Multiple Linear Regression - Estimated Regression Equation |
Y[t] = + 516.289908256881 + 121.810091743119X[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) | 516.289908256881 | 10.333793 | 49.9613 | 0 | 0 |
X | 121.810091743119 | 39.519158 | 3.0823 | 0.002571 | 0.001286 |
Multiple Linear Regression - Regression Statistics | |
Multiple R | 0.276242092860516 |
R-squared | 0.076309693867958 |
Adjusted R-squared | 0.0682776042494186 |
F-TEST (value) | 9.50060289315269 |
F-TEST (DF numerator) | 1 |
F-TEST (DF denominator) | 115 |
p-value | 0.00257126214987702 |
Multiple Linear Regression - Residual Statistics | |
Residual Standard Deviation | 107.887964388953 |
Sum Squared Residuals | 1338578.47889908 |
Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
1 | 395.3 | 516.289908256882 | -120.989908256882 |
2 | 395.1 | 516.289908256881 | -121.189908256881 |
3 | 403.5 | 516.289908256881 | -112.789908256881 |
4 | 403.3 | 516.289908256881 | -112.989908256881 |
5 | 405.7 | 516.289908256881 | -110.589908256881 |
6 | 406.7 | 516.289908256881 | -109.589908256881 |
7 | 407.2 | 516.289908256881 | -109.089908256881 |
8 | 412.4 | 516.289908256881 | -103.889908256881 |
9 | 415.9 | 516.289908256881 | -100.389908256881 |
10 | 414 | 516.289908256881 | -102.289908256881 |
11 | 411.8 | 516.289908256881 | -104.489908256881 |
12 | 409.9 | 516.289908256881 | -106.389908256881 |
13 | 412.4 | 516.289908256881 | -103.889908256881 |
14 | 415.9 | 516.289908256881 | -100.389908256881 |
15 | 416.3 | 516.289908256881 | -99.9899082568807 |
16 | 417.2 | 516.289908256881 | -99.0899082568807 |
17 | 421.8 | 516.289908256881 | -94.4899082568807 |
18 | 421.4 | 516.289908256881 | -94.8899082568807 |
19 | 415.1 | 516.289908256881 | -101.189908256881 |
20 | 412.4 | 516.289908256881 | -103.889908256881 |
21 | 411.8 | 516.289908256881 | -104.489908256881 |
22 | 408.8 | 516.289908256881 | -107.489908256881 |
23 | 404.5 | 516.289908256881 | -111.789908256881 |
24 | 402.5 | 516.289908256881 | -113.789908256881 |
25 | 409.4 | 516.289908256881 | -106.889908256881 |
26 | 410.7 | 516.289908256881 | -105.589908256881 |
27 | 413.4 | 516.289908256881 | -102.889908256881 |
28 | 415.2 | 516.289908256881 | -101.089908256881 |
29 | 417.7 | 516.289908256881 | -98.5899082568807 |
30 | 417.8 | 516.289908256881 | -98.4899082568807 |
31 | 417.9 | 516.289908256881 | -98.3899082568807 |
32 | 418.4 | 516.289908256881 | -97.8899082568807 |
33 | 418.2 | 516.289908256881 | -98.0899082568807 |
34 | 416.6 | 516.289908256881 | -99.6899082568807 |
35 | 418.9 | 516.289908256881 | -97.3899082568807 |
36 | 421 | 516.289908256881 | -95.2899082568807 |
37 | 423.5 | 516.289908256881 | -92.7899082568807 |
38 | 432.3 | 516.289908256881 | -83.9899082568807 |
39 | 432.3 | 516.289908256881 | -83.9899082568807 |
40 | 428.6 | 516.289908256881 | -87.6899082568807 |
