Multiple Linear Regression - Estimated Regression Equation |
NS[t] = -2.44716196396029 + 0.193585990242196month[t] -2.37440482847711MSF[t] -0.557797764230691SSF[t] + 3.95052239705887TOT[t] -0.0146112912472268t + 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) | -2.44716196396029 | 1.145822 | -2.1357 | 0.034393 | 0.017197 |
month | 0.193585990242196 | 0.650917 | 0.2974 | 0.766586 | 0.383293 |
MSF | -2.37440482847711 | 0.038312 | -61.9761 | 0 | 0 |
SSF | -0.557797764230691 | 0.012702 | -43.9144 | 0 | 0 |
TOT | 3.95052239705887 | 0.043838 | 90.1158 | 0 | 0 |
t | -0.0146112912472268 | 0.051418 | -0.2842 | 0.776691 | 0.388345 |
Multiple Linear Regression - Regression Statistics | |
Multiple R | 0.999840787036238 |
R-squared | 0.999681599421244 |
Adjusted R-squared | 0.999670543845593 |
F-TEST (value) | 90423.2968917684 |
F-TEST (DF numerator) | 5 |
F-TEST (DF denominator) | 144 |
p-value | 0 |
Multiple Linear Regression - Residual Statistics | |
Residual Standard Deviation | 0.816490314760329 |
Sum Squared Residuals | 95.9985265100287 |
Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
1 | 100.294 | 100.062484569353 | 0.2315154306471 |
2 | 109.764 | 109.541698346703 | 0.222301653297345 |
3 | 120.711 | 120.688856535591 | 0.0221434644085211 |
4 | 131.551 | 131.709601701732 | -0.158601701732237 |
5 | 145.023 | 145.32193539912 | -0.298935399119653 |
6 | 177.164 | 177.932890802456 | -0.768890802456213 |
7 | 190.269 | 189.736330818211 | 0.532669181789488 |
8 | 219.996 | 219.956829878612 | 0.0391701213882427 |
9 | 218.186 | 218.98850457938 | -0.802504579379976 |
10 | 191.582 | 190.027101305517 | 1.55489869448253 |
11 | 204.484 | 203.327396403277 | 1.15660359672292 |
12 | 219.318 | 220.890010788265 | -1.57201078826448 |
13 | 100.578 | 100.301841545826 | 0.276158454174364 |
14 | 108.502 | 108.264430570687 | 0.237569429313198 |
15 | 121.37 | 121.425852429345 | -0.0558524293446251 |
16 | 131.422 | 131.555657829741 | -0.133657829741355 |
17 | 148.287 | 148.63092326568 | -0.343923265680244 |
18 | 174.947 | 175.760447078825 | -0.813447078825203 |
19 | 196.606 | 195.978341761302 | 0.627658238697549 |
20 | 223.847 | 224.370413470371 | -0.52341347037143 |
21 | 206.917 | 206.836080495782 | 0.0809195042181142 |
22 | 195.727 | 194.184656238445 | 1.54234376155473 |
23 | 208.73 | 209.708169840715 | -0.978169840714512 |
24 | 213.558 | 216.079939819861 | -2.52193981986147 |
25 | 100 | 99.6002941606927 | 0.399705839307351 |
26 | 97.9592 | 97.7058834212779 | 0.25331657872206 |
27 | 109.211 | 108.930614342804 | 0.280385657196027 |
28 | 120.473 | 120.625351638871 | -0.152351638871199 |
29 | 131.112 | 131.38663240982 | -0.274632409820436 |
30 | 147.732 | 148.255806171153 | -0.523806171153366 |
31 | 179.407 | 180.251620382152 | -0.844620382151813 |
32 | 197.796 | 197.193823981812 | 0.602176018187691 |
33 | 227.227 | 225.924679027075 | 1.30232097292501 |
34 | 197.833 | 197.148007258221 | 0.684992741778897 |
35 | 194.766 | 193.339188296662 | 1.4268117033383 |
36 | 210.264 | 211.205232877839 | -0.941232877839145 |
