Multiple Linear Regression - Estimated Regression Equation
Total_Ecological_Footprint[t] = + 2.18708 -0.00107868`Population_(millions)`[t] + 15.1658Urban_Land[t] + 0.0118292Total_Biocapacity[t] + e[t]


Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STAT
H0: parameter = 0		2-tail p-value1-tail p-value
(Intercept)+2.187 0.2683+8.1500e+00 7.776e-14 3.888e-14
`Population_(millions)`-0.001079 0.001131-9.5390e-01 0.3415 0.1708
Urban_Land+15.17 3.014+5.0330e+00 1.229e-06 6.147e-07
Total_Biocapacity+0.01183 0.01362+8.6840e-01 0.3864 0.1932


Multiple Linear Regression - Regression Statistics
Multiple R 0.3691
R-squared 0.1362
Adjusted R-squared 0.1209
F-TEST (value) 8.884
F-TEST (DF numerator)3
F-TEST (DF denominator)169
p-value 1.683e-05
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation 2.163
Sum Squared Residuals 790.7


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 0.79 2.767-1.977
2 2.21 3.108-0.8976
3 2.12 2.608-0.4875
4 0.93 2.801-1.871
5 3.14 3.741-0.6012
6 2.23 3.256-1.026
7 9.31 4.481 4.829
8 6.06 4.489 1.571
9 2.31 3.097-0.787
10 6.84 2.906 3.934
11 7.49 3.709 3.781
12 0.72 3.086-2.366
13 4.48 2.796 1.684
14 5.09 3.585 1.505
15 7.44 6.284 1.156
16 1.41 2.793-1.383
17 4.84 6.04-1.2
18 2.96 3.284-0.3236
19 3.12 2.506 0.6145
20 3.83 2.529 1.301
21 3.11 3.445-0.3351
22 4.06 2.676 1.384
23 3.32 4.185-0.8646
24 1.21 2.939-1.729
25 0.8 2.635-1.835
26 1.17 2.942-1.772
27 8.17 3.4 4.77
28 5.65 2.191 3.459
29 1.24 2.882-1.642
30 1.46 2.956-1.496
31 4.36 4.486-0.1261
32 3.38 2.499 0.8807
33 1.87 3.543-1.673
34 1.03 2.19-1.16
35 1.29 2.766-1.476
36 0.82 2.911-2.091
37 2.84 3.717-0.8766
38 1.27 3.4-2.13
39 3.92 3.126 0.7945
40 1.95 2.639-0.6889
41 4.21 2.948 1.262
42 5.19 4.176 1.014
43 5.51 6.029-0.519
44 2.57 2.199 0.3708
45 1.53 2.941-1.411
46 2.17 3.106-0.9363
47 2.15 4.382-2.232
48 2.07 2.946-0.8758
49 3.97 2.542 1.428
50 0.42 2.499-2.079
51 1.02 3.005-1.985
52 2.9 2.821 0.0792
53 5.14 5.34-0.1997
54 2.34 3.504-1.164
55 4.73 2.203 2.527
56 2.02 2.952-0.9315
57 1.03 2.65-1.62
58 1.58 2.803-1.223
59 5.3 5.764-0.4644
60 1.97 3.237-1.267
61 4.38 3.104 1.276
62 3.23 2.192 1.038
63 1.89 3.244-1.354
64 1.41 2.806-1.396
65 1.53 3.131-1.601
66 3.07 3.884-0.8138
67 0.61 2.634-2.024
68 1.68 3.109-1.429
69 2.92 4.174-1.254
70 1.16 1.617-0.4567
71 1.58 2.846-1.266
72 2.79 3.48-0.6902
73 1.88 2.762-0.8818
74 5.57 4.198 1.372
75 6.22 3.396 2.824
76 4.61 3.044 1.566
77 1.89 2.947-1.057
78 5.02 3.575 1.445
79 2.1 3.244-1.144
80 5.55 2.665 2.885
81 1.03 2.753-1.723
82 1.17 3.077-1.907
83 5.69 3.052 2.638
84 8.13 4.465 3.665
85 1.91 3.41-1.5
86 1.22 3.867-2.647
87 6.29 4.269 2.021
88 3.84 3.096 0.7441
89 1.66 2.346-0.6858
90 1.21 2.668-1.458
91 3.69 2.492 1.198
92 5.83 4.526 1.304
93 15.82 4.33 11.49
94 3.26 2.506 0.754
95 0.99 3.104-2.114
96 0.81 2.936-2.126
97 3.71 3.246 0.4643
98 1.53 3.1-1.57
99 2.08 2.798-0.7179
100 2.54 2.843-0.3026
101 3.46 2.194 1.266
102 2.89 2.83 0.05996
103 1.78 2.648-0.8677
104 6.08 3.128 2.952
105 3.78 2.376 1.404
106 1.68 2.615-0.9354
107 0.87 2.943-2.073
108 1.43 3.82-2.39
109 2.48 2.569-0.08934
110 0.98 3.833-2.853
111 5.28 4.761 0.5189
112 3.58 2.278 1.302
113 5.6 4.274 1.326
114 1.39 2.966-1.576
115 1.56 2.638-1.078
116 1.16 2.772-1.612
117 7.52 5.088 2.432
118 0.79 2.453-1.663
119 2.79 2.521 0.2689
120 1.91 4.197-2.287
121 4.16 4.428-0.2675
122 2.28 3.263-0.9833
123 1.1 2.847-1.747
124 4.44 3.535 0.9046
125 3.88 2.952 0.9282
126 10.8 3.109 7.691
127 3.65 2.188 1.462
128 2.71 4.011-1.301
129 5.69 2.568 3.122
130 0.87 2.939-2.069
131 4.94 2.194 2.746
132 2.45 2.191 0.2591
133 2.77 2.21 0.5603
134 1.49 2.197-0.7072
135 5.61 2.769 2.841
136 1.21 2.488-1.278
137 2.7 2.798-0.0982
138 1.24 2.954-1.714
139 7.97 2.637 5.333
140 4.06 3.578 0.4818
141 5.81 2.819 2.991
142 1.29 5.726-4.436
143 1.24 3.101-1.861
144 3.31 2.751 0.5592
145 3.67 2.758 0.9119
146 1.32 2.928-1.608
147 4.25 4.608-0.3581
148 2.01 3.106-1.096
149 7.25 5.942 1.308
150 5.79 4.014 1.776
151 1.51 2.929-1.419
152 0.91 3.398-2.488
153 1.32 3.058-1.738
154 2.66 3.191-0.5313
155 0.48 2.814-2.334
156 1.13 2.49-1.359
157 2.7 2.204 0.4955
158 7.92 2.204 5.716
159 2.34 2.793-0.453
160 3.33 2.732 0.5981
161 5.47 3.579 1.891
162 1.24 2.761-1.521
163 2.84 3.226-0.3864
164 4.94 4.865 0.07544
165 7.93 2.184 5.746
166 8.22 3.254 4.966
167 2.91 4.884-1.974
168 2.32 3.38-1.06
169 3.57 2.794 0.7757
170 1.65 3.618-1.968
171 1.03 2.774-1.744
172 0.99 2.805-1.815
173 1.37 2.483-1.113


Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
7 0.1717 0.3433 0.8283
8 0.1208 0.2417 0.8792
9 0.05527 0.1105 0.9447
10 0.06327 0.1265 0.9367
11 0.2725 0.545 0.7275
12 0.3081 0.6163 0.6919
13 0.3143 0.6285 0.6857
14 0.234 0.4679 0.766
15 0.1804 0.3609 0.8196
16 0.1449 0.2898 0.8551
17 0.2493 0.4987 0.7507
18 0.3855 0.7711 0.6145
19 0.3155 0.6311 0.6845
20 0.2601 0.5202 0.7399
21 0.2233 0.4466 0.7767
22 0.183 0.3661 0.8169
23 0.1568 0.3135 0.8432
24 0.1413 0.2827 0.8587
25 0.1258 0.2517 0.8742
26 0.1113 0.2226 0.8887
27 0.1337 0.2673 0.8663
28 0.2357 0.4713 0.7643
29 0.2886 0.5772 0.7114
30 0.2628 0.5256 0.7372
31 0.2163 0.4326 0.7837
32 0.2714 0.5428 0.7286
33 0.2591 0.5182 0.7409
34 0.2184 0.4367 0.7816
35 0.2421 0.4842 0.7579
36 0.2374 0.4749 0.7626
37 0.199 0.3979 0.801
38 0.1902 0.3804 0.8098
39 0.1626 0.3253 0.8374
40 0.1315 0.2629 0.8685
41 0.125 0.2499 0.875
42 0.1057 0.2114 0.8943
43 0.0876 0.1752 0.9124
44 0.07091 0.1418 0.9291
45 0.05825 0.1165 0.9417
46 0.04598 0.09196 0.954
47 0.04387 0.08773 0.9561
48 0.03355 0.06711 0.9664
49 0.02864 0.05728 0.9714
50 0.0265 0.053 0.9735
51 0.02341 0.04682 0.9766
52 0.01739 0.03478 0.9826
53 0.01263 0.02525 0.9874
54 0.0456 0.0912 0.9544
55 0.05482 0.1096 0.9452
56 0.04438 0.08875 0.9556
57 0.03897 0.07794 0.961
58 0.03202 0.06404 0.968
59 0.02471 0.04941 0.9753
60 0.02022 0.04044 0.9798
61 0.01732 0.03464 0.9827
62 0.01424 0.02849 0.9858
63 0.01172 0.02344 0.9883
64 0.009629 0.01926 0.9904
65 0.00823 0.01646 0.9918
66 0.006245 0.01249 0.9938
67 0.005873 0.01175 0.9941
68 0.004778 0.009556 0.9952
69 0.003769 0.007539 0.9962
70 0.002679 0.005358 0.9973
71 0.002104 0.004208 0.9979
72 0.001498 0.002997 0.9985
73 0.001074 0.002148 0.9989
74 0.0008992 0.001798 0.9991
75 0.001386 0.002771 0.9986
76 0.00123 0.002459 0.9988
77 0.0009053 0.001811 0.9991
78 0.0007546 0.001509 0.9992
79 0.0005608 0.001122 0.9994
80 0.0008822 0.001764 0.9991
81 0.0007601 0.00152 0.9992
82 0.0006919 0.001384 0.9993
83 0.0009177 0.001835 0.9991
84 0.001985 0.00397 0.998
85 0.001638 0.003277 0.9984
86 0.001975 0.00395 0.998
87 0.001924 0.003847 0.9981
88 0.001422 0.002844 0.9986
89 0.001016 0.002031 0.999
90 0.0008175 0.001635 0.9992
91 0.0006491 0.001298 0.9994
92 0.00051 0.00102 0.9995
93 0.424 0.848 0.576
94 0.387 0.774 0.613
95 0.3837 0.7673 0.6163
96 0.3809 0.7617 0.6191
97 0.3414 0.6829 0.6586
98 0.321 0.6421 0.679
99 0.2862 0.5725 0.7138
100 0.2506 0.5011 0.7494
101 0.2282 0.4563 0.7718
