Repository of Reproducible Computations

Multiple Linear Regression - Estimated Regression Equation

K1[t] = + 2.53514 + 0.0442511K2[t] + 0.0677177K3[t] + 0.268577K4[t] + 0.0244293ITH[t] + e[t]

Warning: you did not specify the column number of the endogenous series! The first column was selected by default.

Multiple Linear Regression - Ordinary Least Squares
Variable	Parameter	S.D.	T-STAT H0: parameter = 0	2-tail p-value	1-tail p-value
(Intercept)	+2.535	0.522	+4.8570e+00	3.131e-06	1.566e-06
K2	+0.04425	0.06452	+6.8580e-01	0.494	0.247
K3	+0.06772	0.06343	+1.0680e+00	0.2876	0.1438
K4	+0.2686	0.06586	+4.0780e+00	7.555e-05	3.778e-05
ITH	+0.02443	0.02438	+1.0020e+00	0.318	0.159

Multiple Linear Regression - Regression Statistics
Multiple R	0.3646
R-squared	0.1329
Adjusted R-squared	0.1083
F-TEST (value)	5.403
F-TEST (DF numerator)	4
F-TEST (DF denominator)	141
p-value	0.0004458
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	0.708
Sum Squared Residuals	70.67

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	5	4.399	0.6007
2	4	3.824	0.1765
3	4	4.092	-0.09208
4	5	4.155	0.8448
5	5	4.233	0.7669
6	5	4.02	0.9802
7	5	4.386	0.614
8	5	4.2	0.8002
9	5	4.156	0.8444
10	4	3.917	0.08339
11	5	4.614	0.3864
12	5	4.81	0.1901
13	4	4.356	-0.356
14	5	4.267	0.7334
15	3	4.009	-1.009
16	5	4.673	0.3275
17	3	4.59	-1.59
18	4	4.073	-0.07322
19	4	4.224	-0.2243
20	5	3.892	1.108
21	4	4.405	-0.4049
22	5	3.896	1.104
23	4	4.16	-0.1598
24	4	4.521	-0.5215
25	4	4.478	-0.4782
26	4	4.135	-0.1352
27	5	4.454	0.5462
28	5	4.38	0.6195
29	5	4.625	0.3754
30	5	4.38	0.6195
31	2	4.317	-2.317
32	4	4.203	-0.2031
33	4	4.356	-0.356
34	4	4.181	-0.181
35	5	3.873	1.127
36	5	4.722	0.2777
37	4	4.049	-0.04864
38	4	3.95	0.04989
39	5	4.472	0.5283
40	5	4.404	0.5961
41	4	4.049	-0.04879
42	4	4.453	-0.4528
43	5	4.336	0.6638
44	5	4.361	0.6393
45	5	4.342	0.6582
46	4	4.693	-0.6933
47	5	4.386	0.614
48	4	4.576	-0.5758
49	5	3.61	1.39
50	5	3.868	1.132
51	4	4.405	-0.4049
52	5	4.269	0.7315
53	3	4.38	-1.38
54	3	4.311	-1.311
55	5	4.649	0.3509
56	4	4.151	-0.1506
57	4	4.448	-0.4482
58	5	4.332	0.6684
59	5	4.546	0.4541
60	5	4.307	0.6928
61	4	4.341	-0.3408
62	4	4.467	-0.4671
63	4	4.298	-0.2975
64	5	4.541	0.4587
65	4	4.107	-0.1073
66	4	4.072	-0.07225
67	4	3.917	0.08339
68	4	3.842	0.1576
69	4	3.818	0.1821
70	4	4.589	-0.5892
71	4	4.307	-0.3072
72	5	4.477	0.5228
73	4	4.385	-0.3851
74	5	4.614	0.3864
75	4	4.424	-0.4238
76	4	4.335	-0.3353
77	3	3.842	-0.8424
78	4	4.233	-0.2331
79	2	3.707	-1.707
80	4	4.185	-0.1852
81	5	4.497	0.5029
82	3	4.698	-1.698
83	4	4.356	-0.356
84	5	4.926	0.07354
85	2	4.136	-2.136
86	5	4.372	0.6284
87	5	4.429	0.5707
88	5	4.79	0.2099
89	4	3.785	0.2152
90	5	4.428	0.5716
91	5	4.648	0.3519
92	4	4.448	-0.4482
93	4	4.766	-0.7656
94	5	4.668	0.3321
95	5	4.312	0.6882
96	4	4.239	-0.2385
97	5	4.361	0.6393
98	5	4.453	0.5472
99	4	4.249	-0.2487
100	5	4.809	0.1911
101	5	4.723	0.2767
102	4	4.537	-0.5371
103	4	4.22	-0.2196
104	4	4.312	-0.3118
105	5	4.341	0.6592
106	5	4.77	0.2298
107	4	4.428	-0.4284
108	5	4.405	0.5951
109	5	4.473	0.5274
110	4	3.842	0.1576
111	4	4.405	-0.4049
112	4	3.759	0.2406
113	4	4.585	-0.5846
114	5	4.277	0.7227
115	5	4.58	0.4196
116	4	3.888	0.1124
117	4	4.117	-0.1165
118	3	4.087	-1.087
119	4	4.362	-0.3616
120	5	4.77	0.2298
121	4	4.164	-0.1644
122	4	3.862	0.1378
123	5	4.74	0.2598
124	3	4.244	-1.244
125	4	4.337	-0.3372
126	1	3.804	-2.804
127	5	4.703	0.2975
128	4	4.069	-0.06861
129	5	4.228	0.7715
130	3	3.975	-0.9755
131	4	4.38	-0.3805
132	4	4.312	-0.3118
133	4	4.341	-0.3408
134	5	4.473	0.5274
135	5	4.224	0.7757
136	5	4.643	0.3575
137	5	4.253	0.7471
138	5	4.403	0.597
139	5	4.337	0.6628
140	4	4.657	-0.6573
141	3	4.273	-1.273
142	4	4.521	-0.5215
143	4	3.799	0.2009
144	5	4.784	0.2155
145	4	4.38	-0.3805
146	4	4.019	-0.01879

