| Multiple Linear Regression - Estimated Regression Equation |
| ITH1[t] = -0.348654 + 0.334464ITH2[t] + 0.352526ITH3[t] + 0.151315ITH4[t] + 0.0396807IKSUM[t] + 0.12895`ITH1(t-1)`[t] + 0.0126931`ITH1(t-2)`[t] -0.0192636`ITH1(t-3)`[t] -0.0164317`ITH1(t-4)`[t] + 0.0233105`ITH1(t-5)`[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) | -0.3487 | 0.8679 | -4.0170e-01 | 0.6885 | 0.3442 |
| ITH2 | +0.3345 | 0.09107 | +3.6720e+00 | 0.0003378 | 0.0001689 |
| ITH3 | +0.3525 | 0.07165 | +4.9200e+00 | 2.331e-06 | 1.166e-06 |
| ITH4 | +0.1513 | 0.06266 | +2.4150e+00 | 0.017 | 0.008499 |
| IKSUM | +0.03968 | 0.03047 | +1.3020e+00 | 0.1949 | 0.09744 |
| `ITH1(t-1)` | +0.129 | 0.06553 | +1.9680e+00 | 0.05103 | 0.02552 |
| `ITH1(t-2)` | +0.01269 | 0.06587 | +1.9270e-01 | 0.8475 | 0.4237 |
| `ITH1(t-3)` | -0.01926 | 0.06543 | -2.9440e-01 | 0.7689 | 0.3844 |
| `ITH1(t-4)` | -0.01643 | 0.06516 | -2.5220e-01 | 0.8013 | 0.4006 |
| `ITH1(t-5)` | +0.02331 | 0.06476 | +3.5990e-01 | 0.7194 | 0.3597 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.6615 |
| R-squared | 0.4376 |
| Adjusted R-squared | 0.4025 |
| F-TEST (value) | 12.45 |
| F-TEST (DF numerator) | 9 |
| F-TEST (DF denominator) | 144 |
| p-value | 1.799e-14 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 0.6508 |
| Sum Squared Residuals | 60.99 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 5 | 5.068 | -0.06752 |
| 2 | 5 | 3.888 | 1.112 |
| 3 | 5 | 4.265 | 0.7351 |
| 4 | 5 | 3.957 | 1.043 |
| 5 | 5 | 4.87 | 0.1299 |
| 6 | 5 | 5.203 | -0.2034 |
| 7 | 5 | 4.739 | 0.2607 |
| 8 | 4 | 3.933 | 0.06678 |
| 9 | 3 | 4.085 | -1.085 |
| 10 | 5 | 4.933 | 0.06718 |
| 11 | 5 | 3.967 | 1.033 |
| 12 | 5 | 3.924 | 1.076 |
| 13 | 4 | 4.414 | -0.4143 |
| 14 | 2 | 3.124 | -1.124 |
| 15 | 5 | 4.451 | 0.5487 |
| 16 | 5 | 4.753 | 0.2473 |
| 17 | 5 | 4.551 | 0.4495 |
| 18 | 4 | 4.041 | -0.04137 |
| 19 | 4 | 4.893 | -0.8929 |
| 20 | 4 | 4.439 | -0.4389 |
| 21 | 5 | 4.689 | 0.3112 |
| 22 | 5 | 4.532 | 0.4684 |
| 23 | 5 | 4.824 | 0.1764 |
| 24 | 5 | 5.236 | -0.2362 |
| 25 | 1 | 1.978 | -0.9782 |
| 26 | 5 | 4.375 | 0.6252 |
| 27 | 4 | 4.577 | -0.5768 |
| 28 | 4 | 4.083 | -0.08254 |
| 29 | 4 | 4.25 | -0.2495 |
| 30 | 5 | 4.405 | 0.5954 |
