Multiple Linear Regression - Estimated Regression Equation |
Y[t] = + 5156.77183908046 + 1866.29530377668X[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) | 5156.77183908046 | 182.028745 | 28.3294 | 0 | 0 |
X | 1866.29530377668 | 412.802393 | 4.521 | 1.6e-05 | 8e-06 |
Multiple Linear Regression - Regression Statistics | |
Multiple R | 0.402065013518833 |
R-squared | 0.161656275095899 |
Adjusted R-squared | 0.153747372030766 |
F-TEST (value) | 20.4397846028196 |
F-TEST (DF numerator) | 1 |
F-TEST (DF denominator) | 106 |
p-value | 1.60881629114318e-05 |
Multiple Linear Regression - Residual Statistics | |
Residual Standard Deviation | 1697.85110548636 |
Sum Squared Residuals | 305566027.898534 |
Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
1 | 4716.99 | 5156.77183908045 | -439.781839080449 |
2 | 4926.65 | 5156.77183908046 | -230.121839080459 |
3 | 4920.1 | 5156.77183908046 | -236.671839080460 |
4 | 5170.09 | 5156.77183908046 | 13.3181609195402 |
5 | 5246.24 | 5156.77183908046 | 89.4681609195398 |
6 | 5283.61 | 5156.77183908046 | 126.838160919540 |
7 | 4979.05 | 5156.77183908046 | -177.72183908046 |
8 | 4825.2 | 5156.77183908046 | -331.57183908046 |
9 | 4695.12 | 5156.77183908046 | -461.65183908046 |
10 | 4711.54 | 5156.77183908046 | -445.23183908046 |
11 | 4727.22 | 5156.77183908046 | -429.551839080460 |
12 | 4384.96 | 5156.77183908046 | -771.81183908046 |
13 | 4378.75 | 5156.77183908046 | -778.02183908046 |
14 | 4472.93 | 5156.77183908046 | -683.84183908046 |
15 | 4564.07 | 5156.77183908046 | -592.70183908046 |
16 | 4310.54 | 5156.77183908046 | -846.23183908046 |
17 | 4171.38 | 5156.77183908046 | -985.39183908046 |
18 | 4049.38 | 5156.77183908046 | -1107.39183908046 |
19 | 3591.37 | 5156.77183908046 | -1565.40183908046 |
20 | 3720.46 | 5156.77183908046 | -1436.31183908046 |
21 | 4107.23 | 5156.77183908046 | -1049.54183908046 |
22 | 4101.71 | 5156.77183908046 | -1055.06183908046 |
23 | 4162.34 | 5156.77183908046 | -994.43183908046 |
24 | 4136.22 | 5156.77183908046 | -1020.55183908046 |
25 | 4125.88 | 5156.77183908046 | -1030.89183908046 |
26 | 4031.48 | 5156.77183908046 | -1125.29183908046 |
27 | 3761.36 | 5156.77183908046 | -1395.41183908046 |
28 | 3408.56 | 5156.77183908046 | -1748.21183908046 |
29 | 3228.47 | 5156.77183908046 | -1928.30183908046 |
30 | 3090.45 | 5156.77183908046 | -2066.32183908046 |
31 | 2741.14 | 5156.77183908046 | -2415.63183908046 |
32 | 2980.44 | 5156.77183908046 | -2176.33183908046 |
33 | 3104.33 | 5156.77183908046 | -2052.44183908046 |
34 | 3181.57 | 5156.77183908046 | -1975.20183908046 |
35 | 2863.86 | 5156.77183908046 | -2292.91183908046 |
36 | 2898.01 | 5156.77183908046 | -2258.76183908046 |
37 | 3112.33 | 5156.77183908046 | -2044.44183908046 |
38 | 3254.33 | 5156.77183908046 | -1902.44183908046 |
39 | 3513.47 | 5156.77183908046 | -1643.30183908046 |
40 | 3587.61 | 5156.77183908046 | -1569.16183908046 |
41 | 3727.45 | 5156.77183908046 | -1429.32183908046 |
42 | 3793.34 | 5156.77183908046 | -1363.43183908046 |
43 | 3817.58 | 5156.77183908046 | -1339.19183908046 |
44 | 3845.13 | 5156.77183908046 | -1311.64183908046 |
45 | 3931.86 | 5156.77183908046 | -1224.91183908046 |
46 | 4197.52 | 5156.77183908046 | -959.25183908046 |
47 | 4307.13 | 5156.77183908046 | -849.64183908046 |
48 | 4229.43 | 5156.77183908046 | -927.34183908046 |
49 | 4362.28 | 5156.77183908046 | -794.49183908046 |
50 | 4217.34 | 5156.77183908046 | -939.43183908046 |
