Multiple Linear Regression - Estimated Regression Equation
Total_Ecological_Footprint[t] = + 2.58433 -0.00563894Grazing_Land[t] -0.0375181Forest_Land[t] + 0.351754Fishing_Water[t] + 0.960884Cropland[t] + e[t]


Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STAT
H0: parameter = 0		2-tail p-value1-tail p-value
(Intercept)+2.584 0.2207+1.1710e+01 1.554e-23 7.769e-24
Grazing_Land-0.005639 0.1737-3.2470e-02 0.9741 0.4871
Forest_Land-0.03752 0.02547-1.4730e+00 0.1426 0.07128
Fishing_Water+0.3518 0.1629+2.1590e+00 0.03224 0.01612
Cropland+0.9609 0.2632+3.6510e+00 0.0003486 0.0001743


Multiple Linear Regression - Regression Statistics
Multiple R 0.3416
R-squared 0.1167
Adjusted R-squared 0.09563
F-TEST (value) 5.547
F-TEST (DF numerator)4
F-TEST (DF denominator)168
p-value 0.0003221
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation 2.194
Sum Squared Residuals 808.6


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 2.813-2.023
2 2.21 3.125-0.9154
3 2.12 2.816-0.6958
4 0.93 2.836-1.906
5 3.14 5.673-2.533
6 2.23 3.009-0.7789
7 9.31 8.806 0.5038
8 6.06 3.189 2.871
9 2.31 3.028-0.7181
10 6.84 5.497 1.343
11 7.49 2.756 4.734
12 0.72 2.842-2.122
13 4.48 2.675 1.805
14 5.09 3.986 1.104
15 7.44 3.126 4.314
16 1.41 3.001-1.591
17 4.84 2.691 2.149
18 2.96 2.637 0.3235
19 3.12 2.829 0.2909
20 3.83 2.699 1.131
21 3.11 3.344-0.2335
22 4.06 2.981 1.079
23 3.32 3.859-0.539
24 1.21 3.054-1.844
25 0.8 2.779-1.979
26 1.17 3.106-1.936
27 8.17 6.428 1.742
28 5.65 2.616 3.034
29 1.24 2.598-1.358
30 1.46 2.923-1.463
31 4.36 3.085 1.275
32 3.38 3.032 0.3484
33 1.87 2.736-0.8656
34 1.03 2.829-1.799
35 1.29 2.54-1.25
36 0.82 2.63-1.81
37 2.84 2.966-0.1264
38 1.27 3.424-2.154
39 3.92 3.295 0.6254
40 1.95 2.881-0.9313
41 4.21 2.776 1.434
42 5.19 3.438 1.752
43 5.51 5.492 0.01842
44 2.57 2.984-0.4143
45 1.53 2.796-1.266
46 2.17 2.876-0.7059
47 2.15 2.957-0.8065
48 2.07 2.88-0.8101
49 3.97 2.947 1.023
50 0.42 2.974-2.554
51 1.02 2.894-1.874
52 2.9 3.033-0.1327
53 5.14 4.191 0.9492
54 2.34 4.734-2.394
55 4.73 2.887 1.843
56 2.02 3.103-1.083
57 1.03 2.91-1.88
58 1.58 2.692-1.112
59 5.3 3.765 1.535
60 1.97 3.237-1.267
61 4.38 3.605 0.7748
62 3.23 2.748 0.4817
63 1.89 2.953-1.063
64 1.41 2.998-1.588
65 1.53 3.66-2.13
66 3.07 2.819 0.2509
67 0.61 2.76-2.15
68 1.68 2.947-1.267
69 2.92 3.788-0.868
70 1.16 2.93-1.77
71 1.58 3.148-1.568
72 2.79 3.11-0.3197
73 1.88 2.755-0.8753
74 5.57 3.893 1.677
75 6.22 2.802 3.418
76 4.61 3.15 1.46
77 1.89 2.773-0.883
78 5.02 2.76 2.26
79 2.1 2.67-0.5696
80 5.55 3.681 1.869
81 1.03 2.781-1.751
82 1.17 2.839-1.669
83 5.69 2.847 2.843
84 8.13 2.734 5.396
85 1.91 3.048-1.138
86 1.22 3.113-1.893
87 6.29 6.087 0.2029
88 3.84 2.739 1.101
89 1.66 2.619-0.9586
90 1.21 2.783-1.573
91 3.69 2.834 0.8564
92 5.83 5.522 0.3077
93 15.82 3.098 12.72
94 3.26 2.921 0.339
95 0.99 2.871-1.881
96 0.81 3.037-2.227
97 3.71 3.573 0.137
98 1.53 3.079-1.549
99 2.08 2.737-0.657
100 2.54 3.148-0.6076
101 3.46 2.915 0.5445
102 2.89 2.97-0.08012
103 1.78 3.151-1.371
104 6.08 2.525 3.555
105 3.78 2.703 1.077
106 1.68 2.931-1.251
107 0.87 2.885-2.015
108 1.43 3.507-2.077
109 2.48 4.371-1.891
110 0.98 2.941-1.961
111 5.28 3.165 2.115
112 3.58 4.459-0.8789
113 5.6 3.138 2.462
114 1.39 3.11-1.72
115 1.56 3.204-1.644
116 1.16 3.07-1.91
117 7.52 3.218 4.302
118 0.79 2.848-2.058
119 2.79 2.862-0.0722
120 1.91 3.087-1.177
121 4.16 4.793-0.633
122 2.28 2.892-0.6119
123 1.1 2.913-1.813
124 4.44 3.603 0.8373
125 3.88 3.028 0.8517
126 10.8 3.005 7.795
127 3.65 2.717 0.9327
128 2.71 3.405-0.6951
129 5.69 3.653 2.037
130 0.87 2.991-2.121
131 4.94 2.769 2.171
132 2.45 2.726-0.2759
133 2.77 3.224-0.4545
134 1.49 2.957-1.467
135 5.61 2.731 2.879
136 1.21 2.828-1.618
137 2.7 3.268-0.5684
138 1.24 3.056-1.816
139 7.97 2.588 5.382
140 4.06 3.197 0.8632
141 5.81 2.869 2.941
142 1.29 3.552-2.262
143 1.24 2.775-1.535
144 3.31 2.976 0.3336
145 3.67 3.284 0.386
146 1.32 2.857-1.537
147 4.25 2.413 1.837
148 2.01 2.82-0.8098
149 7.25 4.362 2.888
150 5.79 2.867 2.923
151 1.51 2.976-1.466
152 0.91 2.865-1.955
153 1.32 3.039-1.719
154 2.66 3.383-0.7235
155 0.48 3.097-2.617
156 1.13 2.916-1.786
157 2.7 3.561-0.8605
158 7.92 3.099 4.821
159 2.34 3.176-0.8357
160 3.33 3.296 0.03395
161 5.47 3.195 2.275
162 1.24 2.933-1.693
163 2.84 4.062-1.222
164 4.94 3.261 1.679
165 7.93 2.766 5.164
166 8.22 4.072 4.148
167 2.91 5.094-2.184
168 2.32 3.13-0.8096
169 3.57 2.733 0.8371
170 1.65 3.163-1.513
171 1.03 2.739-1.709
172 0.99 2.78-1.79
173 1.37 2.726-1.356


Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
8 0.02608 0.05215 0.9739
9 0.005763 0.01153 0.9942
10 0.05045 0.1009 0.9496
11 0.7467 0.5065 0.2533
12 0.6893 0.6215 0.3107
13 0.6865 0.6269 0.3135
14 0.5967 0.8067 0.4033
15 0.7854 0.4292 0.2146
16 0.7598 0.4803 0.2402
17 0.7144 0.5712 0.2856
18 0.7096 0.5807 0.2904
19 0.6373 0.7253 0.3627
20 0.6239 0.7522 0.3761
21 0.5609 0.8783 0.4391
22 0.4915 0.9831 0.5085
23 0.4284 0.8568 0.5716
24 0.4171 0.8342 0.5829
25 0.4095 0.8189 0.5905
26 0.3962 0.7925 0.6038
27 0.3416 0.6833 0.6584
28 0.3956 0.7913 0.6044
29 0.3791 0.7581 0.6209
30 0.3419 0.6838 0.6581
31 0.3011 0.6023 0.6989
32 0.2504 0.5008 0.7496
33 0.2108 0.4215 0.7892
34 0.1988 0.3976 0.8012
35 0.1687 0.3374 0.8313
36 0.1596 0.3191 0.8404
37 0.1266 0.2532 0.8734
38 0.1254 0.2508 0.8746
39 0.1004 0.2008 0.8996
40 0.0809 0.1618 0.9191
41 0.07177 0.1435 0.9282
42 0.06581 0.1316 0.9342
43 0.05074 0.1015 0.9493
44 0.03839 0.07677 0.9616
45 0.03133 0.06266 0.9687
46 0.02365 0.04731 0.9763
47 0.01778 0.03556 0.9822
48 0.01318 0.02635 0.9868
49 0.009855 0.01971 0.9901
50 0.01181 0.02361 0.9882
51 0.01057 0.02114 0.9894
52 0.007449 0.0149 0.9926
53 0.005627 0.01125 0.9944
54 0.007368 0.01474 0.9926
55 0.007017 0.01404 0.993
56 0.005173 0.01035 0.9948
57 0.004873 0.009745 0.9951
58 0.003671 0.007343 0.9963
59 0.0031 0.0062 0.9969
60 0.002433 0.004867 0.9976
61 0.001741 0.003482 0.9983
62 0.001204 0.002408 0.9988
63 0.0008836 0.001767 0.9991
64 0.0007182 0.001436 0.9993
65 0.0007658 0.001532 0.9992
66 0.0006429 0.001286 0.9994
67 0.0006456 0.001291 0.9994
68 0.0004834 0.0009668 0.9995
69 0.0003436 0.0006872 0.9997
70 0.0002972 0.0005944 0.9997
71 0.0002403 0.0004805 0.9998
72 0.0001546 0.0003092 0.9998
73 0.0001038 0.0002076 0.9999
74 9.567e-05 0.0001913 0.9999
75 0.0002465 0.0004931 0.9998
76 0.0002036 0.0004072 0.9998
77 0.0001397 0.0002795 0.9999
78 0.0001629 0.0003258 0.9998
79 0.0001069 0.0002139 0.9999
80 0.0001085 0.000217 0.9999
81 9.249e-05 0.000185 0.9999
82 7.713e-05 0.0001543 0.9999
83 0.000122 0.000244 0.9999
84 0.001271 0.002542 0.9987
85 0.0009607 0.001921 0.999
86 0.0008834 0.001767 0.9991
87 0.0006116 0.001223 0.9994
88 0.0004603 0.0009205 0.9995
89 0.00033 0.0006599 0.9997
90 0.00027 0.00054 0.9997
91 0.0001911 0.0003823 0.9998
92 0.0001319 0.0002639 0.9999
93 0.5174 0.9651 0.4826