| 31 | 4 | 4.51 | -0.51 |
| 32 | 4 | 4.018 | -0.01787 |
| 33 | 5 | 4.137 | 0.8628 |
| 34 | 5 | 5.147 | -0.147 |
| 35 | 5 | 5.088 | -0.08779 |
| 36 | 2 | 2.25 | -0.2497 |
| 37 | 3 | 3.189 | -0.1886 |
| 38 | 4 | 3.972 | 0.0283 |
| 39 | 5 | 4.643 | 0.3573 |
| 40 | 5 | 4.897 | 0.1035 |
| 41 | 4 | 4.308 | -0.3076 |
| 42 | 5 | 4.228 | 0.7724 |
| 43 | 5 | 4.976 | 0.02359 |
| 44 | 4 | 4.345 | -0.3447 |
| 45 | 5 | 4.619 | 0.3807 |
| 46 | 4 | 3.778 | 0.2223 |
| 47 | 4 | 4.176 | -0.1761 |
| 48 | 3 | 3.657 | -0.6567 |
| 49 | 4 | 3.244 | 0.7557 |
| 50 | 4 | 4.581 | -0.5809 |
| 51 | 5 | 4.255 | 0.7449 |
| 52 | 4 | 4.716 | -0.7157 |
| 53 | 4 | 4.448 | -0.4481 |
| 54 | 4 | 4.058 | -0.05786 |
| 55 | 4 | 3.334 | 0.666 |
| 56 | 4 | 4.259 | -0.2592 |
| 57 | 2 | 4.005 | -2.005 |
| 58 | 4 | 4.042 | -0.04206 |
| 59 | 4 | 3.707 | 0.2934 |
| 60 | 5 | 5.113 | -0.1127 |
| 61 | 3 | 3.48 | -0.48 |
| 62 | 3 | 3.609 | -0.6088 |
| 63 | 5 | 4.388 | 0.6122 |
| 64 | 4 | 3.628 | 0.3717 |
| 65 | 5 | 5.034 | -0.03422 |
| 66 | 4 | 4.864 | -0.8641 |
| 67 | 4 | 3.601 | 0.3988 |
| 68 | 5 | 4.413 | 0.5872 |
| 69 | 5 | 5.035 | -0.03536 |
| 70 | 5 | 3.818 | 1.182 |
| 71 | 4 | 3.775 | 0.225 |
| 72 | 5 | 4.094 | 0.9062 |
| 73 | 5 | 5.119 | -0.1188 |
| 74 | 2 | 4.337 | -2.337 |
| 75 | 5 | 4.419 | 0.5808 |
| 76 | 5 | 4.718 | 0.2825 |
| 77 | 5 | 5.341 | -0.3406 |
| 78 | 5 | 4.112 | 0.8882 |
| 79 | 4 | 4.025 | -0.02482 |
| 80 | 4 | 3.926 | 0.07388 |
| 81 | 5 | 4.982 | 0.01759 |
| 82 | 4 | 4.062 | -0.06164 |
| 83 | 5 | 4.959 | 0.04116 |
| 84 | 5 | 4.759 | 0.2406 |
| 85 | 5 | 4.793 | 0.2071 |
| 86 | 4 | 4.23 | -0.2302 |
| 87 | 5 | 5.131 | -0.1305 |
| 88 | 5 | 4.578 | 0.4219 |
| 89 | 3 | 3.607 | -0.6074 |
| 90 | 5 | 4.436 | 0.5635 |
| 91 | 5 | 5.083 | -0.08276 |
| 92 | 5 | 5.083 | -0.08322 |
| 93 | 4 | 4.83 | -0.8299 |
| 94 | 4 | 4.078 | -0.0779 |
| 95 | 4 | 4.223 | -0.2235 |
| 96 | 5 | 4.739 | 0.2613 |
| 97 | 5 | 4.683 | 0.3171 |
| 98 | 4 | 3.712 | 0.2879 |
| 99 | 3 | 4.11 | -1.11 |
| 100 | 3 | 3.416 | -0.416 |
| 101 | 4 | 4.335 | -0.3346 |
| 102 | 4 | 3.683 | 0.3175 |
| 103 | 5 | 4.527 | 0.4734 |
| 104 | 5 | 4.437 | 0.5627 |
| 105 | 4 | 4.707 | -0.7067 |
| 106 | 5 | 5.147 | -0.1469 |
| 107 | 5 | 4.178 | 0.8222 |
| 108 | 4 | 3.841 | 0.1592 |
