Multiple Linear Regression - Estimated Regression Equation
Total_Ecological_Footprint[t] = -1.30022 + 6.28387e-05GDP_per_Capita[t] -0.000423779`Population_(millions)`[t] + 5.40691HDI[t] + e[t]


Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STAT
H0: parameter = 0		2-tail p-value1-tail p-value
(Intercept)-1.3 0.5279-2.4630e+00 0.01479 0.007396
GDP_per_Capita+6.284e-05 6.379e-06+9.8500e+00 2.464e-18 1.232e-18
`Population_(millions)`-0.0004238 0.0006559-6.4620e-01 0.5191 0.2595
HDI+5.407 0.8382+6.4510e+00 1.154e-09 5.77e-10


Multiple Linear Regression - Regression Statistics
Multiple R 0.8453
R-squared 0.7145
Adjusted R-squared 0.7093
F-TEST (value) 139.3
F-TEST (DF numerator)3
F-TEST (DF denominator)167
p-value 0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation 1.256
Sum Squared Residuals 263.6


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 0.79 1.213-0.4229
2 2.21 2.93-0.7204
3 2.12 2.972-0.8518
4 0.93 1.796-0.8658
5 5.38 3.747 1.633
6 3.14 4.021-0.8809
7 2.23 2.861-0.6309
8 9.31 7.904 1.406
9 6.06 6.676-0.6163
10 2.31 3.198-0.8876
11 6.84 4.34 2.5
12 7.49 4.66 2.83
13 0.72 1.716-0.996
14 4.48 3.959 0.5209
15 5.09 3.417 1.673
16 7.44 6.527 0.9131
17 1.41 1.338 0.07223
18 4.84 2.04 2.8
19 2.96 2.351 0.6086
20 3.12 2.941 0.1789
21 3.83 2.916 0.9137
22 3.11 3.503-0.3926
23 4.06 6.255-2.195
24 3.32 3.393-0.07262
25 1.21 0.8437 0.3663
26 0.8 0.8217-0.02169
27 2.52 2.399 0.1211
28 1.21 1.722-0.5124
29 1.17 1.474-0.3039
30 8.17 6.882 1.288
31 1.24 0.7295 0.5105
32 1.46 0.8762 0.5838
33 4.36 4.093 0.2671
34 3.38 2.345 1.034
35 1.87 3.032-1.162
36 1.03 1.457-0.427
37 1.29 1.902-0.612
38 0.82 0.9641-0.1441
39 2.84 3.371-0.5313
40 3.92 4.044-0.1242
41 1.95 3.184-1.234
42 4.21 5.272-1.062
43 5.19 4.761 0.4286
44 5.51 7.531-2.021
45 2.19 1.277 0.9133
46 2.57 3.038-0.4681
47 1.53 2.917-1.387
48 2.17 2.967-0.7966
49 2.15 2.58-0.4305
50 2.07 2.498-0.4279
51 3.97 3.348 0.6224
52 0.42 0.8335-0.4135
53 6.86 4.383 2.478
54 1.02 1.01 0.01028
55 2.9 2.856 0.04361
56 5.87 6.658-0.7878
57 5.14 6.34-1.2
58 2.02 3.075-1.055
59 1.03 1.11-0.07985
60 1.58 2.986-1.406
61 5.3 6.527-1.227
62 1.97 1.873 0.09673
63 4.38 4.978-0.598
64 2.98 3.167-0.1865
65 1.89 2.249-0.3589
66 1.41 0.9406 0.4694
67 1.53 1.013 0.5172
68 3.07 2.311 0.7588
69 0.61 1.338-0.7279
70 1.68 2.137-0.4572
71 2.92 4.007-1.087
72 1.16 1.515-0.355
73 1.58 2.504-0.9237
74 2.79 3.249-0.4586
75 1.88 2.568-0.6879
76 5.57 6.939-1.369
77 6.22 5.628 0.5925
78 4.61 5.792-1.182
79 1.89 2.92-1.03
80 5.02 6.361-1.341
81 2.1 3.042-0.942
82 5.55 3.619 1.931
83 1.03 1.668-0.638
84 5.69 5.009 0.6809
85 8.13 5.761 2.369
86 1.91 2.282-0.3721
87 1.22 1.803-0.5825
88 6.29 3.941 2.349
89 3.84 3.382 0.4583
90 1.66 1.378 0.2817
91 1.21 0.9939 0.2161
92 3.69 3.066 0.6235
93 5.83 4.089 1.741
94 15.82 10.72 5.103
95 3.26 3.025 0.2348
96 0.99 1.477-0.4865
97 0.81 1.049-0.239
98 3.71 3.495 0.215
99 1.53 0.9569 0.5731
100 2.54 1.497 1.043
101 3.46 3.416 0.04374
102 2.89 3.34-0.4499
103 1.78 2.499-0.7189
104 6.08 2.772 3.308
105 3.78 3.481 0.2993
106 1.68 2.236-0.5562
107 0.87 0.9398-0.0698
108 1.43 1.613-0.1833
109 2.48 2.421 0.05935
110 0.98 1.652-0.6719
111 5.28 7.035-1.755
112 5.6 5.974-0.3739
113 1.39 2.206-0.8158
114 1.56 0.5567 1.003
115 1.16 1.496-0.3358
116 4.98 10.07-5.095
117 7.52 4.391 3.129
118 0.79 1.566-0.7761
119 2.79 3.39-0.6
120 1.91 1.518 0.3922
121 4.16 2.543 1.617
122 2.28 2.991-0.7113
123 1.1 2.377-1.277
124 4.44 4.091 0.3493
125 3.88 4.642-0.762
126 10.8 9.543 1.257
127 2.71 3.541-0.831
128 5.69 3.748 1.942
129 0.87 1.33-0.4597
130 4.94 3.515 1.425
131 2.45 3.133-0.6829
132 3.11 2.981 0.1295
133 2.77 2.74 0.02989
134 1.49 1.761-0.2705
135 5.61 4.658 0.9519
136 1.21 1.249-0.03896
137 2.7 3.209-0.5088
138 1.24 0.8914 0.3486
139 7.97 6.956 1.014
140 4.06 4.377-0.3169
141 5.81 5.03 0.7795
142 1.29 1.507-0.2166
143 3.31 2.755 0.5555
144 3.67 5.395-1.725
145 1.32 2.927-1.607
146 4.25 3.053 1.197
147 2.01 1.858 0.1524
148 7.25 7.293-0.04345
149 5.79 9.286-3.496
150 0.91 2.101-1.191
151 1.32 1.485-0.1652
152 2.66 2.909-0.2488
153 0.48 2.268-1.788
154 1.13 1.275-0.1447
155 2.7 2.865-0.1649
156 7.92 4.013 3.907
157 2.34 2.859-0.5187
158 3.33 3.434-0.1036
159 5.47 2.707 2.763
160 1.24 1.317-0.07748
161 2.84 2.907-0.06717
162 4.94 6.114-1.174
163 7.93 5.749 2.181
164 8.22 6.61 1.61
165 2.91 3.865-0.9545
166 2.32 2.408-0.0884
167 3.57 3.46 0.1095
168 1.65 2.326-0.6762
169 1.03 1.475-0.445
170 0.99 1.939-0.9492
171 1.37 1.398-0.02777


Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
7 0.2141 0.4281 0.7859
8 0.2208 0.4415 0.7792
9 0.3505 0.701 0.6495
10 0.2597 0.5193 0.7403
11 0.5091 0.9818 0.4909
12 0.6772 0.6457 0.3228
13 0.7377 0.5245 0.2623
14 0.6569 0.6863 0.3431
15 0.6712 0.6577 0.3288
16 0.5938 0.8125 0.4062
17 0.5169 0.9662 0.4831
18 0.7352 0.5295 0.2648
19 0.672 0.6561 0.328
20 0.6057 0.7886 0.3943
21 0.5421 0.9158 0.4579
22 0.5231 0.9538 0.4769
23 0.7734 0.4533 0.2266
24 0.7297 0.5406 0.2703
25 0.6766 0.6469 0.3234
26 0.6162 0.7676 0.3838
27 0.5559 0.8882 0.4441
28 0.5095 0.981 0.4905
29 0.4508 0.9015 0.5492
30 0.4268 0.8535 0.5732
31 0.3771 0.7543 0.6229
32 0.3311 0.6622 0.6689
33 0.2798 0.5595 0.7202
34 0.3337 0.6675 0.6663
35 0.3443 0.6886 0.6557
36 0.3003 0.6006 0.6997
37 0.2662 0.5324 0.7338
38 0.2224 0.4449 0.7776
39 0.1946 0.3892 0.8054
40 0.1609 0.3219 0.8391
41 0.1646 0.3293 0.8354
42 0.1696 0.3392 0.8304
43 0.1398 0.2795 0.8602
44 0.2246 0.4493 0.7754
45 0.2063 0.4127 0.7937
46 0.1768 0.3536 0.8232
47 0.1868 0.3737 0.8132
48 0.1668 0.3336 0.8332
49 0.1401 0.2802 0.8599
50 0.1163 0.2326 0.8837
51 0.09766 0.1953 0.9023
52 0.08026 0.1605 0.9197
53 0.1536 0.3072 0.8464
54 0.1262 0.2523 0.8738
55 0.1025 0.2049 0.8975
56 0.09223 0.1845 0.9078
57 0.09234 0.1847 0.9077
58 0.08708 0.1742 0.9129
59 0.06954 0.1391 0.9305
60 0.07438 0.1488 0.9256
61 0.07355 0.1471 0.9264
62 0.05846 0.1169 0.9415
63 0.04821 0.09642 0.9518
64 0.03765 0.07531 0.9623
65 0.02955 0.05911 0.9704
66 0.02345 0.04689 0.9766
67 0.01858 0.03715 0.9814
68 0.01564 0.03127 0.9844
69 0.01297 0.02594 0.987
70 0.009964 0.01993 0.99
71 0.009162 0.01832 0.9908
72 0.007609 0.01522 0.9924
73 0.006348 0.0127 0.9937
74 0.004723 0.009445 0.9953
75 0.003708 0.007416 0.9963
76 0.003885 0.00777 0.9961
77 0.003094 0.006189 0.9969
78 0.002886 0.005772 0.9971
79 0.002583 0.005166 0.9974
80 0.002562 0.005124 0.9974
81 0.002199 0.004398 0.9978
82 0.00391 0.00782 0.9961
83 0.003036 0.006072 0.997
84 0.002462 0.004924 0.9975
85 0.006483 0.01297 0.9935
86 0.004841 0.009682 0.9952
87 0.003734 0.007469 0.9963
88 0.008582 0.01716 0.9914
89 0.006579 0.01316 0.9934
90 0.004872 0.009743 0.9951
91 0.003544 0.007088 0.9965
92 0.002745 0.005489 0.9973
93 0.003736 0.007472 0.9963
94 0.1604 0.3208 0.8396
95 0.1363 0.2727 0.8637
96 0.1166 0.2332 0.8834
97 0.09679 0.1936 0.9032
98 0.0797 0.1594 0.9203
99 0.06776 0.1355 0.9322
100 0.06414 0.1283 0.9359
101 0.05142 0.1028 0.9486
