Multiple Linear Regression - Estimated Regression Equation |
Y[t] = + 32.692139819348 + 1.28981479437032X[t] + 0.144892381334993M1[t] + 1.73658903653866M2[t] -0.550465623628254M3[t] + 0.621836851411566M4[t] + 2.96612775017956M5[t] + 3.54060389137733M6[t] + 6.75112864261287M7[t] + 5.90591649878049M8[t] + 0.100824026717422M9[t] + 3.89912416000683M10[t] + 7.93909788953396M11[t] -2.06872918563815t + 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) | 32.692139819348 | 35.621144 | 0.9178 | 0.360424 | 0.180212 |
X | 1.28981479437032 | 0.374494 | 3.4442 | 0.00077 | 0.000385 |
M1 | 0.144892381334993 | 11.663962 | 0.0124 | 0.990108 | 0.495054 |
M2 | 1.73658903653866 | 11.903884 | 0.1459 | 0.884237 | 0.442119 |
M3 | -0.550465623628254 | 11.98989 | -0.0459 | 0.963451 | 0.481726 |
M4 | 0.621836851411566 | 11.919197 | 0.0522 | 0.958472 | 0.479236 |
M5 | 2.96612775017956 | 11.896975 | 0.2493 | 0.803505 | 0.401753 |
M6 | 3.54060389137733 | 11.895701 | 0.2976 | 0.766452 | 0.383226 |
M7 | 6.75112864261287 | 11.899343 | 0.5674 | 0.571445 | 0.285723 |
M8 | 5.90591649878049 | 11.898229 | 0.4964 | 0.620466 | 0.310233 |
M9 | 0.100824026717422 | 12.016082 | 0.0084 | 0.993318 | 0.496659 |
M10 | 3.89912416000683 | 11.899852 | 0.3277 | 0.743691 | 0.371845 |
M11 | 7.93909788953396 | 11.935595 | 0.6652 | 0.507117 | 0.253558 |
t | -2.06872918563815 | 0.52147 | -3.9671 | 0.000119 | 6e-05 |
Multiple Linear Regression - Regression Statistics | |
Multiple R | 0.469536623350642 |
R-squared | 0.220464640667523 |
Adjusted R-squared | 0.143106169894071 |
F-TEST (value) | 2.84990949876923 |
F-TEST (DF numerator) | 13 |
F-TEST (DF denominator) | 131 |
p-value | 0.00122249412706421 |
Multiple Linear Regression - Residual Statistics | |
Residual Standard Deviation | 29.1235780132500 |
Sum Squared Residuals | 111111.946314495 |
Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
1 | 100 | 159.749782452077 | -59.7497824520768 |
2 | 103.53 | 162.652064682893 | -59.1220646828931 |
3 | 108.36 | 164.745354808939 | -56.3853548089388 |
4 | 115.2 | 158.48329855376 | -43.28329855376 |
5 | 123.51 | 158.952332486045 | -35.4423324860454 |
6 | 132.87 | 160.669718279587 | -27.7997182795871 |
7 | 130.55 | 163.140023083386 | -32.5900230833859 |
8 | 136.68 | 162.405868756401 | -25.7258687564012 |
9 | 140.63 | 159.833185903562 | -19.2031859035620 |
10 | 143.47 | 156.945219887367 | -13.4752198873675 |
11 | 124.1 | 158.142575554634 | -34.0425755546343 |
12 | 111.49 | 150.817563251752 | -39.3275632517525 |
13 | 119.93 | 149.048504222774 | -29.1185042227737 |
14 | 131.79 | 153.743629017764 | -21.9536290177642 |
15 | 136.61 | 156.468928393052 | -19.8589283930522 |
16 | 141.79 | 158.719649780717 | -16.9296497807174 |
17 | 142.23 | 155.822267099696 | -13.5922670996963 |
18 | 146.74 | 156.043467731768 | -9.3034677317684 |
19 | 154.85 | 158.500874387624 | -3.65087438762354 |
20 | 148.44 | 158.863062635854 | -10.4230626358536 |
21 | 154.18 | 155.323018687237 | -1.14301868723665 |
