Multiple Linear Regression - Estimated Regression Equation |
PS[t] = + 6.14877022785273 + 0.353909374463323CM[t] -0.340140308890912D[t] + 0.187547743317141PE[t] -0.0218597760694683PC[t] + 0.414511745648744O[t] -0.055790671462666`H `[t] + 1.91304219854686M1[t] + 3.20749012754116M2[t] + 2.29146189157973M3[t] + 1.04229613763446M4[t] + 1.11536866188866M5[t] + 2.25591011160927M6[t] + 0.866676009591269M7[t] + 2.79259992654015M8[t] + 0.816064160614426M9[t] + 0.182942017830659M10[t] + 0.206770309169597M11[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) | 6.14877022785273 | 3.263652 | 1.884 | 0.061622 | 0.030811 |
CM | 0.353909374463323 | 0.058762 | 6.0228 | 0 | 0 |
D | -0.340140308890912 | 0.12035 | -2.8263 | 0.005394 | 0.002697 |
PE | 0.187547743317141 | 0.103963 | 1.804 | 0.073369 | 0.036685 |
PC | -0.0218597760694683 | 0.130768 | -0.1672 | 0.86748 | 0.43374 |
O | 0.414511745648744 | 0.074323 | 5.5771 | 0 | 0 |
`H ` | -0.055790671462666 | 0.132543 | -0.4209 | 0.674451 | 0.337225 |
M1 | 1.91304219854686 | 1.33692 | 1.4309 | 0.154662 | 0.077331 |
M2 | 3.20749012754116 | 1.354492 | 2.368 | 0.01924 | 0.00962 |
M3 | 2.29146189157973 | 1.344833 | 1.7039 | 0.090602 | 0.045301 |
M4 | 1.04229613763446 | 1.36951 | 0.7611 | 0.447885 | 0.223942 |
M5 | 1.11536866188866 | 1.363755 | 0.8179 | 0.414814 | 0.207407 |
M6 | 2.25591011160927 | 1.363916 | 1.654 | 0.100353 | 0.050177 |
M7 | 0.866676009591269 | 1.360019 | 0.6373 | 0.524994 | 0.262497 |
M8 | 2.79259992654015 | 1.354753 | 2.0613 | 0.041108 | 0.020554 |
M9 | 0.816064160614426 | 1.335105 | 0.6112 | 0.542027 | 0.271014 |
M10 | 0.182942017830659 | 1.344702 | 0.136 | 0.891979 | 0.445989 |
M11 | 0.206770309169597 | 1.361999 | 0.1518 | 0.879551 | 0.439775 |
Multiple Linear Regression - Regression Statistics | |
Multiple R | 0.657416140227832 |
R-squared | 0.43219598143206 |
Adjusted R-squared | 0.3637373408955 |
F-TEST (value) | 6.31324224443585 |
F-TEST (DF numerator) | 17 |
F-TEST (DF denominator) | 141 |
p-value | 8.03553890094122e-11 |
Multiple Linear Regression - Residual Statistics | |
Residual Standard Deviation | 3.39580543571185 |
Sum Squared Residuals | 1625.94073256663 |
Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
1 | 24 | 23.8137796249422 | 0.186220375057788 |
2 | 25 | 24.3531080632850 | 0.646891936715029 |
3 | 30 | 24.7878446146897 | 5.21215538531025 |
4 | 19 | 19.8772607017328 | -0.877260701732849 |
5 | 22 | 19.8387111751325 | 2.16128882486746 |
6 | 22 | 24.1705249670097 | -2.17052496700972 |
7 | 25 | 22.0821689363653 | 2.9178310636347 |
8 | 23 | 20.3296682885634 | 2.67033171143661 |
9 | 17 | 18.7192363779055 | -1.71923637790550 |
10 | 21 | 20.585036028063 | 0.414963971936982 |
11 | 19 | 21.6599863942585 | -2.65998639425846 |
12 | 19 | 22.0908852371785 | -3.09088523717846 |
13 | 15 | 23.6632219875176 | -8.66322198751764 |
14 | 16 | 18.7821513979123 | -2.78215139791227 |
15 | 23 | 20.1220839673848 | 2.87791603261521 |
16 | 27 | 23.5168728037248 | 3.48312719627516 |
