Multiple Linear Regression - Estimated Regression Equation
ITHSUM[t] = + 13.2072 -0.0169155IK1[t] + 0.720896IK2[t] -0.0543074IK3[t] -0.463071IK4[t] + 0.19166KVDD1[t] -0.0978236KVDD2[t] + 0.270208KVDD3[t] -0.185305KVDD4[t] -0.460079EP1[t] + 0.575924EP2[t] -0.460701EP3[t] + 0.262505EP4[t] -0.203569EC1[t] + 0.499368EC2[t] + 0.156823EC3[t] + 0.0576426EC4[t] + e[t]


Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STAT
H0: parameter = 0		2-tail p-value1-tail p-value
(Intercept)+13.21 2.964+4.4560e+00 1.952e-05 9.758e-06
IK1-0.01692 0.4504-3.7560e-02 0.9701 0.4851
IK2+0.7209 0.4297+1.6780e+00 0.09612 0.04806
IK3-0.05431 0.4271-1.2720e-01 0.899 0.4495
IK4-0.4631 0.3948-1.1730e+00 0.2433 0.1216
KVDD1+0.1917 0.3327+5.7620e-01 0.5656 0.2828
KVDD2-0.09782 0.2461-3.9750e-01 0.6917 0.3459
KVDD3+0.2702 0.2522+1.0710e+00 0.2862 0.1431
KVDD4-0.1853 0.2578-7.1870e-01 0.4738 0.2369
EP1-0.4601 0.439-1.0480e+00 0.2968 0.1484
EP2+0.5759 0.3906+1.4740e+00 0.1431 0.07156
EP3-0.4607 0.2302-2.0010e+00 0.0477 0.02385
EP4+0.2625 0.2037+1.2890e+00 0.2001 0.1
EC1-0.2036 0.2238-9.0940e-01 0.365 0.1825
EC2+0.4994 0.2023+2.4690e+00 0.01503 0.007515
EC3+0.1568 0.3356+4.6730e-01 0.6412 0.3206
EC4+0.05764 0.2595+2.2210e-01 0.8246 0.4123


Multiple Linear Regression - Regression Statistics
Multiple R 0.3997
R-squared 0.1597
Adjusted R-squared 0.04283
F-TEST (value) 1.366
F-TEST (DF numerator)16
F-TEST (DF denominator)115
p-value 0.1709
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation 2.431
Sum Squared Residuals 679.6


Menu of Residual Diagnostics
DescriptionLink
HistogramCompute
Central TendencyCompute
QQ PlotCompute
Kernel Density PlotCompute
Skewness/Kurtosis TestCompute
Skewness-Kurtosis PlotCompute
Harrell-Davis PlotCompute
Bootstrap Plot -- Central TendencyCompute
Blocked Bootstrap Plot -- Central TendencyCompute
(Partial) Autocorrelation PlotCompute
Spectral AnalysisCompute
Tukey lambda PPCC PlotCompute
Box-Cox Normality PlotCompute
Summary StatisticsCompute


Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolation
Forecast		Residuals
Prediction Error
1 14 15.92-1.922
2 17 16.66 0.3396
3 17 15.94 1.065
4 15 16.29-1.286
5 20 18.24 1.762
6 15 17.02-2.019
7 15 15.26-0.2605
8 19 16.38 2.617
9 20 17.37 2.633
10 18 19.5-1.5
11 15 15.32-0.3197
12 14 16.85-2.855
13 16 16.91-0.905
14 19 17.35 1.653
15 19 16.37 2.629
16 16 16.41-0.4061
17 18 18.02-0.024
18 17 15.2 1.803
19 19 16.47 2.528
20 17 17.22-0.2153
21 19 16.22 2.784
22 20 15.46 4.535
23 5 14.66-9.655
24 19 17.26 1.743
25 16 17.42-1.417
26 15 16.01-1.009
27 16 16.22-0.223
28 18 15.87 2.13
29 16 16.92-0.9161
30 15 15.6-0.5992
31 17 14.96 2.037
32 20 17.72 2.284
33 19 15.78 3.223
34 7 14.69-7.689
35 13 15.52-2.516
36 16 16.2-0.1969
37 18 16.87 1.134
38 18 15.97 2.025
39 16 17.14-1.14
40 17 17.2-0.1988
41 19 16.08 2.92
42 16 14.9 1.101
43 13 15.56-2.559
44 12 17.08-5.077
45 17 16.65 0.3469
46 17 15.41 1.591
47 16 17.11-1.108
48 16 15.89 0.1111
49 14 14.63-0.6327
50 13 14.62-1.623
51 16 14.59 1.41
52 14 16.23-2.232
53 20 17.02 2.981
54 13 15.91-2.907
55 18 17.32 0.6772
56 14 16.84-2.835
57 19 14.77 4.233
58 18 16.43 1.57
59 14 15.68-1.677
60 18 18.25-0.2461
61 19 15.98 3.021
62 15 16.46-1.464
63 14 17.51-3.508
64 19 17.95 1.051
65 13 17.13-4.129
66 19 18.12 0.8791
67 18 17.04 0.9608
68 20 16.64 3.36
69 15 16.16-1.16
70 15 16.51-1.507
71 15 16.25-1.246
72 20 17.35 2.648
73 15 16.32-1.318
74 19 18.07 0.9327
75 18 17.43 0.5658
76 18 15.63 2.365
77 15 16.72-1.72
78 20 16.85 3.155
79 17 15.68 1.315
80 12 15.06-3.061
81 18 16.29 1.712
82 19 18.58 0.4157
83 20 16.64 3.357
84 17 17.22-0.2203
85 16 16.02-0.01731
86 18 17.2 0.8031
87 14 16.78-2.779
88 15 14.86 0.1375
89 12 14.97-2.973
90 17 14.83 2.17
91 18 17.39 0.6078
92 17 16.22 0.7825
93 17 18.84-1.843
94 20 17.09 2.906
95 16 17.12-1.122
96 14 16.36-2.355
97 15 15 0.0006962
98 18 17.65 0.3482
99 20 17.33 2.675
100 17 17.22-0.2162
101 17 17.78-0.7793
102 17 17.08-0.07971
103 15 16.42-1.419
104 18 17.63 0.3665
105 17 17.76-0.7565
106 20 17.76 2.24
107 15 16.68-1.678
108 16 17.39-1.392
109 18 16.82 1.181
110 15 17.06-2.063
111 20 17.08 2.917
112 14 17.84-3.838
113 15 15.61-0.6148
114 17 17.78-0.7819
115 18 15.61 2.389
116 20 16.27 3.732
117 17 17.44-0.4368
118 18 16.75 1.252
119 15 15.54-0.5443
120 16 17.41-1.414
121 15 17.86-2.859
122 18 15.7 2.303
123 16 15.36 0.6368
124 12 16.21-4.209
125 19 15.34 3.661
126 15 16.65-1.651
127 19 17.29 1.713
128 18 16.55 1.446
129 16 14.84 1.158
130 16 16.88-0.8831
131 16 16.29-0.2938
132 14 16.53-2.53


Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
20 0.2829 0.5658 0.7171
21 0.3154 0.6307 0.6846
22 0.5372 0.9255 0.4628
23 0.9728 0.05442 0.02721
24 0.955 0.09003 0.04501
25 0.9349 0.1302 0.06508
26 0.8993 0.2015 0.1007
27 0.8676 0.2648 0.1324
28 0.8207 0.3587 0.1793
29 0.8327 0.3345 0.1673
30 0.7781 0.4437 0.2219
31 0.7265 0.547 0.2735
32 0.7727 0.4546 0.2273
33 0.7772 0.4457 0.2228
34 0.9797 0.04055 0.02028
35 0.9755 0.04904 0.02452
36 0.9816 0.03685 0.01842
37 0.9842 0.0316 0.0158
38 0.9872 0.02567 0.01283
39 0.9823 0.03534 0.01767
40 0.9755 0.04899 0.02449
41 0.9756 0.04873 0.02436
42 0.9655 0.06902 0.03451
43 0.9718 0.05648 0.02824
44 0.9918 0.01633 0.008164
45 0.9881 0.02376 0.01188
46 0.9846 0.03075 0.01538
47 0.9862 0.02769 0.01384
48 0.9815 0.03693 0.01847
49 0.9746 0.05077 0.02539
50 0.9695 0.06108 0.03054
51 0.9621 0.07588 0.03794
52 0.9587 0.0826 0.0413
53 0.9583 0.08347 0.04174
54 0.9612 0.0775 0.03875
55 0.9491 0.1018 0.05088
56 0.9581 0.08387 0.04193
57 0.9794 0.04114 0.02057
58 0.9756 0.04879 0.0244
59 0.9699 0.0601 0.03005
60 0.9618 0.07649 0.03824
61 0.9643 0.07135 0.03568
62 0.9555 0.089 0.0445
63 0.9677 0.06463 0.03232
64 0.9625 0.07501 0.0375
65 0.9814 0.03715 0.01858
66 0.975 0.05008 0.02504
67 0.9674 0.06514 0.03257
68 0.9757 0.04865 0.02433
69 0.9702 0.05953 0.02976
70 0.9674 0.06529 0.03264
71 0.9582 0.08359 0.04179
72 0.9634 0.0731 0.03655
73 0.9578 0.08447 0.04224
74 0.948 0.104 0.05199
75 0.9349 0.1301 0.06506
76 0.9374 0.1252 0.06262
77 0.9265 0.1471 0.07353
78 0.9494 0.1012 0.05062
79 0.9423 0.1154 0.05769
80 0.9698 0.06043 0.03022
81 0.9622 0.07565 0.03783
82 0.9544 0.09121 0.0456
83 0.9619 0.07623 0.03812
84 0.9491 0.1017 0.05086
85 0.9353 0.1295 0.06473
86 0.913 0.1741 0.08703
87 0.9111 0.1777 0.08886
88 0.8959 0.2083 0.1041
89 0.9207 0.1585 0.07926
90 0.9154 0.1693 0.08464
91 0.8872 0.2256 0.1128
92 0.852 0.2959 0.148
93 0.8202 0.3597 0.1798
94 0.8018 0.3964 0.1982
95 0.7654 0.4692 0.2346
96 0.7895 0.421 0.2105
97 0.7968 0.4064 0.2032
98 0.7484 0.5033 0.2516
99 0.7622 0.4757 0.2378
100 0.6948 0.6105 0.3052
101 0.6186 0.7628 0.3814
102 0.5361 0.9279 0.4639
103 0.4694 0.9387 0.5306
104 0.3845 0.7689 0.6155
105 0.2994 0.5988 0.7006
106 0.466 0.932 0.534
107 0.3765 0.7531 0.6235
108 0.3257 0.6513 0.6743
109 0.2634 0.5267 0.7366
110 0.4725 0.9449 0.5275
111 0.7653 0.4694 0.2347
112 0.629 0.742 0.371


Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level0 0OK
5% type I error level170.182796NOK
10% type I error level450.483871NOK


Ramsey RESET F-Test for powers (2 and 3) of fitted values
> reset_test_fitted
	RESET test
data:  mylm
RESET = 1.6116, df1 = 2, df2 = 113, p-value = 0.2041
Ramsey RESET F-Test for powers (2 and 3) of regressors
> reset_test_regressors
	RESET test
data:  mylm
RESET = 0.71919, df1 = 32, df2 = 83, p-value = 0.8515
Ramsey RESET F-Test for powers (2 and 3) of principal components
> reset_test_principal_components
	RESET test
data:  mylm
RESET = 0.044604, df1 = 2, df2 = 113, p-value = 0.9564


Variance Inflation Factors (Multicollinearity)
> vif
     IK1      IK2      IK3      IK4    KVDD1    KVDD2    KVDD3    KVDD4 
1.615338 1.507243 1.663850 1.421215 1.405451 1.222929 1.240410 1.221858 
     EP1      EP2      EP3      EP4      EC1      EC2      EC3      EC4 
2.641173 2.471580 1.094537 1.461922 1.802779 1.571429 1.345985 1.260384