37 | 214.026 | 215.095929942669 | -1.0699299426694 |
38 | 100.254 | 99.9609044142318 | 0.293095585768179 |
39 | 100.107 | 99.8765702954398 | 0.230429704560195 |
40 | 113.097 | 112.759776418755 | 0.337223581244712 |
41 | 122.204 | 122.313259091321 | -0.109259091321414 |
42 | 131.193 | 131.474641053971 | -0.281641053971026 |
43 | 151.23 | 151.96057019587 | -0.730570195870184 |
44 | 181.625 | 183.149781030041 | -1.5247810300406 |
45 | 205.874 | 204.925659291054 | 0.948340708945729 |
46 | 226.757 | 225.513826384278 | 1.2431736157222 |
47 | 194.438 | 192.571539263186 | 1.86646073681386 |
48 | 194.576 | 194.159039958653 | 0.416960041346852 |
49 | 214.211 | 214.9754534821 | -0.764453482099673 |
50 | 225.59 | 227.161004537593 | -1.57100453759254 |
51 | 102.839 | 102.599222822475 | 0.239777177524715 |
52 | 102.865 | 102.643747194985 | 0.221252805014521 |
53 | 112.18 | 111.878564062235 | 0.30143593776465 |
54 | 124.943 | 125.026311408733 | -0.0833114087326177 |
55 | 136.448 | 136.755815103979 | -0.30781510397912 |
56 | 150.278 | 150.972079175181 | -0.694079175181151 |
57 | 188.871 | 190.215225678812 | -1.34422567881211 |
58 | 206.229 | 205.354576214792 | 0.874423785208002 |
59 | 223.928 | 222.714699092515 | 1.21330090748496 |
60 | 202.508 | 201.484528442987 | 1.02347155701299 |
61 | 198.563 | 199.263313264627 | -0.700313264627039 |
62 | 214.169 | 213.73746964467 | 0.431530355329945 |
63 | 227.637 | 229.285356362307 | -1.64835636230737 |
64 | 104.726 | 104.410023690504 | 0.315976309495591 |
65 | 102.719 | 102.460778010625 | 0.258221989375095 |
66 | 114.855 | 114.59971807542 | 0.255281924580432 |
67 | 125.276 | 125.384663805913 | -0.108663805912619 |
68 | 138.433 | 138.78435752288 | -0.351357522880019 |
69 | 154.789 | 155.419700998574 | -0.630700998573696 |
70 | 189.866 | 190.895019555634 | -1.02901955563403 |
71 | 208.473 | 207.855105594316 | 0.617894405684081 |
72 | 220.682 | 220.817303023491 | -0.135303023490964 |
73 | 196.651 | 195.72152628862 | 0.929473711379647 |
74 | 201.679 | 200.787549756518 | 0.891450243482093 |
75 | 213.656 | 213.297702918876 | 0.358297081123666 |
76 | 229 | 229.32515743151 | -0.325157431510075 |
77 | 103.387 | 103.055971827635 | 0.331028172365047 |
78 | 103.921 | 103.695427314606 | 0.22557268539425 |
79 | 114.53 | 114.342224742688 | 0.187775257312414 |
80 | 130.192 | 130.295637957794 | -0.103637957793774 |
81 | 136.323 | 136.842059394865 | -0.519059394864619 |
82 | 153.029 | 153.706623145344 | -0.677623145344154 |
83 | 192.114 | 193.737708240681 | -1.62370824068113 |
84 | 211.102 | 211.074010997153 | 0.0279890028472805 |
85 | 227.654 | 227.293746964081 | 0.360253035919443 |
86 | 191.446 | 191.422510493499 | 0.0234895065009864 |
87 | 201.506 | 199.55065512984 | 1.95534487015961 |
88 | 219.028 | 218.267230940434 | 0.760769059565896 |
89 | 226.841 | 227.736915719855 | -0.89591571985541 |
90 | 101.746 | 101.473469833514 | 0.272530166485707 |
91 | 105.751 | 105.51772833192 | 0.233271668080425 |
92 | 115.328 | 115.143842631635 | 0.184157368365469 |
93 | 131.595 | 131.79794222296 | -0.202942222959919 |
