Repository of Reproducible Computations

Multiple Linear Regression - Estimated Regression Equation

K1[t] = + 2.38799 + 0.0420172K2[t] + 0.0566008K3[t] + 0.28681K4[t] + 0.028565ITH[t] -0.00507587`K1(t-1)`[t] + 0.117242`K1(t-2)`[t] -0.0113644`K1(t-3)`[t] -0.0636007`K1(t-4)`[t] -0.0287444`K1(t-5)`[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)	+2.388	0.9595	+2.4890e+00	0.01407	0.007035
K2	+0.04202	0.0666	+6.3090e-01	0.5292	0.2646
K3	+0.0566	0.06659	+8.4990e-01	0.3969	0.1985
K4	+0.2868	0.06863	+4.1790e+00	5.309e-05	2.655e-05
ITH	+0.02857	0.02524	+1.1320e+00	0.2597	0.1299
`K1(t-1)`	-0.005076	0.08109	-6.2600e-02	0.9502	0.4751
`K1(t-2)`	+0.1172	0.08101	+1.4470e+00	0.1502	0.07511
`K1(t-3)`	-0.01136	0.08154	-1.3940e-01	0.8894	0.4447
`K1(t-4)`	-0.0636	0.08208	-7.7490e-01	0.4398	0.2199
`K1(t-5)`	-0.02874	0.08172	-3.5170e-01	0.7256	0.3628

Multiple Linear Regression - Regression Statistics
Multiple R	0.3938
R-squared	0.1551
Adjusted R-squared	0.09701
F-TEST (value)	2.671
F-TEST (DF numerator)	9
F-TEST (DF denominator)	131
p-value	0.007034
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	0.7178
Sum Squared Residuals	67.5

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	5	4.075	0.9246
2	5	4.494	0.5061
3	5	4.232	0.768
4	5	4.161	0.8388
5	4	3.885	0.1155
6	5	4.605	0.395
7	5	4.698	0.3023
8	4	4.355	-0.3552
9	5	4.315	0.6855
10	3	3.881	-0.8812
11	5	4.695	0.3047
12	3	4.448	-1.448
13	4	4.134	-0.1343
14	4	4.13	-0.1296
15	5	3.824	1.176
16	4	4.422	-0.4223
17	5	3.995	1.005
18	4	4.104	-0.1039
19	4	4.56	-0.5599
20	4	4.438	-0.4381
21	4	4.001	-0.0007358
22	5	4.421	0.5791
23	5	4.359	0.6411
24	5	4.734	0.2656
25	5	4.465	0.5352
26	2	4.36	-2.36
27	4	4.172	-0.172
28	4	3.997	0.00279
29	4	4.126	-0.1257
30	5	3.946	1.054
31	5	4.789	0.2111
32	4	4.12	-0.1204
33	4	4.013	-0.01331
34	5	4.36	0.6398
35	5	4.281	0.7189
36	4	4.119	-0.1191
37	4	4.542	-0.5416
38	5	4.247	0.753
39	5	4.253	0.7469