17 | 22 | 20.7469115341049 | 1.25308846589509 |
18 | 14 | 17.1849983434503 | -3.18499834345029 |
19 | 22 | 23.6308076260435 | -1.63080762604348 |
20 | 23 | 25.4960347074826 | -2.4960347074826 |
21 | 23 | 21.4872006729362 | 1.51279932706383 |
22 | 19 | 21.1350869194662 | -2.13508691946615 |
23 | 18 | 23.1296481378974 | -5.12964813789736 |
24 | 20 | 22.0122834048641 | -2.01228340486415 |
25 | 23 | 22.7869306069099 | 0.213069393090103 |
26 | 25 | 24.9992923672243 | 0.000707632775675614 |
27 | 19 | 24.3870333911222 | -5.38703339112219 |
28 | 24 | 23.4725364815549 | 0.527463518445079 |
29 | 22 | 21.1116262173615 | 0.888373782638507 |
30 | 26 | 24.1150665594054 | 1.88493344059460 |
31 | 29 | 22.4222490962516 | 6.57775090374837 |
32 | 32 | 26.7472607729094 | 5.25273922709065 |
33 | 25 | 20.7794912127753 | 4.22050878722474 |
34 | 29 | 23.9349463204706 | 5.06505367952938 |
35 | 28 | 24.1321758622818 | 3.8678241377182 |
36 | 17 | 15.7868101968747 | 1.21318980312527 |
37 | 28 | 26.9243317875929 | 1.07566821240705 |
38 | 29 | 25.0841475899746 | 3.91585241002544 |
39 | 26 | 28.5858122280069 | -2.58581222800692 |
40 | 25 | 23.0416503234580 | 1.95834967654203 |
41 | 14 | 19.4160261152381 | -5.41602611523811 |
42 | 25 | 22.8924613445657 | 2.10753865543434 |
43 | 26 | 21.2013212833235 | 4.79867871667654 |
44 | 20 | 21.5824076018632 | -1.58240760186320 |
45 | 18 | 21.0227127084867 | -3.02271270848667 |
46 | 32 | 24.1959034928809 | 7.80409650711906 |
47 | 25 | 23.934323425318 | 1.06567657468202 |
48 | 25 | 20.5414826495505 | 4.45851735044952 |
49 | 23 | 22.1176766849051 | 0.882323315094906 |
50 | 21 | 23.908273522058 | -2.90827352205798 |
51 | 20 | 24.9063893658019 | -4.90638936580193 |
52 | 15 | 15.8764028453032 | -0.87640284530316 |
53 | 30 | 26.0255947343067 | 3.97440526569328 |
54 | 24 | 26.5557566659754 | -2.55575666597541 |
55 | 26 | 23.8864918300167 | 2.1135081699833 |
56 | 24 | 22.9578244600350 | 1.04217553996505 |
57 | 22 | 20.8256286249576 | 1.17437137504239 |
58 | 14 | 14.1871184963506 | -0.187118496350568 |
59 | 24 | 20.8905056273397 | 3.1094943726603 |
60 | 24 | 21.7094291759346 | 2.29057082406538 |
61 | 24 | 24.169688300541 | -0.169688300540989 |
62 | 24 | 21.6640801942310 | 2.33591980576903 |
63 | 19 | 19.1169778063536 | -0.116977806353572 |
64 | 31 | 27.1689712914661 | 3.83102870853388 |
65 | 22 | 26.4021944756145 | -4.40219447561446 |
66 | 27 | 22.4219874013483 | 4.57801259865168 |
67 | 19 | 17.1048496095279 | 1.89515039047207 |
68 | 25 | 23.6920947830707 | 1.30790521692927 |
69 | 20 | 24.4773365505020 | -4.47733655050204 |
70 | 21 | 20.2265489158174 | 0.773451084182563 |
71 | 27 | 26.4126917995004 | 0.587308200499596 |
72 | 23 | 23.1423493748509 | -0.142349374850932 |
73 | 25 | 26.4659751165094 | -1.46597511650937 |
74 | 20 | 23.9267728341495 | -3.92677283414946 |
75 | 22 | 23.4983695363039 | -1.49836953630393 |
76 | 23 | 22.8856125644766 | 0.114387435523365 |
77 | 25 | 24.3561623447288 | 0.643837655271192 |
