Repository of Reproducible Computations

Multiple Linear Regression - Estimated Regression Equation

ITHSUM[t] = + 9.42232 + 0.291481SK1[t] + 0.376166SK3[t] + 0.392351SK4[t] + 0.374714SK5[t] + 0.286452SK6[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)	+9.422	2.51	+3.7540e+00	0.0002451	0.0001226
SK1	+0.2915	0.2677	+1.0890e+00	0.2779	0.1389
SK3	+0.3762	0.2447	+1.5370e+00	0.1263	0.06313
SK4	+0.3923	0.334	+1.1750e+00	0.2419	0.1209
SK5	+0.3747	0.3185	+1.1760e+00	0.2412	0.1206
SK6	+0.2864	0.3304	+8.6700e-01	0.3873	0.1936

Multiple Linear Regression - Regression Statistics
Multiple R	0.2264
R-squared	0.05127
Adjusted R-squared	0.02086
F-TEST (value)	1.686
F-TEST (DF numerator)	5
F-TEST (DF denominator)	156
p-value	0.1411
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	2.444
Sum Squared Residuals	932.1

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	14	16.29	-2.289
2	19	16.6	2.403
3	17	17.06	-0.05786
4	17	15.25	1.753
5	15	17.06	-2.058
6	20	16.68	3.323
7	15	15.25	-0.2484
8	19	16.39	2.608
9	15	16.97	-1.968
10	15	17.34	-2.344
11	19	15.93	3.071
12	20	16.2	3.799
13	18	16.68	1.322
14	15	16.22	-1.22
15	14	16.68	-2.678
16	20	16.68	3.322
17	16	16.21	-0.2061
18	16	16.68	-0.6817
19	16	16.29	-0.2858
20	10	16.97	-6.968
21	19	16.97	2.03
22	19	16.68	2.317
23	16	16.97	-0.9696
24	15	16.02	-1.016
25	18	16.28	1.716
26	17	16.31	0.693
27	19	16.76	2.239
28	17	16.6	0.4015
29	19	17.34	1.656
30	20	17.26	2.739
31	5	17.34	-12.34
32	19	16.47	2.525
33	16	15.55	0.4454
34	15	16.39	-1.392
35	16	16.58	-0.5772
36	18	15.93	2.069
37	16	16.68	-0.6831
38	15	16.6	-1.598
39	17	17.34	-0.3443
40	20	17.24	2.757
41	19	16.58	2.418
42	7	16.2	-9.201
43	13	16.31	-3.307
44	16	15.62	0.3754
45	16	16.68	-0.6817
46	18	16.68	1.317
47	18	16.22	1.779
48	16	16.97	-0.9746
49	17	17.34	-0.3443
50	19	16.2	2.799
51	16	16.68	-0.6831
52	19	15.25	3.752
53	13	15.73	-2.729
54	16	16.29	-0.2893
55	13	16.68	-3.682
56	12	16.88	-4.883
57	17	16.39	0.6148
58	17	16.97	0.03185
59	17	15.27	1.734
60	16	17.34	-1.344
61	16	16.31	-0.307
62	14	16	-2.003
63	16	16.29	-0.2893
64	13	16.49	-3.494
65	16	16.28	-0.2843
66	14	15.91	-1.91
67	20	17.45	2.55
68	12	15.93	-3.931
69	13	16.31	-3.307
70	18	17.07	0.926
71	14	15.64	-1.639
72	19	16.68	2.318
73	18	16.66	1.34
74	14	16.68	-2.678
75	18	16.68	1.317
76	19	16.97	2.03
77	15	15.64	-0.6393
78	14	16.68	-2.682
79	17	16.59	0.408
80	19	16.97	2.032
81	13	16.6	-3.598
82	19	16.9	2.099
83	18	17.34	0.6557
84	20	16.68	3.322
85	15	16.02	-1.016
86	15	15.54	-0.5385
87	15	16.4	-1.397
88	20	16.97	3.03
89	15	16.68	-1.682
90	19	16.4	2.605
91	18	16.28	1.716
92	18	16.97	1.03
93	15	16.51	-1.509
94	20	17.65	2.347
95	17	16.97	0.03185
96	12	16.68	-4.678
97	18	17.26	0.7404
98	19	16.97	2.03
99	20	16.88	3.115
100	17	17.65	-0.652
101	15	16.95	-1.952
102	16	15.25	0.748
103	18	16.68	1.317
104	18	16.68	1.317
105	14	16.48	-2.48
106	15	16.31	-1.307
107	12	16.2	-4.201
108	17	16.28	0.7157
109	14	15.91	-1.915
110	18	16.39	1.608
111	17	16.31	0.6916
112	17	16.46	0.5413
113	20	17.64	2.364
114	16	16.02	-0.02053
115	14	16.29	-2.291
116	15	15.91	-0.9096
117	18	16.31	1.693
118	20	16.68	3.318
119	17	15.93	1.069
120	17	16.02	0.9845
121	17	15.91	1.085
122	17	16.59	0.4066
123	15	15.25	-0.247
124	17	15.63	1.372
125	18	15.23	2.769
126	17	16.29	0.7107
127	20	16.58	3.419
128	15	15.24	-0.2434
129	16	16.02	-0.0155
130	15	15.91	-0.9146
131	18	16.97	1.027
132	15	16.68	-1.683
133	18	17.74	0.2583
134	20	17.34	2.656
135	19	16.2	2.799
136	14	16.77	-2.766
137	16	16.68	-0.6831
138	15	15.55	-0.5546
139	17	16.59	0.408
140	18	16.97	1.032
141	20	16.96	3.043
142	17	16.68	0.3169
143	18	16.68	1.317
144	15	14.87	0.1292
145	16	16.4	-0.3967
146	11	15.91	-4.915
147	15	16.59	-1.593
148	18	16.66	1.34
149	17	16.97	0.0304
150	16	17.35	-1.349
151	12	16.31	-4.308
152	19	16.1	2.9
153	18	16.59	1.407
154	15	16.58	-1.576
155	17	16.02	0.9795
156	19	17.08	1.925
157	18	16.22	1.778
158	19	16.21	2.794
159	16	15.55	0.4518
160	16	16.59	-0.5934
161	16	16.68	-0.6817
162	14	16.49	-2.491

