| Multiple Linear Regression - Estimated Regression Equation |
| Y[t] = + 6.7992929704292 -0.595409398402679X[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) | 6.7992929704292 | 1.541765 | 4.4101 | 4.2e-05 | 2.1e-05 |
| X | -0.595409398402679 | 0.214263 | -2.7789 | 0.00721 | 0.003605 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.332800503518977 |
| R-squared | 0.110756175142485 |
| Adjusted R-squared | 0.0964135328060733 |
| F-TEST (value) | 7.72215973491225 |
| F-TEST (DF numerator) | 1 |
| F-TEST (DF denominator) | 62 |
| p-value | 0.00720990438056168 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 1.12614036542989 |
| Sum Squared Residuals | 78.627911604335 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 1.4 | 1.91693590352723 | -0.51693590352723 |
| 2 | 1.2 | 2.03601778320776 | -0.836017783207764 |
| 3 | 1 | 2.33372248240910 | -1.33372248240910 |
| 4 | 1.7 | 2.75050906129098 | -1.05050906129098 |
| 5 | 2.4 | 2.92913188081178 | -0.529131880811783 |
| 6 | 2 | 2.86959094097152 | -0.869590940971516 |
| 7 | 2.1 | 2.27418154256884 | -0.174181542568836 |
| 8 | 2 | 2.03601778320776 | -0.0360177832077644 |
| 9 | 1.8 | 1.97647684336750 | -0.176476843367497 |
| 10 | 2.7 | 2.21464060272857 | 0.485359397271432 |
| 11 | 2.3 | 2.33372248240910 | -0.0337224824091043 |
| 12 | 1.9 | 2.27418154256884 | -0.374181542568837 |
| 13 | 2 | 2.1550996628883 | -0.155099662888300 |
| 14 | 2.3 | 2.1550996628883 | 0.144900337111699 |
| 15 | 2.8 | 2.1550996628883 | 0.6449003371117 |
| 16 | 2.4 | 2.33372248240910 | 0.0662775175908958 |
| 17 | 2.3 | 2.33372248240910 | -0.0337224824091043 |
| 18 | 2.7 | 2.57188624177018 | 0.128113758229824 |
| 19 | 2.7 | 2.33372248240910 | 0.366277517590896 |
| 20 | 2.9 | 2.33372248240910 | 0.566277517590896 |
| 21 | 3 | 2.27418154256884 | 0.725818457431164 |
| 22 | 2.2 | 2.21464060272857 | -0.0146406027285680 |
| 23 | 2.3 | 2.21464060272857 | 0.0853593972714317 |
| 24 | 2.8 | 2.09555872304803 | 0.704441276951968 |
| 25 | 2.8 | 1.97647684336750 | 0.823523156632503 |
| 26 | 2.8 | 1.91693590352723 | 0.88306409647277 |
| 27 | 2.2 | 1.91693590352723 | 0.283064096472771 |
| 28 | 2.6 | 1.91693590352723 | 0.683064096472771 |
| 29 | 2.8 | 2.09555872304803 | 0.704441276951968 |
| 30 | 2.5 | 2.45280436208964 | 0.047195637910360 |
| 31 | 2.4 | 2.69096812145071 | -0.290968121450712 |
| 32 | 2.3 | 2.86959094097152 | -0.569590940971516 |
| 33 | 1.9 | 2.81005000113125 | -0.910050001131247 |
| 34 | 1.7 | 2.69096812145071 | -0.990968121450711 |
| 35 | 2 | 2.63142718161044 | -0.631427181610444 |
| 36 | 2.1 | 2.57188624177018 | -0.471886241770176 |
| 37 | 1.7 | 2.51234530192991 | -0.812345301929908 |
| 38 | 1.8 | 2.57188624177018 | -0.771886241770176 |
| 39 | 1.8 | 2.69096812145071 | -0.890968121450711 |
