0.08522 0.1704 0.9148
68 0.155 0.3099 0.845
69 0.3582 0.7164 0.6418
70 0.2956 0.5912 0.7044
71 0.2521 0.5043 0.7479
72 0.2499 0.4997 0.7501
73 0.28 0.56 0.72
74 0.2381 0.4763 0.7619
75 0.1903 0.3805 0.8097
76 0.2017 0.4033 0.7983
77 0.1567 0.3135 0.8433
78 0.1794 0.3588 0.8206
79 0.1306 0.2613 0.8694
80 0.142 0.284 0.858
81 0.1013 0.2027 0.8987
82 0.07708 0.1542 0.9229
83 0.06935 0.1387 0.9306
84 0.2164 0.4328 0.7836
85 0.184 0.368 0.816
86 0.4736 0.9473 0.5264
87 0.473 0.9459 0.527
88 0.3362 0.6724 0.6638


Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level0 0OK
5% type I error level00OK
10% type I error level00OK


Ramsey RESET F-Test for powers (2 and 3) of fitted values
> reset_test_fitted
	RESET test
data:  mylm
RESET = 2.3145, df1 = 2, df2 = 89, p-value = 0.1047
Ramsey RESET F-Test for powers (2 and 3) of regressors
> reset_test_regressors
	RESET test
data:  mylm
RESET = 1.1975, df1 = 16, df2 = 75, p-value = 0.2902
Ramsey RESET F-Test for powers (2 and 3) of principal components
> reset_test_principal_components
	RESET test
data:  mylm
RESET = 1.9343, df1 = 2, df2 = 89, p-value = 0.1506


Variance Inflation Factors (Multicollinearity)
> vif
    `^M`   `^M-1`   `^M-2`   `^M-3`    `^Gf`  `^Gf-1`  `^Gf-2`  `^Gf-3` 
2.931005 4.689156 4.304951 2.674322 1.486434 1.731101 1.790882 1.460023 












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