| Multiple Linear Regression - Estimated Regression Equation |
| Y[t] = + 103.885297340278 + 18.0026589708333X[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) | 103.885297340278 | 1.912641 | 54.3151 | 0 | 0 |
| X | 18.0026589708333 | 3.312792 | 5.4343 | 0 | 0 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.4667909175743 |
| R-squared | 0.217893760729857 |
| Adjusted R-squared | 0.210515399982025 |
| F-TEST (value) | 29.5314593819359 |
| F-TEST (DF numerator) | 1 |
| F-TEST (DF denominator) | 106 |
| p-value | 3.53844414435756e-07 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 16.2293012130874 |
| Sum Squared Residuals | 27919.3630937027 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 100 | 103.885297340278 | -3.88529734027768 |
| 2 | 108.1560276 | 103.885297340278 | 4.27073025972225 |
| 3 | 114.0150276 | 103.885297340278 | 10.1297302597222 |
| 4 | 102.1880309 | 103.885297340278 | -1.69726644027778 |
| 5 | 110.3672031 | 103.885297340278 | 6.48190575972222 |
| 6 | 96.8602511 | 103.885297340278 | -7.02504624027778 |
| 7 | 94.1944583 | 103.885297340278 | -9.69083904027779 |
| 8 | 99.51621961 | 103.885297340278 | -4.36907773027779 |
| 9 | 94.06333487 | 103.885297340278 | -9.82196247027777 |
| 10 | 97.5541476 | 103.885297340278 | -6.33114974027779 |
| 11 | 78.15062422 | 103.885297340278 | -25.7346731202778 |
| 12 | 81.2434643 | 103.885297340278 | -22.6418330402778 |
| 13 | 92.36262465 | 103.885297340278 | -11.5226726902778 |
| 14 | 96.06324371 | 103.885297340278 | -7.82205363027778 |
| 15 | 114.0523777 | 103.885297340278 | 10.1670803597222 |
| 16 | 110.6616666 | 103.885297340278 | 6.77636925972222 |
| 17 | 104.9171949 | 103.885297340278 | 1.03189755972222 |
| 18 | 90.00187193 | 103.885297340278 | -13.8834254102778 |
| 19 | 95.7008067 | 103.885297340278 | -8.18449064027778 |
| 20 | 86.02741157 | 103.885297340278 | -17.8578857702778 |
| 21 | 84.85287668 | 103.885297340278 | -19.0324206602778 |
| 22 | 100.04328 | 103.885297340278 | -3.84201734027778 |
| 23 | 80.91713823 | 103.885297340278 | -22.9681591102778 |
| 24 | 74.06539709 | 103.885297340278 | -29.8199002502778 |
| 25 | 77.30281369 | 103.885297340278 | -26.5824836502778 |
| 26 | 97.23043249 | 103.885297340278 | -6.65486485027778 |
| 27 | 90.75515676 | 103.885297340278 | -13.1301405802778 |
| 28 | 100.5614455 | 103.885297340278 | -3.32385184027777 |
| 29 | 92.01293267 | 103.885297340278 | -11.8723646702778 |
| 30 | 99.24012138 | 103.885297340278 | -4.64517596027777 |
| 31 | 105.8672755 | 103.885297340278 | 1.98197815972223 |
| 32 | 90.9920463 | 103.885297340278 | -12.8932510402778 |
| 33 | 93.30624423 | 103.885297340278 | -10.5790531102778 |
| 34 | 91.17419413 | 103.885297340278 | -12.7111032102778 |
| 35 | 77.33295039 | 103.885297340278 | -26.5523469502778 |
| 36 | 91.1277721 | 103.885297340278 | -12.7575252402778 |
| 37 | 85.01249943 | 103.885297340278 | -18.8727979102778 |
| 38 | 83.90390242 | 103.885297340278 | -19.9813949202778 |
| 39 | 104.8626302 | 103.885297340278 | 0.97733285972222 |
| 40 | 110.9039108 | 103.885297340278 | 7.01861345972223 |
| 41 | 95.43714373 | 103.885297340278 | -8.44815361027778 |
| 42 | 111.6238727 | 103.885297340278 | 7.73857535972223 |
| 43 | 108.8925403 | 103.885297340278 | 5.00724295972221 |
| 44 | 96.17511682 | 103.885297340278 | -7.71018052027778 |
| 45 | 101.9740205 | 103.885297340278 | -1.91127684027778 |
| 46 | 99.11953031 | 103.885297340278 | -4.76576703027778 |
| 47 | 86.78158147 | 103.885297340278 | -17.1037158702778 |
| 48 | 118.4195003 | 103.885297340278 | 14.5342029597222 |
