Multiple Linear Regression - Estimated Regression Equation |
Y[t] = + 149.610526315789 + 132.070837320574X[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) | 149.610526315789 | 6.665114 | 22.4468 | 0 | 0 |
X | 132.070837320574 | 15.370542 | 8.5925 | 0 | 0 |
Multiple Linear Regression - Regression Statistics | |
Multiple R | 0.625290378654623 |
R-squared | 0.390988057638041 |
Adjusted R-squared | 0.385692301617503 |
F-TEST (value) | 73.8304514259446 |
F-TEST (DF numerator) | 1 |
F-TEST (DF denominator) | 115 |
p-value | 4.84057238736568e-14 |
Multiple Linear Regression - Residual Statistics | |
Residual Standard Deviation | 64.9634949753739 |
Sum Squared Residuals | 485329.403132775 |
Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
1 | 100.01 | 149.610526315790 | -49.6005263157897 |
2 | 103.84 | 149.610526315789 | -45.7705263157892 |
3 | 104.48 | 149.610526315789 | -45.1305263157895 |
4 | 95.43 | 149.610526315789 | -54.1805263157895 |
5 | 104.8 | 149.610526315789 | -44.8105263157895 |
6 | 108.64 | 149.610526315789 | -40.9705263157895 |
7 | 105.65 | 149.610526315789 | -43.9605263157895 |
8 | 108.42 | 149.610526315789 | -41.1905263157895 |
9 | 115.35 | 149.610526315789 | -34.2605263157895 |
10 | 113.64 | 149.610526315789 | -35.9705263157895 |
11 | 115.24 | 149.610526315789 | -34.3705263157895 |
12 | 100.33 | 149.610526315789 | -49.2805263157895 |
13 | 101.29 | 149.610526315789 | -48.3205263157895 |
14 | 104.48 | 149.610526315789 | -45.1305263157895 |
15 | 99.26 | 149.610526315789 | -50.3505263157895 |
16 | 100.11 | 149.610526315789 | -49.5005263157895 |
17 | 103.52 | 149.610526315789 | -46.0905263157895 |
18 | 101.18 | 149.610526315789 | -48.4305263157895 |
19 | 96.39 | 149.610526315789 | -53.2205263157895 |
20 | 97.56 | 149.610526315789 | -52.0505263157895 |
21 | 96.39 | 149.610526315789 | -53.2205263157895 |
22 | 85.1 | 149.610526315789 | -64.5105263157895 |
23 | 79.77 | 149.610526315789 | -69.8405263157895 |
24 | 79.13 | 149.610526315789 | -70.4805263157895 |
25 | 80.84 | 149.610526315789 | -68.7705263157895 |
26 | 82.75 | 149.610526315789 | -66.8605263157895 |
27 | 92.55 | 149.610526315789 | -57.0605263157895 |
28 | 96.6 | 149.610526315789 | -53.0105263157895 |
29 | 96.92 | 149.610526315789 | -52.6905263157895 |
30 | 95.32 | 149.610526315789 | -54.2905263157895 |
31 | 98.52 | 149.610526315789 | -51.0905263157895 |
32 | 100.22 | 149.610526315789 | -49.3905263157895 |
33 | 104.91 | 149.610526315789 | -44.7005263157895 |
34 | 103.1 | 149.610526315789 | -46.5105263157895 |
35 | 97.13 | 149.610526315789 | -52.4805263157895 |
36 | 103.42 | 149.610526315789 | -46.1905263157895 |
37 | 111.72 | 149.610526315789 | -37.8905263157895 |
38 | 118.11 | 149.610526315789 | -31.5005263157895 |
39 | 111.62 | 149.610526315789 | -37.9905263157895 |
40 | 100.22 | 149.610526315789 | -49.3905263157895 |
