Multiple Linear Regression - Estimated Regression Equation |
TOT[t] = + 0.745313423069235 + 0.60534531523025SMF[t] + 0.140579094641995SSF[t] + 0.247134222645753NS[t] + 0.00229224875322625t + 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) | 0.745313423069235 | 0.155805 | 4.7836 | 4e-06 | 2e-06 |
SMF | 0.60534531523025 | 0.004484 | 134.9894 | 0 | 0 |
SSF | 0.140579094641995 | 0.002901 | 48.4561 | 0 | 0 |
NS | 0.247134222645753 | 0.002914 | 84.8121 | 0 | 0 |
t | 0.00229224875322625 | 0.001204 | 1.9044 | 0.058843 | 0.029422 |
Multiple Linear Regression - Regression Statistics | |
Multiple R | 0.999992983326871 |
R-squared | 0.999985966702975 |
Adjusted R-squared | 0.99998557957754 |
F-TEST (value) | 2583105.82522995 |
F-TEST (DF numerator) | 4 |
F-TEST (DF denominator) | 145 |
p-value | 0 |
Multiple Linear Regression - Residual Statistics | |
Residual Standard Deviation | 0.202936009187988 |
Sum Squared Residuals | 5.97153845464634 |
Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
1 | 100 | 100.053468923622 | -0.053468923622119 |
2 | 102 | 102.039353291239 | -0.0393532912385971 |
3 | 103.65 | 103.66957952725 | -0.0195795272501676 |
4 | 104.974 | 105.005577696872 | -0.0315776968717988 |
5 | 104.641 | 104.6866550444 | -0.0456550444002395 |
6 | 104.902 | 104.950275695015 | -0.0482756950153905 |
7 | 105.695 | 105.74348143727 | -0.0484814372695179 |
8 | 106.489 | 106.547680154214 | -0.0586801542143236 |
9 | 107.146 | 107.219249925571 | -0.0732499255709799 |
10 | 107.695 | 107.763594325848 | -0.0685943258476967 |
11 | 107.711 | 107.770830464145 | -0.0598304641446105 |
12 | 108.313 | 108.389201501733 | -0.0762015017331089 |
13 | 108.124 | 108.215553699716 | -0.0915536997162164 |
14 | 109.615 | 109.695749687722 | -0.0807496877224333 |
15 | 111.34 | 111.409553677012 | -0.0695536770119466 |
16 | 110.717 | 110.796336611416 | -0.0793366114157735 |
17 | 111.217 | 111.286097767136 | -0.0690977671357486 |
18 | 111.452 | 111.514134244267 | -0.0621342442668106 |
19 | 111.611 | 111.676369487038 | -0.0653694870381744 |
20 | 111.717 | 111.751808780865 | -0.0348087808646776 |
21 | 112.062 | 112.088634512177 | -0.0266345121773037 |
22 | 112.842 | 112.884697193317 | -0.0426971933168909 |
23 | 113.241 | 113.279847434805 | -0.0388474348054006 |
24 | 113.015 | 113.071178189092 | -0.0561781890923824 |
25 | 113.998 | 114.065472098293 | -0.0674720982930629 |
26 | 114.936 | 114.996091677772 | -0.0600916777718165 |
27 | 114.245 | 114.303879617043 | -0.0588796170430116 |
28 | 114.437 | 114.471426503628 | -0.0344265036276967 |
29 | 115.286 | 115.314337484133 | -0.0283374841332313 |
30 | 116.071 | 116.099247581855 | -0.0282475818552755 |
31 | 117.807 | 117.813928074762 | -0.00692807476175484 |
32 | 118.255 | 118.261750654163 | -0.0067506541630806 |
33 | 118.969 | 118.969123292152 | -0.000123292151803544 |
34 | 120.333 | 120.327983024063 | 0.00501697593727331 |
35 | 121.998 | 121.976769091834 | 0.0212309081663191 |
36 | 123.239 | 123.207317189722 | 0.0316828102782056 |