40	5	4.434	0.5655
41	4	4.794	-0.7936
42	5	4.435	0.5647
43	4	4.456	-0.4563
44	5	3.588	1.412
45	5	3.821	1.179
46	4	4.441	-0.4411
47	5	4.342	0.6575
48	3	4.284	-1.284
49	3	4.309	-1.309
50	5	4.498	0.5015
51	4	3.916	0.08447
52	4	4.584	-0.584
53	5	4.388	0.6122
54	5	4.495	0.5051
55	5	4.362	0.6383
56	4	4.438	-0.4379
57	4	4.462	-0.4623
58	4	4.205	-0.2053
59	5	4.427	0.5726
60	4	4.028	-0.02823
61	4	4.168	-0.1675
62	4	3.865	0.1353
63	4	3.713	0.2872
64	4	3.719	0.2809
65	4	4.563	-0.5629
66	4	4.278	-0.2783
67	5	4.464	0.5358
68	4	4.374	-0.374
69	5	4.709	0.2913
70	4	4.376	-0.3756
71	4	4.362	-0.3616
72	3	3.736	-0.7363
73	4	4.147	-0.1475
74	2	3.517	-1.517
75	4	4.184	-0.1844
76	5	4.307	0.6932
77	3	4.754	-1.754
78	4	4.585	-0.5849
79	5	4.849	0.1509
80	2	4.048	-2.048
81	5	4.544	0.4565
82	5	4.199	0.8011
83	5	4.864	0.1356
84	4	3.963	0.03677
85	5	4.507	0.4931
86	5	4.528	0.472
87	4	4.44	-0.4404
88	4	4.842	-0.8416
89	5	4.575	0.4247
90	5	4.196	0.804
91	4	4.291	-0.2911
92	5	4.456	0.5436
93	5	4.356	0.6444
94	4	4.272	-0.2717
95	5	4.87	0.1303
96	5	4.67	0.3296
97	4	4.572	-0.572
98	4	4.285	-0.2854
99	4	4.218	-0.2184
100	5	4.245	0.7553
101	5	4.746	0.2542
102	4	4.519	-0.5193
103	5	4.498	0.5016
104	5	4.369	0.6309
105	4	3.796	0.2038
106	4	4.47	-0.4697
107	4	3.646	0.3535
108	4	4.455	-0.4554
109	5	4.219	0.7807
110	5	4.575	0.4249
111	4	3.945	0.05547
112	4	4.198	-0.1981
113	3	3.974	-0.9736
114	4	4.277	-0.2772
115	5	4.634	0.3664
116	4	4.142	-0.1417
117	4	3.971	0.02934
118	5	4.739	0.2607
119	3	4.168	-1.168
120	4	4.43	-0.4295
121	1	3.635	-2.635
122	5	4.686	0.314
123	4	3.727	0.2728
124	5	4.371	0.629
125	3	4.124	-1.124
126	4	4.509	-0.5089
127	4	4.136	-0.136
128	4	4.285	-0.2848
129	5	4.484	0.516
130	5	4.247	0.753
131	5	4.72	0.2801
132	5	4.32	0.6797
133	5	4.402	0.5982
134	5	4.344	0.6556
135	4	4.675	-0.6755
136	3	4.246	-1.246
137	4	4.408	-0.4076
138	4	3.539	0.4613
139	5	4.747	0.2534
140	4	4.422	-0.4225
141	4	4.124	-0.124