78 | 25 | 24.5244836050379 | 0.475516394962088 |
79 | 17 | 23.0619840643732 | -6.06198406437317 |
80 | 19 | 23.0605867841818 | -4.06058678418185 |
81 | 25 | 23.1596966911531 | 1.8403033088469 |
82 | 19 | 21.7904476894089 | -2.79044768940894 |
83 | 20 | 22.0052612871699 | -2.00526128716993 |
84 | 26 | 21.1330307795191 | 4.86696922048086 |
85 | 23 | 21.1939394091234 | 1.80606059087655 |
86 | 27 | 26.3285365084981 | 0.671463491501924 |
87 | 17 | 21.7285482193295 | -4.72854821932953 |
88 | 17 | 23.0255857841869 | -6.02558578418692 |
89 | 17 | 19.5722677137679 | -2.57226771376791 |
90 | 22 | 22.9247158231212 | -0.924715823121187 |
91 | 21 | 22.8220553771362 | -1.82205537713623 |
92 | 32 | 30.0162069426751 | 1.98379305732486 |
93 | 21 | 24.4486440456690 | -3.44864404566895 |
94 | 21 | 23.2662700860218 | -2.26627008602179 |
95 | 18 | 20.1513689601983 | -2.15136896019830 |
96 | 18 | 20.0586416129406 | -2.05864161294062 |
97 | 23 | 23.2628299258930 | -0.26282992589297 |
98 | 19 | 22.2712196601799 | -3.27121966017988 |
99 | 20 | 21.5972940494516 | -1.59729404945163 |
100 | 21 | 21.5499573417065 | -0.549957341706525 |
101 | 20 | 23.6147074741298 | -3.61470747412985 |
102 | 17 | 19.9923647998927 | -2.99236479989269 |
103 | 18 | 19.6029285633576 | -1.60292856335762 |
104 | 19 | 21.9742713767137 | -2.97427137671375 |
105 | 22 | 21.4912496252541 | 0.508750374745933 |
106 | 15 | 17.5735081371596 | -2.57350813715963 |
107 | 14 | 17.2600761736985 | -3.26007617369846 |
108 | 18 | 25.186978645569 | -7.18697864556898 |
109 | 24 | 21.7852151560524 | 2.21478484394758 |
110 | 35 | 25.1124633303110 | 9.88753666968903 |
111 | 29 | 19.6529904669363 | 9.34700953306367 |
112 | 21 | 21.6843188351038 | -0.684318835103755 |
113 | 20 | 18.1346889866415 | 1.86531101335854 |
114 | 22 | 24.3299317082594 | -2.32993170825941 |
115 | 13 | 16.2610351212007 | -3.2610351212007 |
116 | 26 | 25.0267827187664 | 0.973217281233622 |
117 | 17 | 16.0709045789130 | 0.929095421087023 |
118 | 25 | 19.0029908103164 | 5.99700918968363 |
119 | 20 | 19.4631200556095 | 0.536879944390472 |
120 | 19 | 16.9993299196298 | 2.00067008037024 |
121 | 21 | 23.1645906951455 | -2.16459069514546 |
122 | 22 | 22.7316573108145 | -0.731657310814519 |
123 | 24 | 23.6054684937591 | 0.394531506240948 |
124 | 21 | 22.5851984251227 | -1.58519842512267 |
125 | 26 | 25.5952644597697 | 0.404735540230294 |
126 | 24 | 21.3827389988765 | 2.61726100112351 |
127 | 16 | 19.5603147467725 | -3.56031474677254 |
128 | 23 | 23.7349476798571 | -0.734947679857064 |
129 | 18 | 20.3710345866985 | -2.37103458669855 |
130 | 16 | 21.1908014811978 | -5.19080148119779 |
131 | 26 | 23.1174877098554 | 2.88251229014461 |
132 | 19 | 17.7258947284971 | 1.27410527150287 |
133 | 21 | 17.1994634315024 | 3.80053656849757 |
134 | 21 | 23.8168540089534 | -2.81685400895344 |
135 | 22 | 19.2632076286628 | 2.73679237133718 |
136 | 23 | 19.5038793472856 | 3.4961206527144 |
137 | 29 | 24.6209624668823 | 4.37903753311771 |
138 | 21 | 19.7877020621918 | 1.21229793780821 |