37 | 124.666 | 124.628219415657 | 0.0377805843430814 |
38 | 126.54 | 126.510004349142 | 0.0299956508581331 |
39 | 127.336 | 127.299101220759 | 0.0368987792413602 |
40 | 127.871 | 127.831470180021 | 0.0395298199789552 |
41 | 130.115 | 130.054691644214 | 0.0603083557858642 |
42 | 132.773 | 132.694905150304 | 0.0780948496958481 |
43 | 134.265 | 134.180541131744 | 0.0844588682560918 |
44 | 134.596 | 134.514536886025 | 0.0814631139748931 |
45 | 134.38 | 134.29039868427 | 0.0896013157302171 |
46 | 135.121 | 135.041752019776 | 0.0792479802238968 |
47 | 135.136 | 135.076608290654 | 0.0593917093456037 |
48 | 135.336 | 135.289980720439 | 0.046019279560806 |
49 | 135.284 | 135.212300806742 | 0.0716991932582532 |
50 | 137.144 | 137.080562980098 | 0.0634370199023919 |
51 | 140.349 | 140.259505283448 | 0.089494716551558 |
52 | 143.264 | 143.165769467153 | 0.09823053284699 |
53 | 144.381 | 144.268267935477 | 0.112732064522862 |
54 | 145.881 | 145.772138072799 | 0.108861927201454 |
55 | 146.497 | 146.416569079575 | 0.0804309204250713 |
56 | 148.857 | 148.786431283685 | 0.0705687163154483 |
57 | 150.78 | 150.714259040807 | 0.0657409591932464 |
58 | 153.293 | 153.228481490109 | 0.0645185098907708 |
59 | 157.641 | 157.570564454631 | 0.0704355453689521 |
60 | 162.182 | 162.103391857216 | 0.0786081427836005 |
61 | 167.86 | 167.771271308994 | 0.0887286910059043 |
62 | 175.245 | 175.119100182587 | 0.1258998174128 |
63 | 179.32 | 179.227537577267 | 0.0924624227326956 |
64 | 184.979 | 184.894429358997 | 0.0845706410028477 |
65 | 188.482 | 188.415941685785 | 0.0660583142147218 |
66 | 192.86 | 192.763958067186 | 0.09604193281394 |
67 | 195.475 | 195.376109268356 | 0.0988907316438793 |
68 | 198.4 | 198.299379610351 | 0.100620389649113 |
69 | 200.598 | 200.464723506962 | 0.133276493038371 |
70 | 202.121 | 202.004955666181 | 0.11604433381895 |
71 | 205.875 | 205.694170946042 | 0.1808290539578 |
72 | 207.085 | 206.920599996748 | 0.164400003252303 |
73 | 209.204 | 209.013563615097 | 0.190436384902739 |
74 | 212.246 | 211.879487932984 | 0.366512067016203 |
75 | 215.466 | 215.105151210584 | 0.360848789415679 |
76 | 216.693 | 216.415996182252 | 0.277003817747888 |
77 | 219.019 | 218.583486651203 | 0.435513348796601 |
78 | 217.924 | 217.616719939681 | 0.307280060319006 |
79 | 217.978 | 217.736063060537 | 0.241936939462883 |
80 | 218.186 | 217.932984200888 | 0.253015799111533 |
81 | 218.54 | 218.378259426883 | 0.161740573116589 |
82 | 217.886 | 218.01971123807 | -0.133711238070151 |
83 | 216.347 | 216.4726124837 | -0.125612483699743 |
84 | 219.825 | 219.950617191516 | -0.125617191515638 |
85 | 221.956 | 222.081209379358 | -0.125209379358221 |
86 | 227.184 | 227.366315725164 | -0.182315725164259 |
87 | 229.247 | 229.421879770897 | -0.174879770896946 |
88 | 233.33 | 233.444606165551 | -0.114606165550622 |
89 | 236.987 | 236.948594415389 | 0.0384055846106389 |
90 | 240.027 | 239.87498096879 | 0.152019031209869 |
91 | 245.433 | 245.457507587089 | -0.0245075870894174 |
