Multiple Linear Regression - Estimated Regression Equation |
Yt[t] = + 7.46043060983698 + 0.328154021465218X1[t] -0.3627366723898X2[t] + 0.186560236681879X3[t] + 0.0233844134026156X4[t] + 0.401270321441297X5[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) | 7.46043060983698 | 2.248109 | 3.3185 | 0.001131 | 0.000565 |
X1 | 0.328154021465218 | 0.055544 | 5.908 | 0 | 0 |
X2 | -0.3627366723898 | 0.107118 | -3.3863 | 9e-04 | 0.00045 |
X3 | 0.186560236681879 | 0.10114 | 1.8446 | 0.067032 | 0.033516 |
X4 | 0.0233844134026156 | 0.128621 | 0.1818 | 0.855973 | 0.427987 |
X5 | 0.401270321441297 | 0.071773 | 5.5908 | 0 | 0 |
Multiple Linear Regression - Regression Statistics | |
Multiple R | 0.605858798778077 |
R-squared | 0.367064884056814 |
Adjusted R-squared | 0.346380729941024 |
F-TEST (value) | 17.7461878306445 |
F-TEST (DF numerator) | 5 |
F-TEST (DF denominator) | 153 |
p-value | 7.54951656745106e-14 |
Multiple Linear Regression - Residual Statistics | |
Residual Standard Deviation | 3.40927289715423 |
Sum Squared Residuals | 1778.34067815237 |
Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
1 | 24 | 23.0236176333508 | 0.976382366649192 |
2 | 25 | 22.3963921073235 | 2.60360789267647 |
3 | 30 | 24.2529863072522 | 5.74701369274783 |
4 | 19 | 20.2962579947228 | -1.29625799472283 |
5 | 22 | 20.5386282852832 | 1.46137171471678 |
6 | 22 | 23.1227812851809 | -1.12278128518093 |
7 | 25 | 22.5736026083869 | 2.42639739161312 |
8 | 23 | 19.4568594581893 | 3.54314054181066 |
9 | 17 | 18.7937770436835 | -1.79377704368349 |
10 | 21 | 21.669677585173 | -0.669677585173036 |
11 | 19 | 22.8153403514384 | -3.8153403514384 |
12 | 19 | 23.3938848919955 | -4.39388489199547 |
13 | 15 | 23.2200335336539 | -8.22003353365394 |
14 | 16 | 17.0860954231925 | -1.08609542319246 |
15 | 23 | 19.4598225179576 | 3.54017748204243 |
16 | 27 | 24.0748423820553 | 2.92515761794465 |
17 | 22 | 21.0019432886847 | 0.998056711315263 |
18 | 14 | 16.535329320714 | -2.535329320714 |
19 | 22 | 24.0873202920243 | -2.08732029202431 |
20 | 23 | 24.0090508616482 | -1.00905086164818 |
21 | 23 | 21.5688381779423 | 1.4311618220577 |
22 | 21 | 24.4545998179461 | -3.45459981794611 |
23 | 19 | 22.4295524471459 | -3.42955244714589 |
24 | 18 | 23.8367869289911 | -5.83678692899107 |
25 | 20 | 23.1800605324662 | -3.18006053246622 |
26 | 23 | 22.4483525596049 | 0.551647440395091 |
27 | 25 | 23.3280787328681 | 1.67192126713187 |
28 | 19 | 23.3532655211774 | -4.35326552117744 |
29 | 24 | 23.839829931247 | 0.160170068753002 |
30 | 22 | 21.5692258736674 | 0.430774126332574 |
31 | 25 | 25.1649483334544 | -0.164948333454416 |
32 | 26 | 23.2232169775374 | 2.77678302246258 |
33 | 29 | 22.7002038848751 | 6.29979611512492 |
34 | 32 | 25.1965595373823 | 6.8034404626177 |
35 | 25 | 21.5830794177202 | 3.41692058227981 |
36 | 29 | 24.4099495065135 | 4.59005049348653 |
37 | 28 | 24.9467056041625 | 3.0532943958375 |
38 | 17 | 17.1062381095522 | -0.106238109552166 |
39 | 28 | 26.0751635208601 | 1.92483647913992 |
40 | 29 | 22.9430722049405 | 6.05692779505949 |