22 | 149.1 | 156.059432243223 | -6.95943224322275 |
23 | 152.22 | 154.948019428567 | -2.72801942856666 |
24 | 149.34 | 147.57141453391 | 1.76858546608999 |
25 | 160.94 | 146.086114759693 | 14.8538852403072 |
26 | 176.16 | 149.285054393214 | 26.8749456067863 |
27 | 195.12 | 148.566548267533 | 46.5534517324671 |
28 | 186.07 | 150.585102992211 | 35.4848970077885 |
29 | 200.78 | 150.125470272550 | 50.6545297274498 |
30 | 208.15 | 149.5727820280 | 58.5772179719998 |
31 | 209.56 | 154.751697899977 | 54.8083021000233 |
32 | 203.33 | 149.928830674838 | 53.4011693251619 |
33 | 198.84 | 143.280333071789 | 55.5596669282113 |
34 | 200.63 | 144.66165402496 | 55.9683459750401 |
35 | 206.47 | 143.627630097966 | 62.8423699020339 |
36 | 196.68 | 134.870923373333 | 61.8090766266668 |
37 | 203.81 | 133.166355084073 | 70.643644915927 |
38 | 190.18 | 134.675637336969 | 55.5043626630313 |
39 | 187.5 | 135.956344142562 | 51.543655857438 |
40 | 187.62 | 136.272343338672 | 51.3476566613283 |
41 | 168.92 | 136.689784679182 | 32.2302153208177 |
42 | 164.78 | 136.330568653788 | 28.4494313462122 |
43 | 175.98 | 141.083845643622 | 34.8961543563779 |
44 | 174.7 | 140.697941311117 | 34.0020586888826 |
45 | 166.95 | 137.183693658388 | 29.7663063416121 |
46 | 161.76 | 136.939847970652 | 24.8201520293475 |
47 | 149.65 | 135.634962936841 | 14.0150370631591 |
48 | 137.42 | 132.927487597805 | 4.49251240219524 |
49 | 142.6 | 131.274511900319 | 11.3254880996806 |
50 | 146.94 | 136.176007062409 | 10.7639929375909 |
51 | 152.52 | 143.338269330331 | 9.18173066966907 |
52 | 147.47 | 137.488953809351 | 9.9810461906494 |
53 | 146.15 | 137.248589604732 | 8.90141039526766 |
54 | 152.04 | 135.393188417868 | 16.6468115821317 |
55 | 144.42 | 139.940095040603 | 4.47990495939671 |
56 | 138.15 | 137.051950007020 | 1.09804999297984 |
57 | 125.94 | 134.208406047363 | -8.26840604736318 |
58 | 112.61 | 132.481273346102 | -19.871273346102 |
59 | 111.48 | 131.137693868459 | -19.6576938684593 |
60 | 95.25 | 127.230690770659 | -31.9806907706587 |
61 | 105.38 | 123.552705846012 | -18.1727058460119 |
62 | 109.59 | 128.596080635482 | -19.0060806354824 |
63 | 99.07 | 131.153704087502 | -32.0837040875022 |
64 | 92.07 | 127.123027426584 | -35.0530274265841 |
65 | 89.1 | 127.73394098625 | -38.6339409862501 |
66 | 86.36 | 130.31550269202 | -43.95550269202 |
67 | 95.39 | 133.637085260103 | -38.2470852601032 |
68 | 95.27 | 133.586532774135 | -38.3165327741348 |
69 | 98.56 | 129.607951795432 | -31.0479517954319 |
70 | 101.79 | 128.035596869495 | -26.2455968694951 |
71 | 102.02 | 128.639637731352 | -26.6196377313516 |
72 | 98.21 | 122.913995773489 | -24.7039957734890 |
73 | 104.42 | 120.809584897974 | -16.3895848979739 |
74 | 105.62 | 124.537348597187 | -18.9173485971867 |
75 | 109.46 | 124.489546164578 | -15.0295461645785 |
76 | 110.94 | 121.955054665130 | -11.0150546651299 |
77 | 113.09 | 121.804977496117 | -8.71497749611747 |