92 | 246.641 | 246.778555896516 | -0.137555896515816 |
93 | 250.328 | 250.587972911182 | -0.259972911181552 |
94 | 250.849 | 251.038503884336 | -0.189503884336324 |
95 | 251.435 | 251.40471396056 | 0.0302860394396804 |
96 | 252.091 | 251.893563693055 | 0.197436306944828 |
97 | 252.946 | 253.208858115749 | -0.262858115749061 |
98 | 252.773 | 253.026535797814 | -0.253535797814479 |
99 | 250.677 | 250.93721870785 | -0.260218707850469 |
100 | 250.105 | 250.034846388617 | 0.0701536113832652 |
101 | 251.788 | 251.80515470318 | -0.0171547031798678 |
102 | 250.212 | 250.227575022966 | -0.0155750229663913 |
103 | 248.073 | 248.056076398848 | 0.0169236011516281 |
104 | 244.468 | 244.676526027044 | -0.208526027044003 |
105 | 244.727 | 244.959737879344 | -0.232737879343539 |
106 | 244.034 | 244.102773069529 | -0.0687730695288894 |
107 | 243.588 | 243.324719252509 | 0.263280747490686 |
108 | 236.447 | 236.470586942982 | -0.0235869429815683 |
109 | 224.906 | 225.100483887179 | -0.1944838871792 |
110 | 221.934 | 222.452917936447 | -0.518917936447114 |
111 | 224.903 | 225.159614429181 | -0.256614429180686 |
112 | 223.798 | 224.070666545012 | -0.272666545011934 |
113 | 218.529 | 218.582334090585 | -0.0533340905851306 |
114 | 217.521 | 217.824706731465 | -0.30370673146501 |
115 | 219.971 | 220.301226649606 | -0.330226649605875 |
116 | 223.841 | 223.941767025971 | -0.100767025971165 |
117 | 223.764 | 223.93876779094 | -0.174767790940088 |
118 | 223.664 | 223.783459409421 | -0.119459409421007 |
119 | 217.678 | 218.126899312379 | -0.448899312379116 |
120 | 218.478 | 218.90180982771 | -0.423809827710211 |
121 | 214.815 | 215.201313886341 | -0.386313886341016 |
122 | 215.143 | 215.272101902515 | -0.129101902515489 |
123 | 218.381 | 218.208549409678 | 0.17245059032194 |
124 | 219.962 | 220.197090414046 | -0.23509041404555 |
125 | 218.933 | 219.447072290941 | -0.514072290941298 |
126 | 218.36 | 219.143416665219 | -0.783416665219369 |
127 | 217.72 | 218.039440809347 | -0.319440809346528 |
128 | 219.934 | 219.823718909999 | 0.110281090001194 |
129 | 220.842 | 220.435245056649 | 0.406754943350537 |
130 | 220.584 | 220.19550679293 | 0.388493207069858 |
131 | 216.346 | 216.626694097259 | -0.280694097259421 |
132 | 220.221 | 219.941479954442 | 0.279520045558104 |
133 | 222.182 | 221.915004844636 | 0.266995155363707 |
134 | 225.455 | 225.226014409564 | 0.228985590436361 |
135 | 226.42 | 226.509524914358 | -0.0895249143579058 |
136 | 228.287 | 228.373801138946 | -0.0868011389464091 |
137 | 231.349 | 231.519039242036 | -0.170039242036341 |
138 | 231.015 | 231.106306945052 | -0.091306945052428 |
139 | 232.241 | 231.962204549983 | 0.27879545001725 |
140 | 233.688 | 233.847080501531 | -0.159080501530606 |
141 | 236.667 | 236.575858897743 | 0.0911411022575046 |
142 | 238.439 | 238.334089200745 | 0.104910799254831 |
143 | 239.488 | 239.09798836874 | 0.390011631260415 |
144 | 238.741 | 238.153273375069 | 0.587726624930835 |
145 | 238.5 | 238.288179425099 | 0.211820574901384 |
146 | 242.116 | 241.708221478477 | 0.407778521523183 |
