| Multiple Linear Regression - Estimated Regression Equation |
| Y[t] = + 13.0633214285714 -1.61912500000001X[t] + 17.0792678571429M1[t] + 14.6398392857143M2[t] + 18.3048392857143M3[t] + 15.1356964285714M4[t] + 10.8335535714285M5[t] + 12.0635535714286M6[t] + 6.52326785714285M7[t] + 5.04398214285713M8[t] + 7.39914285714285M9[t] + 10.0645714285714M10[t] + 5.52071428571428M11[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) | 13.0633214285714 | 0.750462 | 17.407 | 0 | 0 |
| X | -1.61912500000001 | 0.547688 | -2.9563 | 0.004224 | 0.002112 |
| M1 | 17.0792678571429 | 1.04093 | 16.4077 | 0 | 0 |
| M2 | 14.6398392857143 | 1.04093 | 14.0642 | 0 | 0 |
| M3 | 18.3048392857143 | 1.04093 | 17.5851 | 0 | 0 |
| M4 | 15.1356964285714 | 1.04093 | 14.5405 | 0 | 0 |
| M5 | 10.8335535714285 | 1.04093 | 10.4076 | 0 | 0 |
| M6 | 12.0635535714286 | 1.04093 | 11.5892 | 0 | 0 |
| M7 | 6.52326785714285 | 1.04093 | 6.2668 | 0 | 0 |
| M8 | 5.04398214285713 | 1.04093 | 4.8456 | 7e-06 | 4e-06 |
| M9 | 7.39914285714285 | 1.037986 | 7.1284 | 0 | 0 |
| M10 | 10.0645714285714 | 1.037986 | 9.6963 | 0 | 0 |
| M11 | 5.52071428571428 | 1.037986 | 5.3187 | 1e-06 | 1e-06 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.949194746949424 |
| R-squared | 0.90097066763638 |
| Adjusted R-squared | 0.8842333156876 |
| F-TEST (value) | 53.829940984303 |
| F-TEST (DF numerator) | 12 |
| F-TEST (DF denominator) | 71 |
| p-value | 0 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 1.94189343526714 |
| Sum Squared Residuals | 267.737458089287 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 31.514 | 30.1425892857142 | 1.37141071428583 |
| 2 | 27.071 | 27.7031607142857 | -0.632160714285683 |
| 3 | 29.462 | 31.3681607142858 | -1.9061607142858 |
| 4 | 26.105 | 28.1990178571430 | -2.09401785714296 |
| 5 | 22.397 | 23.8968750000001 | -1.49987500000005 |
| 6 | 23.843 | 25.126875 | -1.283875 |
| 7 | 21.705 | 19.5865892857143 | 2.11841071428573 |
| 8 | 18.089 | 18.1073035714286 | -0.0183035714285787 |
| 9 | 20.764 | 20.4624642857143 | 0.30153571428572 |
| 10 | 25.316 | 23.1278928571429 | 2.18810714285715 |
| 11 | 17.704 | 18.5840357142857 | -0.88003571428572 |
| 12 | 15.548 | 13.0633214285714 | 2.48467857142857 |
| 13 | 28.029 | 30.1425892857143 | -2.1135892857143 |
| 14 | 29.383 | 27.7031607142857 | 1.67983928571428 |
| 15 | 36.438 | 31.3681607142857 | 5.0698392857143 |
| 16 | 32.034 | 28.1990178571428 | 3.83498214285716 |
| 17 | 22.679 | 23.896875 | -1.21787499999999 |
| 18 | 24.319 | 25.126875 | -0.807875000000001 |
| 19 | 18.004 | 19.5865892857143 | -1.58258928571429 |
| 20 | 17.537 | 18.1073035714286 | -0.570303571428571 |
| 21 | 20.366 | 20.4624642857143 | -0.0964642857142865 |
| 22 | 22.782 | 23.1278928571429 | -0.345892857142858 |
| 23 | 19.169 | 18.5840357142857 | 0.584964285714287 |
| 24 | 13.807 | 13.0633214285714 | 0.743678571428565 |
| 25 | 29.743 | 30.1425892857143 | -0.399589285714304 |
| 26 | 25.591 | 27.7031607142857 | -2.11216071428572 |
| 27 | 29.096 | 31.3681607142857 | -2.2721607142857 |
| 28 | 26.482 | 28.1990178571428 | -1.71701785714284 |
| 29 | 22.405 | 23.896875 | -1.49187499999999 |
| 30 | 27.044 | 25.126875 | 1.917125 |
| 31 | 17.97 | 19.5865892857143 | -1.61658928571429 |
| 32 | 18.73 | 18.1073035714286 | 0.62269642857143 |
| 33 | 19.684 | 20.4624642857143 | -0.778464285714285 |
