Multiple Linear Regression - Estimated Regression Equation |
Y[t] = + 170.018050942712 -0.185865384723691X[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) | 170.018050942712 | 8.533857 | 19.9228 | 0 | 0 |
X | -0.185865384723691 | 0.042221 | -4.4022 | 2.1e-05 | 1e-05 |
Multiple Linear Regression - Regression Statistics | |
Multiple R | 0.345468222898485 |
R-squared | 0.119348293032637 |
Adjusted R-squared | 0.113189889487411 |
F-TEST (value) | 19.3797454415195 |
F-TEST (DF numerator) | 1 |
F-TEST (DF denominator) | 143 |
p-value | 2.08334234278462e-05 |
Multiple Linear Regression - Residual Statistics | |
Residual Standard Deviation | 29.6276045773387 |
Sum Squared Residuals | 125524.678277733 |
Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
1 | 100 | 151.431512470344 | -51.4315124703439 |
2 | 103.53 | 150.944545162367 | -47.4145451623672 |
3 | 108.36 | 150.015218238749 | -41.6552182387489 |
4 | 115.2 | 150.788418239199 | -35.5884182391994 |
5 | 123.51 | 150.760538431491 | -27.2505384314908 |
6 | 132.87 | 150.297733623529 | -17.4277336235289 |
7 | 130.55 | 150.106292277263 | -19.5562922772635 |
8 | 136.68 | 149.792179777080 | -13.1121797770804 |
9 | 140.63 | 149.028273045866 | -8.39827304586606 |
10 | 143.47 | 149.693671123177 | -6.22367112317687 |
11 | 124.1 | 149.805190354011 | -25.7051903540111 |
12 | 111.49 | 149.418590353786 | -37.9285903537858 |
13 | 119.93 | 149.396286507619 | -29.4662865076190 |
14 | 131.79 | 148.650966314877 | -16.8609663148770 |
15 | 136.61 | 147.630565352744 | -11.0205653527439 |
16 | 141.79 | 147.177053814018 | -5.38705381401811 |
17 | 142.23 | 147.634282660438 | -5.40428266043839 |
18 | 146.74 | 147.387081698756 | -0.64708169875586 |
19 | 154.85 | 147.197499006338 | 7.65250099366229 |
20 | 148.44 | 146.725400929140 | 1.71459907086046 |
21 | 154.18 | 146.100893236468 | 8.07910676353207 |
22 | 149.1 | 146.244009582705 | 2.85599041729482 |
23 | 152.22 | 146.688227852195 | 5.5317721478052 |
24 | 149.34 | 146.309062467358 | 3.03093753264154 |
25 | 160.94 | 146.245868236552 | 14.6941317634476 |
26 | 176.16 | 145.716151890090 | 30.4438481099101 |
27 | 195.12 | 145.192011505169 | 49.9279884948309 |
28 | 186.07 | 144.771955735694 | 41.2980442643065 |
29 | 200.78 | 144.877899004986 | 55.902100995014 |
30 | 208.15 | 144.742217274138 | 63.4077827258623 |
31 | 209.56 | 144.160458619953 | 65.3995413800474 |
32 | 203.33 | 144.435539389344 | 58.8944606106564 |
33 | 198.84 | 144.258967273856 | 54.5810327261438 |
34 | 200.63 | 144.309150927732 | 56.3208490722684 |
35 | 206.47 | 144.742217274138 | 61.7277827258623 |
36 | 196.68 | 144.561927850956 | 52.1180721490442 |
37 | 203.81 | 144.530330735553 | 59.2796692644473 |
38 | 190.18 | 144.244098043078 | 45.9359019569217 |
39 | 187.5 | 143.431866311836 | 44.0681336881643 |
40 | 187.62 | 143.257152850195 | 44.3628471498045 |
41 | 168.92 | 143.236707657876 | 25.6832923421241 |
42 | 164.78 | 143.073146119319 | 21.706853880681 |
43 | 175.98 | 142.552723042093 | 33.4272769579073 |
