Multiple Linear Regression - Estimated Regression Equation
Forest_Footprint[t] = + 0.1978 -0.000144007`Population_(millions)`[t] + 0.14764HDI[t] + 4.14275e-06GDP_per_Capita[t] + 0.00826966Total_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)+0.1978 0.1465+1.3500e+00 0.1789 0.08947
`Population_(millions)`-0.000144 0.0001788-8.0560e-01 0.4217 0.2109
HDI+0.1476 0.2341+6.3050e-01 0.5293 0.2646
GDP_per_Capita+4.143e-06 1.858e-06+2.2300e+00 0.02719 0.0136
Total_Biocapacity+0.00827 0.002933+2.8190e+00 0.005434 0.002717


Multiple Linear Regression - Regression Statistics
Multiple R 0.3595
R-squared 0.1292
Adjusted R-squared 0.107
F-TEST (value) 5.825
F-TEST (DF numerator)4
F-TEST (DF denominator)157
p-value 0.0002137
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation 0.3412
Sum Squared Residuals 18.28


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 0.08 0.2681-0.1881
2 0.25 0.3337-0.08367
3 0.17 0.3274-0.1574
4 0.12 0.312-0.192
5 0.29 0.4277-0.1377
6 0.34 0.3267 0.0133
7 0.89 0.7447 0.1453
8 0.63 0.5643 0.06569
9 0.11 0.3437-0.2337
10 0.19 0.4857-0.2957
11 0.16 0.4241-0.2641
12 0.08 0.2649-0.1849
13 0.14 0.3811-0.2411
14 0.91 0.3708 0.5392
15 0.99 0.5365 0.4535
16 0.26 0.2776-0.01759
17 3.03 0.3383 2.692
18 0.17 0.4399-0.2699
19 0.44 0.338 0.102
20 0.24 0.3602-0.1202
21 0.6 0.4098 0.1902
22 0.26 0.5421-0.2821
23 0.35 0.3671-0.01711
24 0.36 0.2639 0.09611
25 0.45 0.2578 0.1922
26 0.21 0.2877-0.07774
27 1.2 0.6756 0.5244
28 0.26 0.3189-0.05891
29 0.27 0.2752-0.005185
30 0.99 0.408 0.582
31 0.19 0.1321 0.05786
32 0.16 0.3573-0.1973
33 0.18 0.2777-0.09773
34 0.38 0.3796 0.0003956
35 0.51 0.2771 0.2329
36 0.68 0.3592 0.3208
37 0.72 0.4016 0.3184
38 0.09 0.3376-0.2476
39 0.23 0.4563-0.2263
40 0.74 0.4349 0.3051
41 0.77 0.6268 0.1432
42 0.14 0.342-0.202
43 0.12 0.331-0.211
44 0.24 0.3431-0.1031
45 0.17 0.3048-0.1348
46 0.4 0.3147 0.08531
47 0.26 0.4194-0.1594
48 0.06 0.2671-0.2071
49 0.46 0.2544 0.2056
50 0.42 0.341 0.07902
51 0.53 0.5339-0.003911
52 0.79 0.5637 0.2263
53 0.2 0.2714-0.07138
54 0.1 0.333-0.233
55 0.48 0.533-0.05297
56 0.65 0.2962 0.3538
57 0.24 0.4441-0.2041
58 0.58 0.3087 0.2713
59 0.45 0.2759 0.1741
60 0.67 0.2874 0.3826
61 0.77 0.8548-0.08484
62 0.1 0.2725-0.1725
63 0.5 0.3108 0.1892
64 0.36 0.3932-0.03322
65 0.14 0.1183 0.02172
66 0.2 0.2883-0.08835
67 0.07 0.3376-0.2676
68 0.01 0.3157-0.3057
69 0.46 0.5813-0.1213
70 0.36 0.4707-0.1107
71 0.42 0.4855-0.06554
72 0.18 0.3289-0.1489
73 0.27 0.5082-0.2382
74 0.17 0.3284-0.1584
75 0.12 0.3855-0.2655
76 0.27 0.2799-0.009925
77 0.21 0.4278-0.2178
78 0.21 0.4962-0.2862
79 0.09 0.3084-0.2184
80 0.36 0.298 0.06196
81 2.02 0.453 1.567
82 0.25 0.3499-0.09995
83 0.42 0.2804 0.1396
84 0.75 0.2821 0.4679
85 0.14 0.3362-0.1962
86 1.28 0.4263 0.8537
87 1.03 0.818 0.212
88 0.31 0.3407-0.03068
89 0.24 0.2935-0.05353
90 0.2 0.2665-0.0665
91 0.38 0.3697 0.01032
92 0.17 0.2723-0.1023
93 0.21 0.3144-0.1044
94 0.18 0.3537-0.1737
95 0.25 0.3436-0.09357
96 0.15 0.3125-0.1625
97 0.17 0.4472-0.2772
98 0.62 0.3727 0.2473
99 0.14 0.3036-0.1636
100 0.29 0.274 0.01603
101 0.32 0.2883 0.03171
102 0.17 0.3703-0.2003
103 0.21 0.2813-0.07135
104 0.38 0.5629-0.1829
105 1.08 0.5707 0.5093
106 0.42 0.3153 0.1047
107 0.26 0.2575 0.002517
108 0.19 0.2639-0.07392
109 0.15 0.4236-0.2736
110 0.08 0.2582-0.1782
111 0.19 0.3701-0.1801
112 0.36 0.3108 0.04924
113 0.83 0.3975 0.4325
114 0.19 0.3576-0.1676
115 0.09 0.2956-0.2056
116 0.78 0.3906 0.3894
117 0.09 0.4275-0.3375
118 0.15 0.7452-0.5952
119 0.33 0.3687-0.03866
120 0.67 0.4052 0.2648
121 0.25 0.2741-0.02408
122 0.09 0.3658-0.2758
123 0.17 0.3404-0.1704
124 0.27 0.3339-0.06393
125 0.27 0.2919-0.02191
126 0.27 0.4181-0.1481
127 0.21 0.2769-0.06689
128 0.46 0.3456 0.1144
129 0.38 0.2683 0.1117
130 0.91 0.5519 0.3581
131 0.72 0.4184 0.3016
132 0.65 0.4506 0.1994
133 0.09 0.3144-0.2244
134 0.29 0.3307-0.04072
135 0.17 0.4625-0.2925
136 0.16 0.3211-0.1611
137 0.52 1.075-0.5552
138 0.52 0.3024 0.2176
139 1.3 0.6631 0.6369
140 0.38 0.7114-0.3314
141 0.1 0.296-0.196
142 0.23 0.2783-0.04832
143 0.24 0.3274-0.08744
144 0.04 0.3224-0.2824
145 0.27 0.273-0.003024
146 0.14 0.3343-0.1943
147 0.27 0.4-0.13
148 0.28 0.3281-0.04806
149 0.34 0.3552-0.01516
150 0.08 0.3424-0.2624
151 0.54 0.2708 0.2692
152 0.16 0.3341-0.1741
153 0.45 0.5023-0.05229
154 0.38 0.4927-0.1127
155 0.67 0.5235 0.1465
156 0.55 0.4583 0.09173
157 0.08 0.3067-0.2267
158 0.12 0.3717-0.2517
159 0.19 0.2968-0.1068
160 0.04 0.2777-0.2377
161 0.33 0.3071 0.02294
162 0.29 0.2769 0.01312


Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
8 0.005119 0.01024 0.9949
9 0.008285 0.01657 0.9917
10 0.01452 0.02904 0.9855
11 0.01361 0.02721 0.9864
12 0.005336 0.01067 0.9947
13 0.002438 0.004876 0.9976
14 0.1244 0.2489 0.8756
15 0.1753 0.3507 0.8247
16 0.1385 0.2769 0.8615
17 1 3.182e-11 1.591e-11
18 1 8.944e-12 4.472e-12
19 1 2.557e-11 1.279e-11
20 1 5.368e-11 2.684e-11
21 1 5.953e-11 2.977e-11
22 1 9.448e-11 4.724e-11
23 1 2.455e-10 1.227e-10
24 1 5.686e-10 2.843e-10
25 1 1.241e-09 6.205e-10
26 1 2.556e-09 1.278e-09
27 1 1.962e-09 9.811e-10
28 1 3.294e-09 1.647e-09
29 1 7.234e-09 3.617e-09
30 1 2.974e-09 1.487e-09
31 1 5.791e-09 2.895e-09
32 1 9.313e-09 4.657e-09
33 1 1.88e-08 9.401e-09
34 1 3.655e-08 1.828e-08
35 1 5.991e-08 2.996e-08
36 1 7.561e-08 3.781e-08
37 1 9.765e-08 4.883e-08
38 1 1.347e-07 6.736e-08
39 1 2.06e-07 1.03e-07
40 1 2.601e-07 1.3e-07
41 1 4.553e-07 2.276e-07
42 1 6.908e-07 3.454e-07
43 1 1.037e-06 5.184e-07
44 1 1.802e-06 9.008e-07
45 1 3.027e-06 1.514e-06
46 1 5.262e-06 2.631e-06
47 1 7.968e-06 3.984e-06
48 1 1.153e-05 5.767e-06
49 1 1.646e-05 8.23e-06
50 1 2.75e-05 1.375e-05
51 1 4.611e-05 2.306e-05
52 1 6.251e-05 3.126e-05
53 1 0.0001008 5.041e-05
54 0.9999 0.0001319 6.597e-05
55 0.9999 0.0002094 0.0001047
56 0.9999 0.000206 0.000103
57 0.9999 0.0002808 0.0001404
58 0.9998 0.0003328 0.0001664
59 0.9998 0.0004627 0.0002314
60 0.9998 0.0004166 0.0002083
61 0.9998 0.0004562 0.0002281
62 0.9997 0.0006247 0.0003124
63 0.9996 0.0008348 0.0004174
64 0.9994 0.001253 0.0006266
65 0.9991 0.001803 0.0009017
66 0.9987 0.002603 0.001302
67 0.9985 0.00304 0.00152
68 0.9984 0.003288 0.001644
69 0.9978 0.004477 0.002238
70 0.9969 0.006135 0.003067
71 0.9957 0.008554 0.004277
72 0.9944 0.01121 0.005604
73 0.9933 0.01335 0.006673
74 0.9914 0.01711 0.008556
75 0.9903 0.0193 0.009651
76 0.987 0.02605 0.01303
77 0.9846 0.03075 0.01538
78 0.9834 0.03314 0.01657
79 0.9804 0.03914 0.01957
80 0.9746 0.0509 0.02545
81 1 7.336e-06 3.668e-06
82 1 1.206e-05 6.031e-06
83 1 1.765e-05 8.826e-06
84 1 6.799e-06 3.399e-06
85 1 9.603e-06 4.802e-06
86 1 1.214e-07 6.07e-08
87 1 1.327e-07 6.637e-08
88 1 2.544e-07 1.272e-07
89 1 4.738e-07 2.369e-07
90 1 8.685e-07 4.342e-07
91 1 1.598e-06 7.988e-07
92 1 2.826e-06 1.413e-06
93 1 4.937e-06 2.468e-06
94 1 7.494e-06 3.747e-06
95 1 1.249e-05 6.246e-06
96 1 1.928e-05 9.638e-06
97 1 2.354e-05 1.177e-05
98 1 2.715e-05 1.358e-05
99 1 4.178e-05 2.089e-05
100 1 6.757e-05 3.378e-05