41 | 26 | 27.52862185641 | -1.52862185640998 |
42 | 25 | 23.4667094578832 | 1.53329054211676 |
43 | 14 | 19.5469105942641 | -5.54691059426405 |
44 | 25 | 22.1055221703104 | 2.89447782968955 |
45 | 26 | 21.6780393824329 | 4.32196061756713 |
46 | 20 | 20.3008968098917 | -0.300896809891658 |
47 | 18 | 21.4213727878477 | -3.42137278784772 |
48 | 32 | 24.6610362298757 | 7.3389637701243 |
49 | 25 | 25.0045460489836 | -0.00454604898359165 |
50 | 25 | 21.6915513577573 | 3.30844864224273 |
51 | 23 | 20.8454749613068 | 2.15452503869318 |
52 | 21 | 22.1588588066973 | -1.15885880669729 |
53 | 20 | 24.0575114630031 | -4.05751146300312 |
54 | 15 | 16.5269290283781 | -1.52692902837806 |
55 | 30 | 26.717390208988 | 3.28260979101198 |
56 | 24 | 25.3394958960663 | -1.33949589606632 |
57 | 26 | 24.3125491844923 | 1.68745081550775 |
58 | 24 | 21.7172524612978 | 2.28274753870219 |
59 | 22 | 21.4941504714309 | 0.505849528569085 |
60 | 14 | 15.6462203516491 | -1.64622035164913 |
61 | 24 | 22.255359520076 | 1.74464047992401 |
62 | 24 | 22.9203756085798 | 1.07962439142021 |
63 | 24 | 23.3536201567194 | 0.64637984328056 |
64 | 24 | 19.9850555838132 | 4.01494441618681 |
65 | 19 | 18.5129061642547 | 0.487093835745272 |
66 | 31 | 26.8208676764294 | 4.17913232357061 |
67 | 22 | 26.601037521453 | -4.60103752145305 |
68 | 27 | 21.4697621005205 | 5.5302378994795 |
69 | 19 | 17.7359069452234 | 1.26409305477656 |
70 | 25 | 22.3044035896075 | 2.69559641039245 |
71 | 20 | 24.9772106374541 | -4.97721063745406 |
72 | 21 | 21.502677383273 | -0.50267738327296 |
73 | 27 | 27.4823128306108 | -0.482312830610752 |
74 | 23 | 24.3803773473337 | -1.38037734733371 |
75 | 25 | 25.6982731831007 | -0.698273183100738 |
76 | 20 | 22.2330812773097 | -2.23308127730969 |
77 | 21 | 19.2454670687402 | 1.75453293125985 |
78 | 22 | 22.4516157406899 | -0.45161574068992 |
79 | 23 | 23.0320339448358 | -0.0320339448358371 |
80 | 25 | 24.0521764435639 | 0.947823556436075 |
81 | 25 | 23.4230855798854 | 1.57691442011462 |
82 | 17 | 23.8630492300674 | -6.86304923006741 |
83 | 19 | 21.4391304477228 | -2.43913044772283 |
84 | 25 | 23.9709132955503 | 1.02908670444972 |
85 | 19 | 22.3733623294629 | -3.37336232946291 |
86 | 20 | 23.1407040596382 | -3.14070405963825 |
87 | 26 | 22.5238707218134 | 3.47612927818658 |
88 | 23 | 20.8073842775135 | 2.19261572248651 |
89 | 27 | 24.4361957884407 | 2.56380421155931 |
90 | 17 | 20.8970807780462 | -3.8970807780462 |
91 | 17 | 23.3435280898338 | -6.3435280898338 |
92 | 19 | 20.191563551002 | -1.191563551002 |
93 | 17 | 19.7459731472925 | -2.74597314729248 |
94 | 22 | 22.0165688176436 | -0.0165688176435826 |
95 | 21 | 23.5510323826098 | -2.55103238260975 |
96 | 32 | 28.6372448399853 | 3.36275516001471 |
97 | 21 | 24.6834795872242 | -3.6834795872242 |
98 | 21 | 24.3266944626333 | -3.32669446263334 |
99 | 18 | 21.259817450436 | -3.259817450436 |
100 | 18 | 21.2889468496438 | -3.28894684964376 |
101 | 23 | 22.8395308141606 | 0.160469185839441 |
102 | 19 | 20.6492902959521 | -1.64929029595212 |
103 | 20 | 20.9576947616757 | -0.957694761675737 |