| 109 | 4 | 3.94 | 0.06026 |
| 110 | 5 | 4.535 | 0.4654 |
| 111 | 5 | 5.25 | -0.2497 |
| 112 | 5 | 4.343 | 0.6569 |
| 113 | 5 | 4.34 | 0.6598 |
| 114 | 4 | 4.637 | -0.6366 |
| 115 | 5 | 4.157 | 0.8432 |
| 116 | 3 | 4.392 | -1.392 |
| 117 | 5 | 4.31 | 0.6904 |
| 118 | 5 | 4.669 | 0.331 |
| 119 | 4 | 4.715 | -0.7148 |
| 120 | 5 | 5.028 | -0.02796 |
| 121 | 4 | 4.234 | -0.2338 |
| 122 | 4 | 4.097 | -0.0967 |
| 123 | 4 | 4.049 | -0.0489 |
| 124 | 4 | 4.525 | -0.5249 |
| 125 | 2 | 3.021 | -1.021 |
| 126 | 4 | 3.787 | 0.213 |
| 127 | 5 | 4.563 | 0.437 |
| 128 | 5 | 5.162 | -0.1623 |
| 129 | 4 | 4.147 | -0.1474 |
| 130 | 5 | 3.84 | 1.16 |
| 131 | 5 | 4.25 | 0.7503 |
| 132 | 5 | 4.697 | 0.3028 |
| 133 | 5 | 5.18 | -0.1802 |
| 134 | 5 | 4.32 | 0.6798 |
| 135 | 5 | 4.797 | 0.203 |
| 136 | 4 | 4.055 | -0.05507 |
| 137 | 5 | 4.164 | 0.8358 |
| 138 | 3 | 3.402 | -0.4025 |
| 139 | 3 | 4.047 | -1.047 |
| 140 | 4 | 4.624 | -0.6237 |
| 141 | 4 | 4.521 | -0.5208 |
| 142 | 3 | 4.468 | -1.468 |
| 143 | 3 | 3.524 | -0.5242 |
| 144 | 5 | 4.798 | 0.2024 |
| 145 | 5 | 4.746 | 0.2545 |
| 146 | 5 | 4.031 | 0.9688 |
| 147 | 5 | 4.351 | 0.6486 |
| 148 | 5 | 4.926 | 0.07389 |
| 149 | 5 | 4.678 | 0.322 |
| 150 | 5 | 5.052 | -0.0521 |
| 151 | 5 | 4.336 | 0.6644 |
| 152 | 4 | 4.325 | -0.3254 |
| 153 | 4 | 4.318 | -0.3183 |
| 154 | 2 | 4.425 | -2.425 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 13 | 0.7125 | 0.5749 | 0.2875 |
| 14 | 0.7812 | 0.4376 | 0.2188 |
| 15 | 0.8125 | 0.375 | 0.1875 |
| 16 | 0.8587 | 0.2826 | 0.1413 |
| 17 | 0.8174 | 0.3651 | 0.1826 |
| 18 | 0.7669 | 0.4661 | 0.2331 |
| 19 | 0.7035 | 0.5931 | 0.2965 |
| 20 | 0.657 | 0.6859 | 0.343 |
| 21 | 0.5718 | 0.8563 | 0.4282 |
| 22 | 0.489 | 0.9781 | 0.511 |
| 23 | 0.4105 | 0.821 | 0.5895 |
| 24 | 0.3419 | 0.6838 | 0.6581 |
| 25 | 0.3829 | 0.7658 | 0.6171 |
| 26 | 0.3688 | 0.7376 | 0.6312 |
| 27 | 0.3996 | 0.7992 | 0.6004 |
| 28 | 0.3914 | 0.7829 | 0.6086 |
| 29 | 0.3698 | 0.7396 | 0.6302 |
| 30 | 0.5978 | 0.8043 | 0.4022 |
| 31 | 0.5534 | 0.8932 | 0.4466 |
| 32 | 0.4915 | 0.983 | 0.5085 |
| 33 | 0.5825 | 0.835 | 0.4175 |
| 34 | 0.5343 | 0.9314 | 0.4657 |
| 35 | 0.482 | 0.964 | 0.518 |
| 36 | 0.4224 | 0.8449 | 0.5776 |
| 37 | 0.3637 | 0.7273 | 0.6363 |
