| Multiple Linear Regression - Estimated Regression Equation |
| Y[t] = -11.7933478162042 + 0.0118874959627300X[t] -2.72840580123097M1[t] + 5.26960218428549M2[t] + 5.34326942832257M3[t] + 5.45041954136613M4[t] + 2.71934529229835M5[t] + 6.7542162589432M6[t] + 2.47083702763941M7[t] + 1.26704031006233M8[t] + 2.70974721819855M9[t] -0.158659463850549M10[t] -0.449909867577547M11[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) | -11.7933478162042 | 7.137969 | -1.6522 | 0.105022 | 0.052511 |
| X | 0.0118874959627300 | 0.002738 | 4.3409 | 7.3e-05 | 3.6e-05 |
| M1 | -2.72840580123097 | 3.88133 | -0.703 | 0.485478 | 0.242739 |
| M2 | 5.26960218428549 | 3.956646 | 1.3318 | 0.189204 | 0.094602 |
| M3 | 5.34326942832257 | 3.96983 | 1.346 | 0.184635 | 0.092318 |
| M4 | 5.45041954136613 | 3.963075 | 1.3753 | 0.175423 | 0.087712 |
| M5 | 2.71934529229835 | 3.955818 | 0.6874 | 0.495121 | 0.24756 |
| M6 | 6.7542162589432 | 4.039534 | 1.672 | 0.101026 | 0.050513 |
| M7 | 2.47083702763941 | 3.963817 | 0.6233 | 0.536007 | 0.268003 |
| M8 | 1.26704031006233 | 3.95644 | 0.3202 | 0.750171 | 0.375085 |
| M9 | 2.70974721819855 | 3.955467 | 0.6851 | 0.496599 | 0.248299 |
| M10 | -0.158659463850549 | 3.967549 | -0.04 | 0.968268 | 0.484134 |
| M11 | -0.449909867577547 | 3.951867 | -0.1138 | 0.909834 | 0.454917 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.562727797596643 |
| R-squared | 0.316662574187969 |
| Adjusted R-squared | 0.145828217734961 |
| F-TEST (value) | 1.85362347927406 |
| F-TEST (DF numerator) | 12 |
| F-TEST (DF denominator) | 48 |
| p-value | 0.0656190615320313 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 6.24683593753813 |
| Sum Squared Residuals | 1873.10204306486 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 20.3 | 21.3309342061586 | -1.03093420615859 |
| 2 | 20 | 19.0938081677645 | 0.90619183223555 |
| 3 | 19.2 | 19.3695628431679 | -0.169562843167947 |
| 4 | 21.8 | 19.2151880450314 | 2.58481195496855 |
| 5 | 21.3 | 21.0370247496893 | 0.262975250310743 |
| 6 | 21.5 | 19.4253351340374 | 2.07466486596263 |
| 7 | 19.5 | 16.3544804909320 | 3.14551950906797 |
| 8 | 19.5 | 16.3394333696280 | 3.16056663037205 |
| 9 | 19.7 | 20.6113643168939 | -0.911364316893922 |
| 10 | 18.7 | 20.0847943395026 | -1.38479433950263 |
| 11 | 19.7 | 21.0298435158996 | -1.32984351589956 |
| 12 | 20 | 23.2272152899984 | -3.22721528999842 |
| 13 | 19.7 | 20.3086095533638 | -0.608609553363768 |
| 14 | 19.2 | 21.0314700096894 | -1.83147000968945 |
| 15 | 19.7 | 23.7441613574526 | -4.0441613574526 |
| 16 | 22 | 24.2079363493781 | -2.20793634937806 |
| 17 | 21.8 | 22.6537242006205 | -0.853724200620545 |
| 18 | 22.8 | 24.0852335514275 | -1.28523355142753 |
| 19 | 21 | 24.4617527375139 | -3.46175273751391 |
| 20 | 25 | 30.3666786056494 | -5.36667860564939 |
| 21 | 23.3 | 22.7511135901853 | 0.548886409814676 |
| 22 | 25 | 23.4846181848434 | 1.51538181515658 |
| 23 | 26.8 | 14.6224831919881 | 12.1775168080119 |
| 24 | 25.3 | 22.0146907018000 | 3.28530929820005 |
| 25 | 26.5 | 15.7438111036754 | 10.7561888963246 |
| 26 | 27.8 | 22.6719444525462 | 5.12805554745381 |
| 27 | 22 | 20.8317248465837 | 1.16827515341626 |
| 28 | 22.3 | 21.9374246204966 | 0.362575379503377 |
| 29 | 28 | 20.3950999677018 | 7.60490003229815 |
| 30 | 25 | 19.4134476380746 | 5.58655236192537 |
| 31 | 27.3 | 17.7809800064596 | 9.51901999354037 |
| 32 | 25.8 | 17.4211955022364 | 8.37880449776362 |
| 33 | 27.3 | 17.9723402131679 | 9.32765978683215 |
| 34 | 23.5 | 18.3373324329813 | 5.16266756701868 |
| 35 | 24.5 | 15.2287454860873 | 9.2712545139127 |
| 36 | 18 | 14.3710307977645 | 3.62896920223545 |
| 37 | 21.3 | 17.8716728810041 | 3.42832711899589 |