104 | 21 | 22.3255043730554 | -1.32550437305537 |
105 | 20 | 23.8525057494042 | -3.85250574940422 |
106 | 17 | 18.7741072251434 | -1.77410722514342 |
107 | 18 | 20.3006604066273 | -2.30066040662729 |
108 | 19 | 20.749679106004 | -1.74967910600404 |
109 | 22 | 22.0682765809344 | -0.0682765809344119 |
110 | 15 | 18.766441632154 | -3.76644163215395 |
111 | 14 | 18.8510893511519 | -4.8510893511519 |
112 | 18 | 26.6429142940772 | -8.64291429407725 |
113 | 24 | 21.4114487878798 | 2.58855121212023 |
114 | 35 | 23.5620327119435 | 11.4379672880565 |
115 | 29 | 19.2163246027188 | 9.78367539728123 |
116 | 21 | 21.9816944326307 | -0.981694432630689 |
117 | 25 | 20.4953208143283 | 4.50467918567166 |
118 | 20 | 18.4924302963951 | 1.50756970360488 |
119 | 22 | 23.2253187184531 | -1.22531871845307 |
120 | 13 | 16.8359413686559 | -3.83594136865588 |
121 | 26 | 23.2142002181326 | 2.78579978186736 |
122 | 17 | 16.8872223911238 | 0.112777608876169 |
123 | 25 | 20.0947136369743 | 4.90528636302571 |
124 | 20 | 20.7722734892362 | -0.77227348923623 |
125 | 19 | 18.1285543931859 | 0.871445606814121 |
126 | 21 | 22.6212243668162 | -1.62122436681623 |
127 | 22 | 21.0704752877172 | 0.929524712282782 |
128 | 24 | 22.7056739110488 | 1.29432608895116 |
129 | 21 | 22.9951676639565 | -1.99516766395646 |
130 | 26 | 25.482195851486 | 0.517804148514021 |
131 | 24 | 20.5950930960205 | 3.40490690397949 |
132 | 16 | 20.298739799443 | -4.29873979944297 |
133 | 23 | 22.3765319512249 | 0.623468048775057 |
134 | 18 | 20.8107987510593 | -2.81079875105926 |
135 | 16 | 22.3793138772619 | -6.37931387726185 |
136 | 26 | 24.0698543662375 | 1.93014563376249 |
137 | 19 | 19.0560620045677 | -0.0560620045676752 |
138 | 21 | 16.8666199037581 | 4.13338009624188 |
139 | 21 | 22.2168258710245 | -1.21682587102449 |
140 | 22 | 18.5260173770404 | 3.47398262295963 |
141 | 23 | 19.7340241912749 | 3.26597580872508 |
142 | 29 | 24.8124059410788 | 4.18759405892122 |
143 | 21 | 19.2156508743754 | 1.78434912562462 |
144 | 21 | 19.9639464131369 | 1.03605358686309 |
145 | 23 | 21.8927879622684 | 1.1072120377316 |
146 | 27 | 22.996067272599 | 4.00393272740102 |
147 | 25 | 25.3746950753507 | -0.37469507535065 |
148 | 21 | 21.000140913778 | -0.000140913778046401 |
149 | 10 | 17.1119616413152 | -7.1119616413152 |
150 | 20 | 22.6490195793518 | -2.64901957935177 |
151 | 26 | 22.5749237282455 | 3.42507627175453 |
152 | 24 | 23.6474832613484 | 0.352516738651611 |
153 | 29 | 31.6584752151628 | -2.65847521516283 |
154 | 19 | 18.9825826818211 | 0.017417318178872 |
155 | 24 | 22.0940161795511 | 1.90598382044895 |
156 | 19 | 20.7666852307848 | -1.76668523078483 |
157 | 24 | 23.4401554227186 | 0.559844577281407 |
158 | 22 | 21.8244370969672 | 0.17556290303276 |
159 | 17 | 23.7736200572454 | -6.77362005724542 |
Goldfeld-Quandt test for Heteroskedasticity | |||
p-values | Alternative Hypothesis | ||
breakpoint index | greater | 2-sided | less |
9 | 0.303167174871691 | 0.606334349743382 | 0.69683282512831 |
10 | 0.183271906161378 | 0.366543812322756 | 0.816728093838622 |
