Multiple Linear Regression - Estimated Regression Equation |
x(t)[t] = + 3393.98713673818 -0.320686134331667`y(t)`[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) | 3393.98713673818 | 243.730201 | 13.9252 | 0 | 0 |
`y(t)` | -0.320686134331667 | 0.072845 | -4.4023 | 2.1e-05 | 1e-05 |
Multiple Linear Regression - Regression Statistics | |
Multiple R | 0.345471020666261 |
R-squared | 0.119350226120188 |
Adjusted R-squared | 0.113191836093056 |
F-TEST (value) | 19.3801018763631 |
F-TEST (DF numerator) | 1 |
F-TEST (DF denominator) | 143 |
p-value | 2.08300010995366e-05 |
Multiple Linear Regression - Residual Statistics | |
Residual Standard Deviation | 668.425799998675 |
Sum Squared Residuals | 63891406.1648533 |
Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
1 | 1213.8 | 2614.56910782909 | -1400.76910782909 |
2 | 1245.6 | 2587.04461691941 | -1341.44461691941 |
3 | 1306.3 | 2549.41851277827 | -1243.11851277827 |
4 | 1255.8 | 2496.11727039100 | -1240.31727039100 |
5 | 1257.6 | 2431.30980950392 | -1173.70980950392 |
6 | 1287.8 | 2358.39861000227 | -1070.59861000227 |
7 | 1300.4 | 2376.44361878111 | -1076.04361878111 |
8 | 1320.9 | 2328.64214359763 | -1007.74214359763 |
9 | 1370.8 | 2297.92041192866 | -927.120411928661 |
10 | 1327.3 | 2275.77062063037 | -948.470620630373 |
11 | 1320 | 2426.72720464432 | -1106.72720464432 |
12 | 1345.3 | 2525.05278029175 | -1179.75278029175 |
13 | 1346.7 | 2459.22874435883 | -1112.52874435883 |
14 | 1395.4 | 2366.8037935831 | -971.403793583103 |
15 | 1462 | 2329.22899922346 | -867.228999223461 |
16 | 1491.6 | 2288.82254629767 | -797.222546297671 |
17 | 1461.8 | 2285.42327327376 | -823.623273273756 |
18 | 1477.9 | 2250.25041806026 | -772.350418060258 |
19 | 1490.3 | 2187.03035353811 | -696.730353538114 |
20 | 1521.1 | 2237.03173560311 | -715.931735603107 |
21 | 1561.9 | 2192.25433066638 | -630.354330666376 |
22 | 1552.6 | 2231.84944767231 | -679.249447672307 |
23 | 1523.6 | 2207.52540438325 | -683.92540438325 |
24 | 1548.3 | 2230.02153670662 | -681.721536706617 |
25 | 1552.4 | 2139.61690857718 | -587.216908577177 |
26 | 1587 | 2020.97907318118 | -433.979073181176 |
27 | 1621.3 | 1873.15879956099 | -251.858799560995 |
28 | 1648.7 | 1943.70974911396 | -295.009749113961 |
29 | 1641.8 | 1829.10614528785 | -187.306145287854 |
30 | 1650.6 | 1771.6007076795 | -121.000707679499 |
31 | 1688.6 | 1760.67172422148 | -72.071724221476 |
32 | 1670.7 | 1809.21719123660 | -138.517191236603 |
33 | 1682.2 | 1844.21687593756 | -162.016875937562 |
34 | 1678.9 | 1830.26382223279 | -151.363822232791 |
35 | 1650.6 | 1784.76166663247 | -134.161666632471 |
36 | 1662.4 | 1860.99838134714 | -198.598381347138 |
37 | 1664.5 | 1805.43950857418 | -140.939508574176 |
38 | 1683.2 | 1911.67320429423 | -228.473204294228 |
39 | 1736.2 | 1932.57873339131 | -196.378733391309 |
40 | 1747.6 | 1931.64874360175 | -184.048743601747 |
41 | 1749 | 2077.35890245803 | -328.358902458027 |
42 | 1759.7 | 2109.67444421463 | -349.974444214629 |