41 | 102.03 | 149.610526315789 | -47.5805263157895 |
42 | 105.76 | 149.610526315789 | -43.8505263157895 |
43 | 107.68 | 149.610526315789 | -41.9305263157895 |
44 | 110.77 | 149.610526315789 | -38.8405263157895 |
45 | 105.44 | 149.610526315789 | -44.1705263157895 |
46 | 112.26 | 149.610526315789 | -37.3505263157895 |
47 | 114.07 | 149.610526315789 | -35.5405263157895 |
48 | 117.9 | 149.610526315789 | -31.7105263157895 |
49 | 124.72 | 149.610526315789 | -24.8905263157895 |
50 | 126.42 | 149.610526315789 | -23.1905263157895 |
51 | 134.73 | 149.610526315789 | -14.8805263157895 |
52 | 135.79 | 149.610526315789 | -13.8205263157895 |
53 | 143.36 | 149.610526315789 | -6.25052631578946 |
54 | 140.37 | 149.610526315789 | -9.24052631578947 |
55 | 144.74 | 149.610526315789 | -4.87052631578946 |
56 | 151.98 | 149.610526315789 | 2.36947368421052 |
57 | 150.92 | 149.610526315789 | 1.30947368421052 |
58 | 163.38 | 149.610526315789 | 13.7694736842105 |
59 | 154.43 | 149.610526315789 | 4.81947368421054 |
60 | 146.66 | 149.610526315789 | -2.95052631578947 |
61 | 157.95 | 149.610526315789 | 8.33947368421052 |
62 | 162.1 | 149.610526315789 | 12.4894736842105 |
63 | 180.42 | 149.610526315789 | 30.8094736842105 |
64 | 179.57 | 149.610526315789 | 29.9594736842105 |
65 | 171.58 | 149.610526315789 | 21.9694736842105 |
66 | 185.43 | 149.610526315789 | 35.8194736842105 |
67 | 190.64 | 149.610526315789 | 41.0294736842105 |
68 | 203 | 149.610526315789 | 53.3894736842105 |
69 | 202.36 | 149.610526315789 | 52.7494736842105 |
70 | 193.41 | 149.610526315789 | 43.7994736842105 |
71 | 186.17 | 149.610526315789 | 36.5594736842105 |
72 | 192.24 | 149.610526315789 | 42.6294736842105 |
73 | 209.6 | 149.610526315789 | 59.9894736842105 |
74 | 206.41 | 149.610526315789 | 56.7994736842105 |
75 | 209.82 | 149.610526315789 | 60.2094736842105 |
76 | 230.37 | 149.610526315789 | 80.7594736842105 |
77 | 235.8 | 149.610526315789 | 86.1894736842105 |
78 | 232.07 | 149.610526315789 | 82.4594736842105 |
79 | 244.64 | 149.610526315789 | 95.0294736842105 |
80 | 242.19 | 149.610526315789 | 92.5794736842105 |
81 | 217.48 | 149.610526315789 | 67.8694736842105 |
82 | 209.39 | 149.610526315789 | 59.7794736842105 |
83 | 211.73 | 149.610526315789 | 62.1194736842105 |
84 | 221 | 149.610526315789 | 71.3894736842105 |
85 | 203.11 | 149.610526315789 | 53.4994736842105 |
86 | 214.71 | 149.610526315789 | 65.0994736842105 |
87 | 224.19 | 149.610526315789 | 74.5794736842105 |
88 | 238.04 | 149.610526315789 | 88.4294736842105 |
89 | 238.36 | 149.610526315789 | 88.7494736842105 |
90 | 246.24 | 149.610526315789 | 96.6294736842105 |
91 | 259.87 | 149.610526315789 | 110.259473684211 |
92 | 249.97 | 149.610526315789 | 100.359473684211 |
93 | 266.48 | 149.610526315789 | 116.869473684211 |
94 | 282.98 | 149.610526315789 | 133.369473684211 |
95 | 306.31 | 149.610526315789 | 156.699473684211 |