11 | 0.338965752665167 | 0.677931505330333 | 0.661034247334833 |
12 | 0.289608818137534 | 0.579217636275068 | 0.710391181862466 |
13 | 0.866047634514266 | 0.267904730971468 | 0.133952365485734 |
14 | 0.804934375302346 | 0.390131249395308 | 0.195065624697654 |
15 | 0.759902102105923 | 0.480195795788155 | 0.240097897894077 |
16 | 0.69717005828316 | 0.60565988343368 | 0.30282994171684 |
17 | 0.619282751525191 | 0.761434496949617 | 0.380717248474809 |
18 | 0.591038687395453 | 0.817922625209095 | 0.408961312604548 |
19 | 0.524025389127915 | 0.95194922174417 | 0.475974610872085 |
20 | 0.518204023347026 | 0.963591953305947 | 0.481795976652974 |
21 | 0.497824319669455 | 0.99564863933891 | 0.502175680330545 |
22 | 0.430879369865434 | 0.861758739730867 | 0.569120630134566 |
23 | 0.385894677332064 | 0.771789354664128 | 0.614105322667936 |
24 | 0.43499451037991 | 0.86998902075982 | 0.56500548962009 |
25 | 0.447721043082056 | 0.895442086164112 | 0.552278956917944 |
26 | 0.379605715547792 | 0.759211431095584 | 0.620394284452208 |
27 | 0.329281747759595 | 0.658563495519189 | 0.670718252240405 |
28 | 0.345291322953478 | 0.690582645906957 | 0.654708677046522 |
29 | 0.291663451307304 | 0.583326902614607 | 0.708336548692696 |
30 | 0.238502872434837 | 0.477005744869673 | 0.761497127565163 |
31 | 0.191952554345429 | 0.383905108690857 | 0.808047445654571 |
32 | 0.212174113640594 | 0.424348227281188 | 0.787825886359406 |
33 | 0.362084702521348 | 0.724169405042695 | 0.637915297478652 |
34 | 0.596683272280863 | 0.806633455438274 | 0.403316727719137 |
35 | 0.573836653892848 | 0.852326692214304 | 0.426163346107152 |
36 | 0.633997466898335 | 0.73200506620333 | 0.366002533101665 |
37 | 0.625046475135514 | 0.749907049728972 | 0.374953524864486 |
38 | 0.581207101871441 | 0.837585796257118 | 0.418792898128559 |
39 | 0.54926503948919 | 0.90146992102162 | 0.45073496051081 |
40 | 0.634014980726026 | 0.731970038547949 | 0.365985019273974 |
41 | 0.6026968069944 | 0.794606386011199 | 0.397303193005599 |
42 | 0.557493784028079 | 0.885012431943843 | 0.442506215971921 |
43 | 0.644045523161667 | 0.711908953676666 | 0.355954476838333 |
44 | 0.616000997208378 | 0.767998005583244 | 0.383999002791622 |
45 | 0.639204204427411 | 0.721591591145178 | 0.360795795572589 |
46 | 0.589703966450402 | 0.820592067099196 | 0.410296033549598 |
47 | 0.580443349320715 | 0.83911330135857 | 0.419556650679285 |
48 | 0.691689468145315 | 0.61662106370937 | 0.308310531854685 |
49 | 0.650493606472396 | 0.699012787055209 | 0.349506393527605 |
50 | 0.639685672078383 | 0.720628655843235 | 0.360314327921617 |
51 | 0.601176208528055 | 0.79764758294389 | 0.398823791471945 |
52 | 0.560223306122013 | 0.879553387755974 | 0.439776693877987 |
53 | 0.59654801013634 | 0.80690397972732 | 0.40345198986366 |
54 | 0.563409560023509 | 0.873180879952981 | 0.436590439976491 |
55 | 0.6148934247036 | 0.7702131505928 | 0.3851065752964 |
56 | 0.581855444429155 | 0.83628911114169 | 0.418144555570845 |
57 | 0.542133076835251 | 0.915733846329498 | 0.457866923164749 |
58 | 0.511041653464181 | 0.977916693071639 | 0.488958346535819 |