139 | 21 | 20.0509303145513 | 0.949069685448718 |
140 | 23 | 23.1818954345004 | -0.181895434500434 |
141 | 27 | 22.8850403208132 | 4.11495967918679 |
142 | 25 | 24.3836581641059 | 0.616341835894139 |
143 | 21 | 19.7358468313077 | 1.26415316869225 |
144 | 10 | 15.4672663388472 | -5.46726633884718 |
145 | 20 | 23.0429323517082 | -3.04293235170825 |
146 | 26 | 23.9789885207690 | 2.02101147923097 |
147 | 24 | 24.7331758273740 | -0.733175827373961 |
148 | 29 | 31.8117532548780 | -2.81175325487804 |
149 | 19 | 18.5648823023217 | 0.435117697678269 |
150 | 24 | 22.7172677208657 | 1.28273227913428 |
151 | 19 | 20.3128634310799 | -1.31286343107994 |
152 | 24 | 25.2000184493812 | -1.20001844938116 |
153 | 22 | 21.2618240039359 | 0.738175996064113 |
154 | 17 | 22.5276834587409 | -5.52768345874089 |
155 | 24 | 22.1075077355649 | 1.89249226443507 |
156 | 25 | 21.1456179357438 | 3.85438206425619 |
157 | 30 | 24.4094249216569 | 5.59057507834313 |
158 | 19 | 22.0424546916396 | -3.04245469163955 |
159 | 22 | 21.0148044048236 | 0.985195595176392 |
Goldfeld-Quandt test for Heteroskedasticity | |||
p-values | Alternative Hypothesis | ||
breakpoint index | greater | 2-sided | less |
21 | 0.834919278070552 | 0.330161443858897 | 0.165080721929448 |
22 | 0.735821764708785 | 0.52835647058243 | 0.264178235291215 |
23 | 0.630748862484954 | 0.738502275030092 | 0.369251137515046 |
24 | 0.528037286630829 | 0.943925426738342 | 0.471962713369171 |
25 | 0.488176484780283 | 0.976352969560566 | 0.511823515219717 |
26 | 0.393552091921837 | 0.787104183843674 | 0.606447908078163 |
27 | 0.482454556990943 | 0.964909113981885 | 0.517545443009057 |
28 | 0.3986294843707 | 0.7972589687414 | 0.6013705156293 |
29 | 0.354322881225502 | 0.708645762451004 | 0.645677118774498 |
30 | 0.275331014216759 | 0.550662028433518 | 0.724668985783241 |
31 | 0.54026524173632 | 0.91946951652736 | 0.45973475826368 |
32 | 0.706039123092386 | 0.587921753815227 | 0.293960876907614 |
33 | 0.662149423884915 | 0.675701152230169 | 0.337850576115085 |
34 | 0.674498712263519 | 0.651002575472963 | 0.325501287736481 |
35 | 0.715111683409435 | 0.56977663318113 | 0.284888316590565 |
36 | 0.672031748414676 | 0.655936503170648 | 0.327968251585324 |
37 | 0.656273491739658 | 0.687453016520683 | 0.343726508260342 |
38 | 0.682745849520617 | 0.634508300958766 | 0.317254150479383 |
39 | 0.768638231058171 | 0.462723537883657 | 0.231361768941829 |
40 | 0.725679171959634 | 0.548641656080731 | 0.274320828040366 |
41 | 0.739595409268033 | 0.520809181463935 | 0.260404590731967 |
42 | 0.698465829300289 | 0.603068341399423 | 0.301534170699711 |
43 | 0.711553131839049 | 0.576893736321902 | 0.288446868160951 |
44 | 0.6798679788732 | 0.640264042253599 | 0.320132021126800 |
45 | 0.69351783800899 | 0.61296432398202 | 0.30648216199101 |
46 | 0.778357856192638 | 0.443284287614724 | 0.221642143807362 |
47 | 0.736056917680975 | 0.52788616463805 | 0.263943082319025 |
48 | 0.783710488935557 | 0.432579022128887 | 0.216289511064443 |