51 | 4361.28 | 5156.77183908046 | -795.49183908046 |
52 | 4327.74 | 5156.77183908046 | -829.03183908046 |
53 | 4417.65 | 5156.77183908046 | -739.12183908046 |
54 | 4557.68 | 5156.77183908046 | -599.09183908046 |
55 | 4650.35 | 5156.77183908046 | -506.42183908046 |
56 | 4967.18 | 5156.77183908046 | -189.591839080460 |
57 | 5123.42 | 5156.77183908046 | -33.3518390804599 |
58 | 5290.85 | 5156.77183908046 | 134.078160919540 |
59 | 5535.66 | 5156.77183908046 | 378.88816091954 |
60 | 5514.06 | 5156.77183908046 | 357.288160919540 |
61 | 5493.88 | 5156.77183908046 | 337.10816091954 |
62 | 5694.83 | 5156.77183908046 | 538.05816091954 |
63 | 5850.41 | 5156.77183908046 | 693.63816091954 |
64 | 6116.64 | 5156.77183908046 | 959.86816091954 |
65 | 6175 | 5156.77183908046 | 1018.22816091954 |
66 | 6513.58 | 5156.77183908046 | 1356.80816091954 |
67 | 6383.78 | 5156.77183908046 | 1227.00816091954 |
68 | 6673.66 | 5156.77183908046 | 1516.88816091954 |
69 | 6936.61 | 5156.77183908046 | 1779.83816091954 |
70 | 7300.68 | 5156.77183908046 | 2143.90816091954 |
71 | 7392.93 | 5156.77183908046 | 2236.15816091954 |
72 | 7497.31 | 5156.77183908046 | 2340.53816091954 |
73 | 7584.71 | 5156.77183908046 | 2427.93816091954 |
74 | 7160.79 | 5156.77183908046 | 2004.01816091954 |
75 | 7196.19 | 5156.77183908046 | 2039.41816091954 |
76 | 7245.63 | 5156.77183908046 | 2088.85816091954 |
77 | 7347.51 | 5156.77183908046 | 2190.73816091954 |
78 | 7425.75 | 5156.77183908046 | 2268.97816091954 |
79 | 7778.51 | 5156.77183908046 | 2621.73816091954 |
80 | 7822.33 | 5156.77183908046 | 2665.55816091954 |
81 | 8181.22 | 5156.77183908046 | 3024.44816091954 |
82 | 8371.47 | 5156.77183908046 | 3214.69816091954 |
83 | 8347.71 | 5156.77183908046 | 3190.93816091954 |
84 | 8672.11 | 5156.77183908046 | 3515.33816091954 |
85 | 8802.79 | 5156.77183908046 | 3646.01816091954 |
86 | 9138.46 | 5156.77183908046 | 3981.68816091954 |
87 | 9123.29 | 5156.77183908046 | 3966.51816091954 |
88 | 9023.21 | 7023.06714285714 | 2000.14285714286 |
89 | 8850.41 | 7023.06714285714 | 1827.34285714286 |
90 | 8864.58 | 7023.06714285714 | 1841.51285714286 |
91 | 9163.74 | 7023.06714285714 | 2140.67285714286 |
92 | 8516.66 | 7023.06714285714 | 1493.59285714286 |
93 | 8553.44 | 7023.06714285714 | 1530.37285714286 |
94 | 7555.2 | 7023.06714285714 | 532.132857142857 |
95 | 7851.22 | 7023.06714285714 | 828.152857142857 |
96 | 7442 | 7023.06714285714 | 418.932857142857 |
97 | 7992.53 | 7023.06714285714 | 969.462857142857 |
98 | 8264.04 | 7023.06714285714 | 1240.97285714286 |
99 | 7517.39 | 7023.06714285714 | 494.322857142857 |
100 | 7200.4 | 7023.06714285714 | 177.332857142857 |
101 | 7193.69 | 7023.06714285714 | 170.622857142857 |
102 | 6193.58 | 7023.06714285714 | -829.487142857143 |
103 | 5104.21 | 7023.06714285714 | -1918.85714285714 |
104 | 4800.46 | 7023.06714285714 | -2222.60714285714 |
105 | 4461.61 | 7023.06714285714 | -2561.45714285714 |
106 | 4398.59 | 7023.06714285714 | -2624.47714285714 |
107 | 4243.63 | 7023.06714285714 | -2779.43714285714 |
108 | 4293.82 | 7023.06714285714 | -2729.24714285714 |
Goldfeld-Quandt test for Heteroskedasticity | |||
p-values | Alternative Hypothesis | ||
breakpoint index | greater | 2-sided | less |
5 | 0.00386587539863812 | 0.00773175079727623 | 0.996134124601362 |
6 | 0.00083319264282347 | 0.00166638528564694 | 0.999166807357177 |
7 | 0.000104205394468802 | 0.000208410788937605 | 0.999895794605531 |