Goldfeld-Quandt test for Heteroskedasticity
p-values	Alternative Hypothesis
breakpoint index	greater	2-sided	less
9	0.2115	0.423	0.7885
10	0.129	0.2579	0.871
11	0.1801	0.3601	0.8199
12	0.6002	0.7997	0.3998
13	0.485	0.97	0.515
14	0.4765	0.9529	0.5235
15	0.5313	0.9373	0.4687
16	0.5751	0.8498	0.4249
17	0.4981	0.9962	0.5019
18	0.4243	0.8486	0.5757
19	0.3414	0.6828	0.6586
20	0.8273	0.3453	0.1727
21	0.8392	0.3216	0.1608
22	0.8292	0.3416	0.1708
23	0.7811	0.4378	0.2189
24	0.7812	0.4376	0.2188
25	0.7481	0.5038	0.2519
26	0.6916	0.6167	0.3084
27	0.6563	0.6874	0.3437
28	0.5996	0.8009	0.4004
29	0.5925	0.815	0.4075
30	0.6391	0.7218	0.3609
31	0.9991	0.001732	0.0008659
32	0.9989	0.002123	0.001061
33	0.9986	0.002863	0.001431
34	0.9982	0.003534	0.001767
35	0.9973	0.005398	0.002699
36	0.9964	0.007129	0.003564
37	0.9948	0.01042	0.005208
38	0.9931	0.01374	0.006872
39	0.9906	0.01884	0.009419
40	0.9936	0.01288	0.006441
41	0.9931	0.01387	0.006937
42	1	7.514e-05	3.757e-05
43	1	4.917e-05	2.458e-05
44	1	8.146e-05	4.073e-05
45	0.9999	0.0001308	6.54e-05
46	0.9999	0.0001923	9.616e-05
47	0.9999	0.0002456	0.0001228
48	0.9998	0.0003711	0.0001856
49	0.9997	0.0005674	0.0002837
50	0.9997	0.0005051	0.0002526
51	0.9996	0.0007621	0.0003811
52	0.9997	0.0005368	0.0002684
53	0.9998	0.0004048	0.0002024
54	0.9997	0.0006243	0.0003122
55	0.9998	0.000383	0.0001915
56	0.9999	0.0001084	5.42e-05
57	0.9999	0.0001713	8.566e-05
58	0.9999	0.0002632	0.0001316
59	0.9999	0.0002858	0.0001429
60	0.9998	0.0003695	0.0001848
61	0.9997	0.0005728	0.0002864
62	0.9997	0.0006181	0.000309
63	0.9995	0.0009254	0.0004627
64	0.9997	0.0006332	0.0003166
65	0.9995	0.0009514	0.0004757
66	0.9995	0.001078	0.000539
67	0.9995	0.001011	0.0005054
68	0.9998	0.0004958	0.0002479
69	0.9998	0.0003319	0.000166
70	0.9998	0.0004824	0.0002412
71	0.9997	0.0006046	0.0003023
72	0.9997	0.0006331	0.0003166
73	0.9996	0.0008567	0.0004283
74	0.9996	0.0007675	0.0003838
75	0.9995	0.001033	0.0005163
76	0.9994	0.001147	0.0005736
77	0.9992	0.001672	0.0008361
78	0.9993	0.001405	0.0007026
79	0.999	0.002013	0.001007
80	0.9989	0.002286	0.001143
81	0.9994	0.001202	0.0006009
82	0.9993	0.001352	0.0006761
83	0.999	0.001955	0.0009774
84	0.9994	0.001241	0.0006204
85	0.9991	0.001745	0.0008724
86	0.9987	0.002506	0.001253
87	0.9984	0.003182	0.001591
88	0.9988	0.002436	0.001218
89	0.9987	0.002688	0.001344
90	0.9987	0.002669	0.001335
91	0.9984	0.003146	0.001573
92	0.9979	0.004265	0.002132
93	0.9977	0.004573	0.002286