147 | 243.923 | 243.491696778588 | 0.43130322141172 |
148 | 245.813 | 245.727174581886 | 0.0858254181136716 |
149 | 247.143 | 246.936344538267 | 0.206655461733249 |
150 | 246.381 | 246.486383004937 | -0.105383004937036 |
Goldfeld-Quandt test for Heteroskedasticity | |||
p-values | Alternative Hypothesis | ||
breakpoint index | greater | 2-sided | less |
8 | 7.13783364187702e-09 | 1.4275667283754e-08 | 0.999999992862166 |
9 | 1.01174481844702e-11 | 2.02348963689404e-11 | 0.999999999989883 |
10 | 7.80044224220733e-14 | 1.56008844844147e-13 | 0.999999999999922 |
11 | 1.62166449586085e-16 | 3.24332899172171e-16 | 1 |
12 | 2.76753142107478e-19 | 5.53506284214955e-19 | 1 |
13 | 1.18267254802029e-21 | 2.36534509604058e-21 | 1 |
14 | 2.18104347689081e-24 | 4.36208695378163e-24 | 1 |
15 | 1.23134186486247e-26 | 2.46268372972494e-26 | 1 |
16 | 2.11484107122799e-29 | 4.22968214245597e-29 | 1 |
17 | 4.15601605225482e-32 | 8.31203210450964e-32 | 1 |
18 | 1.96562831610367e-34 | 3.93125663220735e-34 | 1 |
19 | 3.99740356152367e-37 | 7.99480712304733e-37 | 1 |
20 | 7.57434889711018e-40 | 1.51486977942204e-39 | 1 |
21 | 1.19991617274403e-42 | 2.39983234548806e-42 | 1 |
22 | 3.28654409575515e-45 | 6.57308819151031e-45 | 1 |
23 | 1.17384452619707e-47 | 2.34768905239415e-47 | 1 |
24 | 2.16682201249319e-50 | 4.33364402498638e-50 | 1 |
25 | 5.44703669791572e-53 | 1.08940733958314e-52 | 1 |
26 | 2.73176669098787e-55 | 5.46353338197575e-55 | 1 |
27 | 5.31278474045217e-58 | 1.06255694809043e-57 | 1 |
28 | 1.45116388701939e-60 | 2.90232777403877e-60 | 1 |
29 | 2.91265857363334e-63 | 5.82531714726667e-63 | 1 |
30 | 7.29125170084228e-66 | 1.45825034016846e-65 | 1 |
31 | 1.27175366860954e-68 | 2.54350733721908e-68 | 1 |
32 | 4.55315506701589e-71 | 9.10631013403178e-71 | 1 |
33 | 9.50727897858636e-74 | 1.90145579571727e-73 | 1 |
34 | 1.92076994388605e-76 | 3.8415398877721e-76 | 1 |
35 | 4.04836205980869e-79 | 8.09672411961738e-79 | 1 |
36 | 6.87678113457234e-82 | 1.37535622691447e-81 | 1 |
37 | 3.92646340550067e-84 | 7.85292681100133e-84 | 1 |
38 | 9.11372682538289e-87 | 1.82274536507658e-86 | 1 |
39 | 1.3929304086514e-89 | 2.78586081730279e-89 | 1 |
40 | 2.07265770251126e-92 | 4.14531540502253e-92 | 1 |
41 | 3.67426221775496e-95 | 7.34852443550991e-95 | 1 |
42 | 5.84130689018066e-98 | 1.16826137803613e-97 | 1 |
43 | 8.12181914986384e-101 | 1.62436382997277e-100 | 1 |
44 | 1.41005295928842e-103 | 2.82010591857683e-103 | 1 |
45 | 8.14665516172048e-106 | 1.6293310323441e-105 | 1 |
46 | 1.21027614510002e-108 | 2.42055229020005e-108 | 1 |
47 | 1.86911975863438e-111 | 3.73823951726876e-111 | 1 |
48 | 2.52739126028995e-114 | 5.0547825205799e-114 | 1 |
49 | 3.912437252766e-117 | 7.82487450553201e-117 | 1 |
50 | 5.06178264474573e-120 | 1.01235652894915e-119 | 1 |
51 | 1.76875392423468e-122 | 3.53750784846936e-122 | 1 |
52 | 2.88905466535945e-125 | 5.7781093307189e-125 | 1 |
53 | 7.58813823036036e-128 | 1.51762764607207e-127 | 1 |
54 | 1.09279772930505e-130 | 2.18559545861009e-130 | 1 |