102 0.1965 0.393 0.8035
103 0.172 0.344 0.828
104 0.1952 0.3903 0.8048
105 0.1771 0.3542 0.8229
106 0.1554 0.3108 0.8446
107 0.1535 0.3071 0.8465
108 0.1577 0.3153 0.8423
109 0.1325 0.2651 0.8675
110 0.1476 0.2953 0.8524
111 0.1272 0.2544 0.8728
112 0.1114 0.2227 0.8886
113 0.1009 0.2019 0.8991
114 0.09158 0.1832 0.9084
115 0.07921 0.1584 0.9208
116 0.07904 0.1581 0.921
117 0.09974 0.1995 0.9003
118 0.1166 0.2332 0.8834
119 0.09578 0.1916 0.9042
120 0.09101 0.182 0.909
121 0.0744 0.1488 0.9256
122 0.06225 0.1245 0.9378
123 0.06699 0.134 0.933
124 0.05487 0.1097 0.9451
125 0.0445 0.08901 0.9555
126 0.414 0.828 0.586
127 0.3819 0.7638 0.6181
128 0.3425 0.685 0.6575
129 0.3335 0.667 0.6665
130 0.3283 0.6565 0.6717
131 0.3432 0.6865 0.6568
132 0.2971 0.5943 0.7029
133 0.2546 0.5093 0.7454
134 0.2223 0.4445 0.7777
135 0.24 0.48 0.76
136 0.2184 0.4369 0.7816
137 0.1805 0.361 0.8195
138 0.165 0.3301 0.835
139 0.3785 0.7569 0.6215
140 0.3375 0.675 0.6625
141 0.4031 0.8061 0.5969
142 0.4569 0.9137 0.5431
143 0.4282 0.8564 0.5718
144 0.3703 0.7406 0.6297
145 0.3192 0.6384 0.6808
146 0.2892 0.5783 0.7108
147 0.3092 0.6184 0.6908
148 0.2579 0.5158 0.7421
149 0.2588 0.5177 0.7412
150 0.3535 0.707 0.6465
151 0.3044 0.6088 0.6956
152 0.266 0.532 0.734
153 0.2428 0.4855 0.7572
154 0.1934 0.3868 0.8066
155 0.1979 0.3958 0.8021
156 0.1798 0.3597 0.8202
157 0.1374 0.2749 0.8626
158 0.3613 0.7226 0.6387
159 0.282 0.564 0.718
160 0.2107 0.4214 0.7893
161 0.248 0.4959 0.752
162 0.2109 0.4217 0.7891
163 0.1418 0.2836 0.8582
164 0.2728 0.5455 0.7272
165 0.9302 0.1396 0.06981
166 0.8462 0.3075 0.1538


Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level25 0.1562NOK
5% type I error level370.23125NOK
10% type I error level470.29375NOK


Ramsey RESET F-Test for powers (2 and 3) of fitted values
> reset_test_fitted
	RESET test
data:  mylm
RESET = 4.8734, df1 = 2, df2 = 167, p-value = 0.008769
Ramsey RESET F-Test for powers (2 and 3) of regressors
> reset_test_regressors
	RESET test
data:  mylm
RESET = 3.1856, df1 = 6, df2 = 163, p-value = 0.005541
Ramsey RESET F-Test for powers (2 and 3) of principal components
> reset_test_principal_components
	RESET test
data:  mylm
RESET = 0.8252, df1 = 2, df2 = 167, p-value = 0.4399


Variance Inflation Factors (Multicollinearity)
> vif
`Population_(millions)`              Urban_Land       Total_Biocapacity 
               1.006998                1.004147                1.003033