Goldfeld-Quandt test for Heteroskedasticity
p-values	Alternative Hypothesis
breakpoint index	greater	2-sided	less
8	0.3102	0.6204	0.6898
9	0.1841	0.3682	0.8159
10	0.1007	0.2014	0.8993
11	0.05149	0.103	0.9485
12	0.04201	0.08402	0.958
13	0.1099	0.2198	0.8901
14	0.06654	0.1331	0.9335
15	0.1699	0.3397	0.8301
16	0.1255	0.2509	0.8745
17	0.5199	0.9603	0.4801
18	0.434	0.868	0.566
19	0.3867	0.7735	0.6133
20	0.4169	0.8339	0.5831
21	0.4084	0.8169	0.5916
22	0.4657	0.9313	0.5343
23	0.4384	0.8767	0.5616
24	0.3944	0.7888	0.6056
25	0.3338	0.6675	0.6662
26	0.4669	0.9337	0.5331
27	0.4406	0.8812	0.5594
28	0.4064	0.8127	0.5936
29	0.3564	0.7127	0.6436
30	0.3214	0.6428	0.6786
31	0.8488	0.3023	0.1512
32	0.8295	0.3409	0.1705
33	0.8079	0.3842	0.1921
34	0.7666	0.4669	0.2334
35	0.7936	0.4128	0.2064
36	0.7679	0.4642	0.2321
37	0.7361	0.5278	0.2639
38	0.6918	0.6163	0.3082
39	0.6628	0.6743	0.3372
40	0.64	0.72	0.36
41	0.5898	0.8204	0.4102
42	0.5605	0.879	0.4395
43	0.549	0.902	0.451
44	0.5358	0.9283	0.4642
45	0.5312	0.9376	0.4688
46	0.5308	0.9385	0.4692
47	0.5155	0.969	0.4845
48	0.4981	0.9962	0.5019
49	0.5833	0.8335	0.4167
50	0.6476	0.7048	0.3524
51	0.6192	0.7617	0.3808
52	0.6229	0.7543	0.3771
53	0.7628	0.4745	0.2372
54	0.852	0.296	0.148
55	0.8345	0.3311	0.1655
56	0.81	0.38	0.19
57	0.7885	0.423	0.2115
58	0.7855	0.4289	0.2145
59	0.7671	0.4657	0.2329
60	0.7674	0.4652	0.2326
61	0.7368	0.5263	0.2632
62	0.7139	0.5721	0.2861
63	0.6788	0.6424	0.3212
64	0.6552	0.6897	0.3448
65	0.626	0.7481	0.374
66	0.5835	0.833	0.4165
67	0.5549	0.8902	0.4451
68	0.5185	0.963	0.4815
69	0.4851	0.9702	0.5149
70	0.4687	0.9374	0.5313
71	0.4313	0.8625	0.5687
72	0.4157	0.8313	0.5843
73	0.3817	0.7634	0.6183
74	0.3545	0.709	0.6455
75	0.3245	0.6491	0.6755
76	0.2909	0.5818	0.7091
77	0.3198	0.6396	0.6802
78	0.2818	0.5636	0.7182
79	0.5119	0.9762	0.4881
80	0.4686	0.9372	0.5314
81	0.4469	0.8939	0.5531
82	0.6712	0.6576	0.3288
83	0.6353	0.7294	0.3647
84	0.5923	0.8154	0.4077
85	0.8841	0.2319	0.1159
86	0.8855	0.229	0.1145