Goldfeld-Quandt test for Heteroskedasticity
p-values	Alternative Hypothesis
breakpoint index	greater	2-sided	less
13	0.3169	0.6338	0.6831
14	0.2156	0.4311	0.7844
15	0.6368	0.7264	0.3632
16	0.5182	0.9635	0.4818
17	0.4282	0.8563	0.5718
18	0.3699	0.7398	0.6301
19	0.4128	0.8256	0.5872
20	0.3213	0.6426	0.6787
21	0.4192	0.8384	0.5808
22	0.4509	0.9018	0.5491
23	0.4174	0.8349	0.5826
24	0.3552	0.7104	0.6448
25	0.2885	0.5769	0.7115
26	0.8975	0.2051	0.1025
27	0.8772	0.2456	0.1228
28	0.8771	0.2458	0.1229
29	0.8401	0.3197	0.1599
30	0.8189	0.3622	0.1811
31	0.7787	0.4427	0.2213
32	0.7776	0.4448	0.2224
33	0.7368	0.5265	0.2632
34	0.7287	0.5425	0.2713
35	0.7163	0.5674	0.2837
36	0.6721	0.6558	0.3279
37	0.6596	0.6808	0.3404
38	0.6863	0.6274	0.3137
39	0.6847	0.6307	0.3153
40	0.6563	0.6875	0.3437
41	0.6554	0.6892	0.3446
42	0.657	0.686	0.343
43	0.6157	0.7685	0.3843
44	0.7026	0.5947	0.2974
45	0.7694	0.4612	0.2306
46	0.7435	0.5129	0.2565
47	0.7328	0.5344	0.2672
48	0.8075	0.3849	0.1925
49	0.8939	0.2122	0.1061
50	0.8809	0.2382	0.1191
51	0.8535	0.2929	0.1465
52	0.8502	0.2997	0.1498
53	0.8333	0.3334	0.1667
54	0.8222	0.3555	0.1778
55	0.8175	0.3651	0.1825
56	0.7924	0.4151	0.2076
57	0.768	0.4641	0.232
58	0.7292	0.5416	0.2708
59	0.715	0.5699	0.285
60	0.6826	0.6349	0.3174
61	0.6444	0.7113	0.3556
62	0.6098	0.7804	0.3902
63	0.5724	0.8552	0.4276
64	0.5382	0.9235	0.4618
65	0.52	0.96	0.48
66	0.4824	0.9647	0.5176
67	0.4601	0.9203	0.5399
68	0.422	0.8439	0.578
69	0.383	0.7659	0.617
70	0.3461	0.6922	0.6539
71	0.3088	0.6175	0.6912
72	0.3217	0.6434	0.6783
73	0.2804	0.5609	0.7196
74	0.4566	0.9132	0.5434
75	0.4167	0.8334	0.5833
76	0.4104	0.8208	0.5896
77	0.6473	0.7054	0.3527
78	0.6339	0.7321	0.3661
79	0.5936	0.8127	0.4064
80	0.8689	0.2623	0.1311
81	0.8745	0.2509	0.1255
82	0.8685	0.2629	0.1315
83	0.8568	0.2864	0.1432
84	0.8406	0.3189	0.1594
85	0.8185	0.3631	0.1815
86	0.7961	0.4079	0.2039
87	0.7814	0.4372	0.2186
88	0.796	0.4079	0.204
89	0.7673	0.4654	0.2327
90	0.7784	0.4433	0.2216
91	0.7375	0.5249	0.2625
92	0.7359	0.5283	0.2641
93	0.7216	0.5569	0.2784
94	0.677	0.6461	0.323
95	0.6266	0.7469	0.3734
96	0.5793	0.8414	0.4207
97	0.5704	0.8592	0.4296
98	0.5195	0.9611	0.4805
99	0.4655	0.9311	0.5345
100	0.4758	0.9516	0.5242
101	0.4239	0.8478	0.5761
102	0.4137	0.8274	0.5863
103	0.4052	0.8104	0.5948
104	0.391	0.782	0.609
105	0.3375	0.6749	0.6625
106	0.2927	0.5854	0.7073
107	0.347	0.694	0.653
108	0.3558	0.7116	0.6442
109	0.369	0.7379	0.631
110	0.315	0.6301	0.685
111	0.2594	0.5188	0.7406
112	0.2288	0.4577	0.7712
113	0.2217	0.4434	0.7783
114	0.174	0.3481	0.826
115	0.1358	0.2716	0.8642
116	0.09963	0.1993	0.9004
117	0.07804	0.1561	0.922
118	0.05686	0.1137	0.9431
119	0.1529	0.3058	0.8471
120	0.1204	0.2408	0.8796
121	0.4736	0.9473	0.5264
122	0.5299	0.9402	0.4701
123	0.471	0.942	0.529
124	0.3772	0.7543	0.6228
125	0.38	0.7599	0.62
126	0.2697	0.5394	0.7303
127	0.1936	0.3872	0.8064
128	0.1092	0.2184	0.8908

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	0	0	OK

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

> reset_test_fitted
	RESET test
data:  mylm
RESET = 0.30653, df1 = 2, df2 = 129, p-value = 0.7365

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

> reset_test_regressors
	RESET test
data:  mylm
RESET = 1.3639, df1 = 18, df2 = 113, p-value = 0.1637

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

> reset_test_principal_components
	RESET test
data:  mylm
RESET = 1.1847, df1 = 2, df2 = 129, p-value = 0.3091

Variance Inflation Factors (Multicollinearity)

> vif
       K2        K3        K4       ITH `K1(t-1)` `K1(t-2)` `K1(t-3)` `K1(t-4)` 
 1.072192  1.121545  1.035371  1.027422  1.024381  1.027083  1.035669  1.049466 
`K1(t-5)` 
 1.045113