59 | 0.463967143941438 | 0.927934287882877 | 0.536032856058562 |
60 | 0.422762276607028 | 0.845524553214056 | 0.577237723392972 |
61 | 0.389856149572537 | 0.779712299145074 | 0.610143850427463 |
62 | 0.350053587354272 | 0.700107174708544 | 0.649946412645728 |
63 | 0.309275961404122 | 0.618551922808244 | 0.690724038595878 |
64 | 0.342214870616303 | 0.684429741232606 | 0.657785129383697 |
65 | 0.300789340611201 | 0.601578681222403 | 0.699210659388799 |
66 | 0.314622189809826 | 0.629244379619651 | 0.685377810190174 |
67 | 0.376722299893158 | 0.753444599786316 | 0.623277700106842 |
68 | 0.453735810270281 | 0.907471620540561 | 0.546264189729719 |
69 | 0.415173598595846 | 0.830347197191692 | 0.584826401404154 |
70 | 0.398962430900143 | 0.797924861800285 | 0.601037569099857 |
71 | 0.465805133548298 | 0.931610267096597 | 0.534194866451702 |
72 | 0.420547218514767 | 0.841094437029534 | 0.579452781485233 |
73 | 0.379420083615661 | 0.758840167231321 | 0.62057991638434 |
74 | 0.343987947421435 | 0.687975894842869 | 0.656012052578565 |
75 | 0.311941642730412 | 0.623883285460823 | 0.688058357269588 |
76 | 0.288322322782673 | 0.576644645565346 | 0.711677677217327 |
77 | 0.26576005410816 | 0.531520108216319 | 0.73423994589184 |
78 | 0.229963664211329 | 0.459927328422658 | 0.770036335788671 |
79 | 0.197609624720245 | 0.395219249440491 | 0.802390375279755 |
80 | 0.170889702903008 | 0.341779405806016 | 0.829110297096992 |
81 | 0.149927711996899 | 0.299855423993797 | 0.850072288003101 |
82 | 0.243958798773799 | 0.487917597547599 | 0.756041201226201 |
83 | 0.225769628132371 | 0.451539256264742 | 0.774230371867629 |
84 | 0.196630524503168 | 0.393261049006336 | 0.803369475496832 |
85 | 0.198635525287207 | 0.397271050574414 | 0.801364474712793 |
86 | 0.194109087922453 | 0.388218175844906 | 0.805890912077547 |
87 | 0.201566756712154 | 0.403133513424309 | 0.798433243287846 |
88 | 0.188441608808055 | 0.37688321761611 | 0.811558391191945 |
89 | 0.176294099046913 | 0.352588198093826 | 0.823705900953087 |
90 | 0.181308594520281 | 0.362617189040561 | 0.81869140547972 |
91 | 0.258552651528514 | 0.517105303057029 | 0.741447348471486 |
92 | 0.224227745019767 | 0.448455490039533 | 0.775772254980233 |
93 | 0.207472771899061 | 0.414945543798122 | 0.792527228100939 |
94 | 0.176647005370814 | 0.353294010741628 | 0.823352994629186 |
95 | 0.161860531291105 | 0.32372106258221 | 0.838139468708895 |
96 | 0.165595947642546 | 0.331191895285092 | 0.834404052357454 |
97 | 0.167373926121472 | 0.334747852242944 | 0.832626073878528 |
98 | 0.163457638314322 | 0.326915276628644 | 0.836542361685678 |
99 | 0.156349521556575 | 0.312699043113149 | 0.843650478443425 |
100 | 0.15119866933871 | 0.30239733867742 | 0.84880133066129 |
101 | 0.124811279134694 | 0.249622558269388 | 0.875188720865306 |
102 | 0.104690768274489 | 0.209381536548978 | 0.895309231725511 |
103 | 0.0848347178153746 | 0.169669435630749 | 0.915165282184625 |
104 | 0.069167695193169 | 0.138335390386338 | 0.930832304806831 |
105 | 0.0739920091905175 | 0.147984018381035 | 0.926007990809482 |
