Multiple Linear Regression - Estimated Regression Equation |
a[t] = + 21.364 -0.345897b[t] -0.0589782c[t] -0.106646d[t] + 0.493261e[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) | +21.36 | 1.351 | +1.5810e+01 | 1.974e-34 | 9.87e-35 |
b | -0.3459 | 0.2378 | -1.4540e+00 | 0.1478 | 0.07392 |
c | -0.05898 | 0.2496 | -2.3630e-01 | 0.8135 | 0.4068 |
d | -0.1066 | 0.2523 | -4.2280e-01 | 0.673 | 0.3365 |
e | +0.4933 | 0.2404 | +2.0520e+00 | 0.04185 | 0.02092 |
Multiple Linear Regression - Regression Statistics | |
Multiple R | 0.1857 |
R-squared | 0.03448 |
Adjusted R-squared | 0.01019 |
F-TEST (value) | 1.42 |
F-TEST (DF numerator) | 4 |
F-TEST (DF denominator) | 159 |
p-value | 0.2299 |
Multiple Linear Regression - Residual Statistics | |
Residual Standard Deviation | 1.772 |
Sum Squared Residuals | 499.4 |
Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
1 | 22 | 21.13 | 0.8747 |
2 | 24 | 20.78 | 3.221 |
3 | 21 | 20.89 | 0.1139 |
4 | 21 | 21.64 | -0.6368 |
5 | 24 | 20.78 | 3.221 |
6 | 20 | 20.78 | -0.7794 |
7 | 22 | 21.33 | 0.6684 |
8 | 19 | 20.89 | -1.886 |
9 | 23 | 21.27 | 1.727 |
10 | 21 | 20.86 | 0.1434 |
11 | 19 | 21.08 | -2.085 |
12 | 19 | 21.13 | -2.125 |
13 | 21 | 20.78 | 0.2206 |
14 | 21 | 21.29 | -0.2909 |
15 | 22 | 20.84 | 1.162 |
16 | 22 | 21.13 | 0.8747 |
17 | 21 | 20.95 | 0.05497 |
18 | 21 | 21.33 | -0.3316 |
19 | 21 | 20.78 | 0.2206 |
20 | 20 | 21.47 | -1.471 |
21 | 22 | 21.13 | 0.8747 |
22 | 22 | 21.29 | 0.7091 |
23 | 24 | 21.27 | 2.727 |
24 | 21 | 21.25 | -0.2502 |
25 | 19 | 21.38 | -2.379 |
26 | 19 | 20.8 | -1.798 |
27 | 23 | 21.23 | 1.768 |
28 | 21 | 21.23 | -0.2319 |
29 | 21 | 21.24 | -0.2433 |
30 | 19 | 20.35 | -1.345 |
31 | 21 | 20.78 | 0.2206 |
32 | 19 | 21.68 | -2.678 |
33 | 21 | 20.78 | 0.2206 |
34 | 21 | 21.27 | -0.2727 |
35 | 23 | 21.29 | 1.709 |
36 | 19 | 20.95 | -1.945 |
37 | 19 | 21.29 | -2.291 |
38 | 19 | 20.74 | -1.739 |
39 | 18 | 21.29 | -3.291 |
40 | 22 | 21.29 | 0.7091 |
41 | 18 | 20.86 | -2.857 |
42 | 22 | 20.39 | 1.607 |
43 | 18 | 20.84 | -2.838 |
44 | 22 | 21.29 | 0.7091 |
45 | 22 | 21.29 | 0.7091 |
46 | 22 | 21.29 | 0.7091 |
47 | 25 | 20.8 | 4.202 |
48 | 19 | 20.78 | -1.779 |
49 | 19 | 21.29 | -2.291 |
