Multiple Linear Regression - Estimated Regression Equation |
Y[t] = + 73.8042336411469 + 0.156334829849718X[t] + 0.0548151015977865M1[t] + 0.297576758775181M2[t] + 0.276411043319977M3[t] + 0.337865016199548M4[t] + 0.341348849186215M5[t] + 0.272164575593166M6[t] + 0.435077360364255M7[t] + 0.356009147021685M8[t] + 0.346983700939432M9[t] + 0.227580410026349M10[t] + 0.126346141928972M11[t] + 0.136100788004864t + 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) | 73.8042336411469 | 3.559799 | 20.7327 | 0 | 0 |
X | 0.156334829849718 | 0.041299 | 3.7854 | 0.000258 | 0.000129 |
M1 | 0.0548151015977865 | 0.21443 | 0.2556 | 0.798745 | 0.399373 |
M2 | 0.297576758775181 | 0.214265 | 1.3888 | 0.167882 | 0.083941 |
M3 | 0.276411043319977 | 0.215965 | 1.2799 | 0.20346 | 0.10173 |
M4 | 0.337865016199548 | 0.223098 | 1.5144 | 0.132982 | 0.066491 |
M5 | 0.341348849186215 | 0.227473 | 1.5006 | 0.136515 | 0.068257 |
M6 | 0.272164575593166 | 0.223346 | 1.2186 | 0.225788 | 0.112894 |
M7 | 0.435077360364255 | 0.219361 | 1.9834 | 0.049986 | 0.024993 |
M8 | 0.356009147021685 | 0.214425 | 1.6603 | 0.099897 | 0.049948 |
M9 | 0.346983700939432 | 0.214793 | 1.6154 | 0.109276 | 0.054638 |
M10 | 0.227580410026349 | 0.217467 | 1.0465 | 0.297776 | 0.148888 |
M11 | 0.126346141928972 | 0.218098 | 0.5793 | 0.563645 | 0.281823 |
t | 0.136100788004864 | 0.007037 | 19.3419 | 0 | 0 |
Multiple Linear Regression - Regression Statistics | |
Multiple R | 0.996923633472064 |
R-squared | 0.993856730975143 |
Adjusted R-squared | 0.993081366923462 |
F-TEST (value) | 1281.79366688516 |
F-TEST (DF numerator) | 13 |
F-TEST (DF denominator) | 103 |
p-value | 0 |
Multiple Linear Regression - Residual Statistics | |
Residual Standard Deviation | 0.46013305322092 |
Sum Squared Residuals | 21.8074099466398 |
Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
1 | 88.74 | 87.9011326458822 | 0.838867354117786 |
2 | 88.92 | 88.2581082148853 | 0.661891785114661 |
3 | 88.77 | 88.3871134221215 | 0.38288657787852 |
4 | 89.17 | 88.780086720318 | 0.389913279681941 |
5 | 89.61 | 89.0400491602939 | 0.569950839706126 |
6 | 89.52 | 89.0850787985267 | 0.434921201473268 |
7 | 89.74 | 89.3887824161982 | 0.351217583801822 |
8 | 89.4 | 89.2347629705634 | 0.165237029436660 |
9 | 89.36 | 89.324317953322 | 0.0356820466779737 |
10 | 89.38 | 89.2894249565634 | 0.0905750434365953 |
11 | 89.36 | 89.4055855879927 | -0.0455855879927416 |
12 | 89.29 | 89.4434805034416 | -0.153480503441577 |
13 | 89.59 | 89.737577380745 | -0.147577380745045 |
14 | 89.79 | 90.1086230844348 | -0.318623084434817 |
15 | 89.86 | 90.234501595074 | -0.374501595073962 |
16 | 90.21 | 90.5008436810923 | -0.290843681092279 |
17 | 90.37 | 90.7139056721132 | -0.343905672113169 |
18 | 90.19 | 90.6995280750031 | -0.509528075003136 |
19 | 90.33 | 90.8515869077203 | -0.521586907720353 |
20 | 90.22 | 90.752284652533 | -0.532284652532929 |
21 | 90.42 | 90.909063612127 | -0.489063612126983 |
22 | 90.54 | 90.9632814683827 | -0.423281468382694 |
23 | 90.73 | 90.9981479882902 | -0.268147988290183 |
24 | 91.02 | 90.9969591962766 | 0.0230408037233981 |
25 | 91.19 | 91.2191420518492 | -0.0291420518491953 |
26 | 91.53 | 91.6277081147029 | -0.097708114702897 |
27 | 91.88 | 91.7520232770435 | 0.127976722956454 |
28 | 92.06 | 92.1356164854491 | -0.0756164854491397 |
29 | 92.32 | 92.3049047241121 | 0.0150952758878739 |
30 | 92.67 | 92.4452986085533 | 0.224701391446699 |
31 | 92.85 | 92.7615090126127 | 0.08849098738727 |
32 | 92.82 | 92.7263040376637 | 0.0936959623363068 |
33 | 93.46 | 92.8580694244818 | 0.601930575518205 |
34 | 93.23 | 92.8184863828277 | 0.411513617172335 |
35 | 93.54 | 92.9643506319285 | 0.575649368071547 |
36 | 93.29 | 92.903754604572 | 0.386245395428029 |
37 | 93.2 | 93.199414830174 | 0.000585169826062811 |
38 | 93.6 | 93.5907840617442 | 0.00921593825581825 |
39 | 93.81 | 93.847983829457 | -0.0379838294570775 |
40 | 94.62 | 94.3066177561905 | 0.313382243809459 |
41 | 95.22 | 94.6494376559867 | 0.570562344013289 |
