| Multiple Linear Regression - Estimated Regression Equation |
| Y[t] = + 0.926377432376777 + 0.20862236830311X[t] + 1.51300377809217Y1[t] -0.848950794851456Y2[t] -0.133140187587768Y3[t] + 0.372615536039044Y4[t] -0.240677055650023M1[t] -0.0853905579208965M2[t] -0.0798213024523612M3[t] -0.233163691979213M4[t] -0.135516619773325M5[t] + 0.438080071005953M6[t] -0.500032999637043M7[t] -0.147424418177767M8[t] + 0.0149030110573563M9[t] -0.136869156770028M10[t] -0.0071194533536342M11[t] -0.00493769282430811t + 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) | 0.926377432376777 | 0.647107 | 1.4316 | 0.160442 | 0.080221 |
| X | 0.20862236830311 | 0.095114 | 2.1934 | 0.034469 | 0.017234 |
| Y1 | 1.51300377809217 | 0.145007 | 10.434 | 0 | 0 |
| Y2 | -0.848950794851456 | 0.274528 | -3.0924 | 0.00371 | 0.001855 |
| Y3 | -0.133140187587768 | 0.274445 | -0.4851 | 0.630372 | 0.315186 |
| Y4 | 0.372615536039044 | 0.14781 | 2.5209 | 0.016022 | 0.008011 |
| M1 | -0.240677055650023 | 0.111247 | -2.1634 | 0.036862 | 0.018431 |
| M2 | -0.0853905579208965 | 0.120872 | -0.7065 | 0.484216 | 0.242108 |
| M3 | -0.0798213024523612 | 0.121187 | -0.6587 | 0.514083 | 0.257042 |
| M4 | -0.233163691979213 | 0.115391 | -2.0206 | 0.050406 | 0.025203 |
| M5 | -0.135516619773325 | 0.115866 | -1.1696 | 0.249445 | 0.124723 |
| M6 | 0.438080071005953 | 0.109585 | 3.9976 | 0.000284 | 0.000142 |
| M7 | -0.500032999637043 | 0.124218 | -4.0254 | 0.000262 | 0.000131 |
| M8 | -0.147424418177767 | 0.159982 | -0.9215 | 0.3626 | 0.1813 |
| M9 | 0.0149030110573563 | 0.146837 | 0.1015 | 0.919692 | 0.459846 |
| M10 | -0.136869156770028 | 0.120038 | -1.1402 | 0.261333 | 0.130667 |
| M11 | -0.0071194533536342 | 0.115911 | -0.0614 | 0.951345 | 0.475673 |
| t | -0.00493769282430811 | 0.003658 | -1.3498 | 0.18506 | 0.09253 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.979836295763954 |
| R-squared | 0.960079166496428 |
| Adjusted R-squared | 0.94221984624483 |
| F-TEST (value) | 53.7578784058433 |
| F-TEST (DF numerator) | 17 |
| F-TEST (DF denominator) | 38 |
| p-value | 0 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 0.158771748288892 |
| Sum Squared Residuals | 0.957921786079023 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 8.6 | 8.64500882573885 | -0.0450088257388447 |
| 2 | 8.5 | 8.57724606270429 | -0.0772460627042843 |
| 3 | 8.2 | 8.3523156841405 | -0.152315684140502 |
| 4 | 8.1 | 7.88623863629586 | 0.213761363704136 |
| 5 | 7.9 | 8.13290844868635 | -0.232908448686345 |
| 6 | 8.6 | 8.48654227318045 | 0.113457726819547 |
| 7 | 8.7 | 8.67391367129502 | 0.0260863287049752 |
| 8 | 8.7 | 8.56798586525684 | 0.132014134743160 |
| 9 | 8.5 | 8.47275928366326 | 0.0272407163367366 |
| 10 | 8.4 | 8.2609655238617 | 0.139034476138309 |
| 11 | 8.5 | 8.44152886921875 | 0.0584711307812455 |
| 12 | 8.7 | 8.70653412456 | -0.00653412455999671 |
| 13 | 8.7 | 8.61741596376992 | 0.0825840362300771 |
| 14 | 8.6 | 8.54739903734177 | 0.052600962658231 |
| 15 | 8.5 | 8.40736373826313 | 0.0926362617368702 |
| 16 | 8.3 | 8.2572014647957 | 0.0427985352042946 |
| 17 | 8 | 8.14551918680277 | -0.145519186802775 |
| 18 | 8.2 | 8.40611967545525 | -0.206119675455255 |