102 0.04245 0.0849 0.9576
103 0.03622 0.07244 0.9638
104 0.1322 0.2644 0.8678
105 0.1109 0.2218 0.8891
106 0.09464 0.1893 0.9054
107 0.07707 0.1542 0.9229
108 0.06216 0.1243 0.9378
109 0.0494 0.0988 0.9506
110 0.04142 0.08284 0.9586
111 0.05159 0.1032 0.9484
112 0.0414 0.08279 0.9586
113 0.03574 0.07149 0.9643
114 0.03429 0.06859 0.9657
115 0.02697 0.05394 0.973
116 0.3758 0.7516 0.6242
117 0.6094 0.7813 0.3906
118 0.5887 0.8226 0.4113
119 0.5508 0.8983 0.4492
120 0.5089 0.9822 0.4911
121 0.5441 0.9117 0.4559
122 0.5105 0.979 0.4895
123 0.5248 0.9503 0.4752
124 0.4769 0.9537 0.5231
125 0.4448 0.8895 0.5552
126 0.4876 0.9753 0.5124
127 0.4684 0.9367 0.5316
128 0.4927 0.9854 0.5073
129 0.4438 0.8877 0.5562
130 0.4585 0.9169 0.5415
131 0.4218 0.8435 0.5782
132 0.3702 0.7405 0.6298
133 0.3204 0.6407 0.6796
134 0.274 0.5481 0.726
135 0.2525 0.5049 0.7475
136 0.211 0.4219 0.789
137 0.1804 0.3608 0.8196
138 0.1555 0.311 0.8445
139 0.1602 0.3204 0.8398
140 0.1297 0.2594 0.8703
141 0.1117 0.2235 0.8883
142 0.08637 0.1727 0.9136
143 0.06818 0.1364 0.9318
144 0.07993 0.1599 0.9201
145 0.1076 0.2152 0.8924
146 0.0984 0.1968 0.9016
147 0.07761 0.1552 0.9224
148 0.06149 0.123 0.9385
149 0.2757 0.5514 0.7243
150 0.2532 0.5063 0.7468
151 0.1994 0.3987 0.8006
152 0.1525 0.305 0.8475
153 0.1979 0.3959 0.8021
154 0.1489 0.2978 0.8511
155 0.1086 0.2173 0.8914
156 0.5142 0.9717 0.4858
157 0.4287 0.8574 0.5713
158 0.3377 0.6754 0.6623
159 0.8178 0.3644 0.1822
160 0.7292 0.5416 0.2708
161 0.6545 0.6911 0.3455
162 0.9451 0.1097 0.05486
163 0.9419 0.1162 0.05812
164 0.8746 0.2509 0.1254


Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level17 0.1076NOK
5% type I error level280.177215NOK
10% type I error level390.246835NOK


Ramsey RESET F-Test for powers (2 and 3) of fitted values
> reset_test_fitted
	RESET test
data:  mylm
RESET = 6.6093, df1 = 2, df2 = 165, p-value = 0.001733
Ramsey RESET F-Test for powers (2 and 3) of regressors
> reset_test_regressors
	RESET test
data:  mylm
RESET = 8.5874, df1 = 6, df2 = 161, p-value = 4.189e-08
Ramsey RESET F-Test for powers (2 and 3) of principal components
> reset_test_principal_components
	RESET test
data:  mylm
RESET = 21.18, df1 = 2, df2 = 165, p-value = 6.497e-09


Variance Inflation Factors (Multicollinearity)
> vif
         GDP_per_Capita `Population_(millions)`                     HDI 
               1.855189                1.003786                1.851080