Multiple Linear Regression - Estimated Regression Equation
Carbon_Footprint[t] = -1.2628 + 0.000107097`Population_(millions)`[t] + 3.22652HDI[t] + 6.37398e-05GDP_per_Capita[t] + e[t]


Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STAT
H0: parameter = 0		2-tail p-value1-tail p-value
(Intercept)-1.263 0.4485-2.8160e+00 0.005484 0.002742
`Population_(millions)`+0.0001071 0.0005463+1.9610e-01 0.8448 0.4224
HDI+3.227 0.7154+4.5100e+00 1.256e-05 6.279e-06
GDP_per_Capita+6.374e-05 5.685e-06+1.1210e+01 7.847e-22 3.924e-22


Multiple Linear Regression - Regression Statistics
Multiple R 0.8459
R-squared 0.7155
Adjusted R-squared 0.7101
F-TEST (value) 132.4
F-TEST (DF numerator)3
F-TEST (DF denominator)158
p-value 0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation 1.045
Sum Squared Residuals 172.4


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 0.2638-0.08377
2 0.87 1.382-0.5119
3 1.14 1.443-0.3028
4 0.2 0.7146-0.5146
5 1.08 2.283-1.203
6 0.89 1.311-0.4213
7 4.85 5.986-1.136
8 4.14 4.846-0.7056
9 1.25 1.611-0.361
10 4.46 2.697 1.763
11 6.19 2.932 3.258
12 0.26 0.6153-0.3553
13 3.28 2.288 0.9916
14 2.57 1.721 0.849
15 4.43 4.673-0.2429
16 0.51 0.3346 0.1754
17 0.63 0.7936-0.1636
18 0.67 0.9792-0.3092
19 1.74 1.393 0.3469
20 2.36 1.457 0.9027
21 0.91 2.022-1.112
22 3.24 4.482-1.242
23 2.08 1.74 0.3399
24 0.12 0.04008 0.07992
25 0.04 0.01424 0.02576
26 0.19 0.4338-0.2438
27 5 5.001-0.0008036
28 0.08-0.03695 0.1169
29 0.01 0.0709-0.0609
30 2.04 2.343-0.303
31 2.32 1.566 0.7545
32 0.67 1.531-0.861
33 0.25 0.4054-0.1554
34 0.47 0.7007-0.2307
35 0.07 0.121-0.05096
36 1.37 1.762-0.3923
37 2.21 2.309-0.09909
38 1.23 1.553-0.3227
39 2.94 3.485-0.5448
40 3.42 2.927 0.4929
41 2.6 5.621-3.021
42 1.47 1.512-0.04209
43 0.86 1.417-0.557
44 1.08 1.425-0.3452
45 1.02 1.159-0.1389
46 0.84 1.103-0.263
47 3.17 2.143 1.028
48 0.03 0.02423 0.005769
49 0.07 0.1586-0.08861
50 1.06 1.328-0.2682
51 2.71 4.511-1.801
52 0.43 1.663-1.233
53 0.21 0.1893 0.0207
54 0.83 1.394-0.5641
55 3.28 4.667-1.387
56 0.43 0.6828-0.2528
57 2.58 3.17-0.5896
58 0.7 0.9454-0.2454
59 0.16 0.09057 0.06943
60 0.09 0.1359-0.04594
61 1.25 0.9784 0.2716
62 0.15 0.3348-0.1848
63 0.6 0.8509-0.2509
64 1.9 2.274-0.3741
65 0.61 0.9021-0.2921
66 0.64 1.193-0.5528
67 1.72 1.676 0.0437
68 1.36 1.211 0.1493
69 3.22 5.043-1.823
70 4.59 3.759 0.8311
71 2.77 3.999-1.229
72 1.09 1.394-0.3037
73 3.69 4.567-0.8773
74 1.09 1.452-0.362
75 4.59 1.974 2.616
76 0.2 0.5518-0.3518
77 4.17 3.154 1.016
78 6.89 4.05 2.84
79 0.95 0.9062 0.04382
80 0.09 0.6236-0.5336
81 1.66 2.226-0.5662
82 2.52 1.773 0.7473
83 0.51 0.3715 0.1385
84 0.14 0.1181 0.02188
85 2.33 1.499 0.831
86 2.15 2.332-0.1817
87 12.65 8.918 3.732
88 2.06 1.455 0.6051
89 0.07 0.4142-0.3442
90 0.07 0.1578-0.08779
91 2.1 1.878 0.2217
92 0.1 0.1089-0.008912
93 0.55 0.448 0.102
94 1.99 1.783 0.2066
95 1.74 1.815-0.07533
96 1.03 1.057-0.02725
97 2.09 1.266 0.8235
98 2.13 1.781 0.3493
99 0.67 0.9419-0.2719
100 0.17 0.09712 0.07288
101 0.09 0.5241-0.4341
102 1.02 1.113-0.09273
103 0.16 0.5271-0.3671
104 3.23 5.123-1.893
105 2.84 4.063-1.223
106 0.45 0.8742-0.4242
107 0.1-0.1378 0.2377
108 0.21 0.535-0.325
109 5.8 2.728 3.072
110 0.38 0.5441-0.1641
111 1.44 1.758-0.3181
112 0.35 0.4705-0.1205
113 0.97 1.126-0.1564
114 0.67 1.458-0.7881
115 0.34 1.029-0.6887
116 2.64 2.329 0.3108
117 2.15 2.896-0.7462
118 9.57 7.818 1.752
119 1.46 1.876-0.4158
120 3.87 2.151 1.719
121 0.07 0.3272-0.2572
122 3.34 1.95 1.39
123 1.56 1.586-0.02575
124 0.96 1.255-0.295
125 0.37 0.6001-0.2301
126 4.21 2.922 1.288
127 0.3 0.2917 0.008335
128 1.66 1.6 0.06002
129 0.07 0.06031 0.009685
130 5.91 5.06 0.8501
131 2.82 2.602 0.218
132 4.27 3.173 1.097
133 0 0.4556-0.4556
134 2.34 1.388 0.952
135 2.22 3.59-1.37
136 0.52 1.343-0.8229
137 3.01 1.55 1.46
138 0.67 0.7443-0.07426
139 3.88 5.427-1.547
140 4.26 7.38-3.12
141 0.13 0.7918-0.6618
142 0.17 0.4366-0.2666
143 1.54 1.417 0.1233
144 0.06 1.003-0.9426
145 0.31 0.2914 0.0186
146 0.88 1.336-0.4564
147 6.89 2.389 4.501
148 1.11 1.336-0.2259
149 1.92 1.863 0.05742
150 4.13 1.269 2.861
151 0.08 0.3282-0.2482
152 1.92 1.359 0.5615
153 3.14 4.26-1.12
154 6.37 4.018 2.352
155 5.9 4.877 1.023
156 0.98 2.194-1.214
157 1.41 1.002 0.4085
158 2.13 1.858 0.2725
159 0.79 0.9741-0.1841
160 0.42 0.436-0.01603
161 0.24 0.721-0.481
162 0.53 0.3749 0.1551


Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
7 0.03881 0.07762 0.9612
8 0.01215 0.0243 0.9879
9 0.003387 0.006773 0.9966
10 0.3072 0.6144 0.6928
11 0.9006 0.1988 0.09939
12 0.9465 0.1069 0.05347
13 0.9291 0.1419 0.07095
14 0.9007 0.1987 0.09935
15 0.8584 0.2832 0.1416
16 0.8059 0.3882 0.1941
17 0.7538 0.4924 0.2462
18 0.7019 0.5961 0.2981
19 0.6319 0.7362 0.3681
20 0.5865 0.827 0.4135
21 0.5222 0.9557 0.4778
22 0.5311 0.9377 0.4689
23 0.4611 0.9223 0.5389
24 0.3958 0.7916 0.6042
25 0.3313 0.6625 0.6687
26 0.2749 0.5497 0.7251
27 0.2307 0.4614 0.7693
28 0.1847 0.3693 0.8153
29 0.1442 0.2885 0.8558
30 0.1186 0.2372 0.8814
31 0.1854 0.3708 0.8146
32 0.1816 0.3632 0.8184
33 0.1445 0.289 0.8555
34 0.1144 0.2287 0.8856
35 0.08793 0.1759 0.9121
36 0.07067 0.1413 0.9293
37 0.05307 0.1061 0.9469
38 0.04111 0.08222 0.9589
39 0.03178 0.06357 0.9682
40 0.02515 0.05031 0.9748
41 0.119 0.238 0.881
42 0.09394 0.1879 0.9061
43 0.08045 0.1609 0.9195
44 0.06497 0.1299 0.935
45 0.05018 0.1004 0.9498
46 0.03866 0.07732 0.9613
47 0.04981 0.09962 0.9502
48 0.03766 0.07533 0.9623
49 0.02812 0.05625 0.9719
50 0.02131 0.04261 0.9787
51 0.0298 0.05959 0.9702
52 0.03307 0.06614 0.9669
53 0.02473 0.04945 0.9753
54 0.0204 0.04081 0.9796
55 0.02072 0.04143 0.9793
56 0.01551 0.03103 0.9845
57 0.01199 0.02398 0.988
58 0.008777 0.01755 0.9912
59 0.006255 0.01251 0.9937
60 0.004382 0.008763 0.9956
61 0.003137 0.006274 0.9969
62 0.00217 0.004339 0.9978
63 0.001505 0.00301 0.9985
64 0.001049 0.002098 0.999
65 0.0007871 0.001574 0.9992
66 0.0005801 0.00116 0.9994
67 0.0003789 0.0007578 0.9996
68 0.0002483 0.0004966 0.9998
69 0.000414 0.0008281 0.9996
70 0.0005459 0.001092 0.9995
71 0.0005521 0.001104 0.9994
72 0.0003801 0.0007602 0.9996
73 0.0003068 0.0006137 0.9997
74 0.000214 0.000428 0.9998
75 0.003102 0.006203 0.9969
76 0.002265 0.004529 0.9977
77 0.00258 0.00516 0.9974
78 0.03896 0.07791 0.961
79 0.03018 0.06035 0.9698
80 0.02495 0.0499 0.975
81 0.0209 0.0418 0.9791
82 0.01812 0.03624 0.9819
83 0.0137 0.0274 0.9863
84 0.01017 0.02034 0.9898
85 0.00892 0.01784 0.9911
86 0.006617 0.01323 0.9934
87 0.1728 0.3455 0.8272
88 0.1545 0.3089 0.8455
89 0.1312 0.2624 0.8688
90 0.1085 0.2169 0.8915
91 0.08974 0.1795 0.9103
92 0.07259 0.1452 0.9274
93 0.05816 0.1163 0.9418
94 0.04659 0.09318 0.9534
95 0.03676 0.07352 0.9632
96 0.02853 0.05705 0.9715
97 0.0256 0.0512 0.9744
98 0.02008 0.04016 0.9799