49 | 0.738732674181637 | 0.522534651636726 | 0.261267325818363 |
50 | 0.713114234534918 | 0.573771530930163 | 0.286885765465082 |
51 | 0.765432502569644 | 0.469134994860713 | 0.234567497430356 |
52 | 0.726385911905444 | 0.547228176189112 | 0.273614088094556 |
53 | 0.770197641166273 | 0.459604717667453 | 0.229802358833727 |
54 | 0.770522069336677 | 0.458955861326646 | 0.229477930663323 |
55 | 0.747139238191423 | 0.505721523617154 | 0.252860761808577 |
56 | 0.707273494354803 | 0.585453011290394 | 0.292726505645197 |
57 | 0.660181951000377 | 0.679636097999245 | 0.339818048999623 |
58 | 0.628791053365127 | 0.742417893269746 | 0.371208946634873 |
59 | 0.657698545723058 | 0.684602908553885 | 0.342301454276942 |
60 | 0.628832463253202 | 0.742335073493596 | 0.371167536746798 |
61 | 0.580552006974226 | 0.838895986051547 | 0.419447993025774 |
62 | 0.555238535377447 | 0.889522929245105 | 0.444761464622552 |
63 | 0.507258786354927 | 0.985482427290146 | 0.492741213645073 |
64 | 0.501077595926743 | 0.997844808146513 | 0.498922404073257 |
65 | 0.611881198362759 | 0.776237603274482 | 0.388118801637241 |
66 | 0.67272290728084 | 0.654554185438321 | 0.327277092719161 |
67 | 0.654535559167333 | 0.690928881665334 | 0.345464440832667 |
68 | 0.612770076587587 | 0.774459846824826 | 0.387229923412413 |
69 | 0.674980139159261 | 0.650039721681478 | 0.325019860840739 |
70 | 0.638713484731596 | 0.722573030536808 | 0.361286515268404 |
71 | 0.590987751764653 | 0.818024496470694 | 0.409012248235347 |
72 | 0.54379915121147 | 0.91240169757706 | 0.45620084878853 |
73 | 0.503111356840559 | 0.993777286318883 | 0.496888643159441 |
74 | 0.52431515055592 | 0.95136969888816 | 0.47568484944408 |
75 | 0.481463578511919 | 0.962927157023838 | 0.518536421488081 |
76 | 0.435208165228557 | 0.870416330457115 | 0.564791834771443 |
77 | 0.385729161569356 | 0.771458323138712 | 0.614270838430644 |
78 | 0.338923536354961 | 0.677847072709923 | 0.661076463645039 |
79 | 0.43713187559011 | 0.87426375118022 | 0.56286812440989 |
80 | 0.464134319828455 | 0.92826863965691 | 0.535865680171545 |
81 | 0.429452556184949 | 0.858905112369897 | 0.570547443815051 |
82 | 0.427236968530507 | 0.854473937061015 | 0.572763031469493 |
83 | 0.398064907927126 | 0.796129815854253 | 0.601935092072874 |
84 | 0.487807024205652 | 0.975614048411304 | 0.512192975794348 |
85 | 0.450240315652623 | 0.900480631305247 | 0.549759684347377 |
86 | 0.411852963549789 | 0.823705927099578 | 0.588147036450211 |
87 | 0.456622041680423 | 0.913244083360847 | 0.543377958319577 |
88 | 0.574571006088161 | 0.850857987823679 | 0.425428993911839 |
89 | 0.556199993917863 | 0.887600012164274 | 0.443800006082137 |
90 | 0.51067332536604 | 0.97865334926792 | 0.48932667463396 |
91 | 0.470826376151094 | 0.941652752302188 | 0.529173623848906 |
92 | 0.459094435916463 | 0.918188871832926 | 0.540905564083537 |
93 | 0.463992811721931 | 0.927985623443862 | 0.536007188278069 |
94 | 0.433592336314196 | 0.867184672628392 | 0.566407663685804 |
