Multiple Linear Regression - Estimated Regression Equation
ITHSUM[t] = + 10.0821 + 0.379265IK1[t] + 0.496624IK2[t] -0.17898IK3[t] -0.280877IK4[t] + e[t]


Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STAT
H0: parameter = 0		2-tail p-value1-tail p-value
(Intercept)+10.08 1.486+6.7850e+00 2.357e-10 1.178e-10
IK1+0.3793 0.2562+1.4800e+00 0.1409 0.07045
IK2+0.4966 0.2816+1.7630e+00 0.07982 0.03991
IK3-0.179 0.2735-6.5450e-01 0.5138 0.2569
IK4-0.2809 0.2603-1.0790e+00 0.2823 0.1412


Multiple Linear Regression - Regression Statistics
Multiple R 0.2026
R-squared 0.04104
Adjusted R-squared 0.01614
F-TEST (value) 1.648
F-TEST (DF numerator)4
F-TEST (DF denominator)154
p-value 0.1651
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation 1.887
Sum Squared Residuals 548.5


Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolation
Forecast		Residuals
Prediction Error
1 11 12.06-1.064
2 14 12.44 1.557
3 12 12.62-0.6221
4 12 11.37 0.6331
5 11 12.44-1.443
6 15 12.44 2.557
7 10 11.67-1.666
8 10 12.62-2.622
9 10 12.16-2.162
10 14 11.53 2.47
11 15 12.06 2.936
12 13 12.44 0.5569
13 11 11.75-0.7462
14 11 11.95-0.9465
15 15 12.06 2.936
16 11 12.13-1.125
17 11 11.67-0.6656
18 12 12.44-0.4431
19 8 11.68-3.685
20 14 12.06 1.936
21 14 11.75 2.254
22 11 12.16-1.162
23 11 11.83-0.8268
24 14 12.34 1.659
25 13 12.03 0.9729
26 14 12.24 1.757
27 12 12.24-0.2428
28 14 12.23 1.773
29 15 12.44 2.557
30 4 11.29-7.286
31 14 12.44 1.557
32 12 12.16-0.1622
33 11 11.75-0.7462
34 12 12.13-0.1254
35 13 11.75 1.254
36 12 12.52-0.5237
37 11 11.75-0.7462
38 12 11.75 0.2538
39 15 12.9 2.097
40 14 11.95 2.054
41 5 11.75-6.746
42 10 11.75-1.746
43 12 11.75 0.2538
44 13 12.44 0.5569
45 13 11.75 1.254
46 12 12.24-0.2428
47 12 12.44-0.4431
48 14 12.24 1.757
49 12 12.24-0.2428
50 14 12.03 1.973
51 9 12.3-3.304
52 12 11.75 0.2538
53 10 12.41-2.406
54 8 12.24-4.243
55 13 12.06 0.9362
56 12 12.06-0.06383
57 13 12.72 0.276
58 12 12.44-0.4431
59 12 12.21-0.206
60 10 11.03-1.034
61 12 12.06-0.06383
62 11 11.75-0.7462
63 12 12.03-0.02706
64 10 12.06-2.064
65 15 12.06 2.936
66 9 11.2-2.203
67 10 12.44-2.443
68 13 12.24 0.7572
69 10 12.9-2.903
70 14 12.44 1.557
71 14 11.78 2.217
72 10 12.16-2.162
73 13 12.44 0.5569
74 14 12.06 1.936
75 10 11.75-1.746
76 10 11.75-1.746
77 12 11.25 0.7504
78 14 12.16 1.838
79 11 12.52-1.524
80 14 11.75 2.254
81 13 12.16 0.8378
82 15 12.16 2.838
83 10 12.06-2.064
84 11 12.48-1.483
85 11 11.53-0.5304
86 15 11.75 3.254
87 11 11.55-0.5459
88 14 12.06 1.936
89 13 12.16 0.8378
90 13 12.16 0.8378
91 11 12.06-1.064
92 15 12.16 2.838
93 12 11.65 0.3522
94 9 12.16-3.162
95 13 12.24 0.7572
96 14 12.16 1.838
97 15 11.65 3.352
98 13 12.16 0.8378
99 11 12.44-1.443
100 12 11.96 0.03807
101 13 12.24 0.7572
102 13 12.24 0.7572
103 10 11.67-1.666
104 12 12.03-0.02706
105 9 11.95-2.946
106 13 11.25 1.75
107 10 11.75-1.746
108 13 11.75 1.254
109 12 12.16-0.1622
110 13 12.62 0.3779
111 15 12.16 2.838
112 11 12.72-1.724
113 10 12.24-2.243
114 11 11.67-0.6656
115 13 12.06 0.9362
116 15 12.44 2.557
117 12 12.02-0.02355
118 12 12.62-0.6221
119 13 12.24 0.7572
120 12 11.75 0.2538
121 12 12.44-0.4431
122 12 12.62-0.6221
123 13 12.24 0.7572
124 13 12.62 0.3779
125 15 11.75 3.254
126 11 12.16-1.162
127 12 11.53 0.4696
128 11 12.24-1.243
129 14 10.95 3.053
130 9 10.49-1.491
131 11 12.24-1.243
132 13 12.06 0.9362
133 15 11.75 3.254
134 10 12.44-2.443
135 10 11.68-1.685
136 12 12.52-0.5237
137 13 12.24 0.7572
138 15 12.9 2.097
139 12 12.24-0.2428
140 13 12.16 0.8378
141 11 11.65-0.6478
142 11 12.16-1.162
143 8 12.44-4.443
144 12 11.97 0.03456
145 14 12.44 1.557
146 13 12.24 0.7572
147 13 12.44 0.5569
148 9 12.16-3.162
149 14 11.67 2.334
150 13 12.44 0.5569
151 10 12.52-2.524
152 12 11.95 0.05353
153 14 12.2 1.797
154 13 12.24 0.7572
155 14 12.06 1.936
156 11 11.85-0.8481
157 12 12.24-0.2428
158 12 12.03-0.02706
159 12 12.72-0.724


Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
8 0.5995 0.801 0.4005
9 0.588 0.8239 0.412
10 0.4834 0.9668 0.5166
11 0.5127 0.9747 0.4873
12 0.3931 0.7863 0.6069
13 0.2908 0.5816 0.7092
14 0.2767 0.5535 0.7232
15 0.2581 0.5161 0.7419
16 0.1909 0.3818 0.8091
17 0.1594 0.3188 0.8406
18 0.1228 0.2457 0.8772
19 0.5477 0.9046 0.4523
20 0.5294 0.9413 0.4706
21 0.5961 0.8078 0.4039
22 0.5326 0.9349 0.4674
23 0.488 0.9761 0.512
24 0.646 0.7081 0.354
25 0.5829 0.8341 0.4171
26 0.5759 0.8482 0.4241
27 0.5112 0.9777 0.4888
28 0.4575 0.9151 0.5425
29 0.4772 0.9545 0.5228
30 0.8941 0.2119 0.1059
31 0.8727 0.2546 0.1273
32 0.8469 0.3062 0.1531
33 0.8116 0.3768 0.1884
34 0.7703 0.4595 0.2297
35 0.759 0.482 0.241
36 0.7731 0.4538 0.2269
37 0.7313 0.5374 0.2687
38 0.6887 0.6226 0.3113
39 0.6655 0.6689 0.3345
40 0.6626 0.6748 0.3374
41 0.9635 0.07306 0.03653
42 0.958 0.08404 0.04202
43 0.9479 0.1042 0.05212
44 0.9338 0.1324 0.0662
45 0.9309 0.1383 0.06914
46 0.9123 0.1755 0.08773
47 0.8968 0.2064 0.1032
48 0.8963 0.2074 0.1037
49 0.872 0.256 0.128
50 0.863 0.2739 0.137
51 0.8996 0.2008 0.1004
52 0.8803 0.2393 0.1197
53 0.9196 0.1608 0.08041
54 0.9688 0.06243 0.03122
55 0.9609 0.07816 0.03908
56 0.95 0.09992 0.04996
57 0.946 0.1081 0.05404
58 0.9338 0.1324 0.06621
59 0.9171 0.1658 0.08291
60 0.9042 0.1917 0.09584
61 0.8828 0.2344 0.1172
62 0.8617 0.2766 0.1383
63 0.8357 0.3287 0.1643
64 0.8464 0.3073 0.1536
65 0.8812 0.2377 0.1188
66 0.8938 0.2123 0.1062
67 0.9126 0.1748 0.0874
68 0.8974 0.2053 0.1026
69 0.9315 0.1369 0.06846
70 0.9271 0.1459 0.07294
71 0.9374 0.1252 0.0626
72 0.9405 0.119 0.05949
73 0.9271 0.1457 0.07287
74 0.926 0.1479 0.07397
75 0.924 0.1519 0.07596
76 0.9227 0.1545 0.07726
77 0.9131 0.1738 0.08691
78 0.9177 0.1647 0.08235
79 0.9136 0.1728 0.08639
80 0.9246 0.1508 0.07542
81 0.912 0.1761 0.08804
82 0.9369 0.1262 0.06312
83 0.9425 0.1149 0.05746
84 0.9436 0.1127 0.05635
85 0.9318 0.1363 0.06816
86 0.9583 0.08335 0.04168
87 0.9531 0.09371 0.04685
88 0.9555 0.089 0.0445
89 0.9467 0.1065 0.05325
90 0.9367 0.1265 0.06326
91 0.926 0.1479 0.07396
92 0.9507 0.0987 0.04935
93 0.9374 0.1252 0.06259
94 0.9598 0.0805 0.04025