| 49 | 118.7441447 | 103.885297340278 | 14.8588473597222 |
| 50 | 106.5296192 | 103.885297340278 | 2.64432185972222 |
| 51 | 134.7772694 | 103.885297340278 | 30.8919720597222 |
| 52 | 104.6778714 | 103.885297340278 | 0.792574059722222 |
| 53 | 105.2954304 | 103.885297340278 | 1.41013305972222 |
| 54 | 139.4139849 | 103.885297340278 | 35.5286875597222 |
| 55 | 103.6060491 | 103.885297340278 | -0.279248240277772 |
| 56 | 99.78182974 | 103.885297340278 | -4.10346760027777 |
| 57 | 103.4610301 | 103.885297340278 | -0.424267240277777 |
| 58 | 120.0594945 | 103.885297340278 | 16.1741971597222 |
| 59 | 96.71377168 | 103.885297340278 | -7.17152566027779 |
| 60 | 107.1308929 | 103.885297340278 | 3.24559555972223 |
| 61 | 105.3608372 | 103.885297340278 | 1.47553985972223 |
| 62 | 111.6942359 | 103.885297340278 | 7.80893855972222 |
| 63 | 132.0519998 | 103.885297340278 | 28.1667024597222 |
| 64 | 126.8037879 | 103.885297340278 | 22.9184905597222 |
| 65 | 154.4824253 | 103.885297340278 | 50.5971279597222 |
| 66 | 141.5570984 | 103.885297340278 | 37.6718010597222 |
| 67 | 109.9506882 | 103.885297340278 | 6.06539085972222 |
| 68 | 127.904198 | 103.885297340278 | 24.0189006597222 |
| 69 | 133.0888617 | 103.885297340278 | 29.2035643597222 |
| 70 | 120.0796299 | 103.885297340278 | 16.1943325597222 |
| 71 | 117.5557142 | 103.885297340278 | 13.6704168597222 |
| 72 | 143.0362309 | 103.885297340278 | 39.1509335597222 |
| 73 | 159.982927 | 121.887956311111 | 38.0949706888889 |
| 74 | 128.5991124 | 121.887956311111 | 6.71115608888889 |
| 75 | 149.7373327 | 121.887956311111 | 27.8493763888889 |
| 76 | 126.8169313 | 121.887956311111 | 4.92897498888888 |
| 77 | 140.9639674 | 121.887956311111 | 19.0760110888889 |
| 78 | 137.6691981 | 121.887956311111 | 15.7812417888889 |
| 79 | 117.9402337 | 121.887956311111 | -3.94772261111112 |
| 80 | 122.3095247 | 121.887956311111 | 0.421568388888889 |
| 81 | 127.7804207 | 121.887956311111 | 5.89246438888889 |
| 82 | 136.1677176 | 121.887956311111 | 14.2797612888889 |
| 83 | 116.2405856 | 121.887956311111 | -5.6473707111111 |
| 84 | 123.1576893 | 121.887956311111 | 1.26973298888889 |
| 85 | 116.3400234 | 121.887956311111 | -5.5479329111111 |
| 86 | 108.6119282 | 121.887956311111 | -13.2760281111111 |
| 87 | 125.8982264 | 121.887956311111 | 4.01027008888889 |
| 88 | 112.8003105 | 121.887956311111 | -9.08764581111111 |
| 89 | 107.5182447 | 121.887956311111 | -14.3697116111111 |
| 90 | 135.0955413 | 121.887956311111 | 13.2075849888889 |
| 91 | 115.5096488 | 121.887956311111 | -6.37830751111111 |
| 92 | 115.8640759 | 121.887956311111 | -6.0238804111111 |
| 93 | 104.5883906 | 121.887956311111 | -17.2995657111111 |
| 94 | 163.7213386 | 121.887956311111 | 41.8333822888889 |
| 95 | 113.4482275 | 121.887956311111 | -8.4397288111111 |
| 96 | 98.0428844 | 121.887956311111 | -23.8450719111111 |
| 97 | 116.7868521 | 121.887956311111 | -5.10110421111110 |
| 98 | 126.5330444 | 121.887956311111 | 4.64508808888889 |
| 99 | 113.0336597 | 121.887956311111 | -8.85429661111111 |
| 100 | 124.3392163 | 121.887956311111 | 2.45125998888890 |
| 101 | 109.8298759 | 121.887956311111 | -12.0580804111111 |
| 102 | 124.4434777 | 121.887956311111 | 2.55552138888889 |
| 103 | 111.5039454 | 121.887956311111 | -10.3840109111111 |
| 104 | 102.0350019 | 121.887956311111 | -19.8529544111111 |
| 105 | 116.8726598 | 121.887956311111 | -5.01529651111111 |
| 106 | 112.2073122 | 121.887956311111 | -9.6806441111111 |
| 107 | 101.1513902 | 121.887956311111 | -20.7365661111111 |