55 | 5.75198774536366e-133 | 1.15039754907273e-132 | 1 |
56 | 8.12657949806779e-136 | 1.62531589961356e-135 | 1 |
57 | 1.08954524549774e-138 | 2.17909049099547e-138 | 1 |
58 | 1.3814424035608e-141 | 2.76288480712161e-141 | 1 |
59 | 1.96640843981138e-143 | 3.93281687962276e-143 | 1 |
60 | 2.77005966377742e-146 | 5.54011932755485e-146 | 1 |
61 | 3.67311364164096e-149 | 7.34622728328192e-149 | 1 |
62 | 5.73499212665023e-152 | 1.14699842533005e-151 | 1 |
63 | 1.21777746844671e-154 | 2.43555493689341e-154 | 1 |
64 | 1.62589041468762e-157 | 3.25178082937525e-157 | 1 |
65 | 2.81466092711487e-160 | 5.62932185422973e-160 | 1 |
66 | 3.92673755456564e-163 | 7.85347510913127e-163 | 1 |
67 | 6.46800968969753e-166 | 1.29360193793951e-165 | 1 |
68 | 8.97844270158552e-169 | 1.7956885403171e-168 | 1 |
69 | 1.98209325900186e-171 | 3.96418651800371e-171 | 1 |
70 | 4.07550109345179e-174 | 8.15100218690357e-174 | 1 |
71 | 1.05627757365008e-176 | 2.11255514730016e-176 | 1 |
72 | 2.40003332098209e-179 | 4.80006664196418e-179 | 1 |
73 | 9.61081516208388e-182 | 1.92216303241678e-181 | 1 |
74 | 1.04209933378133e-56 | 2.08419866756265e-56 | 1 |
75 | 1.76323270327656e-51 | 3.52646540655312e-51 | 1 |
76 | 8.59336685903316e-52 | 1.71867337180663e-51 | 1 |
77 | 1.18279955005642e-45 | 2.36559910011283e-45 | 1 |
78 | 2.40768655061254e-45 | 4.81537310122507e-45 | 1 |
79 | 2.17865478701816e-44 | 4.35730957403633e-44 | 1 |
80 | 3.77501917193752e-43 | 7.55003834387504e-43 | 1 |
81 | 1.56013069515418e-39 | 3.12026139030837e-39 | 1 |
82 | 2.26358664245906e-22 | 4.52717328491811e-22 | 1 |
83 | 9.57287956068603e-16 | 1.91457591213721e-15 | 0.999999999999999 |
84 | 1.30308734812693e-11 | 2.60617469625387e-11 | 0.999999999986969 |
85 | 1.3002513024519e-08 | 2.60050260490379e-08 | 0.999999986997487 |
86 | 1.45616580106319e-06 | 2.91233160212638e-06 | 0.999998543834199 |
87 | 4.64190210665052e-05 | 9.28380421330105e-05 | 0.999953580978933 |
88 | 0.00051017463755059 | 0.00102034927510118 | 0.999489825362449 |
89 | 0.00277235717416483 | 0.00554471434832967 | 0.997227642825835 |
90 | 0.0191351280945021 | 0.0382702561890042 | 0.980864871905498 |
91 | 0.0431555439516459 | 0.0863110879032919 | 0.956844456048354 |
92 | 0.0658536769591559 | 0.131707353918312 | 0.934146323040844 |
93 | 0.0836354318487756 | 0.167270863697551 | 0.916364568151224 |
94 | 0.0963229448268558 | 0.192645889653712 | 0.903677055173144 |
95 | 0.128408623528603 | 0.256817247057206 | 0.871591376471397 |
96 | 0.156271051820717 | 0.312542103641433 | 0.843728948179283 |
97 | 0.176881785556717 | 0.353763571113434 | 0.823118214443283 |
98 | 0.193604569982425 | 0.38720913996485 | 0.806395430017575 |
99 | 0.24816137704951 | 0.49632275409902 | 0.75183862295049 |
100 | 0.25638113597899 | 0.51276227195798 | 0.74361886402101 |
101 | 0.220623447565738 | 0.441246895131475 | 0.779376552434262 |
102 | 0.237940499969509 | 0.475880999939017 | 0.762059500030491 |
103 | 0.310052968087449 | 0.620105936174899 | 0.689947031912551 |