87	0.8785	0.243	0.1215
88	0.8536	0.2927	0.1464
89	0.8365	0.3271	0.1635
90	0.8251	0.3497	0.1749
91	0.7979	0.4043	0.2021
92	0.7775	0.445	0.2225
93	0.8	0.4	0.2
94	0.7679	0.4643	0.2321
95	0.7746	0.4508	0.2254
96	0.7358	0.5283	0.2642
97	0.7355	0.5289	0.2645
98	0.7162	0.5676	0.2838
99	0.6728	0.6543	0.3272
100	0.6278	0.7445	0.3722
101	0.5848	0.8304	0.4152
102	0.5532	0.8937	0.4468
103	0.5018	0.9964	0.4982
104	0.4539	0.9078	0.5461
105	0.4618	0.9235	0.5382
106	0.4106	0.8211	0.5894
107	0.377	0.754	0.623
108	0.3675	0.7349	0.6325
109	0.3398	0.6797	0.6602
110	0.2998	0.5995	0.7002
111	0.2619	0.5238	0.7381
112	0.2644	0.5288	0.7356
113	0.2934	0.5868	0.7066
114	0.3056	0.6113	0.6944
115	0.2673	0.5346	0.7327
116	0.2331	0.4662	0.7669
117	0.1968	0.3936	0.8032
118	0.2257	0.4513	0.7743
119	0.1846	0.3693	0.8154
120	0.1467	0.2935	0.8533
121	0.1203	0.2407	0.8797
122	0.0974	0.1948	0.9026
123	0.07241	0.1448	0.9276
124	0.1097	0.2194	0.8903
125	0.08734	0.1747	0.9127
126	0.6163	0.7675	0.3837
127	0.5656	0.8689	0.4344
128	0.484	0.968	0.516
129	0.5168	0.9664	0.4832
130	0.6234	0.7533	0.3766
131	0.5645	0.871	0.4355
132	0.5288	0.9424	0.4712
133	0.4575	0.9149	0.5425
134	0.4235	0.8471	0.5765
135	0.353	0.7061	0.647
136	0.2462	0.4924	0.7538
137	0.5232	0.9537	0.4768
138	0.4601	0.9202	0.5399

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	0	0	OK
10% type I error level	1	0.00763359	OK

Ramsey RESET F-Test for powers (2 and 3) of fitted values

> reset_test_fitted
	RESET test
data:  mylm
RESET = 0.086865, df1 = 2, df2 = 139, p-value = 0.9169

Ramsey RESET F-Test for powers (2 and 3) of regressors

> reset_test_regressors
	RESET test
data:  mylm
RESET = 1.4181, df1 = 8, df2 = 133, p-value = 0.1945

Ramsey RESET F-Test for powers (2 and 3) of principal components

> reset_test_principal_components
	RESET test
data:  mylm
RESET = 1.6438, df1 = 2, df2 = 139, p-value = 0.197

Variance Inflation Factors (Multicollinearity)

> vif
      K2       K3       K4      ITH 
1.044557 1.060569 1.021999 1.010675