Multiple Linear Regression - Estimated Regression Equation
IKSUM[t] = + 15.2548 + 0.296302ITH1[t] + 0.433327ITH2[t] -0.327263ITH3[t] + 0.0632033ITH4[t] + e[t]


Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STAT
H0: parameter = 0		2-tail p-value1-tail p-value
(Intercept)+15.26 0.9873+1.5450e+01 4.037e-33 2.018e-33
ITH1+0.2963 0.2161+1.3710e+00 0.1724 0.08618
ITH2+0.4333 0.2479+1.7480e+00 0.08247 0.04123
ITH3-0.3273 0.2043-1.6020e+00 0.1112 0.0556
ITH4+0.0632 0.1688+3.7450e-01 0.7086 0.3543


Multiple Linear Regression - Regression Statistics
Multiple R 0.224
R-squared 0.05018
Adjusted R-squared 0.02551
F-TEST (value) 2.034
F-TEST (DF numerator)4
F-TEST (DF denominator)154
p-value 0.09234
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation 1.753
Sum Squared Residuals 473


Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolation
Forecast		Residuals
Prediction Error
1 18 17.15 0.8519
2 19 17.52 1.481
3 18 17.41 0.5866
4 15 17.41-2.413
5 19 17.44 1.556
6 19 17.58 1.417
7 19 17.68 1.323
8 18 17.66 0.3429
9 20 17.68 2.323
10 14 17.52-3.519
11 18 17.58 0.4173
12 19 17.85 1.153
13 16 17.44-1.444
14 18 16.76 1.242
15 18 17.58 0.4173
16 17 17.74-0.7407
17 19 17.37 1.629
18 19 17.12 1.883
19 17 17.81-0.8132
20 18 17.91 0.09004
21 16 17.91-1.91
22 20 17.72 2.28
23 13 17.05-4.054
24 19 17.22 1.777
25 15 17.55-2.55
26 17 17.91-0.91
27 17 17.78-0.7835
28 17 17.91-0.91
29 19 17.58 1.417
30 18 15.78 2.216
31 19 17.91 1.09
32 20 17.49 2.513
33 16 17.05-1.054
34 17 17.12-0.1171
35 16 17.85-1.847
36 16 16.73-0.7267
37 16 17.05-1.054
38 16 17.41-1.413
39 17 17.58-0.5827
40 18 17.52 0.4805
41 16 16.51-0.5132
42 16 16.71-0.7148
43 16 17.88-1.878
44 19 17.85 1.153
45 16 17.46-1.456
46 17 17.12-0.1171
47 19 18.17 0.826
48 17 17.52-0.5195
49 17 17.12-0.1171
50 15 17.91-2.91
51 16 17.69-1.688
52 16 17.12-1.117
53 16 17.08-1.085
54 17 17.25-0.2548
55 18 17.55 0.4496
56 18 17.41 0.5866
57 18 17.55 0.4496
58 19 17.49 1.513
59 14 17.12-3.117
60 13 17.01-4.011
61 18 17.12 0.8829
62 16 16.46-0.4613
63 15 17.49-2.487
64 18 17.38 0.6188
65 18 17.58 0.4173
66 16 16.65-0.6516
67 19 17.08 1.915
68 17 17.09-0.08616
69 17 17.01-0.01106
70 19 17.52 1.481
71 19 17.61 1.386
72 20 17.01 2.989
73 19 18.24 0.7628
74 18 17.52 0.4805
75 16 17.68-1.677
76 16 17.38-1.381
77 15 17.41-2.413
78 20 17.52 2.481
79 16 16.83-0.8314
80 16 17.15-1.149
81 20 17.85 2.153
82 20 17.58 2.417
83 18 17.29 0.713
84 15 17.05-2.054
85 14 17.05-3.054
86 16 17.58-1.583
87 14 17.05-3.054
88 18 17.52 0.4805
89 20 17.85 2.153
90 20 17.09 2.914
91 18 17.05 0.9461
92 20 17.58 2.417
93 14 17.39-3.393
94 20 17.41 2.588
95 17 17.09-0.08616
96 20 17.52 2.481
97 14 17.58-3.583
98 20 16.79 3.21
99 19 17.05 1.946
100 18 17.12 0.8829
101 17 17.46-0.4563
102 17 17.85-0.8468
103 19 17.77 1.228
104 15 16.82-1.821
105 18 17.02 0.9783
106 15 16.79-1.79
107 16 17.38-1.381
108 16 17.85-1.847
109 20 17.41 2.587
110 18 16.79 1.21
111 20 17.58 2.417
112 18 17.35 0.6498
113 17 17.38-0.3812
114 19 17.44 1.556
115 18 17.85 0.1532
116 19 17.58 1.417
117 17 18.17-1.174
118 18 18.17-0.174
119 17 17.55-0.5504
120 16 17.41-1.413
121 19 16.82 2.179
122 18 17.78 0.2165
123 17 17.09-0.08616
124 18 17.55 0.4496
125 16 17.58-1.583
126 20 17.05 2.946
127 14 17.12-3.117
128 17 17.05-0.05392
129 13 16.85-3.853
130 13 16.75-3.746
131 17 17.05-0.05392
132 18 17.09 0.9138
133 16 17.58-1.583
134 19 16.99 2.009
135 17 17.29-0.287
136 16 17.41-1.413
137 17 17.09-0.08616
138 17 17.58-0.5827
139 17 16.65 0.3472
140 20 17.09 2.914
141 14 17.05-3.054
142 20 17.35 2.65
143 19 16.59 2.412
144 16 16.82-0.8208
145 19 17.61 1.386
146 17 17.55-0.5504
147 19 17.64 1.355
148 20 17.02 2.978
149 19 17.52 1.481
150 19 17.85 1.153
151 16 17.29-1.287
152 18 17.41 0.5866
153 16 17.52-1.519
154 17 17.09-0.08616
155 18 17.52 0.4805
156 16 16.96-0.9598
157 17 17.12-0.1171
158 15 16.73-1.727
159 18 16.13 1.866


Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
8 0.3598 0.7196 0.6402
9 0.2595 0.5189 0.7405
10 0.7041 0.5917 0.2959
11 0.5882 0.8236 0.4118
12 0.5551 0.8897 0.4449
13 0.6568 0.6864 0.3432
14 0.6817 0.6366 0.3183
15 0.597 0.806 0.403
16 0.5501 0.8999 0.4499
17 0.5355 0.929 0.4645
18 0.5072 0.9855 0.4928
19 0.457 0.914 0.543
20 0.3787 0.7574 0.6213
21 0.3739 0.7478 0.6261
22 0.3906 0.7811 0.6094
23 0.7653 0.4694 0.2347
24 0.7655 0.469 0.2345
25 0.8032 0.3936 0.1968
26 0.7623 0.4755 0.2377
27 0.7209 0.5582 0.2791
28 0.6716 0.6568 0.3284
29 0.655 0.6899 0.345
30 0.6226 0.7548 0.3774
31 0.5952 0.8097 0.4048
32 0.6449 0.7103 0.3551
33 0.6303 0.7395 0.3697
34 0.5769 0.8462 0.4231
35 0.5774 0.8453 0.4227
36 0.5434 0.9133 0.4566
37 0.516 0.9681 0.484
38 0.5026 0.9947 0.4974
39 0.4503 0.9007 0.5497
40 0.4021 0.8043 0.5979
41 0.3703 0.7406 0.6297
42 0.3319 0.6637 0.6681
43 0.3293 0.6587 0.6707
44 0.3055 0.6109 0.6945
45 0.2919 0.5838 0.7081
46 0.2482 0.4964 0.7518
47 0.2183 0.4365 0.7817
48 0.1839 0.3678 0.8161
49 0.1513 0.3026 0.8487
50 0.204 0.4079 0.796
51 0.2003 0.4007 0.7997
52 0.1792 0.3585 0.8208
53 0.1572 0.3145 0.8428
54 0.1294 0.2589 0.8706
55 0.109 0.2179 0.891
56 0.08928 0.1786 0.9107
57 0.07364 0.1473 0.9264
58 0.07267 0.1453 0.9273
59 0.1173 0.2346 0.8827
60 0.2488 0.4975 0.7512
61 0.2235 0.447 0.7765
62 0.1905 0.381 0.8095
63 0.2212 0.4424 0.7788
64 0.1922 0.3844 0.8078
65 0.1645 0.329 0.8355
66 0.1396 0.2792 0.8604
67 0.1474 0.2948 0.8526
68 0.1218 0.2436 0.8782
69 0.09949 0.199 0.9005
70 0.09542 0.1908 0.9046
71 0.08933 0.1787 0.9107
72 0.1326 0.2652 0.8674
73 0.1131 0.2262 0.8869
74 0.09393 0.1879 0.9061
75 0.09179 0.1836 0.9082
76 0.0844 0.1688 0.9156
77 0.1003 0.2005 0.8997
78 0.1232 0.2464 0.8768
79 0.106 0.212 0.894
80 0.09343 0.1869 0.9066
81 0.103 0.2059 0.897
82 0.1226 0.2453 0.8774
83 0.1044 0.2087 0.8956
84 0.1119 0.2237 0.8881
85 0.1619 0.3239 0.8381
86 0.1546 0.3092 0.8454
87 0.2167 0.4335 0.7833
88 0.187 0.374 0.813
89 0.2013 0.4026 0.7987
90 0.2665 0.5329 0.7335
91 0.2389 0.4778 0.7611
92 0.2779 0.5557 0.7221
93 0.4157 0.8314 0.5843
94 0.4542 0.9084 0.5458
