Multiple Linear Regression - Estimated Regression Equation
V5[t] = + 10.2852 -0.230543V1[t] + 0.441032V2[t] + 0.442236V3[t] -0.099862V4[t] -0.00458843t + e[t]


Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STAT
H0: parameter = 0		2-tail p-value1-tail p-value
(Intercept)+10.29 1.223+8.4070e+00 6.315e-13 3.157e-13
V1-0.2305 0.1353-1.7040e+00 0.09184 0.04592
V2+0.441 0.1299+3.3950e+00 0.001028 0.000514
V3+0.4422 0.1519+2.9120e+00 0.004535 0.002267
V4-0.09986 0.2253-4.4320e-01 0.6587 0.3293
t-0.004588 0.005421-8.4640e-01 0.3996 0.1998


Multiple Linear Regression - Regression Statistics
Multiple R 0.4427
R-squared 0.196
Adjusted R-squared 0.1508
F-TEST (value) 4.338
F-TEST (DF numerator)5
F-TEST (DF denominator)89
p-value 0.001403
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation 1.414
Sum Squared Residuals 177.9


Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolation
Forecast		Residuals
Prediction Error
1 11 11.63-0.6289
2 9 10.28-1.279
3 12 12.04-0.04308
4 12 11.05 0.947
5 12 13.17-1.165
6 11 12.03-1.027
7 12 11.16 0.8409
8 12 10.79 1.207
9 15 13 2.004
10 13 12.22 0.7798
11 12 11.56 0.4359
12 11 13.13-2.134
13 9 11.11-2.112
14 11 12.64-1.643
15 12 12.24-0.2386
16 12 11.85 0.1497
17 12 11.87 0.1342
18 14 12.53 1.474
19 12 11.3 0.7031
20 9 12.42-3.424
21 13 11.77 1.232
22 13 11.17 1.829
23 12 11.95 0.0511
24 12 12.06-0.05735
25 12 11.94 0.06027
26 12 12.06-0.05626
27 11 12.16-1.161
28 13 10.75 2.249
29 13 11.71 1.288
30 10 12.36-2.359
31 13 12.35 0.6456
32 5 10.35-5.353
33 10 10.81-0.8105
34 15 11.9 3.102
35 13 12.09 0.9052
36 12 11.01 0.9928
37 13 11.89 1.114
38 13 11.98 1.018
39 11 11.43-0.4333
40 12 11.97 0.02924
41 12 12.75-0.7496
42 13 11.86 1.138
43 14 11.86 2.142
44 12 11.96 0.03683
45 12 11.85 0.152
46 10 11.96-1.955
47 12 12.69-0.6924
48 12 11.85 0.1458
49 12 11.39 0.6126
50 13 11.51 1.487
51 14 11.84 2.158
52 10 10.26-0.2622
53 13 12.71 0.2854
54 11 11.81-0.8067
55 12 12.03-0.03262
56 12 12.34-0.3396
57 13 11.45 1.547
58 12 12.02-0.01885
59 9 12.13-3.126
60 12 12.45-0.4519
61 14 11.78 2.224
62 11 12.54-1.543
63 12 12.65-0.6486
64 12 11.86 0.1382
65 9 10.43-1.433
66 13 12.21 0.7873
67 10 10.19-0.1922
68 14 12.18 1.815
69 10 11.63-1.627
70 12 11.29 0.709
71 11 11.29-0.2888
72 14 12.63 1.373
73 13 12.6 0.396
74 12 11.37 0.6251
75 10 11.7-1.701
76 12 11.58 0.4226
77 12 11.03 0.9692
78 15 13.25 1.747
79 12 12.5-0.4966
80 12 11.37 0.635
81 10 10.8-0.8019
82 12 12.56-0.5627
83 12 11.88 0.1159
84 12 12.34-0.3418
85 11 12.11-1.105
86 13 12.64 0.3558
87 13 12.54 0.4615
88 11 11.21-0.212
89 10 11.67-1.666
90 9 10.43-1.429
91 13 12.08 0.9221
92 10 12.64-2.635
93 13 11.31 1.685
94 12 11.18 0.8179
95 12 12.05-0.05121


Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
9 0.486 0.972 0.514
10 0.4025 0.8049 0.5975
11 0.3361 0.6723 0.6639
12 0.4269 0.8539 0.5731
13 0.5898 0.8204 0.4102
14 0.5872 0.8256 0.4128
15 0.5262 0.9475 0.4738
16 0.4263 0.8525 0.5737
17 0.3357 0.6715 0.6643
18 0.4165 0.8329 0.5835
19 0.3337 0.6674 0.6663
20 0.4584 0.9168 0.5416
21 0.6098 0.7804 0.3902
22 0.5847 0.8307 0.4153
23 0.5104 0.9791 0.4895
24 0.4398 0.8796 0.5602
25 0.3692 0.7384 0.6308
26 0.3082 0.6163 0.6918
27 0.2678 0.5357 0.7322
28 0.4264 0.8528 0.5736
29 0.3754 0.7508 0.6246
30 0.5125 0.9751 0.4875
31 0.4583 0.9167 0.5417
32 0.9881 0.0239 0.01195
33 0.9854 0.02917 0.01458
34 0.997 0.005989 0.002994
35 0.9956 0.008817 0.004409
36 0.9939 0.0123 0.00615
37 0.9919 0.01623 0.008113
38 0.989 0.022 0.011
39 0.9845 0.03091 0.01545
40 0.9774 0.04528 0.02264
41 0.9713 0.05736 0.02868
42 0.9654 0.06911 0.03456
43 0.9744 0.05123 0.02562
44 0.9635 0.07299 0.0365
45 0.9491 0.1018 0.05091
46 0.9665 0.06699 0.0335
47 0.96 0.08001 0.04
48 0.9445 0.1111 0.05555
49 0.9264 0.1473 0.07365
50 0.9218 0.1564 0.07821
51 0.9486 0.1027 0.05135
52 0.9334 0.1332 0.06659
53 0.9134 0.1733 0.08663
54 0.8996 0.2008 0.1004
55 0.8688 0.2624 0.1312
56 0.8381 0.3237 0.1619
57 0.8491 0.3018 0.1509
58 0.8084 0.3832 0.1916
59 0.9596 0.08076 0.04038
60 0.9484 0.1033 0.05163
61 0.9677 0.06467 0.03234
62 0.9741 0.05184 0.02592
63 0.9772 0.04556 0.02278
64 0.9658 0.06837 0.03419
65 0.9671 0.06577 0.03288
66 0.954 0.092 0.046
67 0.9367 0.1265 0.06325
68 0.9351 0.1298 0.06489
69 0.9521 0.09585 0.04793
70 0.931 0.1379 0.06897
71 0.9066 0.1867 0.09336
72 0.9007 0.1986 0.09931
73 0.8594 0.2813 0.1406
74 0.821 0.358 0.179
75 0.8396 0.3209 0.1604
76 0.7787 0.4426 0.2213
77 0.73 0.5399 0.27
78 0.7964 0.4071 0.2036
79 0.7801 0.4398 0.2199
80 0.7714 0.4572 0.2286
81 0.7307 0.5386 0.2693
82 0.6276 0.7447 0.3724
83 0.5073 0.9854 0.4927
84 0.4317 0.8635 0.5683
85 0.3746 0.7493 0.6254
86 0.238 0.476 0.762


Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level2 0.02564NOK
5% type I error level100.128205NOK
10% type I error level230.294872NOK


Ramsey RESET F-Test for powers (2 and 3) of fitted values
> reset_test_fitted
	RESET test
data:  mylm
RESET = 6.8132, df1 = 2, df2 = 87, p-value = 0.001783
Ramsey RESET F-Test for powers (2 and 3) of regressors
> reset_test_regressors
	RESET test
data:  mylm
RESET = 1.055, df1 = 10, df2 = 79, p-value = 0.4067
Ramsey RESET F-Test for powers (2 and 3) of principal components
> reset_test_principal_components
	RESET test
data:  mylm
RESET = 0.35495, df1 = 2, df2 = 87, p-value = 0.7022


Variance Inflation Factors (Multicollinearity)
> vif
      V1       V2       V3       V4        t 
1.017552 1.054518 1.081245 1.082508 1.050060