50 | 19 | 21.23 | -2.232 |
51 | 19 | 20.78 | -1.779 |
52 | 21 | 21.23 | -0.2319 |
53 | 21 | 21.23 | -0.2319 |
54 | 20 | 20.8 | -0.7977 |
55 | 19 | 21.05 | -2.052 |
56 | 19 | 21.29 | -2.291 |
57 | 22 | 20.45 | 1.548 |
58 | 26 | 21.23 | 4.768 |
59 | 19 | 21.13 | -2.125 |
60 | 21 | 21.13 | -0.1253 |
61 | 21 | 20.29 | 0.7139 |
62 | 20 | 20.78 | -0.7794 |
63 | 23 | 20.9 | 2.096 |
64 | 22 | 20.92 | 1.084 |
65 | 22 | 21.13 | 0.8747 |
66 | 22 | 21.29 | 0.7091 |
67 | 21 | 20.8 | 0.2023 |
68 | 21 | 21.13 | -0.1253 |
69 | 22 | 21.13 | 0.8747 |
70 | 23 | 22.42 | 0.583 |
71 | 18 | 20.78 | -2.779 |
72 | 24 | 21.23 | 2.768 |
73 | 22 | 20.39 | 1.607 |
74 | 21 | 20.78 | 0.2206 |
75 | 21 | 21.62 | -0.6186 |
76 | 21 | 21.27 | -0.2727 |
77 | 23 | 20.78 | 2.221 |
78 | 21 | 21.13 | -0.1253 |
79 | 23 | 21.29 | 1.709 |
80 | 21 | 21.29 | -0.2909 |
81 | 19 | 21.35 | -2.35 |
82 | 21 | 21.27 | -0.2727 |
83 | 21 | 20.74 | 0.2613 |
84 | 21 | 21.29 | -0.2909 |
85 | 23 | 21.27 | 1.727 |
86 | 23 | 21.27 | 1.727 |
87 | 20 | 21.13 | -1.125 |
88 | 20 | 21.16 | -1.158 |
89 | 19 | 20.86 | -1.857 |
90 | 23 | 21.29 | 1.709 |
91 | 22 | 21.74 | 0.2565 |
92 | 19 | 21.13 | -2.125 |
93 | 23 | 21.27 | 1.727 |
94 | 22 | 21.27 | 0.7273 |
95 | 22 | 21.13 | 0.8747 |
96 | 21 | 21.27 | -0.2727 |
97 | 21 | 21.14 | -0.1436 |
98 | 21 | 21.27 | -0.2727 |
99 | 21 | 21.23 | -0.2319 |
100 | 22 | 21.27 | 0.7273 |
101 | 25 | 21.14 | 3.856 |
102 | 21 | 21.29 | -0.2909 |
103 | 23 | 21.27 | 1.727 |
104 | 19 | 20.78 | -1.779 |
105 | 22 | 21.73 | 0.2748 |
106 | 20 | 21.23 | -1.232 |
107 | 21 | 21.23 | -0.2319 |
108 | 25 | 21.33 | 3.668 |
109 | 21 | 20.8 | 0.2023 |
110 | 19 | 20.84 | -1.838 |
111 | 23 | 21.35 | 1.65 |
112 | 22 | 21.29 | 0.7091 |
113 | 21 | 21.29 | -0.2909 |
114 | 24 | 21.27 | 2.727 |
115 | 21 | 20.89 | 0.1139 |
116 | 19 | 21.27 | -2.273 |
117 | 18 | 20.29 | -2.286 |
118 | 19 | 21.23 | -2.232 |
119 | 20 | 21.33 | -1.332 |
120 | 19 | 21.13 | -2.125 |
121 | 22 | 20.78 | 1.221 |
122 | 21 | 21.54 | -0.5449 |
123 | 22 | 20.89 | 1.114 |
124 | 24 | 21.23 | 2.768 |
125 | 28 | 21.29 | 6.709 |
126 | 19 | 20.78 | -1.779 |
127 | 18 | 20.89 | -2.886 |
128 | 23 | 21.23 | 1.768 |
129 | 19 | 20.89 | -1.886 |