106 | 0.0610052105173347 | 0.122010421034669 | 0.938994789482665 |
107 | 0.0539069738399774 | 0.107813947679955 | 0.946093026160023 |
108 | 0.0472209695484173 | 0.0944419390968347 | 0.952779030451583 |
109 | 0.0363985089919587 | 0.0727970179839174 | 0.963601491008041 |
110 | 0.0358992577967031 | 0.0717985155934063 | 0.964100742203297 |
111 | 0.0452125173350232 | 0.0904250346700465 | 0.954787482664977 |
112 | 0.180955683183649 | 0.361911366367299 | 0.81904431681635 |
113 | 0.165054450617797 | 0.330108901235595 | 0.834945549382203 |
114 | 0.597307230948238 | 0.805385538103524 | 0.402692769051762 |
115 | 0.874510148678328 | 0.250979702643343 | 0.125489851321672 |
116 | 0.844979458493553 | 0.310041083012893 | 0.155020541506447 |
117 | 0.894632713617535 | 0.210734572764929 | 0.105367286382465 |
118 | 0.87279443800004 | 0.254411123999921 | 0.12720556199996 |
119 | 0.847689558796055 | 0.30462088240789 | 0.152310441203945 |
120 | 0.877971708479872 | 0.244056583040257 | 0.122028291520128 |
121 | 0.857671657384474 | 0.284656685231052 | 0.142328342615526 |
122 | 0.821949400890632 | 0.356101198218736 | 0.178050599109368 |
123 | 0.850400725233224 | 0.299198549533553 | 0.149599274766776 |
124 | 0.812775955862856 | 0.374448088274287 | 0.187224044137144 |
125 | 0.77727497835217 | 0.445450043295661 | 0.22272502164783 |
126 | 0.732848303780098 | 0.534303392439803 | 0.267151696219902 |
127 | 0.699031978855796 | 0.601936042288407 | 0.300968021144204 |
128 | 0.659625545216797 | 0.680748909566407 | 0.340374454783203 |
129 | 0.603997811521454 | 0.792004376957092 | 0.396002188478546 |
130 | 0.542618005847216 | 0.914763988305567 | 0.457381994152784 |
131 | 0.541396971393463 | 0.917206057213074 | 0.458603028606537 |
132 | 0.541507306832898 | 0.916985386334204 | 0.458492693167102 |
133 | 0.49201842200272 | 0.98403684400544 | 0.50798157799728 |
134 | 0.444298507112976 | 0.888597014225952 | 0.555701492887024 |
135 | 0.596843113757033 | 0.806313772485935 | 0.403156886242967 |
136 | 0.560225537119912 | 0.879548925760177 | 0.439774462880088 |
137 | 0.488060397250348 | 0.976120794500695 | 0.511939602749652 |
138 | 0.500465747071631 | 0.999068505856738 | 0.499534252928369 |
139 | 0.428677355797048 | 0.857354711594096 | 0.571322644202952 |
140 | 0.392394744899589 | 0.784789489799177 | 0.607605255100411 |
141 | 0.357899121912323 | 0.715798243824647 | 0.642100878087677 |
142 | 0.417566057793126 | 0.835132115586252 | 0.582433942206874 |
143 | 0.570950490818346 | 0.858099018363308 | 0.429049509181654 |
144 | 0.497661935280862 | 0.995323870561723 | 0.502338064719138 |
145 | 0.41681494841382 | 0.83362989682764 | 0.58318505158618 |
146 | 0.411934368393863 | 0.823868736787726 | 0.588065631606137 |
147 | 0.360460923669245 | 0.720921847338491 | 0.639539076330754 |
148 | 0.251071208740865 | 0.502142417481731 | 0.748928791259135 |
149 | 0.456567419664047 | 0.913134839328095 | 0.543432580335953 |
150 | 0.385521341064606 | 0.771042682129212 | 0.614478658935394 |
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 | 4 | 0.028169014084507 | OK |