78 | 109.58 | 124.154372538901 | -14.5743725389007 |
79 | 111.41 | 126.934232893348 | -15.5242328933483 |
80 | 109.83 | 125.155328582924 | -15.3253285829237 |
81 | 110.58 | 121.357321675433 | -10.7773216754327 |
82 | 109.04 | 121.822874124601 | -12.782874124601 |
83 | 107.8 | 119.950470581266 | -12.1504705812665 |
84 | 109.79 | 115.978976743747 | -6.18897674374743 |
85 | 110.76 | 114.326001046262 | -3.56600104626201 |
86 | 112.64 | 118.453607331730 | -5.81360733172959 |
87 | 114.17 | 115.748786422719 | -1.57878642271852 |
88 | 115.99 | 117.573868928242 | -1.58386892824155 |
89 | 119.01 | 117.901023233146 | 1.10897676685382 |
90 | 117.92 | 118.444677563811 | -0.524677563810919 |
91 | 115.92 | 122.153204570205 | -6.23320457020526 |
92 | 120.75 | 122.257429859561 | -1.50742985956122 |
93 | 124.94 | 138.761107815459 | -13.8211078154590 |
94 | 129.17 | 141.290363935620 | -12.1203639356198 |
95 | 128.14 | 138.205534485577 | -10.0655344855772 |
96 | 134.18 | 133.266679552280 | 0.913320447719609 |
97 | 131.74 | 133.832185301112 | -2.09218530111194 |
98 | 134.32 | 136.025069395024 | -1.70506939502400 |
99 | 137.8 | 140.65929466598 | -2.85929466598001 |
100 | 141.79 | 137.028460591317 | 4.76153940868333 |
101 | 142.75 | 136.710707499036 | 6.03929250096385 |
102 | 144.3 | 137.293056273532 | 7.00694372646804 |
103 | 145.49 | 144.445388780895 | 1.04461121910497 |
104 | 138.21 | 143.066327056725 | -4.85632705672518 |
105 | 139.02 | 139.281218297178 | -0.261218297177833 |
106 | 141.91 | 137.32191893293 | 4.58808106706998 |
107 | 144.95 | 133.669570973364 | 11.2804290266356 |
108 | 146.11 | 130.162410461819 | 15.9475895381813 |
109 | 150.96 | 125.968499619424 | 24.9915003805762 |
110 | 148.2 | 129.954226277511 | 18.2457737224894 |
111 | 152.12 | 138.935127405495 | 13.1848725945054 |
112 | 154.74 | 132.092654492849 | 22.6473455071509 |
113 | 150.8 | 131.220281038989 | 19.5797189610106 |
114 | 152.6 | 135.156148278848 | 17.4438517211519 |
115 | 158.74 | 137.716740118253 | 21.0232598817473 |
116 | 161.83 | 136.814909868 | 25.0150901320001 |
117 | 162.4 | 135.506245513644 | 26.8937544863564 |
118 | 156.11 | 134.991538719091 | 21.1184612809095 |
119 | 154.93 | 128.501598211910 | 26.4284017880898 |
120 | 157.18 | 126.297150642679 | 30.8828493573214 |
121 | 159.85 | 120.684443526476 | 39.1655564735237 |
122 | 154.4 | 123.909179455885 | 30.4908205441154 |
123 | 151.57 | 124.364404793081 | 27.2055952069192 |
124 | 133.34 | 119.792005918527 | 13.5479940814729 |
125 | 131.2 | 114.095725133722 | 17.1042748662776 |
126 | 124.17 | 117.631749787326 | 6.5382502126738 |
127 | 133.19 | 116.271304651845 | 16.9186953481548 |
128 | 130.94 | 116.130465130271 | 14.8095348697291 |
129 | 119.58 | 112.564624885766 | 7.01537511423354 |
130 | 118.55 | 105.523455231700 | 13.0265447683004 |
131 | 119.96 | 102.606301704925 | 17.3536982950749 |
132 | 108.42 | 101.704567078007 | 6.71543292199257 |
133 | 95.93 | 102.515137637769 | -6.58513763776925 |