104 | 0.501167155226691 | 0.997665689546617 | 0.498832844773309 |
105 | 0.631063621159515 | 0.737872757680969 | 0.368936378840485 |
106 | 0.64951400032161 | 0.700971999356779 | 0.35048599967839 |
107 | 0.605057611728084 | 0.789884776543833 | 0.394942388271916 |
108 | 0.612614465681022 | 0.774771068637957 | 0.387385534318978 |
109 | 0.708644104062195 | 0.58271179187561 | 0.291355895937805 |
110 | 0.911990898102819 | 0.176018203794363 | 0.0880091018971814 |
111 | 0.932668308705531 | 0.134663382588938 | 0.0673316912944692 |
112 | 0.947320642350937 | 0.105358715298126 | 0.052679357649063 |
113 | 0.96233847584463 | 0.0753230483107396 | 0.0376615241553698 |
114 | 0.978146502222659 | 0.0437069955546823 | 0.0218534977773411 |
115 | 0.984788842590037 | 0.0304223148199257 | 0.0152111574099629 |
116 | 0.993399963361423 | 0.0132000732771548 | 0.00660003663857742 |
117 | 0.999267011664842 | 0.00146597667031622 | 0.000732988335158112 |
118 | 0.999480800094435 | 0.00103839981112965 | 0.000519199905564827 |
119 | 0.99986516333009 | 0.000269673339819359 | 0.00013483666990968 |
120 | 0.999876943615183 | 0.000246112769634954 | 0.000123056384817477 |
121 | 0.999800393455071 | 0.00039921308985725 | 0.000199606544928625 |
122 | 0.999884257850114 | 0.000231484299772501 | 0.00011574214988625 |
123 | 0.999990650146791 | 1.86997064179764e-05 | 9.34985320898821e-06 |
124 | 0.999985176659081 | 2.96466818385188e-05 | 1.48233409192594e-05 |
125 | 0.999983201773979 | 3.35964520413588e-05 | 1.67982260206794e-05 |
126 | 0.999989523596024 | 2.09528079514139e-05 | 1.04764039757069e-05 |
127 | 0.999988036970641 | 2.39260587171157e-05 | 1.19630293585579e-05 |
128 | 0.999976706882418 | 4.65862351635365e-05 | 2.32931175817683e-05 |
129 | 0.999985451388826 | 2.9097222348217e-05 | 1.45486111741085e-05 |
130 | 0.999999766957186 | 4.66085627226499e-07 | 2.33042813613249e-07 |
131 | 0.999999178506578 | 1.64298684326175e-06 | 8.21493421630875e-07 |
132 | 0.9999989517563 | 2.09648739940251e-06 | 1.04824369970126e-06 |
133 | 0.999998233382629 | 3.53323474194911e-06 | 1.76661737097456e-06 |
134 | 0.999995937579381 | 8.12484123878753e-06 | 4.06242061939377e-06 |
135 | 0.999982781909618 | 3.44361807640121e-05 | 1.72180903820061e-05 |
136 | 0.999957441450996 | 8.51170980086357e-05 | 4.25585490043179e-05 |
137 | 0.999851823612737 | 0.000296352774525164 | 0.000148176387262582 |
138 | 0.999849775696609 | 0.000300448606782727 | 0.000150224303391364 |
139 | 0.999815602880313 | 0.00036879423937452 | 0.00018439711968726 |
140 | 0.99981982464025 | 0.000360350719500941 | 0.00018017535975047 |
141 | 0.999054201163604 | 0.00189159767279281 | 0.000945798836396406 |
142 | 0.994484576692113 | 0.011030846615774 | 0.00551542330788702 |
Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
Description | # significant tests | % significant tests | OK/NOK |
1% type I error level | 107 | 0.792592592592593 | NOK |
5% type I error level | 112 | 0.82962962962963 | NOK |
10% type I error level | 114 | 0.844444444444444 | NOK |