44 | 174.7 | 142.188426888034 | 32.5115731119657 |
45 | 166.95 | 141.560201887668 | 25.3897981123318 |
46 | 161.76 | 141.844575926295 | 19.9154240737046 |
47 | 149.65 | 142.316674003494 | 7.33332599650641 |
48 | 137.42 | 141.264675925958 | -3.84467592595752 |
49 | 142.6 | 141.225644195166 | 1.37435580483446 |
50 | 146.94 | 140.450585540868 | 6.48941445913226 |
51 | 152.52 | 138.790807655285 | 13.7291923447148 |
52 | 147.47 | 139.504530732624 | 7.96546926737584 |
53 | 146.15 | 139.578876886514 | 6.57112311348637 |
54 | 152.04 | 139.630919194236 | 12.4090808057637 |
55 | 144.42 | 139.140234578566 | 5.27976542143426 |
56 | 138.15 | 139.136517270871 | -0.986517270871246 |
57 | 125.94 | 138.411642270449 | -12.4716422704489 |
58 | 112.61 | 138.909761501508 | -26.2997615015083 |
59 | 111.48 | 139.387435540248 | -27.9074355402482 |
60 | 95.25 | 138.508292270505 | -43.2582922705052 |
61 | 105.38 | 138.761069193729 | -33.3810691937294 |
62 | 109.59 | 137.965565347112 | -28.375565347112 |
63 | 99.07 | 136.969326884993 | -37.899326884993 |
64 | 92.07 | 137.420979769872 | -45.3509797698716 |
65 | 89.1 | 137.372654769843 | -48.2726547698434 |
66 | 86.36 | 136.785320154117 | -50.4253201541166 |
67 | 95.39 | 136.471207653934 | -41.0812076539335 |
68 | 95.27 | 136.058586499847 | -40.7885864998469 |
69 | 98.56 | 135.497273037981 | -36.9372730379814 |
70 | 101.79 | 135.973088422874 | -34.183088422874 |
71 | 102.02 | 136.170105730681 | -34.1501057306812 |
72 | 98.21 | 135.553032653399 | -37.3430326533985 |
73 | 104.42 | 135.579053807260 | -31.1590538072598 |
74 | 105.62 | 134.973132653061 | -29.3531326530606 |
75 | 109.46 | 134.352342268083 | -24.8923422680835 |
76 | 110.94 | 134.588391306683 | -23.6483913066826 |
77 | 113.09 | 134.649726883641 | -21.5597268836414 |
78 | 109.58 | 134.095848037165 | -24.5158480371648 |
79 | 111.41 | 133.859798998566 | -22.4497989985657 |
80 | 109.83 | 133.696237460009 | -23.8662374600088 |
81 | 110.58 | 133.108902844282 | -22.5289028442820 |
82 | 109.04 | 133.291050921311 | -24.2510509213112 |
83 | 107.8 | 133.844929767788 | -26.0449297677878 |
84 | 109.79 | 132.975079767281 | -23.1850797672809 |
85 | 110.76 | 132.936048036489 | -22.1760480364889 |
86 | 112.64 | 132.272508613025 | -19.6325086130254 |
87 | 114.17 | 132.034600920579 | -17.8646009205790 |
88 | 115.99 | 131.642424958812 | -15.6524249588121 |
89 | 119.01 | 131.634990343423 | -12.6249903434231 |
90 | 117.92 | 131.341323035560 | -13.4213230355597 |
91 | 115.92 | 130.971450919960 | -15.0514509199595 |
92 | 120.75 | 130.536525919706 | -9.7865259197061 |
93 | 124.94 | 127.023670148428 | -2.08367014842835 |
94 | 129.17 | 126.908433609900 | 2.26156639010033 |
95 | 128.14 | 127.637025918017 | 0.502974081983463 |
96 | 134.18 | 126.906574956052 | 7.27342504394758 |
97 | 131.74 | 126.547854763536 | 5.19214523646431 |
98 | 134.32 | 126.163113417158 | 8.15688658284233 |
99 | 137.8 | 124.867631685634 | 12.9323683143665 |
100 | 141.79 | 125.261666301248 | 16.5283336987522 |
101 | 142.75 | 125.347164378221 | 17.4028356217793 |