134 | 88.83 | 104.192095813933 | -15.3620958139332 |
135 | 84.98 | 104.853691518229 | -19.8736915182287 |
136 | 81.61 | 111.515579502640 | -29.9055795026404 |
137 | 72.84 | 112.074900470532 | -39.2349004705318 |
138 | 74.72 | 113.224767754550 | -38.5047677545505 |
139 | 83.4 | 120.325507670139 | -36.9255076701387 |
140 | 87.42 | 119.591353343154 | -32.171353343154 |
141 | 86.33 | 121.042892648750 | -34.7128926487502 |
142 | 94.28 | 122.346824714259 | -28.0668247142592 |
143 | 98.81 | 125.466004425138 | -26.6560044251378 |
144 | 100.96 | 121.288140220519 | -20.3281402205195 |
145 | 99.14 | 124.446173706035 | -25.3061737060353 |
Goldfeld-Quandt test for Heteroskedasticity | |||
p-values | Alternative Hypothesis | ||
breakpoint index | greater | 2-sided | less |
17 | 0.00466609395647789 | 0.00933218791295578 | 0.995333906043522 |
18 | 0.00235012749651757 | 0.00470025499303514 | 0.997649872503482 |
19 | 0.000397503160361459 | 0.000795006320722918 | 0.999602496839639 |
20 | 0.000219373660454627 | 0.000438747320909255 | 0.999780626339545 |
21 | 6.85159217903825e-05 | 0.000137031843580765 | 0.99993148407821 |
22 | 4.54154331249988e-05 | 9.08308662499977e-05 | 0.999954584566875 |
23 | 2.27113173819099e-05 | 4.54226347638197e-05 | 0.999977288682618 |
24 | 4.54853812350786e-05 | 9.09707624701572e-05 | 0.999954514618765 |
25 | 6.29302029737019e-05 | 0.000125860405947404 | 0.999937069797026 |
26 | 0.000110823645130869 | 0.000221647290261738 | 0.99988917635487 |
27 | 0.000280215093412296 | 0.000560430186824592 | 0.999719784906588 |
28 | 0.000168025484843652 | 0.000336050969687305 | 0.999831974515156 |
29 | 0.000261543204288888 | 0.000523086408577776 | 0.999738456795711 |
30 | 0.000246920739119622 | 0.000493841478239244 | 0.99975307926088 |
31 | 0.000262430796347758 | 0.000524861592695516 | 0.999737569203652 |
32 | 0.000129309685724667 | 0.000258619371449334 | 0.999870690314275 |
33 | 8.72186896849832e-05 | 0.000174437379369966 | 0.999912781310315 |
34 | 4.69367364643406e-05 | 9.38734729286811e-05 | 0.999953063263536 |
35 | 3.44459612235950e-05 | 6.889192244719e-05 | 0.999965554038776 |
36 | 2.34915126026657e-05 | 4.69830252053315e-05 | 0.999976508487397 |
37 | 2.00178196198469e-05 | 4.00356392396938e-05 | 0.99997998218038 |
38 | 9.22043344337917e-05 | 0.000184408668867583 | 0.999907795665566 |
39 | 0.000545518394658858 | 0.00109103678931772 | 0.999454481605341 |
40 | 0.00149441438681749 | 0.00298882877363497 | 0.998505585613183 |
41 | 0.01714860786237 | 0.03429721572474 | 0.98285139213763 |
42 | 0.0959213738318002 | 0.191842747663600 | 0.9040786261682 |
43 | 0.191258915943445 | 0.38251783188689 | 0.808741084056555 |
44 | 0.306650102276662 | 0.613300204553324 | 0.693349897723338 |
45 | 0.500459076941334 | 0.999081846117332 | 0.499540923058666 |
46 | 0.682348767807298 | 0.635302464385403 | 0.317651232192702 |
47 | 0.815305024771566 | 0.369389950456869 | 0.184694975228434 |
48 | 0.91515894607564 | 0.169682107848721 | 0.0848410539243603 |