42 | 95.38 | 94.7695080125474 | 0.610491987452565 |
43 | 95.31 | 94.9934808669955 | 0.316519133004485 |
44 | 95.3 | 95.0645835763443 | 0.23541642365571 |
45 | 95.57 | 95.182278828476 | 0.387721171524078 |
46 | 95.42 | 95.2505668194181 | 0.169433180581896 |
47 | 95.53 | 95.2713632046391 | 0.258636795360883 |
48 | 95.33 | 95.1826269079097 | 0.147373092090312 |
49 | 95.9 | 95.6799590640178 | 0.22004093598222 |
50 | 96.06 | 95.9243735555293 | 0.135626444470715 |
51 | 96.31 | 96.1221660878993 | 0.187833912100703 |
52 | 96.34 | 96.3322276351717 | 0.007772364828292 |
53 | 96.49 | 96.565613154073 | -0.0756131540730777 |
54 | 96.22 | 96.4933916699186 | -0.27339166991864 |
55 | 96.53 | 96.806475377381 | -0.276475377381066 |
56 | 96.5 | 96.7978473235065 | -0.297847323506479 |
57 | 96.77 | 97.0359203946224 | -0.265920394622396 |
58 | 96.66 | 97.0135341842517 | -0.353534184251747 |
59 | 96.58 | 97.0546540973532 | -0.474654097353221 |
60 | 96.63 | 96.9737345421163 | -0.343734542116279 |
61 | 97.06 | 97.3256753064641 | -0.265675306464133 |
62 | 97.73 | 97.7764517733773 | -0.04645177337726 |
63 | 98.01 | 97.9601741710608 | 0.0498258289392028 |
64 | 97.76 | 98.239023043467 | -0.479023043467086 |
65 | 97.49 | 98.3973678440406 | -0.907367844040594 |
66 | 97.77 | 98.5361983801833 | -0.766198380183278 |
67 | 97.96 | 98.8258318631682 | -0.86583186316825 |
68 | 98.23 | 98.8953712242185 | -0.665371224218511 |
69 | 98.51 | 99.1865981374833 | -0.676598137483325 |
70 | 98.19 | 98.992243614278 | -0.802243614277995 |
71 | 98.37 | 99.028673482484 | -0.658673482483973 |
72 | 98.31 | 98.9305570959636 | -0.620557095963563 |
73 | 98.6 | 99.28406120861 | -0.684061208609927 |
74 | 98.97 | 99.6848105299711 | -0.714810529971143 |
75 | 99.11 | 99.8544627929682 | -0.744462792968203 |
76 | 99.64 | 100.188028855822 | -0.548028855821893 |
77 | 100.03 | 100.390147408753 | -0.360147408753312 |
78 | 99.98 | 100.442993788479 | -0.462993788478649 |
79 | 100.32 | 100.701360305494 | -0.381360305493685 |
80 | 100.44 | 100.678662116933 | -0.23866211693262 |
81 | 100.51 | 100.802610762258 | -0.292610762258228 |
82 | 101 | 100.78804129338 | 0.211958706619928 |
83 | 100.88 | 100.877625003735 | 0.0023749962650349 |
84 | 100.55 | 100.837352504259 | -0.287352504258947 |
85 | 100.83 | 101.106435808786 | -0.276435808786456 |
86 | 101.51 | 101.615056162744 | -0.105056162743974 |
87 | 102.16 | 101.969183524964 | 0.190816475036287 |
88 | 102.39 | 102.176118375639 | 0.213881624360874 |
89 | 102.54 | 102.422010680928 | 0.117989319071539 |
90 | 102.85 | 102.396689645729 | 0.453310354271046 |
91 | 103.47 | 102.581578792715 | 0.888421207285392 |
92 | 103.57 | 102.651118153765 | 0.918881846235113 |
93 | 103.69 | 102.631238755629 | 1.05876124437124 |
94 | 103.5 | 102.657316342512 | 0.84268365748848 |
95 | 103.47 | 102.784420412030 | 0.685579587969658 |
96 | 103.45 | 102.761344743838 | 0.68865525616221 |
97 | 103.48 | 102.997597734097 | 0.482402265903143 |
98 | 103.93 | 103.482767863577 | 0.447232136423077 |
99 | 103.89 | 103.611773070813 | 0.278226929186937 |
100 | 104.4 | 103.915635515995 | 0.484364484004697 |
101 | 104.79 | 104.230315146419 | 0.559684853581482 |
102 | 104.77 | 104.231571032293 | 0.538428967706538 |
103 | 105.13 | 104.561851571039 | 0.56814842896064 |
104 | 105.26 | 104.662657898060 | 0.597342101940437 |
105 | 104.96 | 104.917927800459 | 0.0420721995410439 |
106 | 104.75 | 104.897104938387 | -0.147104938386800 |
107 | 105.01 | 105.085179591547 | -0.075179591547005 |
108 | 105.15 | 104.990189901624 | 0.159810098376415 |
109 | 105.2 | 105.339003969374 | -0.139003969374454 |
110 | 105.77 | 105.741316639034 | 0.0286833609658205 |
111 | 105.78 | 105.840618228599 | -0.0606182285988618 |
112 | 106.26 | 106.275801930855 | -0.0158019308548665 |
113 | 106.13 | 106.276248553280 | -0.146248553280158 |
114 | 106.12 | 106.369741988766 | -0.249741988766414 |
115 | 106.57 | 106.737542886676 | -0.167542886676257 |
116 | 106.44 | 106.716408046414 | -0.276408046413688 |
117 | 106.54 | 106.941974331142 | -0.401974331141612 |