96 | 301.73 | 281.681363636364 | 20.0486363636364 |
97 | 314.62 | 281.681363636364 | 32.9386363636364 |
98 | 332.62 | 281.681363636364 | 50.9386363636364 |
99 | 355.51 | 281.681363636364 | 73.8286363636363 |
100 | 370.32 | 281.681363636364 | 88.6386363636364 |
101 | 408.13 | 281.681363636364 | 126.448636363636 |
102 | 433.58 | 281.681363636364 | 151.898636363636 |
103 | 440.51 | 281.681363636364 | 158.828636363636 |
104 | 386.29 | 281.681363636364 | 104.608636363636 |
105 | 342.84 | 281.681363636364 | 61.1586363636363 |
106 | 254.97 | 281.681363636364 | -26.7113636363636 |
107 | 203.42 | 281.681363636364 | -78.2613636363637 |
108 | 170.09 | 281.681363636364 | -111.591363636364 |
109 | 174.03 | 281.681363636364 | -107.651363636364 |
110 | 167.85 | 281.681363636364 | -113.831363636364 |
111 | 177.01 | 281.681363636364 | -104.671363636364 |
112 | 188.19 | 281.681363636364 | -93.4913636363636 |
113 | 211.2 | 281.681363636364 | -70.4813636363637 |
114 | 240.91 | 281.681363636364 | -40.7713636363636 |
115 | 230.26 | 281.681363636364 | -51.4213636363637 |
116 | 251.25 | 281.681363636364 | -30.4313636363636 |
117 | 241.66 | 281.681363636364 | -40.0213636363636 |
Goldfeld-Quandt test for Heteroskedasticity | |||
p-values | Alternative Hypothesis | ||
breakpoint index | greater | 2-sided | less |
5 | 0.00048472802182107 | 0.00096945604364214 | 0.999515271978179 |
6 | 7.31723676365988e-05 | 0.000146344735273198 | 0.999926827632363 |
7 | 5.6607439472176e-06 | 1.13214878944352e-05 | 0.999994339256053 |
8 | 6.2943650041166e-07 | 1.25887300082332e-06 | 0.9999993705635 |
9 | 3.56081257305129e-07 | 7.12162514610259e-07 | 0.999999643918743 |
10 | 7.28297869214755e-08 | 1.45659573842951e-07 | 0.999999927170213 |
11 | 1.69045081912576e-08 | 3.38090163825151e-08 | 0.999999983095492 |
12 | 2.54426366729059e-09 | 5.08852733458117e-09 | 0.999999997455736 |
13 | 3.19724219524526e-10 | 6.39448439049051e-10 | 0.999999999680276 |
14 | 3.03980953308348e-11 | 6.07961906616696e-11 | 0.999999999969602 |
15 | 4.73697507364262e-12 | 9.47395014728523e-12 | 0.999999999995263 |
16 | 6.16671362886054e-13 | 1.23334272577211e-12 | 0.999999999999383 |
17 | 5.74617002750737e-14 | 1.14923400550147e-13 | 0.999999999999942 |
18 | 6.22213169458994e-15 | 1.24442633891799e-14 | 0.999999999999994 |
19 | 1.46552900218537e-15 | 2.93105800437074e-15 | 0.999999999999999 |
20 | 2.48851809380292e-16 | 4.97703618760584e-16 | 1 |
21 | 4.98807768521791e-17 | 9.97615537043582e-17 | 1 |
22 | 2.17514825403231e-16 | 4.35029650806461e-16 | 1 |
23 | 1.65212044607174e-15 | 3.30424089214347e-15 | 0.999999999999998 |
24 | 4.87975326436531e-15 | 9.75950652873061e-15 | 0.999999999999995 |
25 | 5.75786211918379e-15 | 1.15157242383676e-14 | 0.999999999999994 |
26 | 3.90801084301792e-15 | 7.81602168603585e-15 | 0.999999999999996 |
27 | 8.79156212255708e-16 | 1.75831242451142e-15 | 1 |