41 | 426.7 | 516.289908256881 | -89.5899082568807 |
42 | 427.3 | 516.289908256881 | -88.9899082568807 |
43 | 428.5 | 516.289908256881 | -87.7899082568807 |
44 | 437 | 516.289908256881 | -79.2899082568807 |
45 | 442 | 516.289908256881 | -74.2899082568807 |
46 | 444.9 | 516.289908256881 | -71.3899082568807 |
47 | 441.4 | 516.289908256881 | -74.8899082568807 |
48 | 440.3 | 516.289908256881 | -75.9899082568807 |
49 | 447.1 | 516.289908256881 | -69.1899082568807 |
50 | 455.3 | 516.289908256881 | -60.9899082568807 |
51 | 478.6 | 516.289908256881 | -37.6899082568807 |
52 | 486.5 | 516.289908256881 | -29.7899082568807 |
53 | 487.8 | 516.289908256881 | -28.4899082568807 |
54 | 485.9 | 516.289908256881 | -30.3899082568808 |
55 | 483.8 | 516.289908256881 | -32.4899082568807 |
56 | 488.4 | 516.289908256881 | -27.8899082568808 |
57 | 494 | 516.289908256881 | -22.2899082568807 |
58 | 493.6 | 516.289908256881 | -22.6899082568807 |
59 | 487.3 | 516.289908256881 | -28.9899082568807 |
60 | 482.1 | 516.289908256881 | -34.1899082568807 |
61 | 484.2 | 516.289908256881 | -32.0899082568807 |
62 | 496.8 | 516.289908256881 | -19.4899082568807 |
63 | 501.1 | 516.289908256881 | -15.1899082568807 |
64 | 499.8 | 516.289908256881 | -16.4899082568807 |
65 | 495.5 | 516.289908256881 | -20.7899082568807 |
66 | 498.1 | 516.289908256881 | -18.1899082568807 |
67 | 503.8 | 516.289908256881 | -12.4899082568807 |
68 | 516.2 | 516.289908256881 | -0.0899082568806833 |
69 | 526.1 | 516.289908256881 | 9.8100917431193 |
70 | 527.1 | 516.289908256881 | 10.8100917431193 |
71 | 525.1 | 516.289908256881 | 8.8100917431193 |
72 | 528.9 | 516.289908256881 | 12.6100917431192 |
73 | 540.1 | 516.289908256881 | 23.8100917431193 |
74 | 549 | 516.289908256881 | 32.7100917431193 |
75 | 556 | 516.289908256881 | 39.7100917431193 |
76 | 568.9 | 516.289908256881 | 52.6100917431192 |
77 | 589.1 | 516.289908256881 | 72.8100917431193 |
78 | 590.3 | 516.289908256881 | 74.0100917431192 |
79 | 603.3 | 516.289908256881 | 87.0100917431192 |
80 | 638.8 | 516.289908256881 | 122.510091743119 |
81 | 643 | 516.289908256881 | 126.710091743119 |
82 | 656.7 | 516.289908256881 | 140.410091743119 |
83 | 656.1 | 516.289908256881 | 139.810091743119 |
84 | 654.1 | 516.289908256881 | 137.810091743119 |
85 | 659.9 | 516.289908256881 | 143.610091743119 |
86 | 662.1 | 516.289908256881 | 145.810091743119 |
87 | 669.2 | 516.289908256881 | 152.910091743119 |
88 | 673.1 | 516.289908256881 | 156.810091743119 |
89 | 678.3 | 516.289908256881 | 162.010091743119 |
90 | 677.4 | 516.289908256881 | 161.110091743119 |
91 | 678.5 | 516.289908256881 | 162.210091743119 |
92 | 672.4 | 516.289908256881 | 156.110091743119 |
93 | 665.3 | 516.289908256881 | 149.010091743119 |
94 | 667.9 | 516.289908256881 | 151.610091743119 |
95 | 672.1 | 516.289908256881 | 155.810091743119 |