94 | 137.453 | 137.959344557349 | -0.506344557349233 |
95 | 157.658 | 158.420402318091 | -0.762402318090834 |
96 | 189.665 | 190.858864778182 | -1.19386477818178 |
97 | 211.503 | 211.96854988597 | -0.46554988596951 |
98 | 218.398 | 218.29754574331 | 0.100454256690227 |
99 | 190.056 | 189.106405364598 | 0.949594635402304 |
100 | 204.453 | 201.397190291563 | 3.05580970843667 |
101 | 217.602 | 217.194489072519 | 0.407510927480726 |
102 | 221.488 | 221.344609263322 | 0.143390736677625 |
103 | 100.371 | 100.16911722683 | 0.201882773170276 |
104 | 106.746 | 106.483597687383 | 0.262402312617354 |
105 | 117.973 | 117.848721254301 | 0.124278745699441 |
106 | 133.091 | 133.317017350179 | -0.226017350178627 |
107 | 137.072 | 137.484478680748 | -0.412478680747637 |
108 | 161.039 | 161.769010971747 | -0.730010971747048 |
109 | 191.006 | 191.920450090548 | -0.914450090547994 |
110 | 218.055 | 217.771156951552 | 0.283843048447874 |
111 | 213.639 | 213.770203602686 | -0.131203602685985 |
112 | 190.322 | 189.318827282272 | 1.0031727177284 |
113 | 206.552 | 205.220986074274 | 1.33101392572622 |
114 | 220.635 | 221.606608954818 | -0.971608954818042 |
115 | 101.337 | 101.100823106274 | 0.236176893725509 |
116 | 108.454 | 108.308879884284 | 0.145120115716369 |
117 | 117.863 | 117.77935733172 | 0.0836426682795824 |
118 | 133.167 | 133.411418201358 | -0.244418201357652 |
119 | 139.485 | 139.84754335329 | -0.362543353289645 |
120 | 165.599 | 166.274353171104 | -0.675353171103964 |
121 | 186.398 | 187.531630853148 | -1.13363085314775 |
122 | 221.076 | 220.315564295438 | 0.760435704562395 |
123 | 212.71 | 211.959275154938 | 0.750724845061709 |
124 | 203.701 | 203.304009904884 | 0.396990095115507 |
125 | 205.642 | 206.053866895497 | -0.411866895497264 |
126 | 222.011 | 221.31466055304 | 0.696339446959644 |
127 | 102.307 | 102.013887282095 | 0.293112717905061 |
128 | 107.724 | 107.674447896917 | 0.049552103082794 |
129 | 116.582 | 116.61109957869 | -0.0290995786899651 |
130 | 131.858 | 132.206530950713 | -0.348530950712608 |
131 | 142.049 | 142.371588805241 | -0.322588805241041 |
132 | 171.248 | 171.963915013617 | -0.715915013616749 |
133 | 189.577 | 190.290944975565 | -0.713944975564737 |
134 | 226.743 | 225.44390516454 | 1.29909483545978 |
135 | 217.355 | 216.405721251067 | 0.949278748933447 |
136 | 200.524 | 199.959633313448 | 0.5643666865516 |
137 | 205.679 | 207.274047810601 | -1.59504781060108 |
138 | 224.948 | 225.220258920477 | -0.272258920477377 |
139 | 101.794 | 101.577415508982 | 0.216584491017972 |
140 | 108.936 | 108.816952455157 | 0.119047544842654 |
141 | 117.645 | 117.717497244868 | -0.0724972448678101 |
142 | 132.5 | 132.822508494308 | -0.322508494308118 |
143 | 141.315 | 141.728926354835 | -0.413926354835221 |
144 | 172.249 | 172.909733405925 | -0.660733405925316 |
145 | 190.244 | 189.821857555075 | 0.422142444924961 |
146 | 223.179 | 222.295539465309 | 0.883460534690984 |
147 | 217.786 | 217.456992573263 | 0.329007426737222 |
148 | 200.524 | 200.179301026763 | 0.344698973237023 |
149 | 204.583 | 206.166683779262 | -1.58368377926224 |