| 34 | 19.785 | 23.1278928571429 | -3.34289285714286 |
| 35 | 18.479 | 18.5840357142857 | -0.105035714285713 |
| 36 | 10.698 | 13.0633214285714 | -2.36532142857143 |
| 37 | 31.956 | 30.1425892857143 | 1.81341071428570 |
| 38 | 29.506 | 27.7031607142857 | 1.80283928571428 |
| 39 | 34.506 | 31.3681607142857 | 3.1378392857143 |
| 40 | 27.165 | 28.1990178571428 | -1.03401785714284 |
| 41 | 26.736 | 23.896875 | 2.83912500000001 |
| 42 | 23.691 | 25.126875 | -1.435875 |
| 43 | 18.157 | 19.5865892857143 | -1.42958928571429 |
| 44 | 17.328 | 18.1073035714286 | -0.779303571428571 |
| 45 | 18.205 | 20.4624642857143 | -2.25746428571429 |
| 46 | 20.995 | 23.1278928571429 | -2.13289285714286 |
| 47 | 17.382 | 18.5840357142857 | -1.20203571428571 |
| 48 | 9.367 | 13.0633214285714 | -3.69632142857143 |
| 49 | 31.124 | 30.1425892857143 | 0.981410714285696 |
| 50 | 26.551 | 27.7031607142857 | -1.15216071428572 |
| 51 | 30.651 | 31.3681607142857 | -0.7171607142857 |
| 52 | 25.859 | 28.1990178571428 | -2.34001785714284 |
| 53 | 25.1 | 23.896875 | 1.20312500000001 |
| 54 | 25.778 | 25.126875 | 0.651124999999998 |
| 55 | 20.418 | 19.5865892857143 | 0.831410714285713 |
| 56 | 18.688 | 18.1073035714286 | 0.580696428571428 |
| 57 | 20.424 | 20.4624642857143 | -0.0384642857142866 |
| 58 | 24.776 | 23.1278928571429 | 1.64810714285714 |
| 59 | 19.814 | 18.5840357142857 | 1.22996428571429 |
| 60 | 12.738 | 13.0633214285714 | -0.325321428571436 |
| 61 | 31.566 | 30.1425892857143 | 1.42341071428570 |
| 62 | 30.111 | 27.7031607142857 | 2.40783928571428 |
| 63 | 30.019 | 31.3681607142857 | -1.3491607142857 |
| 64 | 31.934 | 28.1990178571428 | 3.73498214285716 |
| 65 | 25.826 | 23.896875 | 1.92912500000001 |
| 66 | 26.835 | 25.126875 | 1.708125 |
| 67 | 20.205 | 19.5865892857143 | 0.618410714285712 |
| 68 | 17.789 | 18.1073035714286 | -0.318303571428569 |
| 69 | 20.52 | 18.8433392857143 | 1.67666071428571 |
| 70 | 22.518 | 21.5087678571429 | 1.00923214285714 |
| 71 | 15.572 | 16.9649107142857 | -1.39291071428571 |
| 72 | 11.509 | 11.4441964285714 | 0.0648035714285629 |
| 73 | 25.447 | 28.5234642857143 | -3.07646428571431 |
| 74 | 24.09 | 26.0840357142857 | -1.99403571428572 |
| 75 | 27.786 | 29.7490357142857 | -1.96303571428570 |
| 76 | 26.195 | 26.5798928571428 | -0.384892857142838 |
| 77 | 20.516 | 22.27775 | -1.76174999999999 |
| 78 | 22.759 | 23.50775 | -0.748749999999998 |
| 79 | 19.028 | 17.9674642857143 | 1.06053571428571 |
| 80 | 16.971 | 16.4881785714286 | 0.482821428571429 |
| 81 | 20.036 | 18.8433392857143 | 1.19266071428571 |
| 82 | 22.485 | 21.5087678571429 | 0.976232142857142 |
| 83 | 18.73 | 16.9649107142857 | 1.76508928571429 |
| 84 | 14.538 | 11.4441964285714 | 3.09380357142856 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 16 | 0.996452077148394 | 0.0070958457032111 | 0.00354792285160555 |
| 17 | 0.991388538875865 | 0.0172229222482710 | 0.00861146112413552 |
| 18 | 0.981624836201743 | 0.0367503275965147 | 0.0183751637982573 |
| 19 | 0.981091124784194 | 0.0378177504316111 | 0.0189088752158056 |
| 20 | 0.965184086533379 | 0.0696318269332425 | 0.0348159134666213 |
| 21 | 0.94014138456684 | 0.119717230866318 | 0.059858615433159 |
| 22 | 0.922504861198616 | 0.154990277602769 | 0.0774951388013844 |
| 23 | 0.889021227912969 | 0.221957544174062 | 0.110978772087031 |