130 | 23 | 21.29 | 1.709 |
131 | 19 | 21.27 | -2.273 |
132 | 22 | 20.86 | 1.143 |
133 | 21 | 21.23 | -0.2319 |
134 | 19 | 22.4 | -3.402 |
135 | 22 | 22.04 | -0.0417 |
136 | 21 | 21.23 | -0.2319 |
137 | 23 | 21.13 | 1.875 |
138 | 22 | 21.29 | 0.7091 |
139 | 19 | 20.78 | -1.779 |
140 | 22 | 21.47 | 0.5288 |
141 | 21 | 20.74 | 0.2613 |
142 | 20 | 21.23 | -1.232 |
143 | 23 | 20.39 | 2.607 |
144 | 22 | 21.23 | 0.7681 |
145 | 23 | 21.27 | 1.727 |
146 | 22 | 21.14 | 0.8564 |
147 | 21 | 21.27 | -0.2727 |
148 | 20 | 20.78 | -0.7794 |
149 | 18 | 20.98 | -2.978 |
150 | 18 | 20.78 | -2.779 |
151 | 20 | 21.23 | -1.232 |
152 | 19 | 20.78 | -1.779 |
153 | 21 | 21.27 | -0.2727 |
154 | 24 | 21.33 | 2.668 |
155 | 19 | 20.78 | -1.779 |
156 | 20 | 20.74 | -0.7387 |
157 | 19 | 20.84 | -1.838 |
158 | 23 | 21.65 | 1.348 |
159 | 22 | 21.23 | 0.7681 |
160 | 21 | 21.13 | -0.1253 |
161 | 24 | 20.69 | 3.309 |
162 | 21 | 21.23 | -0.2319 |
163 | 21 | 20.8 | 0.2023 |
164 | 22 | 20.29 | 1.714 |
Goldfeld-Quandt test for Heteroskedasticity | |||
p-values | Alternative Hypothesis | ||
breakpoint index | greater | 2-sided | less |
8 | 0.7396 | 0.5207 | 0.2604 |
9 | 0.6478 | 0.7045 | 0.3522 |
10 | 0.5136 | 0.9729 | 0.4864 |
11 | 0.4353 | 0.8707 | 0.5647 |
12 | 0.6041 | 0.7918 | 0.3959 |
13 | 0.5222 | 0.9555 | 0.4778 |
14 | 0.4217 | 0.8434 | 0.5783 |
15 | 0.3358 | 0.6716 | 0.6642 |
16 | 0.2642 | 0.5284 | 0.7358 |
17 | 0.1935 | 0.3869 | 0.8065 |
18 | 0.1849 | 0.3698 | 0.8151 |
19 | 0.1417 | 0.2834 | 0.8583 |
20 | 0.1106 | 0.2213 | 0.8894 |
21 | 0.08408 | 0.1682 | 0.9159 |
22 | 0.07577 | 0.1515 | 0.9242 |
23 | 0.09298 | 0.186 | 0.907 |
24 | 0.0923 | 0.1846 | 0.9077 |
25 | 0.1191 | 0.2382 | 0.8809 |
26 | 0.122 | 0.2439 | 0.878 |
27 | 0.1685 | 0.337 | 0.8315 |
28 | 0.1303 | 0.2605 | 0.8697 |
29 | 0.1035 | 0.2071 | 0.8965 |
30 | 0.1101 | 0.2203 | 0.8899 |
31 | 0.08353 | 0.1671 | 0.9165 |
32 | 0.139 | 0.2779 | 0.861 |
33 | 0.1088 | 0.2176 | 0.8912 |
34 | 0.08759 | 0.1752 | 0.9124 |
35 | 0.1028 | 0.2055 | 0.8972 |
36 | 0.1125 | 0.225 | 0.8875 |
37 | 0.1183 | 0.2367 | 0.8817 |
38 | 0.1104 | 0.2208 | 0.8896 |
39 | 0.1606 | 0.3212 | 0.8394 |
40 | 0.1483 | 0.2966 | 0.8517 |
41 | 0.1648 | 0.3295 | 0.8352 |
