Multiple Linear Regression - Estimated Regression Equation
^QP[t] = + 2.70262 + 2.48764`^M`[t] + 0.856761`^M-1`[t] + 1.46887`^M-2`[t] + 0.600318`^M-3`[t] + 0.70018`^Gf`[t] + 0.160499`^Gf-1`[t] -0.472344`^Gf-2`[t] -0.650205`^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)+2.703 0.6306+4.2860e+00 4.689e-05 2.344e-05
`^M`+2.488 0.5122+4.8560e+00 5.226e-06 2.613e-06
`^M-1`+0.8568 0.6882+1.2450e+00 0.2165 0.1082
`^M-2`+1.469 0.6918+2.1230e+00 0.03657 0.01828
`^M-3`+0.6003 0.5432+1.1050e+00 0.2722 0.1361
`^Gf`+0.7002 0.2448+2.8600e+00 0.0053 0.00265
`^Gf-1`+0.1605 0.2663+6.0270e-01 0.5483 0.2741
`^Gf-2`-0.4723 0.2685-1.7590e+00 0.08201 0.04101
`^Gf-3`-0.6502 0.2441-2.6630e+00 0.009219 0.00461


Multiple Linear Regression - Regression Statistics
Multiple R 0.8504
R-squared 0.7232
Adjusted R-squared 0.6977
F-TEST (value) 28.41
F-TEST (DF numerator)8
F-TEST (DF denominator)87
p-value 0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation 3.792
Sum Squared Residuals 1251


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 6.116-0.1156
2 7.5 3.64 3.86
3 7 3.347 3.653
4 1.4 0.6247 0.7753
5-5.4-1.421-3.979
6-3.5 0.4946-3.995
7 1.9-0.32 2.22
8 4.4 1.518 2.882
9 4.4 2.851 1.549
10 9.5 6.343 3.157
11 17.7 9.926 7.774
12 11.5 13.26-1.758
13 14.1 15.89-1.794
14 7.9 12.35-4.452
15 6.7 7.944-1.244
16 4.2 8.02-3.82
17 2.7 6.911-4.211
18 7.2 8.606-1.406
19 9.7 8.787 0.9133
20 9.2 7.528 1.672
21 6.1 5.846 0.2541
22 3.3 7.323-4.023
23-1 3.577-4.577
24-5.3 2.794-8.094
25-0.6 1.192-1.792
26-0.2 0.1006-0.3006
27 4.4 6.619-2.219
28 8.9 11.89-2.986
29 12.6 13.14-0.5381
30 8 9.847-1.847
31 8.6 9.481-0.8814
32 6.2 6.842-0.6417
33 1.8 5.699-3.899
34 5.6 4.702 0.8977
35 5.1 3.824 1.276
36 8.6 4.871 3.729
37 8.1 6.225 1.875
38 2.1 4.108-2.008
39 7.1 1.315 5.785
40-5.4-1.113-4.287
41-7.2 3.154-10.35
42 3.9 7.084-3.184
43 13.2 7.184 6.016
44 13.1 9.354 3.746
45 10 9.324 0.6761
46 10 9.287 0.7131
47 5 9.379-4.379
48 5 3.968 1.032
49 5 2.411 2.589
50 4.3 1.368 2.932
51 1.7 6.365-4.665
52-3.2 3.584-6.784
53 3.4 5.285-1.885
54 11 6.647 4.353
55 9 7.094 1.906
56 14.4 8.967 5.433
57 11.6 9.249 2.351
58 8.5 7.454 1.046
59 6.2 3.286 2.914
60 5.4 5.02 0.3796
61 7.7 7.248 0.4517
62 8.7 6.368 2.332
63 11.1 10.49 0.6089
64 10.6 12.46-1.865
65 12.9 10.22 2.682
66 8.7 7.762 0.9375
67 8.8 10.58-1.784
68 6 13.38-7.384
69 20 12.47 7.534
70 12.9 13.54-0.6449
71 14.7 13.47 1.227
72 20.8 16.58 4.217
73 21.3 15.63 5.668
74 11.5 14.66-3.163
75 10.6 9.22 1.38
76 14.3 7.4 6.9
77 5.8 7.263-1.463
78 7.9 7.918-0.01776
79 17.1 15.49 1.607
80 17.6 15.71 1.887
81 17.9 18.38-0.4803
82 26 19.09 6.91
83 17.7 18.02-0.3151
84 15.4 19.37-3.968
85 20.9 19.47 1.43
86 16.2 17.99-1.79
87 17.9 15.53 2.365
88 6.7 12.8-6.095
89 10 11.17-1.174
90 14.3 9.346 4.954
91 17.3 13.73 3.572
92 22.9 19.19 3.709
93 22.8 22.6 0.2021
94 19.6 24.6-5.003
95 17.7 23.78-6.082
96 19.2 20.79-1.585


Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
12 0.4649 0.9297 0.5351
13 0.3123 0.6245 0.6877
14 0.3677 0.7354 0.6323
15 0.6501 0.6999 0.3499
16 0.5775 0.8449 0.4225
17 0.5052 0.9896 0.4948
18 0.4088 0.8177 0.5912
19 0.3585 0.717 0.6415
20 0.2706 0.5413 0.7294
21 0.1997 0.3993 0.8003
22 0.2107 0.4214 0.7893
23 0.3205 0.6411 0.6795
24 0.6233 0.7535 0.3767
25 0.5686 0.8628 0.4314
26 0.5021 0.9958 0.4979
27 0.4992 0.9984 0.5008
28 0.5458 0.9084 0.4542
29 0.4764 0.9529 0.5236
30 0.408 0.816 0.592
31 0.3387 0.6775 0.6613
32 0.2756 0.5513 0.7244
33 0.2654 0.5308 0.7346
34 0.2134 0.4269 0.7866
35 0.1775 0.355 0.8225
36 0.1784 0.3569 0.8216
37 0.1416 0.2831 0.8584
38 0.1149 0.2297 0.8851
39 0.1563 0.3127 0.8437
40 0.1694 0.3389 0.8306
41 0.5723 0.8554 0.4277
42 0.5625 0.875 0.4375
43 0.6129 0.7742 0.3871
44 0.6064 0.7872 0.3936
45 0.5486 0.9028 0.4514
46 0.4866 0.9731 0.5134
47 0.5111 0.9778 0.4889
48 0.453 0.9061 0.547
49 0.4682 0.9363 0.5318
50 0.4359 0.8718 0.5641
51 0.529 0.9419 0.471
52 0.6964 0.6072 0.3036
53 0.7105 0.5789 0.2895
54 0.707 0.5859 0.293
55 0.667 0.6661 0.333
56 0.6878 0.6245 0.3122
57 0.6399 0.7203 0.3601
58 0.5933 0.8133 0.4067
59 0.5697 0.8606 0.4303
60 0.5876 0.8249 0.4124
61 0.5246 0.9508 0.4754
62 0.4691 0.9382 0.5309
63 0.4091 0.8182 0.5909
64 0.4324 0.8648 0.5676
65 0.4263 0.8525 0.5737
66 0.3578 0.7156 0.6422
67 0.3767 0.7535 0.6233
68 0.5946 0.8108 0.4054
69 0.7488 0.5025 0.2512
70 0.721 0.5581 0.279
71 0.6729 0.6542 0.3271
72 0.6634 0.6731 0.3366
73 0.8049 0.3903 0.1951
74 0.7519 0.4963 0.2481
75 0.6881 0.6237 0.3119
76 0.7221 0.5558 0.2779
77 0.6419 0.7162 0.3581
78 0.7992 0.4016 0.2008
79 0.7134 0.5733 0.2866
80 0.8102 0.3796 0.1898
81 0.7253 0.5494 0.2747
82 0.8205 0.359 0.1795
83 0.9969 0.006174 0.003087
84 0.9842 0.03163 0.01581


Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level1 0.0137NOK
5% type I error level20.0273973OK
10% type I error level20.0273973OK


Ramsey RESET F-Test for powers (2 and 3) of fitted values
> reset_test_fitted
	RESET test
data:  mylm
RESET = 1.7749, df1 = 2, df2 = 85, p-value = 0.1757
Ramsey RESET F-Test for powers (2 and 3) of regressors
> reset_test_regressors
	RESET test
data:  mylm
RESET = 1.1593, df1 = 16, df2 = 71, p-value = 0.3215
Ramsey RESET F-Test for powers (2 and 3) of principal components
> reset_test_principal_components
	RESET test
data:  mylm
RESET = 1.3781, df1 = 2, df2 = 85, p-value = 0.2576


Variance Inflation Factors (Multicollinearity)
> vif
    `^M`   `^M-1`   `^M-2`   `^M-3`    `^Gf`  `^Gf-1`  `^Gf-2`  `^Gf-3` 
2.579924 4.645671 4.464674 2.517397 1.568928 1.860056 1.896317 1.557756