43 | 1793.6 | 2022.32916180671 | -228.729161806713 |
44 | 1817.4 | 2032.36022408861 | -214.960224088607 |
45 | 1858.4 | 2092.75825062863 | -234.358250628633 |
46 | 1839.9 | 2133.23525450398 | -293.335254503976 |
47 | 1809.1 | 2227.60356325376 | -418.503563253756 |
48 | 1877.7 | 2322.9243098225 | -445.224309822501 |
49 | 1880.3 | 2282.57237353955 | -402.272373539547 |
50 | 1930.9 | 2248.73677950621 | -317.836779506213 |
51 | 2039.3 | 2205.22608480009 | -165.926084800092 |
52 | 1992.7 | 2244.59351465065 | -251.893514650648 |
53 | 1987.8 | 2254.87471211732 | -267.074712117321 |
54 | 1984.4 | 2208.97490571043 | -224.574905710430 |
55 | 2016.5 | 2268.37880523403 | -251.878805234028 |
56 | 2016.7 | 2317.21930349274 | -300.519303492741 |
57 | 2064.1 | 2412.39574130104 | -348.295741301036 |
58 | 2031.5 | 2516.27560079509 | -484.775600795093 |
59 | 2000.3 | 2525.10409007324 | -524.804090073244 |
60 | 2057.8 | 2651.61156320574 | -593.811563205743 |
61 | 2041.2 | 2572.61694773582 | -531.416947735823 |
62 | 2093.2 | 2539.84282480713 | -446.642824807127 |
63 | 2158.3 | 2621.81661446499 | -463.516614464988 |
64 | 2128.8 | 2676.37494649883 | -547.574946498834 |
65 | 2131.9 | 2699.56055401101 | -567.660554011014 |
66 | 2170.3 | 2720.90221625079 | -550.602216250786 |
67 | 2190.8 | 2650.46350684484 | -459.663506844835 |
68 | 2217.7 | 2651.44159955455 | -433.741599554547 |
69 | 2254.4 | 2625.7931225307 | -371.3931225307 |
70 | 2223.3 | 2600.58719237223 | -377.287192372231 |
71 | 2210.5 | 2598.82341863341 | -388.323418633407 |
72 | 2250.8 | 2628.53498897924 | -377.734988979236 |
73 | 2249.1 | 2580.1370375859 | -331.037037585901 |
74 | 2288.6 | 2570.74414071133 | -282.144140711326 |
75 | 2329.2 | 2540.84336554624 | -211.643365546242 |
76 | 2313.8 | 2529.32752646239 | -215.527526462391 |
77 | 2309.8 | 2512.58129652759 | -202.781296527592 |
78 | 2345.9 | 2539.89734144996 | -193.997341449963 |
79 | 2361.3 | 2525.66849766967 | -164.368497669667 |
80 | 2372 | 2537.9603971986 | -165.9603971986 |
81 | 2410.4 | 2532.08542721764 | -121.685427217644 |
82 | 2398.5 | 2544.09191608702 | -145.591916087022 |
83 | 2362.3 | 2553.77984420518 | -191.479844205181 |
84 | 2419.1 | 2538.24580785816 | -119.145807858155 |
85 | 2421.6 | 2530.68082194927 | -109.080821949271 |
86 | 2465 | 2516.05432736240 | -51.0543273624039 |
87 | 2480.5 | 2504.1568717787 | -23.6568717786991 |
88 | 2506.1 | 2489.91199369169 | 16.1880063083135 |
89 | 2506.6 | 2466.38325201577 | 40.2167479842279 |
90 | 2525.8 | 2474.87502085287 | 50.9249791471256 |
91 | 2550 | 2490.48281501080 | 59.5171849892032 |
92 | 2578.3 | 2452.85350400832 | 125.446495991681 |
93 | 2807.8 | 2420.2108623947 | 387.589137605302 |
94 | 2815.3 | 2387.19301800391 | 428.10698199609 |
95 | 2767.7 | 2395.27110172772 | 372.428898272275 |
96 | 2815.4 | 2348.13344684231 | 467.266553157687 |
97 | 2838.8 | 2367.21747869639 | 471.58252130361 |
98 | 2864 | 2347.09763062842 | 516.902369371578 |
99 | 2948.6 | 2319.97720424799 | 628.622795752007 |