8 | 1.76408811240380e-05 | 3.52817622480760e-05 | 0.999982359118876 |
9 | 4.83299699929965e-06 | 9.6659939985993e-06 | 0.999995167003001 |
10 | 1.03730720163209e-06 | 2.07461440326419e-06 | 0.999998962692798 |
11 | 1.9017653217698e-07 | 3.8035306435396e-07 | 0.999999809823468 |
12 | 2.00468676949373e-07 | 4.00937353898745e-07 | 0.999999799531323 |
13 | 1.22150316652121e-07 | 2.44300633304242e-07 | 0.999999877849683 |
14 | 3.8681971028116e-08 | 7.7363942056232e-08 | 0.99999996131803 |
15 | 8.5218669285961e-09 | 1.70437338571922e-08 | 0.999999991478133 |
16 | 4.41973977526035e-09 | 8.8394795505207e-09 | 0.99999999558026 |
17 | 3.53411828546817e-09 | 7.06823657093634e-09 | 0.999999996465882 |
18 | 3.69187023893153e-09 | 7.38374047786306e-09 | 0.99999999630813 |
19 | 2.35486569933385e-08 | 4.70973139866771e-08 | 0.999999976451343 |
20 | 3.51800137012001e-08 | 7.03600274024001e-08 | 0.999999964819986 |
21 | 1.44502534467465e-08 | 2.8900506893493e-08 | 0.999999985549747 |
22 | 5.7655327651551e-09 | 1.15310655303102e-08 | 0.999999994234467 |
23 | 2.00116463288809e-09 | 4.00232926577618e-09 | 0.999999997998835 |
24 | 7.05926352202411e-10 | 1.41185270440482e-09 | 0.999999999294074 |
25 | 2.46950405100206e-10 | 4.93900810200411e-10 | 0.99999999975305 |
26 | 1.00413978200115e-10 | 2.00827956400231e-10 | 0.999999999899586 |
27 | 7.73114166708188e-11 | 1.54622833341638e-10 | 0.999999999922689 |
28 | 1.7140715224743e-10 | 3.4281430449486e-10 | 0.999999999828593 |
29 | 5.327347041672e-10 | 1.0654694083344e-09 | 0.999999999467265 |
30 | 1.85492649864778e-09 | 3.70985299729557e-09 | 0.999999998145074 |
31 | 1.40870654481176e-08 | 2.81741308962351e-08 | 0.999999985912934 |
32 | 3.35277371633315e-08 | 6.70554743266631e-08 | 0.999999966472263 |
33 | 5.15867452475614e-08 | 1.03173490495123e-07 | 0.999999948413255 |
34 | 6.39256096138433e-08 | 1.27851219227687e-07 | 0.99999993607439 |
35 | 1.45627018457859e-07 | 2.91254036915719e-07 | 0.999999854372982 |
36 | 2.84062364311938e-07 | 5.68124728623876e-07 | 0.999999715937636 |
37 | 3.65361132474051e-07 | 7.30722264948103e-07 | 0.999999634638868 |
38 | 3.85621805641011e-07 | 7.71243611282022e-07 | 0.999999614378194 |
39 | 3.06762615661152e-07 | 6.13525231322305e-07 | 0.999999693237384 |
40 | 2.35309129812231e-07 | 4.70618259624462e-07 | 0.99999976469087 |
41 | 1.66512336136506e-07 | 3.33024672273013e-07 | 0.999999833487664 |
42 | 1.1690093419261e-07 | 2.3380186838522e-07 | 0.999999883099066 |
43 | 8.43651206713238e-08 | 1.68730241342648e-07 | 0.99999991563488 |
44 | 6.28265197535801e-08 | 1.25653039507160e-07 | 0.99999993717348 |
45 | 4.68115822839482e-08 | 9.36231645678964e-08 | 0.999999953188418 |
46 | 3.32534873483773e-08 | 6.65069746967545e-08 | 0.999999966746513 |
47 | 2.44525035962369e-08 | 4.89050071924739e-08 | 0.999999975547496 |
48 | 1.90830671003401e-08 | 3.81661342006802e-08 | 0.999999980916933 |
49 | 1.55759856972772e-08 | 3.11519713945544e-08 | 0.999999984424014 |
50 | 1.39210980960704e-08 | 2.78421961921409e-08 | 0.999999986078902 |
51 | 1.30911604925300e-08 | 2.61823209850601e-08 | 0.99999998690884 |
52 | 1.35130485479267e-08 | 2.70260970958534e-08 | 0.999999986486951 |
53 | 1.51758859736619e-08 | 3.03517719473238e-08 | 0.999999984824114 |
54 | 1.87734261297878e-08 | 3.75468522595755e-08 | 0.999999981226574 |
55 | 2.59113568543129e-08 | 5.18227137086258e-08 | 0.999999974088643 |
56 | 4.38888268330831e-08 | 8.77776536661662e-08 | 0.999999956111173 |