150 | 225.566 | 225.939145234042 | -0.373145234042176 |
Goldfeld-Quandt test for Heteroskedasticity | |||
p-values | Alternative Hypothesis | ||
breakpoint index | greater | 2-sided | less |
9 | 0.331322311662486 | 0.662644623324972 | 0.668677688337514 |
10 | 0.418219875444455 | 0.83643975088891 | 0.581780124555545 |
11 | 0.300653930422322 | 0.601307860844644 | 0.699346069577678 |
12 | 0.809767112860655 | 0.380465774278691 | 0.190232887139346 |
13 | 0.724352960156259 | 0.551294079687481 | 0.27564703984374 |
14 | 0.629693121162976 | 0.740613757674047 | 0.370306878837024 |
15 | 0.532143312179173 | 0.935713375641655 | 0.467856687820827 |
16 | 0.433754218914488 | 0.867508437828976 | 0.566245781085512 |
17 | 0.364056793887739 | 0.728113587775478 | 0.635943206112261 |
18 | 0.359340780308186 | 0.718681560616372 | 0.640659219691814 |
19 | 0.453011526482248 | 0.906023052964497 | 0.546988473517752 |
20 | 0.376779128804398 | 0.753558257608797 | 0.623220871195602 |
21 | 0.302105401043866 | 0.604210802087732 | 0.697894598956134 |
22 | 0.339304960746476 | 0.678609921492952 | 0.660695039253524 |
23 | 0.375982458862764 | 0.751964917725529 | 0.624017541137236 |
24 | 0.832334393367822 | 0.335331213264356 | 0.167665606632178 |
25 | 0.795592367308213 | 0.408815265383574 | 0.204407632691787 |
26 | 0.749207991062899 | 0.501584017874203 | 0.250792008937101 |
27 | 0.694293346471164 | 0.611413307057672 | 0.305706653528836 |
28 | 0.639478610403946 | 0.721042779192108 | 0.360521389596054 |
29 | 0.583052917442005 | 0.83389416511599 | 0.416947082557995 |
30 | 0.53579192050437 | 0.92841615899126 | 0.46420807949563 |
31 | 0.501464334608465 | 0.997071330783071 | 0.498535665391535 |
32 | 0.555354776652601 | 0.889290446694798 | 0.444645223347399 |
33 | 0.757936012104236 | 0.484127975791528 | 0.242063987895764 |
34 | 0.731489844788326 | 0.537020310423347 | 0.268510155211674 |
35 | 0.784616884658147 | 0.430766230683706 | 0.215383115341853 |
36 | 0.786826612230041 | 0.426346775539919 | 0.213173387769959 |
37 | 0.7836851665798 | 0.432629666840399 | 0.2163148334202 |
38 | 0.741405373190317 | 0.517189253619366 | 0.258594626809683 |
39 | 0.698748029608503 | 0.602503940782993 | 0.301251970391497 |
40 | 0.651696582251597 | 0.696606835496806 | 0.348303417748403 |
41 | 0.599270356640551 | 0.801459286718898 | 0.400729643359449 |
42 | 0.547755839014886 | 0.904488321970228 | 0.452244160985114 |
43 | 0.530906939211368 | 0.938186121577264 | 0.469093060788632 |
44 | 0.659245558704882 | 0.681508882590235 | 0.340754441295118 |
45 | 0.699498737817795 | 0.60100252436441 | 0.300501262182205 |
46 | 0.775749542308706 | 0.448500915382588 | 0.224250457691294 |
47 | 0.890501589296817 | 0.218996821406365 | 0.109498410703183 |
48 | 0.868639939823656 | 0.262720120352687 | 0.131360060176344 |
49 | 0.859889720375119 | 0.280220559249762 | 0.140110279624881 |
50 | 0.902840625046748 | 0.194318749906504 | 0.0971593749532521 |
51 | 0.880172156002696 | 0.239655687994607 | 0.119827843997304 |
52 | 0.855806292938587 | 0.288387414122827 | 0.144193707061413 |