| 40 | 1.8 | 2.63142718161044 | -0.831427181610444 |
| 41 | 1.3 | 2.75050906129098 | -1.45050906129098 |
| 42 | 1.3 | 2.98867282065205 | -1.68867282065205 |
| 43 | 1.3 | 2.81005000113125 | -1.51005000113125 |
| 44 | 1.2 | 2.86959094097152 | -1.66959094097152 |
| 45 | 1.4 | 2.98867282065205 | -1.58867282065205 |
| 46 | 2.2 | 3.04821376049232 | -0.848213760492319 |
| 47 | 2.9 | 3.10775470033259 | -0.207754700332587 |
| 48 | 3.1 | 2.92913188081178 | 0.170868119188217 |
| 49 | 3.5 | 2.75050906129098 | 0.74949093870902 |
| 50 | 3.6 | 2.75050906129098 | 0.84949093870902 |
| 51 | 4.4 | 2.98867282065205 | 1.41132717934795 |
| 52 | 4.1 | 3.16729564017286 | 0.932704359827144 |
| 53 | 5.1 | 3.34591845969366 | 1.75408154030634 |
| 54 | 5.8 | 3.16729564017285 | 2.63270435982714 |
| 55 | 5.9 | 2.51234530192991 | 3.38765469807009 |
| 56 | 5.4 | 2.45280436208964 | 2.94719563791036 |
| 57 | 5.5 | 2.69096812145071 | 2.80903187854929 |
| 58 | 4.8 | 3.16729564017286 | 1.63270435982714 |
| 59 | 3.2 | 3.34591845969366 | -0.145918459693659 |
| 60 | 2.7 | 3.10775470033259 | -0.407754700332587 |
| 61 | 2.1 | 2.57188624177018 | -0.471886241770176 |
| 62 | 1.9 | 2.21464060272857 | -0.314640602728568 |
| 63 | 0.6 | 2.09555872304803 | -1.49555872304803 |
| 64 | 0.7 | 2.21464060272857 | -1.51464060272857 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 5 | 0.05487476495759 | 0.10974952991518 | 0.94512523504241 |
| 6 | 0.0157044852129962 | 0.0314089704259924 | 0.984295514787004 |
| 7 | 0.0149770288416100 | 0.0299540576832201 | 0.98502297115839 |
| 8 | 0.0110406487266641 | 0.0220812974533281 | 0.988959351273336 |
| 9 | 0.00463431173573053 | 0.00926862347146106 | 0.99536568826427 |
| 10 | 0.0103383092331128 | 0.0206766184662256 | 0.989661690766887 |
| 11 | 0.00566546122926184 | 0.0113309224585237 | 0.994334538770738 |
| 12 | 0.00225509298357368 | 0.00451018596714736 | 0.997744907016426 |
| 13 | 0.000903231939007924 | 0.00180646387801585 | 0.999096768060992 |
| 14 | 0.000489914960487134 | 0.000979829920974268 | 0.999510085039513 |
| 15 | 0.000743763628348365 | 0.00148752725669673 | 0.999256236371652 |
| 16 | 0.000371620036632543 | 0.000743240073265086 | 0.999628379963367 |
| 17 | 0.000160199831138948 | 0.000320399662277897 | 0.999839800168861 |
| 18 | 0.000102128858814047 | 0.000204257717628095 | 0.999897871141186 |
| 19 | 7.07488441709346e-05 | 0.000141497688341869 | 0.99992925115583 |
| 20 | 6.85276338702973e-05 | 0.000137055267740595 | 0.99993147236613 |
| 21 | 7.7246112161872e-05 | 0.000154492224323744 | 0.999922753887838 |
| 22 | 3.04108332078833e-05 | 6.08216664157665e-05 | 0.999969589166792 |
| 23 | 1.19134891270325e-05 | 2.38269782540651e-05 | 0.999988086510873 |
| 24 | 8.93929302917981e-06 | 1.78785860583596e-05 | 0.99999106070697 |