96 | 662.5 | 516.289908256881 | 146.210091743119 |
97 | 682.3 | 516.289908256881 | 166.010091743119 |
98 | 692.1 | 516.289908256881 | 175.810091743119 |
99 | 702.7 | 516.289908256881 | 186.410091743119 |
100 | 721.4 | 516.289908256881 | 205.110091743119 |
101 | 733.2 | 516.289908256881 | 216.910091743119 |
102 | 747.7 | 516.289908256881 | 231.410091743119 |
103 | 737.6 | 516.289908256881 | 221.310091743119 |
104 | 729.3 | 516.289908256881 | 213.010091743119 |
105 | 706.1 | 516.289908256881 | 189.810091743119 |
106 | 674.3 | 516.289908256881 | 158.010091743119 |
107 | 659 | 516.289908256881 | 142.710091743119 |
108 | 645.7 | 516.289908256881 | 129.410091743119 |
109 | 646.1 | 516.289908256881 | 129.810091743119 |
110 | 633 | 638.1 | -5.09999999999999 |
111 | 622.3 | 638.1 | -15.8000000000000 |
112 | 628.2 | 638.1 | -9.89999999999995 |
113 | 637.3 | 638.1 | -0.80000000000004 |
114 | 639.6 | 638.1 | 1.50000000000003 |
115 | 638.5 | 638.1 | 0.400000000000006 |
116 | 650.5 | 638.1 | 12.4 |
117 | 655.4 | 638.1 | 17.3 |
Goldfeld-Quandt test for Heteroskedasticity | |||
p-values | Alternative Hypothesis | ||
breakpoint index | greater | 2-sided | less |
5 | 0.000215854676623502 | 0.000431709353247005 | 0.999784145323376 |
6 | 1.64807411532695e-05 | 3.29614823065390e-05 | 0.999983519258847 |
7 | 1.21591717907825e-06 | 2.43183435815651e-06 | 0.99999878408282 |
8 | 2.13637548064001e-07 | 4.27275096128003e-07 | 0.999999786362452 |
9 | 5.31805738106365e-08 | 1.06361147621273e-07 | 0.999999946819426 |
10 | 6.89822643182639e-09 | 1.37964528636528e-08 | 0.999999993101774 |
11 | 6.27107798508578e-10 | 1.25421559701716e-09 | 0.999999999372892 |
12 | 4.68168980977308e-11 | 9.36337961954617e-11 | 0.999999999953183 |
13 | 4.184376634378e-12 | 8.368753268756e-12 | 0.999999999995816 |
14 | 5.75403257940686e-13 | 1.15080651588137e-12 | 0.999999999999425 |
15 | 7.69772821937148e-14 | 1.53954564387430e-13 | 0.999999999999923 |
16 | 1.09489170470793e-14 | 2.18978340941586e-14 | 0.99999999999999 |
17 | 3.22872443093611e-15 | 6.45744886187222e-15 | 0.999999999999997 |
18 | 7.18917829030674e-16 | 1.43783565806135e-15 | 1 |
19 | 6.88014452965067e-17 | 1.37602890593013e-16 | 1 |
20 | 5.67716850457109e-18 | 1.13543370091422e-17 | 1 |
21 | 4.57214132233776e-19 | 9.14428264467551e-19 | 1 |
22 | 3.76449677491932e-20 | 7.52899354983863e-20 | 1 |
23 | 4.29966457470694e-21 | 8.59932914941388e-21 | 1 |
24 | 6.32171994565715e-22 | 1.26434398913143e-21 | 1 |
25 | 5.25674342644445e-23 | 1.05134868528889e-22 | 1 |
26 | 4.36955144606109e-24 | 8.73910289212219e-24 | 1 |
27 | 4.04685621221371e-25 | 8.09371242442741e-25 | 1 |
28 | 4.38652391470248e-26 | 8.77304782940496e-26 | 1 |
29 | 6.54117706638642e-27 | 1.30823541327728e-26 | 1 |
30 | 9.80204016986107e-28 | 1.96040803397221e-27 | 1 |