100 | 2922.8 | 2288.84820118842 | 633.951798811582 |
101 | 2917.2 | 2281.37300739715 | 635.826992602853 |
102 | 2936.8 | 2269.29917443956 | 667.500825560441 |
103 | 2993.4 | 2259.97682851454 | 733.423171485462 |
104 | 3007.8 | 2316.78637721139 | 691.013622788608 |
105 | 3046.3 | 2310.43679175163 | 735.863208248375 |
106 | 3011.5 | 2287.89255650811 | 723.60744349189 |
107 | 2958.6 | 2264.24516096249 | 694.354839037508 |
108 | 3019.8 | 2255.21784628106 | 764.582153718944 |
109 | 2998.5 | 2217.34160695514 | 781.158393044857 |
110 | 3040.4 | 2238.87568087551 | 801.524319124486 |
111 | 3166 | 2208.33994716445 | 957.660052835547 |
112 | 3110 | 2187.91865413021 | 922.081345869788 |
113 | 3099.2 | 2218.64679952187 | 880.553200478127 |
114 | 3150.3 | 2204.62640172889 | 945.673598271108 |
115 | 3163.6 | 2156.71268639840 | 1006.88731360160 |
116 | 3182.6 | 2132.67726063024 | 1049.92273936976 |
117 | 3244.4 | 2128.24537825378 | 1116.15462174622 |
118 | 3223.2 | 2177.21094410488 | 1045.98905589512 |
119 | 3143.6 | 2186.42425674423 | 957.175743255773 |
120 | 3217 | 2168.86027716688 | 1048.13972283312 |
121 | 3182.3 | 2148.08302252353 | 1034.21697747647 |
122 | 3217.2 | 2190.55790101576 | 1026.64209898424 |
123 | 3262.5 | 2212.64676194853 | 1049.85323805147 |
124 | 3227.9 | 2354.72354690283 | 873.176453097171 |
125 | 3171.6 | 2371.37677785867 | 800.223222141328 |
126 | 3219 | 2426.16279704789 | 792.837202952106 |
127 | 3195.4 | 2355.86198267971 | 839.538017320294 |
128 | 3221.6 | 2373.39389364362 | 848.206106356381 |
129 | 3262.1 | 2461.93854219394 | 800.161457806065 |
130 | 3179.5 | 2469.97814358163 | 709.52185641837 |
131 | 3133.6 | 2458.98181603540 | 674.618183964603 |
132 | 3219.2 | 2548.93748357677 | 670.262516423227 |
133 | 3245 | 2646.3298625733 | 598.6701374267 |
134 | 3265.3 | 2701.61294527074 | 563.687054729264 |
135 | 3312.5 | 2731.62275372149 | 580.877246278506 |
136 | 3383.6 | 2757.91260301400 | 625.687396985996 |
137 | 3386.3 | 2826.24119765605 | 560.058802343948 |
138 | 3411.1 | 2811.62432365321 | 599.475676346785 |
139 | 3467.2 | 2743.96596303192 | 723.23403696808 |
140 | 3487.7 | 2712.59003164891 | 775.10996835109 |
141 | 3575.5 | 2721.09783479273 | 854.402165207272 |
142 | 3571.5 | 2659.17013539194 | 912.32986460806 |
143 | 3582.3 | 2623.83693711128 | 958.463062888723 |
144 | 3637.1 | 2607.05863856304 | 1030.04136143696 |
145 | 3685 | 2621.28427548200 | 1063.71572451800 |
Goldfeld-Quandt test for Heteroskedasticity | |||
p-values | Alternative Hypothesis | ||
breakpoint index | greater | 2-sided | less |
5 | 0.00025730356803941 | 0.00051460713607882 | 0.99974269643196 |
6 | 1.24915824225179e-05 | 2.49831648450358e-05 | 0.999987508417578 |
7 | 6.33444809067848e-07 | 1.26688961813570e-06 | 0.99999936655519 |
8 | 3.40605276110422e-08 | 6.81210552220843e-08 | 0.999999965939472 |
9 | 5.8809910282726e-09 | 1.17619820565452e-08 | 0.99999999411901 |
10 | 3.06540670146565e-10 | 6.1308134029313e-10 | 0.99999999969346 |