95 0.4076 0.8153 0.5924
96 0.4516 0.9031 0.5484
97 0.5845 0.8311 0.4155
98 0.6924 0.6153 0.3076
99 0.696 0.6081 0.304
100 0.6656 0.6689 0.3344
101 0.6303 0.7395 0.3697
102 0.5967 0.8066 0.4033
103 0.5824 0.8351 0.4176
104 0.5836 0.8328 0.4164
105 0.5429 0.9142 0.4571
106 0.5454 0.9092 0.4546
107 0.5285 0.9431 0.4715
108 0.54 0.9201 0.46
109 0.6181 0.7639 0.3819
110 0.5923 0.8154 0.4077
111 0.6507 0.6986 0.3493
112 0.6076 0.7847 0.3924
113 0.5613 0.8774 0.4387
114 0.5703 0.8595 0.4297
115 0.518 0.964 0.482
116 0.5181 0.9638 0.4819
117 0.4838 0.9676 0.5162
118 0.4303 0.8607 0.5697
119 0.3882 0.7764 0.6118
120 0.3544 0.7087 0.6456
121 0.3921 0.7842 0.6079
122 0.3478 0.6956 0.6522
123 0.2994 0.5987 0.7006
124 0.2524 0.5047 0.7476
125 0.2307 0.4614 0.7693
126 0.294 0.588 0.706
127 0.373 0.7459 0.627
128 0.3187 0.6374 0.6813
129 0.4586 0.9173 0.5414
130 0.7568 0.4865 0.2432
131 0.7097 0.5806 0.2903
132 0.6731 0.6539 0.3269
133 0.6484 0.7032 0.3516
134 0.6416 0.7168 0.3584
135 0.5766 0.8468 0.4234
136 0.5881 0.8238 0.4119
137 0.5155 0.969 0.4845
138 0.4492 0.8984 0.5508
139 0.3751 0.7502 0.6249
140 0.5396 0.9208 0.4604
141 0.8067 0.3866 0.1933
142 0.8779 0.2441 0.1221
143 0.8694 0.2613 0.1306
144 0.8777 0.2446 0.1223
145 0.8231 0.3537 0.1769
146 0.8251 0.3498 0.1749
147 0.8571 0.2858 0.1429
148 0.8292 0.3417 0.1708
149 0.8202 0.3596 0.1798
150 0.7521 0.4959 0.2479
151 0.5932 0.8136 0.4068


Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level0 0OK
5% type I error level00OK
10% type I error level00OK


Ramsey RESET F-Test for powers (2 and 3) of fitted values
> reset_test_fitted
	RESET test
data:  mylm
RESET = 1.7912, df1 = 2, df2 = 152, p-value = 0.1703
Ramsey RESET F-Test for powers (2 and 3) of regressors
> reset_test_regressors
	RESET test
data:  mylm
RESET = 1.157, df1 = 8, df2 = 146, p-value = 0.3292
Ramsey RESET F-Test for powers (2 and 3) of principal components
> reset_test_principal_components
	RESET test
data:  mylm
RESET = 0.72981, df1 = 2, df2 = 152, p-value = 0.4837


Variance Inflation Factors (Multicollinearity)
> vif
    ITH1     ITH2     ITH3     ITH4 
1.698025 1.446255 1.616083 1.249129