95 0.9501 0.09971 0.04985
96 0.9528 0.09449 0.04724
97 0.9737 0.05251 0.02625
98 0.9681 0.06378 0.03189
99 0.9637 0.07262 0.03631
100 0.9537 0.09269 0.04634
101 0.9426 0.1147 0.05737
102 0.9296 0.1407 0.07036
103 0.9286 0.1428 0.07142
104 0.9099 0.1802 0.09011
105 0.9433 0.1135 0.05673
106 0.9368 0.1263 0.06316
107 0.942 0.1159 0.05796
108 0.931 0.138 0.06899
109 0.9123 0.1754 0.08771
110 0.8904 0.2191 0.1096
111 0.9259 0.1483 0.07413
112 0.9217 0.1565 0.07825
113 0.9317 0.1365 0.06827
114 0.9179 0.1641 0.08207
115 0.9078 0.1844 0.09218
116 0.9378 0.1244 0.06218
117 0.9333 0.1334 0.06671
118 0.9179 0.1642 0.08212
119 0.8993 0.2014 0.1007
120 0.8731 0.2538 0.1269
121 0.8416 0.3167 0.1584
122 0.8132 0.3735 0.1868
123 0.7799 0.4403 0.2201
124 0.7343 0.5315 0.2657
125 0.8019 0.3963 0.1981
126 0.771 0.4581 0.229
127 0.7247 0.5505 0.2753
128 0.6939 0.6122 0.3061
129 0.6911 0.6179 0.3089
130 0.7147 0.5706 0.2853
131 0.6839 0.6322 0.3161
132 0.6576 0.6849 0.3424
133 0.7189 0.5622 0.2811
134 0.7389 0.5221 0.2611
135 0.7029 0.5941 0.2971
136 0.6396 0.7207 0.3604
137 0.5785 0.843 0.4215
138 0.6575 0.685 0.3425
139 0.5834 0.8332 0.4166
140 0.5167 0.9666 0.4833
141 0.4786 0.9572 0.5214
142 0.4258 0.8516 0.5742
143 0.7417 0.5166 0.2583
144 0.6615 0.677 0.3385
145 0.6585 0.6831 0.3415
146 0.5722 0.8557 0.4278
147 0.4997 0.9993 0.5003
148 0.9625 0.07498 0.03749
149 0.9236 0.1527 0.07636
150 0.8424 0.3152 0.1576
151 0.8557 0.2887 0.1443


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 level170.118056NOK


Ramsey RESET F-Test for powers (2 and 3) of fitted values
> reset_test_fitted
	RESET test
data:  mylm
RESET = 0.82485, df1 = 2, df2 = 152, p-value = 0.4403
Ramsey RESET F-Test for powers (2 and 3) of regressors
> reset_test_regressors
	RESET test
data:  mylm
RESET = 1.0142, df1 = 8, df2 = 146, p-value = 0.4279
Ramsey RESET F-Test for powers (2 and 3) of principal components
> reset_test_principal_components
	RESET test
data:  mylm
RESET = 0.56174, df1 = 2, df2 = 152, p-value = 0.5714


Variance Inflation Factors (Multicollinearity)
> vif
     IK1      IK2      IK3      IK4 
1.258859 1.315234 1.390740 1.139902