31 | 1.48339429083147e-28 | 2.96678858166293e-28 | 1 |
32 | 2.41312040807779e-29 | 4.82624081615557e-29 | 1 |
33 | 3.82344056394588e-30 | 7.64688112789176e-30 | 1 |
34 | 5.0641019737419e-31 | 1.01282039474838e-30 | 1 |
35 | 9.14561919695966e-32 | 1.82912383939193e-31 | 1 |
36 | 2.35933833103317e-32 | 4.71867666206634e-32 | 1 |
37 | 9.88292578396888e-33 | 1.97658515679378e-32 | 1 |
38 | 4.12243261655865e-32 | 8.2448652331173e-32 | 1 |
39 | 9.99167652199906e-32 | 1.99833530439981e-31 | 1 |
40 | 7.6437757575562e-32 | 1.52875515151124e-31 | 1 |
41 | 3.92200798148844e-32 | 7.84401596297689e-32 | 1 |
42 | 2.2122950652129e-32 | 4.4245901304258e-32 | 1 |
43 | 1.51863872100385e-32 | 3.03727744200770e-32 | 1 |
44 | 5.46334847562186e-32 | 1.09266969512437e-31 | 1 |
45 | 4.56286983617537e-31 | 9.12573967235074e-31 | 1 |
46 | 4.5175481725295e-30 | 9.035096345059e-30 | 1 |
47 | 1.51201424132605e-29 | 3.02402848265211e-29 | 1 |
48 | 3.74106555839698e-29 | 7.48213111679395e-29 | 1 |
49 | 2.48005158493425e-28 | 4.96010316986849e-28 | 1 |
50 | 5.15622022793929e-27 | 1.03124404558786e-26 | 1 |
51 | 5.01838327639068e-24 | 1.00367665527814e-23 | 1 |
52 | 2.40016230937660e-21 | 4.80032461875321e-21 | 1 |
53 | 2.51679643232849e-19 | 5.03359286465697e-19 | 1 |
54 | 7.68673778369329e-18 | 1.53734755673866e-17 | 1 |
55 | 1.11031770672159e-16 | 2.22063541344317e-16 | 1 |
56 | 1.59613808529198e-15 | 3.19227617058397e-15 | 0.999999999999998 |
57 | 2.37169437235536e-14 | 4.74338874471072e-14 | 0.999999999999976 |
58 | 2.46223930794818e-13 | 4.92447861589637e-13 | 0.999999999999754 |
59 | 1.56952528541959e-12 | 3.13905057083918e-12 | 0.99999999999843 |
60 | 8.08397132030437e-12 | 1.61679426406087e-11 | 0.999999999991916 |
61 | 4.57055532653194e-11 | 9.14111065306389e-11 | 0.999999999954294 |
62 | 3.68943325095777e-10 | 7.37886650191554e-10 | 0.999999999631057 |
63 | 3.09776467556148e-09 | 6.19552935112296e-09 | 0.999999996902235 |
64 | 2.35530616060263e-08 | 4.71061232120526e-08 | 0.999999976446938 |
65 | 1.68543352411099e-07 | 3.37086704822198e-07 | 0.999999831456648 |
66 | 1.30306132460379e-06 | 2.60612264920757e-06 | 0.999998696938675 |
67 | 1.08160935530978e-05 | 2.16321871061955e-05 | 0.999989183906447 |
68 | 9.2414117118286e-05 | 0.000184828234236572 | 0.999907585882882 |
69 | 0.000715913491860645 | 0.00143182698372129 | 0.99928408650814 |
70 | 0.00456052373907773 | 0.00912104747815546 | 0.995439476260922 |
71 | 0.0243135785881895 | 0.0486271571763789 | 0.97568642141181 |
72 | 0.103009138790898 | 0.206018277581796 | 0.896990861209102 |
73 | 0.305627213126341 | 0.611254426252682 | 0.694372786873659 |
74 | 0.615487016524533 | 0.769025966950934 | 0.384512983475467 |
75 | 0.874563462507507 | 0.250873074984985 | 0.125436537492493 |
76 | 0.977330638808823 | 0.0453387223823545 | 0.0226693611911772 |