53 | 0.828107513614667 | 0.343784972770666 | 0.171892486385333 |
54 | 0.794386726094287 | 0.411226547811426 | 0.205613273905713 |
55 | 0.761062408093693 | 0.477875183812615 | 0.238937591906307 |
56 | 0.757744473104362 | 0.484511053791277 | 0.242255526895638 |
57 | 0.836113388062204 | 0.327773223875592 | 0.163886611937796 |
58 | 0.842228075942545 | 0.31554384811491 | 0.157771924057455 |
59 | 0.876981276156603 | 0.246037447686795 | 0.123018723843397 |
60 | 0.885805764558909 | 0.228388470882183 | 0.114194235441091 |
61 | 0.884655983786279 | 0.230688032427441 | 0.115344016213721 |
62 | 0.872763651175761 | 0.254472697648478 | 0.127236348824239 |
63 | 0.929412702532284 | 0.141174594935432 | 0.0705872974677162 |
64 | 0.913642877711832 | 0.172714244576337 | 0.0863571222881683 |
65 | 0.895371178171117 | 0.209257643657765 | 0.104628821828883 |
66 | 0.873943262509458 | 0.252113474981084 | 0.126056737490542 |
67 | 0.847544929590946 | 0.304910140818109 | 0.152455070409054 |
68 | 0.823361053670729 | 0.353277892658541 | 0.176638946329271 |
69 | 0.813975114463967 | 0.372049771072065 | 0.186024885536033 |
70 | 0.841211092017119 | 0.317577815965762 | 0.158788907982881 |
71 | 0.825237817811878 | 0.349524364376243 | 0.174762182188122 |
72 | 0.794720579630752 | 0.410558840738496 | 0.205279420369248 |
73 | 0.80308228513795 | 0.393835429724099 | 0.19691771486205 |
74 | 0.809745328028673 | 0.380509343942655 | 0.190254671971327 |
75 | 0.786625931360869 | 0.426748137278263 | 0.213374068639131 |
76 | 0.766876165319208 | 0.466247669361584 | 0.233123834680792 |
77 | 0.735760434903832 | 0.528479130192337 | 0.264239565096168 |
78 | 0.700589945551977 | 0.598820108896045 | 0.299410054448023 |
79 | 0.66044154684695 | 0.6791169063061 | 0.33955845315305 |
80 | 0.615959241830281 | 0.768081516339439 | 0.384040758169719 |
81 | 0.595615431837575 | 0.808769136324849 | 0.404384568162425 |
82 | 0.585513297934188 | 0.828973404131625 | 0.414486702065812 |
83 | 0.734730018604779 | 0.530539962790442 | 0.265269981395221 |
84 | 0.69562477721844 | 0.608750445563119 | 0.30437522278156 |
85 | 0.655320685190354 | 0.689358629619293 | 0.344679314809646 |
86 | 0.609107688738355 | 0.78178462252329 | 0.390892311261645 |
87 | 0.794248206383219 | 0.411503587233561 | 0.205751793616781 |
88 | 0.782690741535067 | 0.434618516929866 | 0.217309258464933 |
89 | 0.815793331473425 | 0.36841333705315 | 0.184206668526575 |
90 | 0.785942306241559 | 0.428115387516882 | 0.214057693758441 |
91 | 0.754217721492166 | 0.491564557015667 | 0.245782278507834 |
92 | 0.717033207487333 | 0.565933585025335 | 0.282966792512667 |
93 | 0.6792348079316 | 0.6415303841368 | 0.3207651920684 |
94 | 0.670102750599482 | 0.659794498801036 | 0.329897249400518 |
95 | 0.674946692531989 | 0.650106614936021 | 0.325053307468011 |
96 | 0.743803621340761 | 0.512392757318478 | 0.256196378659239 |
97 | 0.744298579440601 | 0.511402841118798 | 0.255701420559399 |
98 | 0.716925810450197 | 0.566148379099605 | 0.283074189549803 |
99 | 0.728369285254546 | 0.543261429490909 | 0.271630714745454 |