| 38 | 0.3112 | 0.6223 | 0.6888 |
| 39 | 0.2766 | 0.5532 | 0.7234 |
| 40 | 0.2304 | 0.4607 | 0.7696 |
| 41 | 0.1934 | 0.3868 | 0.8066 |
| 42 | 0.1991 | 0.3983 | 0.8009 |
| 43 | 0.1633 | 0.3266 | 0.8367 |
| 44 | 0.1453 | 0.2906 | 0.8547 |
| 45 | 0.1186 | 0.2372 | 0.8814 |
| 46 | 0.1048 | 0.2097 | 0.8952 |
| 47 | 0.08346 | 0.1669 | 0.9165 |
| 48 | 0.08479 | 0.1696 | 0.9152 |
| 49 | 0.1112 | 0.2225 | 0.8888 |
| 50 | 0.1261 | 0.2522 | 0.8739 |
| 51 | 0.1263 | 0.2527 | 0.8737 |
| 52 | 0.1487 | 0.2974 | 0.8513 |
| 53 | 0.1352 | 0.2704 | 0.8648 |
| 54 | 0.1095 | 0.2191 | 0.8905 |
| 55 | 0.1094 | 0.2188 | 0.8906 |
| 56 | 0.09228 | 0.1846 | 0.9077 |
| 57 | 0.3893 | 0.7787 | 0.6107 |
| 58 | 0.3408 | 0.6817 | 0.6592 |
| 59 | 0.3072 | 0.6144 | 0.6928 |
| 60 | 0.2751 | 0.5502 | 0.7249 |
| 61 | 0.257 | 0.5141 | 0.743 |
| 62 | 0.2452 | 0.4904 | 0.7548 |
| 63 | 0.2665 | 0.533 | 0.7335 |
| 64 | 0.2382 | 0.4764 | 0.7618 |
| 65 | 0.2018 | 0.4035 | 0.7982 |
| 66 | 0.2358 | 0.4716 | 0.7642 |
| 67 | 0.2161 | 0.4322 | 0.7839 |
| 68 | 0.2038 | 0.4076 | 0.7962 |
| 69 | 0.1704 | 0.3408 | 0.8296 |
| 70 | 0.2476 | 0.4951 | 0.7524 |
| 71 | 0.2154 | 0.4307 | 0.7846 |
| 72 | 0.2512 | 0.5024 | 0.7488 |
| 73 | 0.2142 | 0.4284 | 0.7858 |
| 74 | 0.7761 | 0.4478 | 0.2239 |
| 75 | 0.79 | 0.42 | 0.21 |
| 76 | 0.7618 | 0.4764 | 0.2382 |
| 77 | 0.7411 | 0.5178 | 0.2589 |
| 78 | 0.7705 | 0.459 | 0.2295 |
| 79 | 0.7531 | 0.4938 | 0.2469 |
| 80 | 0.713 | 0.574 | 0.287 |
| 81 | 0.6728 | 0.6545 | 0.3272 |
| 82 | 0.6282 | 0.7436 | 0.3718 |
| 83 | 0.5812 | 0.8375 | 0.4188 |
| 84 | 0.5378 | 0.9243 | 0.4622 |
| 85 | 0.4987 | 0.9974 | 0.5013 |
| 86 | 0.4575 | 0.9151 | 0.5425 |
| 87 | 0.4107 | 0.8214 | 0.5893 |
| 88 | 0.3863 | 0.7725 | 0.6137 |
| 89 | 0.3729 | 0.7459 | 0.6271 |
| 90 | 0.3871 | 0.7743 | 0.6129 |
| 91 | 0.3426 | 0.6852 | 0.6574 |
| 92 | 0.2994 | 0.5987 | 0.7006 |
| 93 | 0.3173 | 0.6346 | 0.6827 |
| 94 | 0.2764 | 0.5528 | 0.7236 |
| 95 | 0.2412 | 0.4823 | 0.7588 |
| 96 | 0.2075 | 0.415 | 0.7925 |
| 97 | 0.1784 | 0.3568 | 0.8216 |
| 98 | 0.1566 | 0.3132 | 0.8434 |
| 99 | 0.2281 | 0.4562 | 0.7719 |
| 100 | 0.2073 | 0.4145 | 0.7927 |
| 101 | 0.1795 | 0.359 | 0.8205 |
| 102 | 0.1656 | 0.3311 | 0.8344 |