28 | 1.64344644644816e-16 | 3.28689289289632e-16 | 1 |
29 | 3.04137388539923e-17 | 6.08274777079846e-17 | 1 |
30 | 5.93124971368902e-18 | 1.18624994273780e-17 | 1 |
31 | 1.07230205932075e-18 | 2.1446041186415e-18 | 1 |
32 | 1.94327332851606e-19 | 3.88654665703212e-19 | 1 |
33 | 4.11956678338408e-20 | 8.23913356676815e-20 | 1 |
34 | 8.04235538153628e-21 | 1.60847107630726e-20 | 1 |
35 | 1.55228813499191e-21 | 3.10457626998381e-21 | 1 |
36 | 3.14545229293883e-22 | 6.29090458587766e-22 | 1 |
37 | 1.32526694357231e-22 | 2.65053388714463e-22 | 1 |
38 | 1.44808212890779e-22 | 2.89616425781558e-22 | 1 |
39 | 5.48766773778129e-23 | 1.09753354755626e-22 | 1 |
40 | 1.19683616441403e-23 | 2.39367232882807e-23 | 1 |
41 | 2.67476718060503e-24 | 5.34953436121007e-24 | 1 |
42 | 6.82301943675543e-25 | 1.36460388735109e-24 | 1 |
43 | 1.99908452290207e-25 | 3.99816904580414e-25 | 1 |
44 | 7.77233479273144e-26 | 1.55446695854629e-25 | 1 |
45 | 2.16022997242336e-26 | 4.32045994484673e-26 | 1 |
46 | 1.04192228920349e-26 | 2.08384457840697e-26 | 1 |
47 | 6.31748918294017e-27 | 1.26349783658803e-26 | 1 |
48 | 6.53558574642678e-27 | 1.30711714928536e-26 | 1 |
49 | 2.11463898728146e-26 | 4.22927797456293e-26 | 1 |
50 | 7.46528863506722e-26 | 1.49305772701344e-25 | 1 |
51 | 1.05886037567485e-24 | 2.1177207513497e-24 | 1 |
52 | 1.03801504140092e-23 | 2.07603008280183e-23 | 1 |
53 | 2.52992332841287e-22 | 5.05984665682573e-22 | 1 |
54 | 1.91372722370825e-21 | 3.82745444741651e-21 | 1 |
55 | 1.87353200639182e-20 | 3.74706401278365e-20 | 1 |
56 | 3.25718515836391e-19 | 6.51437031672782e-19 | 1 |
57 | 2.81906632189366e-18 | 5.63813264378733e-18 | 1 |
58 | 7.23130772619588e-17 | 1.44626154523918e-16 | 1 |
59 | 3.8128921205544e-16 | 7.6257842411088e-16 | 1 |
60 | 9.1244318802457e-16 | 1.82488637604914e-15 | 1 |
61 | 4.42723690604022e-15 | 8.85447381208043e-15 | 0.999999999999996 |
62 | 2.34950076943267e-14 | 4.69900153886534e-14 | 0.999999999999976 |
63 | 4.1323837891569e-13 | 8.2647675783138e-13 | 0.999999999999587 |
64 | 3.72813838590814e-12 | 7.45627677181627e-12 | 0.999999999996272 |
65 | 1.41084139898519e-11 | 2.82168279797038e-11 | 0.999999999985892 |
66 | 9.34754297869421e-11 | 1.86950859573884e-10 | 0.999999999906525 |
67 | 5.79788497577165e-10 | 1.15957699515433e-09 | 0.999999999420212 |
68 | 4.83094583555844e-09 | 9.66189167111688e-09 | 0.999999995169054 |
69 | 2.47500859808822e-08 | 4.95001719617644e-08 | 0.999999975249914 |
70 | 6.62985012693096e-08 | 1.32597002538619e-07 | 0.999999933701499 |
71 | 1.25221099603167e-07 | 2.50442199206333e-07 | 0.9999998747789 |
72 | 2.52439537672405e-07 | 5.04879075344811e-07 | 0.999999747560462 |
73 | 7.35666394940612e-07 | 1.47133278988122e-06 | 0.999999264333605 |
74 | 1.61643793293688e-06 | 3.23287586587375e-06 | 0.999998383562067 |
75 | 3.35972962182597e-06 | 6.71945924365193e-06 | 0.999996640270378 |