102 | 144.3 | 125.047921108816 | 19.2520788911845 |
103 | 145.49 | 124.181788416003 | 21.3082115839969 |
104 | 138.21 | 123.960608608182 | 14.2493913918181 |
105 | 139.02 | 123.371415338608 | 15.6485846613922 |
106 | 141.91 | 123.902990338918 | 18.0070096610824 |
107 | 144.95 | 124.713363416313 | 20.2366365836871 |
108 | 146.11 | 123.776601877305 | 22.3333981226945 |
109 | 150.96 | 124.103724954419 | 26.8562750455808 |
110 | 148.2 | 123.460630723275 | 24.7393692767248 |
111 | 152.12 | 121.538782645232 | 30.5812173547678 |
112 | 154.74 | 122.395622068808 | 32.3443779311916 |
113 | 150.8 | 122.561042261213 | 28.2389577387875 |
114 | 152.6 | 121.778548991526 | 30.8214510084742 |
115 | 158.74 | 121.574097068330 | 37.1659029316703 |
116 | 161.83 | 121.284147068161 | 40.5458529318392 |
117 | 162.4 | 120.338092259917 | 42.0619077400828 |
118 | 156.11 | 120.661498029336 | 35.4485019706636 |
119 | 154.93 | 121.880774953124 | 33.0492250468762 |
120 | 157.18 | 120.756289375546 | 36.4237106244545 |
121 | 159.85 | 121.287864375855 | 38.5621356241447 |
122 | 154.4 | 120.754430721698 | 33.6455692783017 |
123 | 151.57 | 120.061152836679 | 31.5088471633211 |
124 | 133.34 | 120.590869183141 | 12.7491308168586 |
125 | 131.2 | 121.451425914412 | 9.74857408558788 |
126 | 124.17 | 120.726550913990 | 3.44344908601028 |
127 | 133.19 | 121.087129760354 | 12.1028702396463 |
128 | 130.94 | 120.687519183198 | 10.2524808168023 |
129 | 119.58 | 120.066728798221 | -0.486728798220618 |
130 | 118.55 | 121.330613414342 | -2.78061341434171 |
131 | 119.96 | 122.035043222445 | -2.0750432224445 |
132 | 108.42 | 120.722833606295 | -12.3028336062952 |
133 | 95.93 | 120.328798990681 | -24.398798990681 |
134 | 88.83 | 120.018403798192 | -31.1884037981925 |
135 | 84.98 | 119.295387451617 | -34.3153874516173 |
136 | 81.61 | 118.206216297136 | -36.5962162971365 |
137 | 72.84 | 118.165325912497 | -45.3253259124973 |
138 | 74.72 | 117.784301873814 | -43.0643018738137 |
139 | 83.4 | 116.925603796390 | -33.5256037963902 |
140 | 87.42 | 116.611491296207 | -29.1914912962072 |
141 | 86.33 | 115.267684564655 | -28.9376845646549 |
142 | 94.28 | 115.329020141614 | -21.0490201416137 |
143 | 98.81 | 115.163599949210 | -16.3535999492097 |
144 | 100.96 | 114.323488410259 | -13.3634884102586 |
145 | 99.14 | 113.591178794447 | -14.4511787944472 |
Goldfeld-Quandt test for Heteroskedasticity | |||
p-values | Alternative Hypothesis | ||
breakpoint index | greater | 2-sided | less |
5 | 0.0543336217108625 | 0.108667243421725 | 0.945666378289137 |
6 | 0.0481150990737843 | 0.0962301981475685 | 0.951884900926216 |
7 | 0.0206389496865986 | 0.0412778993731972 | 0.979361050313401 |
8 | 0.00799378093007457 | 0.0159875618601491 | 0.992006219069925 |
9 | 0.00273576178032791 | 0.00547152356065582 | 0.997264238219672 |
10 | 0.00140573783459866 | 0.00281147566919732 | 0.998594262165401 |
11 | 0.000595578619164258 | 0.00119115723832852 | 0.999404421380836 |
12 | 0.00186585911491275 | 0.00373171822982551 | 0.998134140885087 |