57 | 8.63113297212975e-08 | 1.72622659442595e-07 | 0.99999991368867 |
58 | 1.97184110097417e-07 | 3.94368220194834e-07 | 0.99999980281589 |
59 | 5.53526236840371e-07 | 1.10705247368074e-06 | 0.999999446473763 |
60 | 1.42112839320398e-06 | 2.84225678640796e-06 | 0.999998578871607 |
61 | 3.4747544798025e-06 | 6.949508959605e-06 | 0.99999652524552 |
62 | 9.44636004492853e-06 | 1.88927200898571e-05 | 0.999990553639955 |
63 | 2.67072750991714e-05 | 5.34145501983428e-05 | 0.9999732927249 |
64 | 8.23418052466462e-05 | 0.000164683610493292 | 0.999917658194753 |
65 | 0.000227043663561289 | 0.000454087327122578 | 0.999772956336439 |
66 | 0.000672716691635665 | 0.00134543338327133 | 0.999327283308364 |
67 | 0.00153461281846401 | 0.00306922563692802 | 0.998465387181536 |
68 | 0.00352614515032068 | 0.00705229030064136 | 0.99647385484968 |
69 | 0.00780305793073897 | 0.0156061158614779 | 0.99219694206926 |
70 | 0.0171364262651728 | 0.0342728525303457 | 0.982863573734827 |
71 | 0.0318580767610296 | 0.0637161535220592 | 0.96814192323897 |
72 | 0.0523035936331341 | 0.104607187266268 | 0.947696406366866 |
73 | 0.0774208224617841 | 0.154841644923568 | 0.922579177538216 |
74 | 0.0956097089205235 | 0.191219417841047 | 0.904390291079477 |
75 | 0.114319933388210 | 0.228639866776420 | 0.88568006661179 |
76 | 0.133474719218696 | 0.266949438437392 | 0.866525280781304 |
77 | 0.153391587934711 | 0.306783175869421 | 0.84660841206529 |
78 | 0.173632581358604 | 0.347265162717208 | 0.826367418641396 |
79 | 0.196962651703467 | 0.393925303406934 | 0.803037348296533 |
80 | 0.21814319407973 | 0.43628638815946 | 0.78185680592027 |
81 | 0.242372222334677 | 0.484744444669354 | 0.757627777665323 |
82 | 0.265427968078179 | 0.530855936156358 | 0.734572031921821 |
83 | 0.281593764256394 | 0.563187528512789 | 0.718406235743606 |
84 | 0.299429126214282 | 0.598858252428563 | 0.700570873785718 |
85 | 0.313175781983826 | 0.626351563967652 | 0.686824218016174 |
86 | 0.329119486359628 | 0.658238972719255 | 0.670880513640372 |
87 | 0.334859333252534 | 0.669718666505068 | 0.665140666747466 |
88 | 0.340817706638682 | 0.681635413277365 | 0.659182293361318 |
89 | 0.34365874710204 | 0.68731749420408 | 0.65634125289796 |
90 | 0.358229112206268 | 0.716458224412536 | 0.641770887793732 |
91 | 0.421101484740138 | 0.842202969480276 | 0.578898515259862 |
92 | 0.439392261215678 | 0.878784522431356 | 0.560607738784322 |
93 | 0.480923902889451 | 0.961847805778901 | 0.519076097110549 |
94 | 0.44628549964359 | 0.89257099928718 | 0.55371450035641 |
95 | 0.442206505514392 | 0.884413011028784 | 0.557793494485608 |
96 | 0.413191176383495 | 0.82638235276699 | 0.586808823616505 |
97 | 0.460127606376481 | 0.920255212752962 | 0.539872393623519 |
98 | 0.613426452213427 | 0.773147095573146 | 0.386573547786573 |
99 | 0.700071629674654 | 0.599856740650692 | 0.299928370325346 |
100 | 0.790980211169657 | 0.418039577660685 | 0.209019788830343 |
101 | 0.949735211381868 | 0.100529577236265 | 0.0502647886181324 |
102 | 0.994238534688944 | 0.011522930622113 | 0.0057614653110565 |
103 | 0.994712106824188 | 0.0105757863516245 | 0.00528789317581225 |
Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
Description | # significant tests | % significant tests | OK/NOK |
1% type I error level | 64 | 0.646464646464647 | NOK |
5% type I error level | 68 | 0.686868686868687 | NOK |
10% type I error level | 69 | 0.696969696969697 | NOK |