101 0.9999 0.00011 5.498e-05
102 0.9999 0.0001604 8.021e-05
103 0.9999 0.0002632 0.0001316
104 0.9998 0.0003786 0.0001893
105 0.9999 0.0001052 5.26e-05
106 0.9999 0.0001565 7.827e-05
107 0.9999 0.0002482 0.0001241
108 0.9998 0.0004028 0.0002014
109 0.9998 0.0004874 0.0002437
110 0.9997 0.0006469 0.0003234
111 0.9995 0.0009277 0.0004639
112 0.9993 0.001373 0.0006865
113 0.9997 0.0005408 0.0002704
114 0.9996 0.0008019 0.000401
115 0.9995 0.0009952 0.0004976
116 0.9997 0.0006136 0.0003068
117 0.9997 0.0006065 0.0003033
118 1 9.257e-05 4.628e-05
119 0.9999 0.000167 8.352e-05
120 0.9999 0.0001484 7.421e-05
121 0.9999 0.0002683 0.0001342
122 0.9998 0.0003232 0.0001616
123 0.9997 0.0005209 0.0002605
124 0.9995 0.000914 0.000457
125 0.9992 0.00157 0.0007849
126 0.9988 0.002381 0.00119
127 0.998 0.003979 0.00199
128 0.9973 0.005384 0.002692
129 0.9962 0.007544 0.003772
130 0.9967 0.006518 0.003259
131 0.998 0.00406 0.00203
132 0.9983 0.003332 0.001666
133 0.9977 0.0046 0.0023
134 0.996 0.007941 0.003971
135 0.9951 0.009782 0.004891
136 0.9918 0.01631 0.008155
137 0.9999 0.0002265 0.0001132
138 0.9999 0.0001735 8.674e-05
139 1 1.038e-05 5.192e-06
140 1 9.492e-06 4.746e-06
141 1 2.59e-05 1.295e-05
142 1 7.216e-05 3.608e-05
143 0.9999 0.0001908 9.54e-05
144 0.9999 0.0001598 7.989e-05
145 0.9998 0.0004639 0.0002319
146 0.9994 0.001286 0.0006428
147 0.9983 0.00343 0.001715
148 0.9974 0.005195 0.002598
149 0.9963 0.007411 0.003705
150 0.9933 0.01335 0.006677
151 0.9979 0.004234 0.002117
152 0.9923 0.0153 0.007651
153 0.9775 0.04495 0.02247
154 0.9438 0.1123 0.05616


Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level125 0.8503NOK
5% type I error level1420.965986NOK
10% type I error level1430.972789NOK


Ramsey RESET F-Test for powers (2 and 3) of fitted values
> reset_test_fitted
	RESET test
data:  mylm
RESET = 4.7239, df1 = 2, df2 = 155, p-value = 0.0102
Ramsey RESET F-Test for powers (2 and 3) of regressors
> reset_test_regressors
	RESET test
data:  mylm
RESET = 4.5707, df1 = 8, df2 = 149, p-value = 5.342e-05
Ramsey RESET F-Test for powers (2 and 3) of principal components
> reset_test_principal_components
	RESET test
data:  mylm
RESET = 0.19068, df1 = 2, df2 = 155, p-value = 0.8266


Variance Inflation Factors (Multicollinearity)
> vif
`Population_(millions)`                     HDI          GDP_per_Capita 
               1.007334                1.857608                1.855642 
      Total_Biocapacity 
               1.007501