13 | 0.00118440319504998 | 0.00236880639009996 | 0.99881559680495 |
14 | 0.000537723878008446 | 0.00107544775601689 | 0.999462276121992 |
15 | 0.000263010128489922 | 0.000526020256979843 | 0.99973698987151 |
16 | 0.000103358197089751 | 0.000206716394179502 | 0.99989664180291 |
17 | 3.73003912277326e-05 | 7.46007824554652e-05 | 0.999962699608772 |
18 | 1.33461383485114e-05 | 2.66922766970228e-05 | 0.999986653861652 |
19 | 5.93858773318676e-06 | 1.18771754663735e-05 | 0.999994061412267 |
20 | 2.04075595374329e-06 | 4.08151190748657e-06 | 0.999997959244046 |
21 | 6.6504338572235e-07 | 1.3300867714447e-06 | 0.999999334956614 |
22 | 2.37136201376090e-07 | 4.74272402752179e-07 | 0.999999762863799 |
23 | 7.42122166915262e-08 | 1.48424433383052e-07 | 0.999999925787783 |
24 | 2.41498551227396e-08 | 4.82997102454793e-08 | 0.999999975850145 |
25 | 9.29196852313395e-09 | 1.85839370462679e-08 | 0.999999990708031 |
26 | 1.13489341433591e-08 | 2.26978682867182e-08 | 0.999999988651066 |
27 | 1.01878887898270e-07 | 2.03757775796540e-07 | 0.999999898121112 |
28 | 6.01899630032177e-08 | 1.20379926006435e-07 | 0.999999939810037 |
29 | 2.02048673220298e-07 | 4.04097346440596e-07 | 0.999999797951327 |
30 | 8.70470962682326e-07 | 1.74094192536465e-06 | 0.999999129529037 |
31 | 1.27733751278629e-06 | 2.55467502557257e-06 | 0.999998722662487 |
32 | 1.22309891374483e-06 | 2.44619782748966e-06 | 0.999998776901086 |
33 | 8.0817365147768e-07 | 1.61634730295536e-06 | 0.999999191826348 |
34 | 6.12885517880207e-07 | 1.22577103576041e-06 | 0.999999387114482 |
35 | 1.07257126921125e-06 | 2.14514253842250e-06 | 0.99999892742873 |
36 | 8.2359946401838e-07 | 1.64719892803676e-06 | 0.999999176400536 |
37 | 1.02103442185417e-06 | 2.04206884370833e-06 | 0.999998978965578 |
38 | 8.76865649238785e-07 | 1.75373129847757e-06 | 0.99999912313435 |
39 | 1.70977582206830e-06 | 3.41955164413659e-06 | 0.999998290224178 |
40 | 3.63299791760851e-06 | 7.26599583521701e-06 | 0.999996367002082 |
41 | 3.15095786303396e-05 | 6.30191572606792e-05 | 0.99996849042137 |
42 | 0.000227058925574136 | 0.000454117851148271 | 0.999772941074426 |
43 | 0.000691531958936874 | 0.00138306391787375 | 0.999308468041063 |
44 | 0.00219679790088322 | 0.00439359580176643 | 0.997803202099117 |
45 | 0.0102322677908677 | 0.0204645355817354 | 0.989767732209132 |
46 | 0.0293131396797708 | 0.0586262793595416 | 0.97068686032023 |
47 | 0.0716507837019145 | 0.143301567403829 | 0.928349216298086 |
48 | 0.222995354377805 | 0.445990708755611 | 0.777004645622195 |
49 | 0.364080575790869 | 0.728161151581739 | 0.63591942420913 |
50 | 0.49637064025509 | 0.99274128051018 | 0.50362935974491 |
51 | 0.629249935711324 | 0.741500128577352 | 0.370750064288676 |
52 | 0.715747591003395 | 0.568504817993211 | 0.284252408996605 |
53 | 0.777301713384288 | 0.445396573231424 | 0.222698286615712 |
54 | 0.81823161353911 | 0.363536772921782 | 0.181768386460891 |
55 | 0.858407445367312 | 0.283185109265376 | 0.141592554632688 |
56 | 0.891205847357055 | 0.217588305285890 | 0.108794152642945 |