42 | 0.1619 | 0.3239 | 0.8381 |
43 | 0.2313 | 0.4625 | 0.7687 |
44 | 0.2158 | 0.4317 | 0.7842 |
45 | 0.1987 | 0.3974 | 0.8013 |
46 | 0.1806 | 0.3613 | 0.8194 |
47 | 0.4432 | 0.8863 | 0.5568 |
48 | 0.4607 | 0.9214 | 0.5393 |
49 | 0.4743 | 0.9485 | 0.5257 |
50 | 0.4936 | 0.9872 | 0.5064 |
51 | 0.5045 | 0.9909 | 0.4955 |
52 | 0.4552 | 0.9104 | 0.5448 |
53 | 0.4068 | 0.8135 | 0.5932 |
54 | 0.3654 | 0.7309 | 0.6346 |
55 | 0.3629 | 0.7259 | 0.6371 |
56 | 0.3745 | 0.749 | 0.6255 |
57 | 0.3677 | 0.7355 | 0.6323 |
58 | 0.68 | 0.6399 | 0.32 |
59 | 0.6988 | 0.6023 | 0.3012 |
60 | 0.6563 | 0.6874 | 0.3437 |
61 | 0.6153 | 0.7694 | 0.3847 |
62 | 0.5823 | 0.8354 | 0.4177 |
63 | 0.6099 | 0.7802 | 0.3901 |
64 | 0.5982 | 0.8036 | 0.4018 |
65 | 0.5653 | 0.8695 | 0.4347 |
66 | 0.5311 | 0.9378 | 0.4689 |
67 | 0.4852 | 0.9704 | 0.5148 |
68 | 0.4391 | 0.8782 | 0.5609 |
69 | 0.4055 | 0.811 | 0.5945 |
70 | 0.3768 | 0.7535 | 0.6232 |
71 | 0.444 | 0.888 | 0.556 |
72 | 0.5091 | 0.9818 | 0.4909 |
73 | 0.4961 | 0.9922 | 0.5039 |
74 | 0.4508 | 0.9016 | 0.5492 |
75 | 0.4104 | 0.8209 | 0.5896 |
76 | 0.3673 | 0.7346 | 0.6327 |
77 | 0.3891 | 0.7781 | 0.6109 |
78 | 0.3461 | 0.6922 | 0.6539 |
79 | 0.3452 | 0.6904 | 0.6548 |
80 | 0.3054 | 0.6108 | 0.6946 |
81 | 0.3394 | 0.6789 | 0.6606 |
82 | 0.2995 | 0.5989 | 0.7005 |
83 | 0.2634 | 0.5269 | 0.7366 |
84 | 0.2295 | 0.459 | 0.7705 |
85 | 0.2273 | 0.4547 | 0.7727 |
86 | 0.2246 | 0.4491 | 0.7754 |
87 | 0.2044 | 0.4088 | 0.7956 |
88 | 0.1863 | 0.3726 | 0.8137 |
89 | 0.2033 | 0.4066 | 0.7967 |
90 | 0.2 | 0.4001 | 0.8 |
91 | 0.1713 | 0.3426 | 0.8287 |
92 | 0.1835 | 0.3669 | 0.8165 |
93 | 0.1821 | 0.3642 | 0.8179 |
94 | 0.1584 | 0.3168 | 0.8416 |
95 | 0.1388 | 0.2777 | 0.8612 |
96 | 0.1155 | 0.2311 | 0.8845 |
97 | 0.09657 | 0.1931 | 0.9034 |
98 | 0.07867 | 0.1573 | 0.9213 |
99 | 0.0633 | 0.1266 | 0.9367 |
100 | 0.05283 | 0.1057 | 0.9472 |
101 | 0.1085 | 0.2171 | 0.8915 |
102 | 0.08973 | 0.1795 | 0.9103 |
103 | 0.09097 | 0.1819 | 0.909 |
104 | 0.09004 | 0.1801 | 0.91 |
105 | 0.07403 | 0.1481 | 0.926 |
106 | 0.06463 | 0.1293 | 0.9354 |
107 | 0.05121 | 0.1024 | 0.9488 |
108 | 0.1011 | 0.2022 | 0.8989 |
109 | 0.08229 | 0.1646 | 0.9177 |