| 25 | 6.5612137106992e-06 | 1.31224274213984e-05 | 0.99999343878629 |
| 26 | 4.53730720429082e-06 | 9.07461440858165e-06 | 0.999995462692796 |
| 27 | 1.74666609901726e-06 | 3.49333219803453e-06 | 0.9999982533339 |
| 28 | 8.91585774884334e-07 | 1.78317154976867e-06 | 0.999999108414225 |
| 29 | 5.93523608934406e-07 | 1.18704721786881e-06 | 0.99999940647639 |
| 30 | 2.29458732742378e-07 | 4.58917465484755e-07 | 0.999999770541267 |
| 31 | 8.02944229432409e-08 | 1.60588845886482e-07 | 0.999999919705577 |
| 32 | 2.84238599628386e-08 | 5.68477199256773e-08 | 0.99999997157614 |
| 33 | 1.33303409033169e-08 | 2.66606818066338e-08 | 0.99999998666966 |
| 34 | 7.9033183298663e-09 | 1.58066366597326e-08 | 0.999999992096682 |
| 35 | 2.8188469665673e-09 | 5.6376939331346e-09 | 0.999999997181153 |
| 36 | 8.95697248669437e-10 | 1.79139449733887e-09 | 0.999999999104303 |
| 37 | 4.58176425368841e-10 | 9.16352850737683e-10 | 0.999999999541824 |
| 38 | 1.92631040055146e-10 | 3.85262080110292e-10 | 0.99999999980737 |
| 39 | 8.34724264386317e-11 | 1.66944852877263e-10 | 0.999999999916528 |
| 40 | 3.4904774995334e-11 | 6.9809549990668e-11 | 0.999999999965095 |
| 41 | 5.5523985823355e-11 | 1.1104797164671e-10 | 0.999999999944476 |
| 42 | 1.05284507464494e-10 | 2.10569014928988e-10 | 0.999999999894716 |
| 43 | 1.85088336377084e-10 | 3.70176672754168e-10 | 0.999999999814912 |
| 44 | 5.74345941235107e-10 | 1.14869188247021e-09 | 0.999999999425654 |
| 45 | 1.72209793056495e-09 | 3.44419586112990e-09 | 0.999999998277902 |
| 46 | 3.05692268830710e-09 | 6.11384537661421e-09 | 0.999999996943077 |
| 47 | 1.27728054792601e-08 | 2.55456109585201e-08 | 0.999999987227195 |
| 48 | 2.92461738331463e-08 | 5.84923476662926e-08 | 0.999999970753826 |
| 49 | 7.99498084186314e-08 | 1.59899616837263e-07 | 0.999999920050192 |
| 50 | 1.81279966049386e-07 | 3.62559932098772e-07 | 0.999999818720034 |
| 51 | 1.85820561814267e-06 | 3.71641123628534e-06 | 0.999998141794382 |
| 52 | 3.85187723798283e-06 | 7.70375447596566e-06 | 0.999996148122762 |
| 53 | 1.91228242940512e-05 | 3.82456485881023e-05 | 0.999980877175706 |
| 54 | 0.000193112610894195 | 0.00038622522178839 | 0.999806887389106 |
| 55 | 0.00935106277678388 | 0.0187021255535678 | 0.990648937223216 |
| 56 | 0.121507883855253 | 0.243015767710505 | 0.878492116144747 |
| 57 | 0.740995289848867 | 0.518009420302267 | 0.259004710151133 |
| 58 | 0.94533912984641 | 0.109321740307179 | 0.0546608701535897 |
| 59 | 0.861129536419469 | 0.277740927161062 | 0.138870463580531 |
| Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
| Description | # significant tests | % significant tests | OK/NOK |
| 1% type I error level | 44 | 0.8 | NOK |
| 5% type I error level | 50 | 0.909090909090909 | NOK |
| 10% type I error level | 50 | 0.909090909090909 | NOK |