57 | 0.926312932663523 | 0.147374134672954 | 0.0736870673364772 |
58 | 0.955741725607158 | 0.0885165487856848 | 0.0442582743928424 |
59 | 0.970394207742918 | 0.0592115845141645 | 0.0296057922570823 |
60 | 0.986712207412366 | 0.0265755851752688 | 0.0132877925876344 |
61 | 0.990663141078824 | 0.0186737178423512 | 0.00933685892117559 |
62 | 0.992242198846722 | 0.0155156023065567 | 0.00775780115327834 |
63 | 0.994636541165487 | 0.0107269176690251 | 0.00536345883451255 |
64 | 0.9966628802517 | 0.00667423949660182 | 0.00333711974830091 |
65 | 0.997959082275746 | 0.00408183544850744 | 0.00204091772425372 |
66 | 0.998794491529132 | 0.0024110169417349 | 0.00120550847086745 |
67 | 0.998957315692915 | 0.00208536861417031 | 0.00104268430708515 |
68 | 0.999060368971588 | 0.00187926205682379 | 0.000939631028411894 |
69 | 0.999035234907788 | 0.00192953018442359 | 0.000964765092211796 |
70 | 0.998915973637327 | 0.00216805272534543 | 0.00108402636267272 |
71 | 0.998771823584617 | 0.00245635283076509 | 0.00122817641538255 |
72 | 0.998721436592671 | 0.00255712681465780 | 0.00127856340732890 |
73 | 0.998468406748182 | 0.00306318650363502 | 0.00153159325181751 |
74 | 0.998122421921552 | 0.00375515615689553 | 0.00187757807844777 |
75 | 0.997553120177472 | 0.00489375964505651 | 0.00244687982252825 |
76 | 0.996796461937967 | 0.00640707612406659 | 0.00320353806203329 |
77 | 0.99575663162761 | 0.00848673674477976 | 0.00424336837238988 |
78 | 0.994701910567166 | 0.0105961788656685 | 0.00529808943283426 |
79 | 0.993323775705369 | 0.0133524485892626 | 0.00667622429463132 |
80 | 0.991938066609506 | 0.0161238667809889 | 0.00806193339049445 |
81 | 0.990316761249846 | 0.0193664775003075 | 0.00968323875015375 |
82 | 0.989000812142191 | 0.0219983757156172 | 0.0109991878578086 |
83 | 0.98842637182737 | 0.0231472563452595 | 0.0115736281726298 |
84 | 0.987710013473071 | 0.0245799730538583 | 0.0122899865269291 |
85 | 0.987422983283562 | 0.0251540334328763 | 0.0125770167164381 |
86 | 0.987202504783559 | 0.0255949904328824 | 0.0127974952164412 |
87 | 0.987380116180003 | 0.0252397676399943 | 0.0126198838199971 |
88 | 0.987883273937457 | 0.0242334521250859 | 0.0121167260625429 |
89 | 0.988719352382597 | 0.0225612952348060 | 0.0112806476174030 |
90 | 0.990846139358769 | 0.0183077212824628 | 0.00915386064123138 |
91 | 0.994171846651562 | 0.0116563066968761 | 0.00582815334843803 |
92 | 0.996572837397685 | 0.00685432520463089 | 0.00342716260231545 |
93 | 0.996853100444787 | 0.00629379911042673 | 0.00314689955521336 |
94 | 0.996959448451295 | 0.00608110309741047 | 0.00304055154870524 |
95 | 0.997619633688807 | 0.00476073262238515 | 0.00238036631119258 |
96 | 0.997775851068017 | 0.00444829786396683 | 0.00222414893198341 |
97 | 0.99807375608026 | 0.00385248783948217 | 0.00192624391974109 |
98 | 0.998231567774051 | 0.00353686445189765 | 0.00176843222594882 |
99 | 0.997950965955145 | 0.00409806808971032 | 0.00204903404485516 |
100 | 0.997634697014862 | 0.00473060597027667 | 0.00236530298513833 |