11 | 2.53845731115398e-11 | 5.07691462230795e-11 | 0.999999999974615 |
12 | 2.35196063901642e-11 | 4.70392127803285e-11 | 0.99999999997648 |
13 | 4.68724463319644e-12 | 9.37448926639288e-12 | 0.999999999995313 |
14 | 1.84561219447523e-12 | 3.69122438895046e-12 | 0.999999999998154 |
15 | 3.48408004309138e-12 | 6.96816008618276e-12 | 0.999999999996516 |
16 | 3.01035221966244e-12 | 6.02070443932487e-12 | 0.99999999999699 |
17 | 6.77696283037e-13 | 1.35539256607400e-12 | 0.999999999999322 |
18 | 1.25171829932686e-13 | 2.50343659865373e-13 | 0.999999999999875 |
19 | 1.60092431110596e-14 | 3.20184862221191e-14 | 0.999999999999984 |
20 | 4.52014222256845e-15 | 9.0402844451369e-15 | 0.999999999999996 |
21 | 1.29195856483808e-15 | 2.58391712967616e-15 | 0.999999999999999 |
22 | 4.29573211095298e-16 | 8.59146422190595e-16 | 1 |
23 | 6.50090879103388e-17 | 1.30018175820678e-16 | 1 |
24 | 1.62692371029784e-17 | 3.25384742059569e-17 | 1 |
25 | 2.10334068272262e-18 | 4.20668136544525e-18 | 1 |
26 | 3.26067156082248e-19 | 6.52134312164496e-19 | 1 |
27 | 1.11052697145758e-19 | 2.22105394291517e-19 | 1 |
28 | 1.30403617118243e-20 | 2.60807234236485e-20 | 1 |
29 | 2.99922883491230e-21 | 5.99845766982461e-21 | 1 |
30 | 7.78857743064804e-22 | 1.55771548612961e-21 | 1 |
31 | 1.02169623883964e-22 | 2.04339247767928e-22 | 1 |
32 | 1.22983578458375e-23 | 2.45967156916751e-23 | 1 |
33 | 1.43374844161615e-24 | 2.8674968832323e-24 | 1 |
34 | 1.63225894849174e-25 | 3.26451789698349e-25 | 1 |
35 | 2.75373341821379e-26 | 5.50746683642758e-26 | 1 |
36 | 3.30299201065432e-27 | 6.60598402130864e-27 | 1 |
37 | 4.24923756985437e-28 | 8.49847513970874e-28 | 1 |
38 | 8.54496078034033e-29 | 1.70899215606807e-28 | 1 |
39 | 8.181852434768e-29 | 1.6363704869536e-28 | 1 |
40 | 8.66943087118318e-29 | 1.73388617423664e-28 | 1 |
41 | 1.66670730402225e-27 | 3.33341460804449e-27 | 1 |
42 | 3.79600318023699e-26 | 7.59200636047399e-26 | 1 |
43 | 2.03552408962039e-25 | 4.07104817924077e-25 | 1 |
44 | 1.58891537437172e-24 | 3.17783074874344e-24 | 1 |
45 | 6.18158694957136e-23 | 1.23631738991427e-22 | 1 |
46 | 1.16672039763891e-21 | 2.33344079527781e-21 | 1 |
47 | 2.23265135398511e-20 | 4.46530270797022e-20 | 1 |
48 | 2.98778961900883e-18 | 5.97557923801766e-18 | 1 |
49 | 7.63784874933946e-17 | 1.52756974986789e-16 | 1 |
50 | 1.61085373173482e-15 | 3.22170746346965e-15 | 0.999999999999998 |
51 | 5.790374204176e-14 | 1.1580748408352e-13 | 0.999999999999942 |
52 | 7.72930290411725e-13 | 1.54586058082345e-12 | 0.999999999999227 |
53 | 7.05582278391672e-12 | 1.41116455678334e-11 | 0.999999999992944 |
54 | 4.13896200428869e-11 | 8.27792400857737e-11 | 0.99999999995861 |
55 | 3.16722399396553e-10 | 6.33444798793106e-10 | 0.999999999683278 |
56 | 2.22059209325622e-09 | 4.44118418651244e-09 | 0.999999997779408 |
57 | 1.96601563773828e-08 | 3.93203127547657e-08 | 0.999999980339844 |
58 | 1.16432286277879e-07 | 2.32864572555757e-07 | 0.999999883567714 |
59 | 4.43465088947712e-07 | 8.86930177895423e-07 | 0.99999955653491 |