| 103 | 0.1497 | 0.2993 | 0.8503 |
| 104 | 0.1417 | 0.2835 | 0.8583 |
| 105 | 0.1619 | 0.3238 | 0.8381 |
| 106 | 0.1332 | 0.2664 | 0.8668 |
| 107 | 0.1451 | 0.2902 | 0.8549 |
| 108 | 0.1214 | 0.2429 | 0.8786 |
| 109 | 0.1014 | 0.2028 | 0.8986 |
| 110 | 0.09205 | 0.1841 | 0.9079 |
| 111 | 0.07359 | 0.1472 | 0.9264 |
| 112 | 0.08675 | 0.1735 | 0.9133 |
| 113 | 0.09825 | 0.1965 | 0.9018 |
| 114 | 0.09298 | 0.186 | 0.907 |
| 115 | 0.1356 | 0.2711 | 0.8644 |
| 116 | 0.2068 | 0.4136 | 0.7932 |
| 117 | 0.3135 | 0.627 | 0.6865 |
| 118 | 0.2704 | 0.5408 | 0.7296 |
| 119 | 0.2591 | 0.5181 | 0.7409 |
| 120 | 0.2155 | 0.431 | 0.7845 |
| 121 | 0.228 | 0.456 | 0.772 |
| 122 | 0.1969 | 0.3938 | 0.8031 |
| 123 | 0.1663 | 0.3327 | 0.8337 |
| 124 | 0.149 | 0.298 | 0.851 |
| 125 | 0.1406 | 0.2812 | 0.8594 |
| 126 | 0.1574 | 0.3147 | 0.8426 |
| 127 | 0.1558 | 0.3115 | 0.8442 |
| 128 | 0.1217 | 0.2435 | 0.8783 |
| 129 | 0.1034 | 0.2069 | 0.8966 |
| 130 | 0.09528 | 0.1906 | 0.9047 |
| 131 | 0.1029 | 0.2058 | 0.8971 |
| 132 | 0.07352 | 0.147 | 0.9265 |
| 133 | 0.04961 | 0.09923 | 0.9504 |
| 134 | 0.03933 | 0.07865 | 0.9607 |
| 135 | 0.02413 | 0.04826 | 0.9759 |
| 136 | 0.01463 | 0.02925 | 0.9854 |
| 137 | 0.05726 | 0.1145 | 0.9427 |
| 138 | 0.03904 | 0.07809 | 0.961 |
| 139 | 0.02986 | 0.05972 | 0.9701 |
| 140 | 0.03344 | 0.06689 | 0.9666 |
| 141 | 0.0153 | 0.0306 | 0.9847 |
| 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 | 3 | 0.0232558 | OK |
| 10% type I error level | 8 | 0.0620155 | OK |
| Ramsey RESET F-Test for powers (2 and 3) of fitted values |
> reset_test_fitted RESET test data: mylm RESET = 3.4694, df1 = 2, df2 = 142, p-value = 0.0338 |
| Ramsey RESET F-Test for powers (2 and 3) of regressors |
> reset_test_regressors RESET test data: mylm RESET = 1.3351, df1 = 18, df2 = 126, p-value = 0.1773 |
| Ramsey RESET F-Test for powers (2 and 3) of principal components |
> reset_test_principal_components RESET test data: mylm RESET = 0.4779, df1 = 2, df2 = 142, p-value = 0.6211 |
| Variance Inflation Factors (Multicollinearity) |
> vif
ITH2 ITH3 ITH4 IKSUM `ITH1(t-1)` `ITH1(t-2)`
1.397461 1.404727 1.244711 1.065544 1.045168 1.058944
`ITH1(t-3)` `ITH1(t-4)` `ITH1(t-5)`
1.047730 1.038997 1.040432
|
