Multiple Linear Regression - Estimated Regression Equation |
I.P.C.N.[t] = + 17.888666290104 + 0.593242377727027T.I.P.[t] + 0.205154983132475`y(t-1)`[t] + 0.115152970700046`y(t-2)`[t] + 1.45879444891353M1[t] -2.14950402416358M2[t] -1.21608635241408M3[t] -1.28121836133136M4[t] + 10.7917317668094M5[t] + 4.87747224861314M6[t] -7.95768982198348M7[t] -4.4592279731663M8[t] -3.79312308338613M9[t] + 0.925313075396348M10[t] + 6.08788829036565M11[t] -0.0896622450989522t + 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) | 17.888666290104 | 11.042792 | 1.6199 | 0.11273 | 0.056365 |
T.I.P. | 0.593242377727027 | 0.109649 | 5.4104 | 3e-06 | 1e-06 |
`y(t-1)` | 0.205154983132475 | 0.117405 | 1.7474 | 0.087875 | 0.043937 |
`y(t-2)` | 0.115152970700046 | 0.116605 | 0.9875 | 0.329031 | 0.164515 |
M1 | 1.45879444891353 | 2.868214 | 0.5086 | 0.613689 | 0.306844 |
M2 | -2.14950402416358 | 2.497623 | -0.8606 | 0.394334 | 0.197167 |
M3 | -1.21608635241408 | 2.806613 | -0.4333 | 0.667019 | 0.333509 |
M4 | -1.28121836133136 | 2.863701 | -0.4474 | 0.656886 | 0.328443 |
M5 | 10.7917317668094 | 3.040126 | 3.5498 | 0.000966 | 0.000483 |
M6 | 4.87747224861314 | 2.721254 | 1.7924 | 0.08028 | 0.04014 |
M7 | -7.95768982198348 | 2.744783 | -2.8992 | 0.005926 | 0.002963 |
M8 | -4.4592279731663 | 2.985327 | -1.4937 | 0.142725 | 0.071363 |
M9 | -3.79312308338613 | 2.56813 | -1.477 | 0.147136 | 0.073568 |
M10 | 0.925313075396348 | 2.713631 | 0.341 | 0.734813 | 0.367407 |
M11 | 6.08788829036565 | 2.746191 | 2.2168 | 0.032102 | 0.016051 |
t | -0.0896622450989522 | 0.033877 | -2.6467 | 0.011394 | 0.005697 |
Multiple Linear Regression - Regression Statistics | |
Multiple R | 0.90677540764535 |
R-squared | 0.82224163991039 |
Adjusted R-squared | 0.758756511306957 |
F-TEST (value) | 12.9517204737289 |
F-TEST (DF numerator) | 15 |
F-TEST (DF denominator) | 42 |
p-value | 3.16493498075943e-11 |
Multiple Linear Regression - Residual Statistics | |
Residual Standard Deviation | 3.71652920335122 |
Sum Squared Residuals | 580.128751413224 |
Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
1 | 116.7 | 116.793696026955 | -0.0936960269545418 |
2 | 112.5 | 112.865685087896 | -0.365685087895517 |
3 | 113 | 111.118957740513 | 1.88104225948693 |
4 | 126.4 | 119.95632806921 | 6.4436719307901 |
5 | 114.1 | 115.169270746585 | -1.06927074658506 |
6 | 112.5 | 116.964979688501 | -4.46497968850098 |
7 | 112.4 | 112.677267470406 | -0.277267470405828 |
8 | 113.1 | 111.550637465283 | 1.54936253471653 |
9 | 116.3 | 113.979576196496 | 2.32042380350424 |
10 | 111.7 | 115.489377680468 | -3.78937768046757 |
11 | 118.8 | 118.029367387670 | 0.770632612330493 |
12 | 116.5 | 113.787225609361 | 2.71277439063879 |
13 | 125.1 | 124.282074634301 | 0.817925365698576 |
14 | 113.1 | 113.303607748095 | -0.203607748094541 |
15 | 119.6 | 118.133648800264 | 1.46635119973557 |
16 | 114.4 | 120.718765463526 | -6.31876546352575 |
17 | 114 | 115.061064314200 | -1.06106431419986 |
18 | 117.8 | 117.334245013689 | 0.465754986310517 |
19 | 117 | 113.626314447114 | 3.37368555288624 |
20 | 120.9 | 118.317083395122 | 2.58291660487787 |
21 | 115 | 117.465835537643 | -2.46583553764268 |
22 | 117.3 | 114.866949719350 | 2.43305028064981 |
23 | 119.4 | 122.105286134203 | -2.70528613420306 |
24 | 114.9 | 116.208143231518 | -1.30814323151784 |