| 108 | 124.4255108 | 121.887956311111 | 2.53755448888889 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 5 | 0.0787621459489388 | 0.157524291897878 | 0.921237854051061 |
| 6 | 0.0608673300550259 | 0.121734660110052 | 0.939132669944974 |
| 7 | 0.0524970373291991 | 0.104994074658398 | 0.94750296267080 |
| 8 | 0.0242007698072505 | 0.048401539614501 | 0.97579923019275 |
| 9 | 0.0170988855224703 | 0.0341977710449407 | 0.98290111447753 |
| 10 | 0.00806685693399365 | 0.0161337138679873 | 0.991933143066006 |
| 11 | 0.0529571894476661 | 0.105914378895332 | 0.947042810552334 |
| 12 | 0.080376905281759 | 0.160753810563518 | 0.919623094718241 |
| 13 | 0.0531355764199753 | 0.106271152839951 | 0.946864423580025 |
| 14 | 0.0313333000292319 | 0.0626666000584639 | 0.968666699970768 |
| 15 | 0.0388281831857341 | 0.0776563663714681 | 0.961171816814266 |
| 16 | 0.0334811211090817 | 0.0669622422181635 | 0.966518878890918 |
| 17 | 0.0214190042818892 | 0.0428380085637783 | 0.97858099571811 |
| 18 | 0.0167603065561136 | 0.0335206131122272 | 0.983239693443886 |
| 19 | 0.0101287447552609 | 0.0202574895105219 | 0.98987125524474 |
| 20 | 0.0101689434662982 | 0.0203378869325964 | 0.989831056533702 |
| 21 | 0.0107489191315675 | 0.0214978382631350 | 0.989251080868432 |
| 22 | 0.0063843752719433 | 0.0127687505438866 | 0.993615624728057 |
| 23 | 0.00950466856588625 | 0.0190093371317725 | 0.990495331434114 |
| 24 | 0.0253257833238490 | 0.0506515666476979 | 0.974674216676151 |
| 25 | 0.0403065992860307 | 0.0806131985720614 | 0.95969340071397 |
| 26 | 0.0281869950852667 | 0.0563739901705335 | 0.971813004914733 |
| 27 | 0.0212865245061066 | 0.0425730490122132 | 0.978713475493893 |
| 28 | 0.0149645781628233 | 0.0299291563256465 | 0.985035421837177 |
| 29 | 0.0108460157570762 | 0.0216920315141525 | 0.989153984242924 |
| 30 | 0.00734898567943645 | 0.0146979713588729 | 0.992651014320564 |
| 31 | 0.00585599677205853 | 0.0117119935441171 | 0.994144003227941 |
| 32 | 0.00439666802741335 | 0.0087933360548267 | 0.995603331972587 |
| 33 | 0.00307856369259617 | 0.00615712738519234 | 0.996921436307404 |
| 34 | 0.00231943102872675 | 0.0046388620574535 | 0.997680568971273 |
| 35 | 0.00523983629130157 | 0.0104796725826031 | 0.994760163708698 |
| 36 | 0.0042283107680864 | 0.0084566215361728 | 0.995771689231914 |
| 37 | 0.0048982100307368 | 0.0097964200614736 | 0.995101789969263 |
| 38 | 0.00641345089555615 | 0.0128269017911123 | 0.993586549104444 |
| 39 | 0.00552971063102585 | 0.0110594212620517 | 0.994470289368974 |
| 40 | 0.00623641653045005 | 0.0124728330609001 | 0.99376358346955 |
| 41 | 0.00505677097399696 | 0.0101135419479939 | 0.994943229026003 |
| 42 | 0.00574088931181939 | 0.0114817786236388 | 0.99425911068818 |
| 43 | 0.00546022080244678 | 0.0109204416048936 | 0.994539779197553 |
| 44 | 0.00454938218488873 | 0.00909876436977746 | 0.995450617815111 |
| 45 | 0.00366736859211772 | 0.00733473718423545 | 0.996332631407882 |
| 46 | 0.00301960571050053 | 0.00603921142100107 | 0.9969803942895 |
| 47 | 0.00462140526685546 | 0.00924281053371092 | 0.995378594733145 |
| 48 | 0.00771545813885953 | 0.0154309162777191 | 0.99228454186114 |
| 49 | 0.0116318344730961 | 0.0232636689461923 | 0.988368165526904 |
| 50 | 0.0103157418822994 | 0.0206314837645988 | 0.9896842581177 |
| 51 | 0.0472571861082816 | 0.0945143722165632 | 0.952742813891718 |
| 52 | 0.0416647248854043 | 0.0833294497708086 | 0.958335275114596 |
| 53 | 0.0370736014932048 | 0.0741472029864096 | 0.962926398506795 |
| 54 | 0.133790707391586 | 0.267581414783172 | 0.866209292608414 |
| 55 | 0.122781688376571 | 0.245563376753143 | 0.877218311623429 |
