Multiple Linear Regression - Estimated Regression Equation
Carbon_Footprint[t] = -1.26537 + 0.000122018`Population_(millions)`[t] + 3.20593HDI[t] + 6.38132e-05GDP_per_Capita[t] + 0.00416326Total_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)-1.265 0.4496-2.8140e+00 0.005512 0.002756
`Population_(millions)`+0.000122 0.0005486+2.2240e-01 0.8243 0.4121
HDI+3.206 0.7185+4.4620e+00 1.542e-05 7.711e-06
GDP_per_Capita+6.381e-05 5.702e-06+1.1190e+01 9.532e-22 4.766e-22
Total_Biocapacity+0.004163 0.009001+4.6250e-01 0.6444 0.3222


Multiple Linear Regression - Regression Statistics
Multiple R 0.8461
R-squared 0.7159
Adjusted R-squared 0.7086
F-TEST (value) 98.89
F-TEST (DF numerator)4
F-TEST (DF denominator)157
p-value 0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation 1.047
Sum Squared Residuals 172.1


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 0.18 0.2543-0.0743
2 0.87 1.37-0.4996
3 1.14 1.429-0.2887
4 0.2 0.7126-0.5126
5 1.08 2.293-1.213
6 0.89 1.298-0.4077
7 4.85 6.038-1.188
8 4.14 4.842-0.7016
9 1.25 1.597-0.3472
10 4.46 2.72 1.74
11 6.19 2.917 3.273
12 0.26 0.6051-0.3451
13 3.28 2.271 1.009
14 2.57 1.718 0.8523
15 4.43 4.661-0.2306
16 0.51 0.326 0.184
17 0.63 0.801-0.171
18 0.67 1.033-0.3632
19 1.74 1.383 0.3573
20 2.36 1.456 0.9045
21 0.91 2.046-1.136
22 3.24 4.477-1.237
23 2.08 1.734 0.346
24 0.12 0.03385 0.08615
25 0.04 0.005131 0.03487
26 0.19 0.4284-0.2384
27 5 5.051-0.0505
28 0.08-0.01427 0.09427
29 0.01 0.06901-0.05901
30 2.04 2.34-0.2997
31 2.32 1.573 0.7465
32 0.67 1.53-0.8599
33 0.25 0.3939-0.1439
34 0.47 0.732-0.262
35 0.07 0.1235-0.05353
36 1.37 1.751-0.3811
37 2.21 2.302-0.09242
38 1.23 1.538-0.308
39 2.94 3.468-0.5284
40 3.42 2.919 0.5014
41 2.6 5.624-3.024
42 1.47 1.5-0.0295
43 0.86 1.403-0.5428
44 1.08 1.417-0.3374
45 1.02 1.146-0.1259
46 0.84 1.09-0.2497
47 3.17 2.148 1.022
48 0.03 0.01916 0.01084
49 0.07 0.151-0.08099
50 1.06 1.321-0.261
51 2.71 4.508-1.798
52 0.43 1.757-1.327
53 0.21 0.1811 0.02886
54 0.83 1.381-0.5513
55 3.28 4.659-1.379
56 0.43 0.6746-0.2446
57 2.58 3.158-0.5781
58 0.7 0.9346-0.2346
59 0.16 0.08845 0.07155
60 0.09 0.1374-0.04741
61 1.25 1.24 0.009714
62 0.15 0.3236-0.1736