110 | 0.08726 | 0.1745 | 0.9127 |
111 | 0.07894 | 0.1579 | 0.9211 |
112 | 0.06403 | 0.1281 | 0.936 |
113 | 0.05105 | 0.1021 | 0.949 |
114 | 0.0797 | 0.1594 | 0.9203 |
115 | 0.06329 | 0.1266 | 0.9367 |
116 | 0.06491 | 0.1298 | 0.9351 |
117 | 0.07919 | 0.1584 | 0.9208 |
118 | 0.08449 | 0.169 | 0.9155 |
119 | 0.07559 | 0.1512 | 0.9244 |
120 | 0.07837 | 0.1567 | 0.9216 |
121 | 0.06839 | 0.1368 | 0.9316 |
122 | 0.05457 | 0.1091 | 0.9454 |
123 | 0.04625 | 0.0925 | 0.9537 |
124 | 0.06983 | 0.1397 | 0.9302 |
125 | 0.5479 | 0.9041 | 0.4521 |
126 | 0.5408 | 0.9184 | 0.4592 |
127 | 0.62 | 0.7599 | 0.38 |
128 | 0.6444 | 0.7113 | 0.3556 |
129 | 0.6492 | 0.7016 | 0.3508 |
130 | 0.6404 | 0.7191 | 0.3596 |
131 | 0.6522 | 0.6955 | 0.3478 |
132 | 0.5997 | 0.8005 | 0.4003 |
133 | 0.5403 | 0.9194 | 0.4597 |
134 | 0.7483 | 0.5034 | 0.2517 |
135 | 0.728 | 0.544 | 0.272 |
136 | 0.6713 | 0.6575 | 0.3287 |
137 | 0.7161 | 0.5677 | 0.2839 |
138 | 0.6594 | 0.6813 | 0.3406 |
139 | 0.642 | 0.716 | 0.358 |
140 | 0.6267 | 0.7466 | 0.3733 |
141 | 0.561 | 0.8781 | 0.439 |
142 | 0.5062 | 0.9876 | 0.4938 |
143 | 0.6161 | 0.7679 | 0.3839 |
144 | 0.5782 | 0.8436 | 0.4218 |
145 | 0.6235 | 0.7529 | 0.3765 |
146 | 0.5434 | 0.9133 | 0.4566 |
147 | 0.4651 | 0.9301 | 0.5349 |
148 | 0.3804 | 0.7609 | 0.6196 |
149 | 0.4893 | 0.9786 | 0.5107 |
150 | 0.51 | 0.98 | 0.49 |
151 | 0.45 | 0.9 | 0.55 |
152 | 0.3959 | 0.7917 | 0.6041 |
153 | 0.2898 | 0.5796 | 0.7102 |
154 | 0.3619 | 0.7239 | 0.6381 |
155 | 0.2844 | 0.5689 | 0.7156 |
156 | 0.3142 | 0.6284 | 0.6858 |
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 | 0.00671141 | OK |
Ramsey RESET F-Test for powers (2 and 3) of fitted values |
> reset_test_fitted RESET test data: mylm RESET = 2.1976, df1 = 2, df2 = 157, p-value = 0.1145 |
Ramsey RESET F-Test for powers (2 and 3) of regressors |
> reset_test_regressors RESET test data: mylm RESET = 1.3192, df1 = 8, df2 = 151, p-value = 0.2379 |
Ramsey RESET F-Test for powers (2 and 3) of principal components |
> reset_test_principal_components RESET test data: mylm RESET = 2.7209, df1 = 2, df2 = 157, p-value = 0.06892 |
Variance Inflation Factors (Multicollinearity) |
> vif b c d e 1.270755 1.283208 1.362280 1.159302 |