100 | 0.986814560076488 | 0.0263708798470242 | 0.0131854399235121 |
101 | 0.982099918936404 | 0.0358001621271916 | 0.0179000810635958 |
102 | 0.975246455543728 | 0.0495070889125446 | 0.0247535444562723 |
103 | 0.966927559390012 | 0.0661448812199767 | 0.0330724406099884 |
104 | 0.958846116627966 | 0.0823077667440687 | 0.0411538833720344 |
105 | 0.946252143454913 | 0.107495713090173 | 0.0537478565450865 |
106 | 0.932045777991453 | 0.135908444017095 | 0.0679542220085473 |
107 | 0.91842773603438 | 0.16314452793124 | 0.0815722639656202 |
108 | 0.916671962288244 | 0.166656075423512 | 0.0833280377117559 |
109 | 0.937029274118766 | 0.125941451762468 | 0.0629707258812342 |
110 | 0.922312486205169 | 0.155375027589662 | 0.077687513794831 |
111 | 0.91188450735435 | 0.176230985291301 | 0.0881154926456503 |
112 | 0.949883207407885 | 0.100233585184231 | 0.0501167925921154 |
113 | 0.985240956079628 | 0.0295180878407436 | 0.0147590439203718 |
114 | 0.987851250158111 | 0.0242974996837784 | 0.0121487498418892 |
115 | 0.982518092626067 | 0.0349638147478653 | 0.0174819073739327 |
116 | 0.975174842724899 | 0.0496503145502021 | 0.024825157275101 |
117 | 0.96470585585256 | 0.07058828829488 | 0.03529414414744 |
118 | 0.954200310483095 | 0.0915993790338091 | 0.0457996895169046 |
119 | 0.937981708147614 | 0.124036583704773 | 0.0620182918523864 |
120 | 0.924224663940286 | 0.151550672119429 | 0.0757753360597144 |
121 | 0.972496556770565 | 0.0550068864588699 | 0.0275034432294349 |
122 | 0.964764223637588 | 0.0704715527248247 | 0.0352357763624123 |
123 | 0.951251139410561 | 0.0974977211788785 | 0.0487488605894393 |
124 | 0.942394484904677 | 0.115211030190646 | 0.057605515095323 |
125 | 0.919047780720841 | 0.161904438558317 | 0.0809522192791587 |
126 | 0.931738498831651 | 0.136523002336698 | 0.0682615011683489 |
127 | 0.908181853342158 | 0.183636293315685 | 0.0918181466578425 |
128 | 0.875654544559856 | 0.248690910880287 | 0.124345455440143 |
129 | 0.837113104468654 | 0.325773791062692 | 0.162886895531346 |
130 | 0.784849592706378 | 0.430300814587243 | 0.215150407293622 |
131 | 0.717529681473269 | 0.564940637053462 | 0.282470318526731 |
132 | 0.735909667962515 | 0.52818066407497 | 0.264090332037485 |
133 | 0.864773472530248 | 0.270453054939505 | 0.135226527469752 |
134 | 0.817078203678154 | 0.365843592643692 | 0.182921796321846 |
135 | 0.754575962152579 | 0.490848075694842 | 0.245424037847421 |
136 | 0.834702316798451 | 0.330595366403099 | 0.165297683201549 |
137 | 0.843645541811034 | 0.312708916377931 | 0.156354458188965 |
138 | 0.75344994759723 | 0.493100104805541 | 0.24655005240277 |
139 | 0.637796634651525 | 0.724406730696949 | 0.362203365348475 |
140 | 0.5178975631417 | 0.9642048737166 | 0.4821024368583 |
141 | 0.395168525659215 | 0.790337051318429 | 0.604831474340785 |
Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
Description | # significant tests | % significant tests | OK/NOK |
1% type I error level | 0 | 0 | OK |
5% type I error level | 7 | 0.0526315789473684 | NOK |
10% type I error level | 14 | 0.105263157894737 | NOK |