99 0.01542 0.03084 0.9846
100 0.01149 0.02298 0.9885
101 0.008885 0.01777 0.9911
102 0.006462 0.01292 0.9935
103 0.00482 0.00964 0.9952
104 0.009843 0.01969 0.9902
105 0.01146 0.02293 0.9885
106 0.008895 0.01779 0.9911
107 0.006676 0.01335 0.9933
108 0.004905 0.009811 0.9951
109 0.03853 0.07705 0.9615
110 0.0301 0.06019 0.9699
111 0.0237 0.0474 0.9763
112 0.01772 0.03545 0.9823
113 0.01322 0.02644 0.9868
114 0.01196 0.02393 0.988
115 0.01062 0.02123 0.9894
116 0.007798 0.0156 0.9922
117 0.006892 0.01378 0.9931
118 0.02325 0.04651 0.9767
119 0.02042 0.04084 0.9796
120 0.02448 0.04896 0.9755
121 0.01812 0.03624 0.9819
122 0.02018 0.04037 0.9798
123 0.01502 0.03004 0.985
124 0.01177 0.02355 0.9882
125 0.008423 0.01685 0.9916
126 0.008626 0.01725 0.9914
127 0.005987 0.01197 0.994
128 0.004251 0.008503 0.9957
129 0.002948 0.005896 0.9971
130 0.003169 0.006338 0.9968
131 0.002089 0.004179 0.9979
132 0.00186 0.003719 0.9981
133 0.001227 0.002454 0.9988
134 0.0009688 0.001938 0.999
135 0.001212 0.002423 0.9988
136 0.001466 0.002932 0.9985
137 0.00156 0.00312 0.9984
138 0.0009483 0.001897 0.9991
139 0.0008835 0.001767 0.9991
140 0.01476 0.02952 0.9852
141 0.01152 0.02303 0.9885
142 0.007398 0.0148 0.9926
143 0.004536 0.009072 0.9955
144 0.00469 0.00938 0.9953
145 0.002788 0.005576 0.9972
146 0.002062 0.004123 0.9979
147 0.1799 0.3597 0.8201
148 0.1329 0.2659 0.8671
149 0.09094 0.1819 0.9091
150 0.4642 0.9284 0.5358
151 0.3739 0.7478 0.6261
152 0.3525 0.705 0.6475
153 0.6925 0.6149 0.3075
154 0.8653 0.2694 0.1347
155 0.791 0.418 0.209


Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level37 0.2483NOK
5% type I error level820.550336NOK
10% type I error level1000.671141NOK


Ramsey RESET F-Test for powers (2 and 3) of fitted values
> reset_test_fitted
	RESET test
data:  mylm
RESET = 27.973, df1 = 2, df2 = 156, p-value = 4.152e-11
Ramsey RESET F-Test for powers (2 and 3) of regressors
> reset_test_regressors
	RESET test
data:  mylm
RESET = 14.261, df1 = 6, df2 = 152, p-value = 7.432e-13
Ramsey RESET F-Test for powers (2 and 3) of principal components
> reset_test_principal_components
	RESET test
data:  mylm
RESET = 32.691, df1 = 2, df2 = 156, p-value = 1.389e-12


Variance Inflation Factors (Multicollinearity)
> vif
`Population_(millions)`                     HDI          GDP_per_Capita 
               1.003850                1.850481                1.854204