| 38 | 21.8 | 22.1013446463351 | -0.301344646335149 |
| 39 | 20.5 | 18.9772754763979 | 1.52272452360214 |
| 40 | 22.3 | 16.2195390624235 | 6.08046093757652 |
| 41 | 18.7 | 21.0845747335402 | -2.38457473354018 |
| 42 | 22.3 | 19.5442100936647 | 2.75578990633534 |
| 43 | 17.7 | 15.2013933825472 | 2.49860661745278 |
| 44 | 19.7 | 19.4301823199378 | 0.269817680062238 |
| 45 | 20.5 | 19.8505645752792 | 0.649435424720801 |
| 46 | 18.5 | 14.0816088783240 | 4.41839112167603 |
| 47 | 10 | 20.9704060360859 | -10.9704060360859 |
| 48 | 14.2 | 12.8137688266469 | 1.38623117335308 |
| 49 | 15.5 | 16.5640483251038 | -1.06404832510381 |
| 50 | 16.5 | 20.4014327236648 | -3.90143272366476 |
| 51 | 20.5 | 18.9772754763979 | 1.52272452360214 |
| 52 | 15.7 | 22.5199119226704 | -6.8199119226704 |
| 53 | 11.7 | 16.3295763484482 | -4.62957634844817 |
| 54 | 7.5 | 16.6317735827958 | -9.1317735827958 |
| 55 | 3.5 | 15.2013933825472 | -11.7013933825472 |
| 56 | 4.5 | 10.9425102025485 | -6.44251020254852 |
| 57 | 2.2 | 11.8146173044737 | -9.6146173044737 |
| 58 | 5 | 14.7116461643487 | -9.71164616434866 |
| 59 | 2.3 | 11.4485217699392 | -9.14852176993915 |
| 60 | 6.1 | 11.1732943837902 | -5.07329438379017 |
| 61 | 3.3 | 14.7809239306943 | -11.4809239306943 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 16 | 0.000301552809064524 | 0.000603105618129048 | 0.999698447190935 |
| 17 | 1.88149035008250e-05 | 3.76298070016499e-05 | 0.999981185096499 |
| 18 | 2.52142447205668e-06 | 5.04284894411336e-06 | 0.999997478575528 |
| 19 | 1.58881285602661e-07 | 3.17762571205321e-07 | 0.999999841118714 |
| 20 | 4.85145410800488e-07 | 9.70290821600976e-07 | 0.99999951485459 |
| 21 | 1.01889402747616e-06 | 2.03778805495233e-06 | 0.999998981105973 |
| 22 | 9.23095697472539e-06 | 1.84619139494508e-05 | 0.999990769043025 |
| 23 | 0.000419190414576797 | 0.000838380829153594 | 0.999580809585423 |
| 24 | 0.000380816501967928 | 0.000761633003935856 | 0.999619183498032 |
| 25 | 0.00137837552418469 | 0.00275675104836938 | 0.998621624475815 |
| 26 | 0.00287348673473148 | 0.00574697346946296 | 0.997126513265268 |
| 27 | 0.00140479018916747 | 0.00280958037833494 | 0.998595209810833 |
| 28 | 0.000561716794522487 | 0.00112343358904497 | 0.999438283205478 |
| 29 | 0.00081196457930109 | 0.00162392915860218 | 0.999188035420699 |
| 30 | 0.000490320671869349 | 0.000980641343738698 | 0.99950967932813 |
| 31 | 0.000994583129193421 | 0.00198916625838684 | 0.999005416870807 |
| 32 | 0.000808250408777578 | 0.00161650081755516 | 0.999191749591222 |
| 33 | 0.00127117475292252 | 0.00254234950584504 | 0.998728825247077 |
| 34 | 0.000680222706057348 | 0.00136044541211470 | 0.999319777293943 |
| 35 | 0.00358039474925363 | 0.00716078949850727 | 0.996419605250746 |
| 36 | 0.00288411937768409 | 0.00576823875536818 | 0.997115880622316 |
| 37 | 0.00250988896747196 | 0.00501977793494391 | 0.997490111032528 |
| 38 | 0.00118603450319490 | 0.00237206900638980 | 0.998813965496805 |
| 39 | 0.000490602589862517 | 0.000981205179725034 | 0.999509397410137 |
| 40 | 0.0017051355275955 | 0.003410271055191 | 0.998294864472405 |
| 41 | 0.00109821467629287 | 0.00219642935258574 | 0.998901785323707 |
| 42 | 0.00116496769842403 | 0.00232993539684805 | 0.998835032301576 |
| 43 | 0.00674271223324974 | 0.0134854244664995 | 0.99325728776675 |
| 44 | 0.00328662818044431 | 0.00657325636088863 | 0.996713371819556 |
| 45 | 0.00297657320254801 | 0.00595314640509602 | 0.997023426797452 |
| Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
| Description | # significant tests | % significant tests | OK/NOK |
| 1% type I error level | 29 | 0.966666666666667 | NOK |
| 5% type I error level | 30 | 1 | NOK |
| 10% type I error level | 30 | 1 | NOK |