95 | 0.407036037196958 | 0.814072074393916 | 0.592963962803042 |
96 | 0.369243081538924 | 0.738486163077848 | 0.630756918461076 |
97 | 0.325425736580925 | 0.650851473161851 | 0.674574263419075 |
98 | 0.332386283644305 | 0.66477256728861 | 0.667613716355695 |
99 | 0.314565939992685 | 0.62913187998537 | 0.685434060007315 |
100 | 0.270473612397624 | 0.540947224795249 | 0.729526387602376 |
101 | 0.287119175123308 | 0.574238350246616 | 0.712880824876692 |
102 | 0.281764682042339 | 0.563529364084679 | 0.71823531795766 |
103 | 0.242397028980858 | 0.484794057961716 | 0.757602971019142 |
104 | 0.226176360049068 | 0.452352720098135 | 0.773823639950932 |
105 | 0.188778205531510 | 0.377556411063021 | 0.81122179446849 |
106 | 0.165091937884378 | 0.330183875768757 | 0.834908062115622 |
107 | 0.15645348702027 | 0.31290697404054 | 0.84354651297973 |
108 | 0.264324537756426 | 0.528649075512852 | 0.735675462243574 |
109 | 0.242648327455489 | 0.485296654910978 | 0.757351672544511 |
110 | 0.634117109524736 | 0.731765780950528 | 0.365882890475264 |
111 | 0.850748440179161 | 0.298503119641677 | 0.149251559820839 |
112 | 0.813991460914741 | 0.372017078170518 | 0.186008539085259 |
113 | 0.775961587889093 | 0.448076824221813 | 0.224038412110907 |
114 | 0.785535562925224 | 0.428928874149551 | 0.214464437074776 |
115 | 0.77694695745727 | 0.446106085085461 | 0.223053042542730 |
116 | 0.726454167130456 | 0.547091665739088 | 0.273545832869544 |
117 | 0.671628640130856 | 0.656742719738289 | 0.328371359869144 |
118 | 0.900533100326208 | 0.198933799347585 | 0.0994668996737924 |
119 | 0.878609190337074 | 0.242781619325853 | 0.121390809662926 |
120 | 0.84705266095313 | 0.305894678093742 | 0.152947339046871 |
121 | 0.836737336277846 | 0.326525327444309 | 0.163262663722154 |
122 | 0.789953056187223 | 0.420093887625554 | 0.210046943812777 |
123 | 0.732614758710528 | 0.534770482578944 | 0.267385241289472 |
124 | 0.688155056079555 | 0.62368988784089 | 0.311844943920445 |
125 | 0.66990367787515 | 0.6601926442497 | 0.33009632212485 |
126 | 0.61047188315979 | 0.77905623368042 | 0.38952811684021 |
127 | 0.612700584558427 | 0.774598830883147 | 0.387299415441573 |
128 | 0.533411166716481 | 0.933177666567037 | 0.466588833283519 |
129 | 0.467590806165785 | 0.93518161233157 | 0.532409193834215 |
130 | 0.42405274731003 | 0.84810549462006 | 0.57594725268997 |
131 | 0.442297826861988 | 0.884595653723976 | 0.557702173138012 |
132 | 0.431134923207977 | 0.862269846415955 | 0.568865076792023 |
133 | 0.430633254966308 | 0.861266509932617 | 0.569366745033692 |
134 | 0.337669836929723 | 0.675339673859447 | 0.662330163070276 |
135 | 0.291511978229051 | 0.583023956458103 | 0.708488021770949 |
136 | 0.41486161057856 | 0.82972322115712 | 0.58513838942144 |
137 | 0.306110846397526 | 0.612221692795051 | 0.693889153602474 |
138 | 0.72925737627067 | 0.54148524745866 | 0.27074262372933 |
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 | 0 | 0 | OK |
10% type I error level | 0 | 0 | OK |