76 | 1.02947722105163e-05 | 2.05895444210326e-05 | 0.99998970522779 |
77 | 2.85944451995365e-05 | 5.7188890399073e-05 | 0.9999714055548 |
78 | 5.84605009753412e-05 | 0.000116921001950682 | 0.999941539499025 |
79 | 0.000134551480047376 | 0.000269102960094752 | 0.999865448519953 |
80 | 0.000245625183268714 | 0.000491250366537428 | 0.999754374816731 |
81 | 0.000278278814603072 | 0.000556557629206144 | 0.999721721185397 |
82 | 0.000284251069932799 | 0.000568502139865598 | 0.999715748930067 |
83 | 0.000289977136983161 | 0.000579954273966321 | 0.999710022863017 |
84 | 0.000310850136339447 | 0.000621700272678894 | 0.99968914986366 |
85 | 0.000298345491604685 | 0.000596690983209369 | 0.999701654508395 |
86 | 0.000300460193372097 | 0.000600920386744195 | 0.999699539806628 |
87 | 0.000316248366056102 | 0.000632496732112204 | 0.999683751633944 |
88 | 0.000359797756145173 | 0.000719595512290345 | 0.999640202243855 |
89 | 0.000396227269911444 | 0.000792454539822888 | 0.999603772730089 |
90 | 0.000448887614038224 | 0.000897775228076448 | 0.999551112385962 |
91 | 0.000547529637405546 | 0.00109505927481109 | 0.999452470362594 |
92 | 0.000592195284580845 | 0.00118439056916169 | 0.999407804715419 |
93 | 0.000702134317727738 | 0.00140426863545548 | 0.999297865682272 |
94 | 0.00091067046934893 | 0.00182134093869786 | 0.999089329530651 |
95 | 0.00136303964510411 | 0.00272607929020822 | 0.998636960354896 |
96 | 0.000813788002333593 | 0.00162757600466719 | 0.999186211997666 |
97 | 0.000499951187883899 | 0.000999902375767797 | 0.999500048812116 |
98 | 0.000345439318111100 | 0.000690878636222201 | 0.99965456068189 |
99 | 0.000316832916946861 | 0.000633665833893721 | 0.999683167083053 |
100 | 0.000391946377667383 | 0.000783892755334767 | 0.999608053622333 |
101 | 0.00133417427090552 | 0.00266834854181104 | 0.998665825729094 |
102 | 0.0127345773925759 | 0.0254691547851518 | 0.987265422607424 |
103 | 0.18789147109276 | 0.37578294218552 | 0.81210852890724 |
104 | 0.638467968394752 | 0.723064063210496 | 0.361532031605248 |
105 | 0.95256940095151 | 0.0948611980969797 | 0.0474305990484898 |
106 | 0.96090598683853 | 0.078188026322939 | 0.0390940131614695 |
107 | 0.939615263034742 | 0.120769473930515 | 0.0603847369652577 |
108 | 0.937666681701115 | 0.12466663659777 | 0.062333318298885 |
109 | 0.930181211062104 | 0.139637577875792 | 0.0698187889378962 |
110 | 0.943433154432817 | 0.113133691134366 | 0.0565668455671829 |
111 | 0.95601321839941 | 0.0879735632011797 | 0.0439867816005899 |
112 | 0.974498682285613 | 0.0510026354287742 | 0.0255013177143871 |
Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
Description | # significant tests | % significant tests | OK/NOK |
1% type I error level | 97 | 0.898148148148148 | NOK |
5% type I error level | 98 | 0.907407407407407 | NOK |
10% type I error level | 102 | 0.944444444444444 | NOK |