63 0.6 0.8434-0.2434
64 1.9 2.265-0.3648
65 0.61 0.9076-0.2976
66 0.64 1.185-0.5454
67 1.72 1.664 0.05649
68 1.36 1.197 0.1631
69 3.22 5.041-1.821
70 4.59 3.742 0.848
71 2.77 3.987-1.217
72 1.09 1.379-0.2885
73 3.69 4.555-0.8647
74 1.09 1.435-0.3453
75 4.59 1.971 2.619
76 0.2 0.541-0.341
77 4.17 3.138 1.032
78 6.89 4.036 2.854
79 0.95 0.8958 0.0542
80 0.09 0.6164-0.5264
81 1.66 2.248-0.5877
82 2.52 1.757 0.7634
83 0.51 0.3624 0.1476
84 0.14 0.1177 0.02231
85 2.33 1.485 0.8454
86 2.15 2.337-0.1868
87 12.65 8.912 3.738
88 2.06 1.444 0.6162
89 0.07 0.4124-0.3424
90 0.07 0.1494-0.07938
91 2.1 1.871 0.229
92 0.1 0.1047-0.004748
93 0.55 0.454 0.09602
94 1.99 1.769 0.2214
95 1.74 1.805-0.06515
96 1.03 1.044-0.0142
97 2.09 1.315 0.7752
98 2.13 1.776 0.3543
99 0.67 0.9302-0.2602
100 0.17 0.09509 0.07491
101 0.09 0.5192-0.4292
102 1.02 1.127-0.1065
103 0.16 0.5163-0.3563
104 3.23 5.111-1.881
105 2.84 4.087-1.247
106 0.45 0.8683-0.4183
107 0.1-0.1419 0.2419
108 0.21 0.5278-0.3178
109 5.8 2.719 3.081
110 0.38 0.5349-0.1549
111 1.44 1.753-0.3126
112 0.35 0.4742-0.1242
113 0.97 1.154-0.1842
114 0.67 1.458-0.7879
115 0.34 1.016-0.6764
116 2.64 2.32 0.3204
117 2.15 2.885-0.7347
118 9.57 7.81 1.76
119 1.46 1.868-0.4076
120 3.87 2.163 1.707
121 0.07 0.3172-0.2472
122 3.34 1.936 1.404
123 1.56 1.57-0.01013
124 0.96 1.246-0.2864
125 0.37 0.5899-0.2199
126 4.21 2.907 1.303
127 0.3 0.2843 0.01573
128 1.66 1.588 0.07242
129 0.07 0.05479 0.01521
130 5.91 5.043 0.8672
131 2.82 2.595 0.2252
132 4.27 3.164 1.106
133 0 0.461-0.461
134 2.34 1.378 0.962
135 2.22 3.577-1.357
136 0.52 1.327-0.8073
137 3.01 1.905 1.105
138 0.67 0.7348-0.06479
139 3.88 5.455-1.575
140 4.26 7.37-3.11
141 0.13 0.7788-0.6488
142 0.17 0.4288-0.2588
143 1.54 1.406 0.1341
144 0.06 0.9955-0.9355
145 0.31 0.2815 0.0285
146 0.88 1.325-0.4454
147 6.89 2.378 4.512
148 1.11 1.323-0.2128
149 1.92 1.853 0.06744
150 4.13 1.264 2.866
151 0.08 0.3187-0.2387
152 1.92 1.351 0.5689
153 3.14 4.248-1.108
154 6.37 4.004 2.366
155 5.9 4.88 1.02
156 0.98 2.219-1.239
157 1.41 0.9895 0.4205
158 2.13 1.852 0.278
159 0.79 0.9636-0.1736
160 0.42 0.4257-0.005688
161 0.24 0.7161-0.4761
162 0.53 0.365 0.165


Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
8 0.01925 0.03851 0.9807
9 0.004609 0.009219 0.9954
10 0.328 0.6559 0.672
11 0.9355 0.129 0.0645
12 0.9588 0.0824 0.0412
13 0.9385 0.123 0.0615
14 0.9154 0.1692 0.0846
15 0.8849 0.2303 0.1151
16 0.837 0.326 0.163
17 0.7818 0.4364 0.2182
18 0.7184 0.5632 0.2816
19 0.6478 0.7044 0.3522
20 0.6016 0.7968 0.3984
21 0.5408 0.9183 0.4592
22 0.5664 0.8672 0.4336
23 0.4951 0.9903 0.5049
24 0.4267 0.8535 0.5733
25 0.359 0.718 0.641
26 0.2996 0.5992 0.7004
27 0.2633 0.5267 0.7367
28 0.2151 0.4301 0.7849
29 0.1697 0.3394 0.8303
30 0.1406 0.2811 0.8594
31 0.2001 0.4002 0.7999
32 0.1949 0.3898 0.8051
33 0.1561 0.3121 0.8439
34 0.1224 0.2448 0.8776
35 0.09425 0.1885 0.9057
36 0.07686 0.1537 0.9231
37 0.05797 0.1159 0.942
38 0.04556 0.09112 0.9544
39 0.03643 0.07287 0.9636
40 0.02854 0.05707 0.9715
41 0.1373 0.2746 0.8627
42 0.1093 0.2185 0.8907
43 0.09423 0.1885 0.9058
44 0.07652 0.153 0.9235
45 0.05958 0.1192 0.9404
46 0.04624 0.09248 0.9538
47 0.0585 0.117 0.9415
48 0.04451 0.08902 0.9555
49 0.03347 0.06694 0.9665
50 0.02547 0.05095 0.9745
51 0.03537 0.07075 0.9646
52 0.03548 0.07096 0.9645
53 0.02652 0.05305 0.9735
54 0.02204 0.04408 0.978
55 0.02293 0.04586 0.9771
56 0.01725 0.0345 0.9828
57 0.01339 0.02678 0.9866
58 0.009845 0.01969 0.9902
59 0.007024 0.01405 0.993
60 0.00493 0.00986 0.9951
61 0.003976 0.007952 0.996
62 0.002765 0.00553 0.9972
63 0.001927 0.003854 0.9981
64 0.001347 0.002693 0.9987
65 0.001006 0.002012 0.999
66 0.000744 0.001488 0.9993
67 0.0004884 0.0009768 0.9995
68 0.0003217 0.0006434 0.9997
69 0.0005293 0.001059 0.9995
70 0.0006924 0.001385 0.9993
71 0.000693 0.001386 0.9993
72 0.0004768 0.0009536 0.9995
73 0.0003836 0.0007673 0.9996
74 0.0002667 0.0005334 0.9997
75 0.003672 0.007345 0.9963
76 0.002685 0.00537 0.9973
77 0.003057 0.006113 0.9969
78 0.0436 0.08719 0.9564
79 0.0339 0.06779 0.9661
80 0.02806 0.05612 0.9719
81 0.02364 0.04729 0.9764
82 0.02059 0.04118 0.9794
83 0.01561 0.03122 0.9844
84 0.01163 0.02325 0.9884
85 0.01025 0.02051 0.9897
86 0.007627 0.01525 0.9924
87 0.1813 0.3626 0.8187
88 0.1623 0.3246 0.8377
89 0.1382 0.2763 0.8618
90 0.1145 0.2289 0.8855
91 0.09478 0.1896 0.9052
92 0.0768 0.1536 0.9232
93 0.0616 0.1232 0.9384
94 0.04932 0.09864 0.9507
95 0.0389 0.07779 0.9611
96 0.03014 0.06027 0.9699
97 0.02715 0.0543 0.9729
98 0.02131 0.04262 0.9787
99 0.01634 0.03268 0.9837
100 0.01218 0.02435 0.9878
101 0.009417 0.01883 0.9906
102 0.006858 0.01372 0.9931
103 0.005107 0.01021 0.9949
104 0.01026 0.02052 0.9897
105 0.01207 0.02415 0.9879
106 0.009337 0.01867 0.9907
107 0.006995 0.01399 0.993
108 0.005145 0.01029 0.9949
109 0.04056 0.08113 0.9594
110 0.03173 0.06346 0.9683
111 0.02488 0.04976 0.9751
112 0.0186 0.03721 0.9814
113 0.01397 0.02794 0.986
114 0.01259 0.02519 0.9874
115 0.01109 0.02219 0.9889
116 0.008119 0.01624 0.9919
117 0.007068 0.01414 0.9929
118 0.02358 0.04716 0.9764
119 0.02041 0.04083 0.9796
120 0.02424 0.04849 0.9758
121 0.01788 0.03576 0.9821
122 0.02016 0.04032 0.9798
123 0.01483 0.02966 0.9852
124 0.01146 0.02291 0.9885
125 0.008133 0.01627 0.9919
126 0.00845 0.0169 0.9916
127 0.005838 0.01168 0.9942
128 0.004069 0.008137 0.9959
129 0.002801 0.005602 0.9972
130 0.003126 0.006252 0.9969
131 0.002038 0.004075 0.998
132 0.001875 0.003749 0.9981
133 0.001233 0.002465 0.9988
134 0.0009777 0.001955 0.999
135 0.001155 0.002311 0.9988
136 0.001289 0.002577 0.9987
137 0.002021 0.004042 0.998
138 0.001229 0.002459 0.9988
139 0.0009996 0.001999 0.999
140 0.01694 0.03388 0.9831
141 0.01433 0.02867 0.9857
142 0.009146 0.01829 0.9909
143 0.00567 0.01134 0.9943
144 0.005541 0.01108 0.9945
145 0.003237 0.006474 0.9968
146 0.002724 0.005449 0.9973
147 0.1771 0.3541 0.8229
148 0.1391 0.2781 0.8609
149 0.09864 0.1973 0.9014
150 0.5239 0.9523 0.4761
151 0.4168 0.8336 0.5832
152 0.3457 0.6914 0.6543
153 0.9975 0.005039 0.00252
154 0.9886 0.02275 0.01137


Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level34 0.2313NOK
5% type I error level810.55102NOK
10% type I error level1010.687075NOK


Ramsey RESET F-Test for powers (2 and 3) of fitted values
> reset_test_fitted
	RESET test
data:  mylm
RESET = 27.945, df1 = 2, df2 = 155, p-value = 4.328e-11
Ramsey RESET F-Test for powers (2 and 3) of regressors
> reset_test_regressors
	RESET test
data:  mylm
RESET = 11.408, df1 = 8, df2 = 149, p-value = 1.519e-12
Ramsey RESET F-Test for powers (2 and 3) of principal components
> reset_test_principal_components
	RESET test
data:  mylm
RESET = 32.554, df1 = 2, df2 = 155, p-value = 1.572e-12


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