60 | 1.74770806210928e-06 | 3.49541612421856e-06 | 0.999998252291938 |
61 | 4.91478308609973e-06 | 9.82956617219947e-06 | 0.999995085216914 |
62 | 1.37683131767708e-05 | 2.75366263535416e-05 | 0.999986231686823 |
63 | 3.78687863859841e-05 | 7.57375727719682e-05 | 0.999962131213614 |
64 | 7.96774173055367e-05 | 0.000159354834611073 | 0.999920322582694 |
65 | 0.000149123066176847 | 0.000298246132353693 | 0.999850876933823 |
66 | 0.000268358439173098 | 0.000536716878346197 | 0.999731641560827 |
67 | 0.000486406349577535 | 0.00097281269915507 | 0.999513593650422 |
68 | 0.00085994707698849 | 0.00171989415397698 | 0.999140052923011 |
69 | 0.00152648994766878 | 0.00305297989533755 | 0.998473510052331 |
70 | 0.002592601457628 | 0.005185202915256 | 0.997407398542372 |
71 | 0.00432802947089734 | 0.00865605894179467 | 0.995671970529103 |
72 | 0.0071191939189483 | 0.0142383878378966 | 0.992880806081052 |
73 | 0.0119027127899542 | 0.0238054255799083 | 0.988097287210046 |
74 | 0.0197848289409112 | 0.0395696578818224 | 0.980215171059089 |
75 | 0.032636478849242 | 0.065272957698484 | 0.967363521150758 |
76 | 0.0526028044869238 | 0.105205608973848 | 0.947397195513076 |
77 | 0.0833336536298606 | 0.166667307259721 | 0.91666634637014 |
78 | 0.127048536381416 | 0.254097072762832 | 0.872951463618584 |
79 | 0.188050962068534 | 0.376101924137068 | 0.811949037931466 |
80 | 0.268740333850418 | 0.537480667700837 | 0.731259666149582 |
81 | 0.366839395045751 | 0.733678790091503 | 0.633160604954249 |
82 | 0.484402061753869 | 0.968804123507738 | 0.515597938246131 |
83 | 0.624130529417493 | 0.751738941165015 | 0.375869470582507 |
84 | 0.751088330828 | 0.497823338344001 | 0.248911669172001 |
85 | 0.859957532379599 | 0.280084935240802 | 0.140042467620401 |
86 | 0.932324157810621 | 0.135351684378758 | 0.0676758421893788 |
87 | 0.973692229206258 | 0.0526155415874844 | 0.0263077707937422 |
88 | 0.99193073986122 | 0.0161385202775608 | 0.00806926013878042 |
89 | 0.998249335715949 | 0.00350132856810291 | 0.00175066428405145 |
90 | 0.999759965304652 | 0.000480069390695039 | 0.000240034695347519 |
91 | 0.99998271788931 | 3.45642213789657e-05 | 1.72821106894828e-05 |
92 | 0.999999281628529 | 1.43674294266677e-06 | 7.18371471333387e-07 |
93 | 0.999999891442591 | 2.17114817164660e-07 | 1.08557408582330e-07 |
94 | 0.999999982880482 | 3.4239035138495e-08 | 1.71195175692475e-08 |
95 | 0.99999999853428 | 2.93144045851656e-09 | 1.46572022925828e-09 |
96 | 0.99999999980964 | 3.80719795278956e-10 | 1.90359897639478e-10 |
97 | 0.999999999977353 | 4.52940037771534e-11 | 2.26470018885767e-11 |
98 | 0.999999999996746 | 6.50883527428368e-12 | 3.25441763714184e-12 |
99 | 0.999999999998933 | 2.13488744242964e-12 | 1.06744372121482e-12 |
100 | 0.99999999999966 | 6.8089761184797e-13 | 3.40448805923985e-13 |
101 | 0.999999999999894 | 2.11204235072192e-13 | 1.05602117536096e-13 |
102 | 0.99999999999996 | 8.14353281229227e-14 | 4.07176640614613e-14 |