94	0.9975	0.00491	0.002455
95	0.9965	0.007065	0.003533
96	0.9988	0.002435	0.001217
97	0.9983	0.003498	0.001749
98	0.998	0.003906	0.001953
99	0.9984	0.003191	0.001596
100	0.9979	0.004225	0.002112
101	0.9979	0.004232	0.002116
102	0.997	0.006028	0.003014
103	0.9961	0.007805	0.003903
104	0.995	0.009996	0.004998
105	0.9957	0.008558	0.004279
106	0.9946	0.0108	0.005399
107	0.9981	0.003719	0.001859
108	0.9973	0.005497	0.002749
109	0.9972	0.00557	0.002785
110	0.9968	0.006412	0.003206
111	0.9957	0.00869	0.004345
112	0.9948	0.01048	0.005238
113	0.9938	0.0124	0.006198
114	0.991	0.01803	0.009016
115	0.9924	0.01519	0.007596
116	0.99	0.01994	0.00997
117	0.9882	0.02359	0.0118
118	0.991	0.01802	0.009008
119	0.988	0.02397	0.01198
120	0.9849	0.03022	0.01511
121	0.9791	0.04179	0.02089
122	0.9708	0.05833	0.02916
123	0.9601	0.07985	0.03993
124	0.9491	0.1018	0.05092
125	0.9497	0.1005	0.05026
126	0.9324	0.1352	0.0676
127	0.9387	0.1226	0.06132
128	0.9184	0.1633	0.08164
129	0.8936	0.2127	0.1064
130	0.8669	0.2662	0.1331
131	0.8312	0.3376	0.1688
132	0.8079	0.3843	0.1921
133	0.7597	0.4807	0.2403
134	0.7533	0.4934	0.2467
135	0.7656	0.4687	0.2344
136	0.7869	0.4263	0.2131
137	0.7352	0.5296	0.2648
138	0.6736	0.6528	0.3264
139	0.604	0.792	0.396
140	0.536	0.9281	0.4641
141	0.5511	0.8978	0.4489
142	0.4742	0.9484	0.5258
143	0.4241	0.8482	0.5759
144	0.345	0.69	0.655
145	0.2692	0.5383	0.7308
146	0.5417	0.9166	0.4583
147	0.4748	0.9495	0.5252
148	0.4054	0.8107	0.5946
149	0.3113	0.6226	0.6887
150	0.2325	0.4651	0.7675
151	0.8912	0.2177	0.1088
152	0.9127	0.1746	0.08732
153	0.8306	0.3388	0.1694

Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description	# significant tests	% significant tests	OK/NOK
1% type I error level	75	0.5172	NOK
5% type I error level	91	0.627586	NOK
10% type I error level	93	0.641379	NOK

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

> reset_test_fitted
	RESET test
data:  mylm
RESET = 0.8606, df1 = 2, df2 = 154, p-value = 0.4249

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

> reset_test_regressors
	RESET test
data:  mylm
RESET = 0.78783, df1 = 10, df2 = 146, p-value = 0.6405

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

> reset_test_principal_components
	RESET test
data:  mylm
RESET = 1.0393, df1 = 2, df2 = 154, p-value = 0.3562

Variance Inflation Factors (Multicollinearity)

> vif
     SK1      SK3      SK4      SK5      SK6 
1.019622 1.033103 1.019654 1.046954 1.045610