101 | 0.997299118827654 | 0.00540176234469261 | 0.00270088117234631 |
102 | 0.996779666088247 | 0.00644066782350664 | 0.00322033391175332 |
103 | 0.99581600798613 | 0.00836798402774238 | 0.00418399201387119 |
104 | 0.99477665279039 | 0.0104466944192181 | 0.00522334720960907 |
105 | 0.993082319312398 | 0.0138353613752042 | 0.00691768068760212 |
106 | 0.991144521992295 | 0.0177109560154091 | 0.00885547800770456 |
107 | 0.989549969924612 | 0.0209000601507757 | 0.0104500300753878 |
108 | 0.986395757477453 | 0.027208485045094 | 0.013604242522547 |
109 | 0.982446373262624 | 0.0351072534747528 | 0.0175536267373764 |
110 | 0.976808693286236 | 0.0463826134275281 | 0.0231913067137641 |
111 | 0.971785823174737 | 0.0564283536505258 | 0.0282141768252629 |
112 | 0.964421728751552 | 0.0711565424968953 | 0.0355782712484477 |
113 | 0.953185912000697 | 0.0936281759986054 | 0.0468140879993027 |
114 | 0.942872944868137 | 0.114254110263726 | 0.0571270551318631 |
115 | 0.939563092562403 | 0.120873814875194 | 0.060436907437597 |
116 | 0.944865105865242 | 0.110269788269516 | 0.0551348941347578 |
117 | 0.962528003337122 | 0.074943993325756 | 0.037471996662878 |
118 | 0.968356250990519 | 0.0632874980189618 | 0.0316437490094809 |
119 | 0.966731389843521 | 0.0665372203129576 | 0.0332686101564788 |
120 | 0.976673444592531 | 0.0466531108149373 | 0.0233265554074687 |
121 | 0.986470700187803 | 0.0270585996243936 | 0.0135292998121968 |
122 | 0.993266193470603 | 0.0134676130587944 | 0.00673380652939718 |
123 | 0.998018238552218 | 0.00396352289556364 | 0.00198176144778182 |
124 | 0.998009465604993 | 0.0039810687900133 | 0.00199053439500665 |
125 | 0.99756868519775 | 0.00486262960450201 | 0.00243131480225101 |
126 | 0.996697764168193 | 0.0066044716636146 | 0.0033022358318073 |
127 | 0.99757314463477 | 0.00485371073046069 | 0.00242685536523034 |
128 | 0.998729601111119 | 0.00254079777776206 | 0.00127039888888103 |
129 | 0.998871907594588 | 0.00225618481082306 | 0.00112809240541153 |
130 | 0.999057645184 | 0.00188470963199957 | 0.000942354815999787 |
131 | 0.999790907700383 | 0.000418184599233913 | 0.000209092299616957 |
132 | 0.999963173478877 | 7.3653042245963e-05 | 3.68265211229815e-05 |
133 | 0.999984338999673 | 3.13220006532921e-05 | 1.56610003266460e-05 |
134 | 0.999992436194005 | 1.51276119891310e-05 | 7.56380599456552e-06 |
135 | 0.999997203443047 | 5.59311390682643e-06 | 2.79655695341322e-06 |
136 | 0.999993376158204 | 1.32476835912680e-05 | 6.62384179563402e-06 |
137 | 0.999958389802188 | 8.32203956239369e-05 | 4.16101978119684e-05 |
138 | 0.999811725498136 | 0.000376549003728766 | 0.000188274501864383 |
139 | 0.998756440558705 | 0.00248711888258927 | 0.00124355944129464 |
140 | 0.991726866379096 | 0.016546267241808 | 0.008273133620904 |
Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
Description | # significant tests | % significant tests | OK/NOK |
1% type I error level | 79 | 0.580882352941177 | NOK |
5% type I error level | 111 | 0.816176470588235 | NOK |
10% type I error level | 121 | 0.889705882352941 | NOK |