| 56 | 0.122062047883039 | 0.244124095766078 | 0.877937952116961 |
| 57 | 0.117982545739986 | 0.235965091479971 | 0.882017454260014 |
| 58 | 0.123970415073652 | 0.247940830147305 | 0.876029584926348 |
| 59 | 0.147593333261397 | 0.295186666522794 | 0.852406666738603 |
| 60 | 0.148935580984675 | 0.297871161969349 | 0.851064419015325 |
| 61 | 0.161496699523163 | 0.322993399046325 | 0.838503300476837 |
| 62 | 0.169790134247940 | 0.339580268495879 | 0.83020986575206 |
| 63 | 0.228722367136195 | 0.457444734272389 | 0.771277632863805 |
| 64 | 0.254764908355812 | 0.509529816711625 | 0.745235091644188 |
| 65 | 0.582584176854118 | 0.834831646291763 | 0.417415823145882 |
| 66 | 0.695816514858851 | 0.608366970282298 | 0.304183485141149 |
| 67 | 0.689278457524662 | 0.621443084950677 | 0.310721542475338 |
| 68 | 0.685551509441902 | 0.628896981116196 | 0.314448490558098 |
| 69 | 0.701387759397603 | 0.597224481204795 | 0.298612240602397 |
| 70 | 0.678362178601241 | 0.643275642797517 | 0.321637821398759 |
| 71 | 0.68617681831603 | 0.62764636336794 | 0.31382318168397 |
| 72 | 0.726914674971448 | 0.546170650057104 | 0.273085325028552 |
| 73 | 0.868582869815772 | 0.262834260368455 | 0.131417130184227 |
| 74 | 0.858357231250921 | 0.283285537498158 | 0.141642768749079 |
| 75 | 0.915328865301453 | 0.169342269397094 | 0.0846711346985468 |
| 76 | 0.900722355879453 | 0.198555288241095 | 0.0992776441205473 |
| 77 | 0.918872672913806 | 0.162254654172387 | 0.0811273270861937 |
| 78 | 0.927924440852928 | 0.144151118294143 | 0.0720755591470715 |
| 79 | 0.912493649175098 | 0.175012701649804 | 0.0875063508249022 |
| 80 | 0.890100064910757 | 0.219799870178487 | 0.109899935089243 |
| 81 | 0.870059934539163 | 0.259880130921674 | 0.129940065460837 |
| 82 | 0.882007780552894 | 0.235984438894212 | 0.117992219447106 |
| 83 | 0.853369913580667 | 0.293260172838665 | 0.146630086419333 |
| 84 | 0.819114939704816 | 0.361770120590368 | 0.180885060295184 |
| 85 | 0.776925065059802 | 0.446149869880396 | 0.223074934940198 |
| 86 | 0.752012419240148 | 0.495975161519704 | 0.247987580759852 |
| 87 | 0.709017808118574 | 0.581964383762852 | 0.290982191881426 |
| 88 | 0.65599546729325 | 0.6880090654135 | 0.34400453270675 |
| 89 | 0.623548262080461 | 0.752903475839079 | 0.376451737919539 |
| 90 | 0.636939273258257 | 0.726121453483485 | 0.363060726741743 |
| 91 | 0.564906251543936 | 0.870187496912128 | 0.435093748456064 |
| 92 | 0.487886389176181 | 0.975772778352363 | 0.512113610823819 |
| 93 | 0.462806317325371 | 0.925612634650742 | 0.537193682674629 |
| 94 | 0.982103362894111 | 0.0357932742117773 | 0.0178966371058886 |
| 95 | 0.967971722006086 | 0.0640565559878277 | 0.0320282779939139 |
| 96 | 0.9817479482404 | 0.036504103519199 | 0.0182520517595995 |
| 97 | 0.96489012471753 | 0.0702197505649413 | 0.0351098752824707 |
| 98 | 0.962759830354305 | 0.0744803392913907 | 0.0372401696456954 |
| 99 | 0.929030183115254 | 0.141939633769492 | 0.0709698168847458 |
| 100 | 0.914925680949316 | 0.170148638101369 | 0.0850743190506845 |
| 101 | 0.847977570706551 | 0.304044858586898 | 0.152022429293449 |
| 102 | 0.831214362401126 | 0.337571275197748 | 0.168785637598874 |
| 103 | 0.688484830059195 | 0.623030339881609 | 0.311515169940805 |
| Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
| Description | # significant tests | % significant tests | OK/NOK |
| 1% type I error level | 9 | 0.090909090909091 | NOK |
| 5% type I error level | 36 | 0.363636363636364 | NOK |
| 10% type I error level | 48 | 0.484848484848485 | NOK |