103 | 0.999999999999974 | 5.25465737113448e-14 | 2.62732868556724e-14 |
104 | 0.999999999999984 | 3.11611238691446e-14 | 1.55805619345723e-14 |
105 | 0.999999999999987 | 2.63479887390193e-14 | 1.31739943695097e-14 |
106 | 0.99999999999999 | 1.93550777800765e-14 | 9.67753889003823e-15 |
107 | 0.999999999999996 | 8.93295583916259e-15 | 4.46647791958129e-15 |
108 | 0.999999999999996 | 7.80764418809254e-15 | 3.90382209404627e-15 |
109 | 0.999999999999997 | 6.45722179618088e-15 | 3.22861089809044e-15 |
110 | 0.999999999999996 | 7.00368036305973e-15 | 3.50184018152987e-15 |
111 | 0.999999999999993 | 1.49132007435717e-14 | 7.45660037178586e-15 |
112 | 0.999999999999984 | 3.14501122896670e-14 | 1.57250561448335e-14 |
113 | 0.999999999999969 | 6.20924601006834e-14 | 3.10462300503417e-14 |
114 | 0.999999999999923 | 1.54867765234234e-13 | 7.7433882617117e-14 |
115 | 0.999999999999793 | 4.14166558554622e-13 | 2.07083279277311e-13 |
116 | 0.999999999999438 | 1.12325457969237e-12 | 5.61627289846187e-13 |
117 | 0.999999999998782 | 2.43583281421926e-12 | 1.21791640710963e-12 |
118 | 0.999999999996675 | 6.64960048277667e-12 | 3.32480024138833e-12 |
119 | 0.9999999999894 | 2.12004947651702e-11 | 1.06002473825851e-11 |
120 | 0.999999999969256 | 6.14877878155799e-11 | 3.07438939077899e-11 |
121 | 0.999999999903335 | 1.93329587922834e-10 | 9.66647939614172e-11 |
122 | 0.999999999713713 | 5.72574791404592e-10 | 2.86287395702296e-10 |
123 | 0.999999999349579 | 1.30084313304240e-09 | 6.50421566521201e-10 |
124 | 0.99999999772371 | 4.55257871244986e-09 | 2.27628935622493e-09 |
125 | 0.99999999206344 | 1.58731192460118e-08 | 7.93655962300588e-09 |
126 | 0.999999972298527 | 5.54029460919337e-08 | 2.77014730459669e-08 |
127 | 0.999999901986201 | 1.96027597644302e-07 | 9.8013798822151e-08 |
128 | 0.9999996551238 | 6.89752398817254e-07 | 3.44876199408627e-07 |
129 | 0.99999881744132 | 2.36511735846387e-06 | 1.18255867923193e-06 |
130 | 0.999997046953737 | 5.90609252502384e-06 | 2.95304626251192e-06 |
131 | 0.999997341082518 | 5.3178349647797e-06 | 2.65891748238985e-06 |
132 | 0.999998974606162 | 2.05078767627521e-06 | 1.02539383813761e-06 |
133 | 0.999999756880239 | 4.86239522588166e-07 | 2.43119761294083e-07 |
134 | 0.999999955412835 | 8.91743293686793e-08 | 4.45871646843396e-08 |
135 | 0.999999991735366 | 1.65292673096122e-08 | 8.2646336548061e-09 |
136 | 0.999999977454485 | 4.50910297964555e-08 | 2.25455148982277e-08 |
137 | 0.999999630967503 | 7.38064993856182e-07 | 3.69032496928091e-07 |
138 | 0.999994276146762 | 1.14477064751576e-05 | 5.72385323757881e-06 |
139 | 0.99992841167797 | 0.000143176644058216 | 7.15883220291079e-05 |
140 | 0.99951580301089 | 0.000968393978217516 | 0.000484196989108758 |
Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
Description | # significant tests | % significant tests | OK/NOK |
1% type I error level | 119 | 0.875 | NOK |
5% type I error level | 123 | 0.904411764705882 | NOK |
10% type I error level | 125 | 0.919117647058823 | NOK |