77 | 0.997027864643628 | 0.00594427071274433 | 0.00297213535637217 |
78 | 0.999791949738726 | 0.000416100522548955 | 0.000208050261274477 |
79 | 0.999988133337831 | 2.37333243371322e-05 | 1.18666621685661e-05 |
80 | 0.999998150964626 | 3.69807074837933e-06 | 1.84903537418967e-06 |
81 | 0.99999962294059 | 7.54118818990046e-07 | 3.77059409495023e-07 |
82 | 0.999999877214427 | 2.45571145520027e-07 | 1.22785572760013e-07 |
83 | 0.999999950047372 | 9.99052561396703e-08 | 4.99526280698351e-08 |
84 | 0.999999976815732 | 4.63685362009822e-08 | 2.31842681004911e-08 |
85 | 0.999999985915375 | 2.81692497392974e-08 | 1.40846248696487e-08 |
86 | 0.999999989758994 | 2.04820118193421e-08 | 1.02410059096711e-08 |
87 | 0.999999990490512 | 1.90189751493123e-08 | 9.50948757465615e-09 |
88 | 0.999999989539383 | 2.09212334751242e-08 | 1.04606167375621e-08 |
89 | 0.99999998660059 | 2.67988202275636e-08 | 1.33994101137818e-08 |
90 | 0.999999981058754 | 3.78824925947177e-08 | 1.89412462973589e-08 |
91 | 0.999999970612415 | 5.8775169801245e-08 | 2.93875849006225e-08 |
92 | 0.999999954174464 | 9.16510728957403e-08 | 4.58255364478701e-08 |
93 | 0.999999935262035 | 1.29475929580598e-07 | 6.47379647902991e-08 |
94 | 0.999999901311645 | 1.97376709766211e-07 | 9.86883548831053e-08 |
95 | 0.99999983267539 | 3.34649220093995e-07 | 1.67324610046998e-07 |
96 | 0.999999784286504 | 4.31426992885191e-07 | 2.15713496442595e-07 |
97 | 0.999999554052646 | 8.91894708227204e-07 | 4.45947354113602e-07 |
98 | 0.999998960581953 | 2.07883609450927e-06 | 1.03941804725464e-06 |
99 | 0.99999751296796 | 4.97406408124844e-06 | 2.48703204062422e-06 |
100 | 0.999995375040132 | 9.249919735495e-06 | 4.6249598677475e-06 |
101 | 0.999994236241354 | 1.15275172920555e-05 | 5.76375864602777e-06 |
102 | 0.999997572116119 | 4.85576776256499e-06 | 2.42788388128250e-06 |
103 | 0.99999918823615 | 1.6235276980218e-06 | 8.117638490109e-07 |
104 | 0.999999919686762 | 1.60626476200699e-07 | 8.03132381003495e-08 |
105 | 0.99999999450275 | 1.09945003912364e-08 | 5.49725019561818e-09 |
106 | 0.999999990994174 | 1.80116518479478e-08 | 9.00582592397388e-09 |
107 | 0.999999943505276 | 1.12989448670926e-07 | 5.64947243354631e-08 |
108 | 0.999999389050932 | 1.22189813673235e-06 | 6.10949068366174e-07 |
109 | 0.999993730631205 | 1.2538737589268e-05 | 6.269368794634e-06 |
110 | 0.999943026641626 | 0.000113946716748002 | 5.69733583740012e-05 |
111 | 0.999806874138193 | 0.000386251723614204 | 0.000193125861807102 |
112 | 0.999137885716748 | 0.00172422856650356 | 0.000862114283251778 |
Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
Description | # significant tests | % significant tests | OK/NOK |
1% type I error level | 102 | 0.944444444444444 | NOK |
5% type I error level | 104 | 0.962962962962963 | NOK |
10% type I error level | 104 | 0.962962962962963 | NOK |