| 19 | 8.1 | 8.00972138997547 | 0.0902786100245288 |
| 20 | 8.1 | 8.00172069089945 | 0.0982793091005472 |
| 21 | 8 | 8.10559280846615 | -0.105592808466147 |
| 22 | 7.9 | 7.88541969597182 | 0.0145803040281778 |
| 23 | 7.9 | 7.90656485463593 | -0.00656485463593173 |
| 24 | 8 | 8.00695571340918 | -0.00695571340918026 |
| 25 | 8 | 7.88869380789894 | 0.111306192101061 |
| 26 | 7.9 | 7.9168859797147 | -0.0168859797147071 |
| 27 | 8 | 7.75290314579094 | 0.247096854209059 |
| 28 | 7.7 | 7.86808007433805 | -0.168080074338047 |
| 29 | 7.2 | 7.4353072595656 | -0.235307259565607 |
| 30 | 7.5 | 7.45157403456724 | 0.0484259654327551 |
| 31 | 7.3 | 7.46410341183356 | -0.164103411833555 |
| 32 | 7 | 7.20927373937682 | -0.209273739376821 |
| 33 | 7 | 6.85630267703442 | 0.143697322965576 |
| 34 | 7 | 7.09269075316744 | -0.092690753167435 |
| 35 | 7.2 | 7.18292171282804 | 0.0170782871719581 |
| 36 | 7.3 | 7.37591956816409 | -0.0759195681640908 |
| 37 | 7.1 | 7.11181503852869 | -0.0118150385286856 |
| 38 | 6.8 | 6.84803997081237 | -0.0480399708123695 |
| 39 | 6.4 | 6.62576964744827 | -0.225769647448267 |
| 40 | 6.1 | 6.18086288343713 | -0.0808628834371325 |
| 41 | 6.5 | 6.12467039640016 | 0.375329603599837 |
| 42 | 7.7 | 7.49468755827083 | 0.205312441729166 |
| 43 | 7.9 | 7.91855685243427 | -0.0185568524342709 |
| 44 | 7.5 | 7.59366917532222 | -0.0936691753222164 |
| 45 | 6.9 | 6.96534523083617 | -0.065345230836166 |
| 46 | 6.6 | 6.66092402699905 | -0.0609240269990517 |
| 47 | 6.9 | 6.96898456331727 | -0.0689845633172719 |
| 48 | 7.7 | 7.61059059386673 | 0.0894094061332678 |
| 49 | 8 | 8.1370663640636 | -0.137066364063608 |
| 50 | 8 | 7.91042894942687 | 0.0895710505731298 |
| 51 | 7.7 | 7.66164778435716 | 0.03835221564284 |
| 52 | 7.3 | 7.30761694113325 | -0.00761694113325208 |
| 53 | 7.4 | 7.16159470854511 | 0.238405291454889 |
| 54 | 8.1 | 8.26107645852621 | -0.161076458526213 |
| 55 | 8.3 | 8.23370467446168 | 0.0662953255383225 |
| 56 | 8.2 | 8.12735052914467 | 0.0726494708553302 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 21 | 0.657508608422047 | 0.684982783155906 | 0.342491391577953 |
| 22 | 0.495025960157948 | 0.990051920315897 | 0.504974039842052 |
| 23 | 0.336593124927146 | 0.673186249854292 | 0.663406875072854 |
| 24 | 0.211896594784979 | 0.423793189569959 | 0.78810340521502 |
| 25 | 0.170759066963023 | 0.341518133926046 | 0.829240933036977 |
| 26 | 0.0981557360692562 | 0.196311472138512 | 0.901844263930744 |
| 27 | 0.348587938086083 | 0.697175876172165 | 0.651412061913917 |
| 28 | 0.35730491177147 | 0.71460982354294 | 0.64269508822853 |
| 29 | 0.460783859741081 | 0.921567719482161 | 0.539216140258919 |
| 30 | 0.40192411972055 | 0.8038482394411 | 0.59807588027945 |
| 31 | 0.398995728660289 | 0.797991457320577 | 0.601004271339711 |
| 32 | 0.349453213245483 | 0.698906426490966 | 0.650546786754517 |
| 33 | 0.484682808797050 | 0.969365617594099 | 0.515317191202950 |
| 34 | 0.461195560239746 | 0.922391120479491 | 0.538804439760254 |
| 35 | 0.686633146375482 | 0.626733707249036 | 0.313366853624518 |
| 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 | 0 | 0 | OK |