| 24 | 0.855952620916544 | 0.288094758166912 | 0.144047379083456 |
| 25 | 0.798584199691953 | 0.402831600616094 | 0.201415800308047 |
| 26 | 0.79797920393451 | 0.404041592130979 | 0.202020796065489 |
| 27 | 0.837919859971912 | 0.324160280056176 | 0.162080140028088 |
| 28 | 0.827053913887561 | 0.345892172224879 | 0.172946086112439 |
| 29 | 0.791747573420803 | 0.416504853158394 | 0.208252426579197 |
| 30 | 0.79479489702622 | 0.410410205947560 | 0.205205102973780 |
| 31 | 0.768451037076802 | 0.463097925846396 | 0.231548962923198 |
| 32 | 0.710491989340525 | 0.579016021318951 | 0.289508010659475 |
| 33 | 0.64890818020313 | 0.70218363959374 | 0.35109181979687 |
| 34 | 0.760146344545893 | 0.479707310908214 | 0.239853655454107 |
| 35 | 0.696503505810225 | 0.60699298837955 | 0.303496494189775 |
| 36 | 0.743224461099177 | 0.513551077801645 | 0.256775538900823 |
| 37 | 0.726054222146344 | 0.547891555707312 | 0.273945777853656 |
| 38 | 0.708049795362201 | 0.583900409275598 | 0.291950204637799 |
| 39 | 0.790174599681153 | 0.419650800637693 | 0.209825400318847 |
| 40 | 0.74810434324724 | 0.503791313505519 | 0.251895656752759 |
| 41 | 0.800956967524654 | 0.398086064950691 | 0.199043032475346 |
| 42 | 0.774743978443535 | 0.45051204311293 | 0.225256021556465 |
| 43 | 0.751867495675459 | 0.496265008649083 | 0.248132504324541 |
| 44 | 0.699079762558832 | 0.601840474882336 | 0.300920237441168 |
| 45 | 0.730722744443732 | 0.538554511112535 | 0.269277255556268 |
| 46 | 0.772436835955547 | 0.455126328088905 | 0.227563164044453 |
| 47 | 0.75037437209353 | 0.499251255812939 | 0.249625627906470 |
| 48 | 0.918036784486678 | 0.163926431026644 | 0.081963215513322 |
| 49 | 0.894239485433059 | 0.211521029133882 | 0.105760514566941 |
| 50 | 0.877764105225785 | 0.24447178954843 | 0.122235894774215 |
| 51 | 0.841689272042906 | 0.316621455914188 | 0.158310727957094 |
| 52 | 0.931563338692568 | 0.136873322614864 | 0.068436661307432 |
| 53 | 0.905099462385064 | 0.189801075229873 | 0.0949005376149363 |
| 54 | 0.867456033996794 | 0.265087932006411 | 0.132543966003206 |
| 55 | 0.824190700206719 | 0.351618599586563 | 0.175809299793281 |
| 56 | 0.763249642796169 | 0.473500714407662 | 0.236750357203831 |
| 57 | 0.782816464911793 | 0.434367070176413 | 0.217183535088207 |
| 58 | 0.739691417513658 | 0.520617164972683 | 0.260308582486342 |
| 59 | 0.671127437078936 | 0.657745125842128 | 0.328872562921064 |
| 60 | 0.796128995997742 | 0.407742008004515 | 0.203871004002258 |
| 61 | 0.78055036207199 | 0.438899275856019 | 0.219449637928009 |
| 62 | 0.791340317625888 | 0.417319364748225 | 0.208659682374112 |
| 63 | 0.726352692751407 | 0.547294614497186 | 0.273647307248593 |
| 64 | 0.76114872695177 | 0.47770254609646 | 0.23885127304823 |
| 65 | 0.786223290055095 | 0.427553419889809 | 0.213776709944905 |
| 66 | 0.790677879610403 | 0.418644240779194 | 0.209322120389597 |
| 67 | 0.660526496930659 | 0.678947006138682 | 0.339473503069341 |
| 68 | 0.487497997955959 | 0.974995995911917 | 0.512502002044041 |
| Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
| Description | # significant tests | % significant tests | OK/NOK |
| 1% type I error level | 1 | 0.0188679245283019 | NOK |
| 5% type I error level | 4 | 0.0754716981132075 | NOK |
| 10% type I error level | 5 | 0.0943396226415094 | OK |