49 | 0.955060252940817 | 0.089879494118367 | 0.0449397470591835 |
50 | 0.971206813175793 | 0.0575863736484131 | 0.0287931868242065 |
51 | 0.975885436188704 | 0.0482291276225917 | 0.0241145638112959 |
52 | 0.981835308977988 | 0.0363293820440239 | 0.0181646910220119 |
53 | 0.985470239953471 | 0.0290595200930572 | 0.0145297600465286 |
54 | 0.990435551253888 | 0.0191288974922249 | 0.00956444874611244 |
55 | 0.993529285577033 | 0.0129414288459335 | 0.00647071442296675 |
56 | 0.995953495963839 | 0.00809300807232269 | 0.00404650403616135 |
57 | 0.997642255194865 | 0.00471548961026926 | 0.00235774480513463 |
58 | 0.998981390379034 | 0.00203721924193125 | 0.00101860962096563 |
59 | 0.999434226208897 | 0.00113154758220628 | 0.00056577379110314 |
60 | 0.999684597993083 | 0.000630804013833893 | 0.000315402006916946 |
61 | 0.999755621840267 | 0.000488756319465642 | 0.000244378159732821 |
62 | 0.999770978995327 | 0.000458042009346071 | 0.000229021004673036 |
63 | 0.999868637837674 | 0.000262724324653007 | 0.000131362162326503 |
64 | 0.9999459703881 | 0.000108059223800941 | 5.40296119004704e-05 |
65 | 0.999977487406744 | 4.50251865129332e-05 | 2.25125932564666e-05 |
66 | 0.999990325522576 | 1.93489548476382e-05 | 9.67447742381908e-06 |
67 | 0.999994049823632 | 1.19003527353767e-05 | 5.95017636768837e-06 |
68 | 0.99999576444737 | 8.47110526090719e-06 | 4.23555263045359e-06 |
69 | 0.999995197334924 | 9.60533015255845e-06 | 4.80266507627922e-06 |
70 | 0.999993876198967 | 1.22476020659492e-05 | 6.1238010329746e-06 |
71 | 0.99999259446481 | 1.48110703808655e-05 | 7.40553519043273e-06 |
72 | 0.999991090451117 | 1.78190977662922e-05 | 8.90954888314612e-06 |
73 | 0.999986686617917 | 2.66267641657596e-05 | 1.33133820828798e-05 |
74 | 0.999982660035133 | 3.46799297341047e-05 | 1.73399648670523e-05 |
75 | 0.99997516312954 | 4.96737409182542e-05 | 2.48368704591271e-05 |
76 | 0.999961169741207 | 7.7660517586249e-05 | 3.88302587931245e-05 |
77 | 0.999937100172971 | 0.000125799654057645 | 6.28998270288226e-05 |
78 | 0.999903356370831 | 0.000193287258337537 | 9.66436291687684e-05 |
79 | 0.999860616007487 | 0.000278767985025181 | 0.000139383992512590 |
80 | 0.999805048192847 | 0.000389903614305939 | 0.000194951807152970 |
81 | 0.999690540780698 | 0.000618918438603204 | 0.000309459219301602 |
82 | 0.99953841942285 | 0.000923161154299814 | 0.000461580577149907 |
83 | 0.999375863161697 | 0.00124827367660652 | 0.00062413683830326 |
84 | 0.99914825444997 | 0.00170349110005937 | 0.000851745550029687 |
85 | 0.998817548702945 | 0.00236490259411082 | 0.00118245129705541 |
86 | 0.998488414074782 | 0.00302317185043616 | 0.00151158592521808 |
87 | 0.997854179841976 | 0.00429164031604817 | 0.00214582015802409 |
88 | 0.996984429405176 | 0.00603114118964812 | 0.00301557059482406 |
89 | 0.99572519656439 | 0.00854960687121791 | 0.00427480343560896 |
90 | 0.99397432300185 | 0.0120513539962988 | 0.00602567699814939 |