25 | 125.8 | 124.904671349021 | 0.895328650978752 |
26 | 117.6 | 115.390533381706 | 2.20946661829429 |
27 | 117.6 | 117.705560936027 | -0.105560936026953 |
28 | 114.9 | 121.293127106314 | -6.39312710631384 |
29 | 121.9 | 118.069409805040 | 3.83059019495955 |
30 | 117 | 120.131595722189 | -3.13159572218863 |
31 | 106.4 | 111.931494519179 | -5.53149451917855 |
32 | 110.5 | 118.47450128476 | -7.9745012847599 |
33 | 113.6 | 113.272952233548 | 0.327047766452163 |
34 | 114.2 | 111.119710151043 | 3.08028984895724 |
35 | 125.4 | 123.020383761642 | 2.37961623835808 |
36 | 124.6 | 120.455469812908 | 4.14453018709217 |
37 | 120.2 | 121.170464168876 | -0.970464168875852 |
38 | 120.8 | 120.927016981310 | -0.127016981309563 |
39 | 111.4 | 116.522604829398 | -5.12260482939777 |
40 | 124.1 | 118.5424936849 | 5.5575063150999 |
41 | 120.2 | 120.243288612376 | -0.0432886123761048 |
42 | 125.5 | 117.156026178118 | 8.3439738218825 |
43 | 116 | 114.954547108653 | 1.04545289134670 |
44 | 117 | 116.372118501824 | 0.627881498176462 |
45 | 105.7 | 106.389912151036 | -0.689912151036261 |
46 | 102 | 105.790051599615 | -3.79005159961503 |
47 | 106.4 | 106.844962716486 | -0.444962716485515 |
48 | 96.9 | 102.449161346213 | -5.5491613462131 |
49 | 107.6 | 108.249093820847 | -0.649093820846937 |
50 | 98.8 | 100.313156800995 | -1.51315680099467 |
51 | 101.1 | 99.2192276937978 | 1.88077230620222 |
52 | 105.7 | 104.989285676050 | 0.710714323949584 |
53 | 104.6 | 106.256966521799 | -1.65696652179852 |
54 | 103.2 | 104.413153397503 | -1.21315339750342 |
55 | 101.6 | 100.210376454649 | 1.38962354535145 |
56 | 106.7 | 103.485659353011 | 3.21434064698903 |
57 | 99.5 | 98.9917238812775 | 0.508276118722535 |
58 | 101 | 98.9339108495244 | 2.06608915047556 |
Goldfeld-Quandt test for Heteroskedasticity | |||
p-values | Alternative Hypothesis | ||
breakpoint index | greater | 2-sided | less |
19 | 0.805132733379345 | 0.38973453324131 | 0.194867266620655 |
20 | 0.705033605057932 | 0.589932789884136 | 0.294966394942068 |
21 | 0.587103703547356 | 0.825792592905288 | 0.412896296452644 |
22 | 0.618023772919378 | 0.763952454161244 | 0.381976227080622 |
23 | 0.514044815618347 | 0.971910368763307 | 0.485955184381653 |
24 | 0.426210961569951 | 0.852421923139902 | 0.573789038430049 |
25 | 0.324705111367582 | 0.649410222735164 | 0.675294888632418 |
26 | 0.292710787574653 | 0.585421575149307 | 0.707289212425346 |
27 | 0.216816586543329 | 0.433633173086658 | 0.783183413456671 |
28 | 0.274251341845868 | 0.548502683691736 | 0.725748658154132 |
29 | 0.336332320304827 | 0.672664640609654 | 0.663667679695173 |
30 | 0.276751170445045 | 0.553502340890089 | 0.723248829554955 |
31 | 0.224220336901904 | 0.448440673803808 | 0.775779663098096 |
32 | 0.549431459998418 | 0.901137080003163 | 0.450568540001582 |
33 | 0.455382583853671 | 0.910765167707343 | 0.544617416146329 |
34 | 0.402350090750459 | 0.804700181500918 | 0.597649909249541 |
35 | 0.305533197228286 | 0.611066394456572 | 0.694466802771714 |
36 | 0.451352713699889 | 0.902705427399778 | 0.548647286300111 |
37 | 0.344178946023515 | 0.688357892047031 | 0.655821053976485 |
38 | 0.229864827054047 | 0.459729654108094 | 0.770135172945953 |
39 | 0.309920199360235 | 0.61984039872047 | 0.690079800639765 |
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 |