91 | 0.992790944738787 | 0.0144181105224258 | 0.0072090552612129 |
92 | 0.991716366903705 | 0.0165672661925904 | 0.00828363309629519 |
93 | 0.995790857797706 | 0.00841828440458832 | 0.00420914220229416 |
94 | 0.997242402515649 | 0.00551519496870281 | 0.00275759748435140 |
95 | 0.998302284300695 | 0.00339543139861066 | 0.00169771569930533 |
96 | 0.998791478775342 | 0.00241704244931664 | 0.00120852122465832 |
97 | 0.999280260530135 | 0.00143947893973079 | 0.000719739469865396 |
98 | 0.999475245862342 | 0.00104950827531573 | 0.000524754137657867 |
99 | 0.999588711086559 | 0.000822577826882706 | 0.000411288913441353 |
100 | 0.999538810395198 | 0.000922379209603499 | 0.000461189604801749 |
101 | 0.999410082839271 | 0.00117983432145734 | 0.000589917160728671 |
102 | 0.999187183587936 | 0.00162563282412803 | 0.000812816412064014 |
103 | 0.999192488996213 | 0.00161502200757341 | 0.000807511003786706 |
104 | 0.99956311311339 | 0.000873773773219914 | 0.000436886886609957 |
105 | 0.999746636729578 | 0.000506726540843991 | 0.000253363270421995 |
106 | 0.999877974552133 | 0.000244050895733151 | 0.000122025447866575 |
107 | 0.99995847418004 | 8.30516399209289e-05 | 4.15258199604644e-05 |
108 | 0.99999010241836 | 1.97951632820818e-05 | 9.8975816410409e-06 |
109 | 0.999996443618963 | 7.11276207496605e-06 | 3.55638103748303e-06 |
110 | 0.99999806328208 | 3.87343584077805e-06 | 1.93671792038903e-06 |
111 | 0.999999069925442 | 1.86014911527108e-06 | 9.3007455763554e-07 |
112 | 0.999998039430377 | 3.92113924660873e-06 | 1.96056962330437e-06 |
113 | 0.999995939902913 | 8.12019417388826e-06 | 4.06009708694413e-06 |
114 | 0.999990502388005 | 1.89952239904769e-05 | 9.49761199523846e-06 |
115 | 0.999982480349997 | 3.50393000055203e-05 | 1.75196500027602e-05 |
116 | 0.999966581676123 | 6.68366477550678e-05 | 3.34183238775339e-05 |
117 | 0.999917577154765 | 0.000164845690468883 | 8.24228452344413e-05 |
118 | 0.99993189657231 | 0.000136206855378252 | 6.81034276891262e-05 |
119 | 0.99997461993141 | 5.07601371811786e-05 | 2.53800685905893e-05 |
120 | 0.999996781978523 | 6.43604295389104e-06 | 3.21802147694552e-06 |
121 | 0.999994828481464 | 1.03430370724634e-05 | 5.17151853623171e-06 |
122 | 0.9999813795936 | 3.72408127995358e-05 | 1.86204063997679e-05 |
123 | 0.9999454913634 | 0.000109017273198957 | 5.45086365994783e-05 |
124 | 0.999863844774914 | 0.000272310450172826 | 0.000136155225086413 |
125 | 0.99944000488547 | 0.00111999022906019 | 0.000559995114530093 |
126 | 0.998243409326439 | 0.00351318134712291 | 0.00175659067356145 |
127 | 0.993141138615833 | 0.0137177227683350 | 0.00685886138416749 |
128 | 0.970080422804408 | 0.0598391543911847 | 0.0299195771955923 |
Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
Description | # significant tests | % significant tests | OK/NOK |
1% type I error level | 92 | 0.821428571428571 | NOK |
5% type I error level | 102 | 0.910714285714286 | NOK |
10% type I error level | 105 | 0.9375 | NOK |