94 0.474 0.948 0.526
95 0.4623 0.9246 0.5377
96 0.4626 0.9252 0.5374
97 0.4193 0.8386 0.5807
98 0.3958 0.7917 0.6042
99 0.3581 0.7161 0.6419
100 0.3262 0.6525 0.6738
101 0.2883 0.5766 0.7117
102 0.2511 0.5022 0.7489
103 0.2286 0.4571 0.7714
104 0.282 0.5639 0.718
105 0.2526 0.5052 0.7474
106 0.2284 0.4568 0.7716
107 0.2211 0.4423 0.7789
108 0.2152 0.4304 0.7848
109 0.2254 0.4508 0.7746
110 0.218 0.436 0.782
111 0.2124 0.4248 0.7876
112 0.3091 0.6181 0.6909
113 0.3511 0.7023 0.6489
114 0.3389 0.6779 0.6611
115 0.3121 0.6241 0.6879
116 0.2983 0.5966 0.7017
117 0.3344 0.6687 0.6656
118 0.3292 0.6583 0.6708
119 0.2886 0.5772 0.7114
120 0.2729 0.5459 0.7271
121 0.2728 0.5457 0.7272
122 0.2346 0.4692 0.7654
123 0.2252 0.4504 0.7748
124 0.1998 0.3997 0.8002
125 0.1728 0.3455 0.8272
126 0.4984 0.9968 0.5016
127 0.4559 0.9117 0.5441
128 0.408 0.8159 0.592
129 0.3861 0.7722 0.6139
130 0.3799 0.7599 0.6201
131 0.3649 0.7298 0.6351
132 0.3179 0.6358 0.6821
133 0.2731 0.5463 0.7269
134 0.2563 0.5127 0.7437
135 0.2775 0.555 0.7225
136 0.2566 0.5132 0.7434
137 0.2161 0.4322 0.7839
138 0.2022 0.4044 0.7978
139 0.4335 0.867 0.5665
140 0.3885 0.777 0.6115
141 0.455 0.9099 0.545
142 0.5251 0.9498 0.4749
143 0.4867 0.9735 0.5133
144 0.431 0.862 0.569
145 0.3743 0.7486 0.6257
146 0.338 0.676 0.662
147 0.324 0.6479 0.676
148 0.2685 0.5369 0.7315
149 0.2767 0.5534 0.7233
150 0.3077 0.6154 0.6923
151 0.2566 0.5133 0.7434
152 0.2215 0.4431 0.7785
153 0.1843 0.3686 0.8157
154 0.1413 0.2826 0.8587
155 0.2866 0.5732 0.7134
156 0.2478 0.4956 0.7522
157 0.2212 0.4424 0.7788
158 0.2045 0.409 0.7955
159 0.1562 0.3123 0.8438
160 0.1064 0.2129 0.8936
161 0.7753 0.4494 0.2247
162 0.674 0.6521 0.326
163 0.6036 0.7929 0.3964
164 0.4644 0.9287 0.5356
165 0.9361 0.1278 0.0639


Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level36 0.2278NOK
5% type I error level480.303797NOK
10% type I error level510.322785NOK


Ramsey RESET F-Test for powers (2 and 3) of fitted values
> reset_test_fitted
	RESET test
data:  mylm
RESET = 0.23611, df1 = 2, df2 = 166, p-value = 0.79
Ramsey RESET F-Test for powers (2 and 3) of regressors
> reset_test_regressors
	RESET test
data:  mylm
RESET = 2.0188, df1 = 8, df2 = 160, p-value = 0.04734
Ramsey RESET F-Test for powers (2 and 3) of principal components
> reset_test_principal_components
	RESET test
data:  mylm
RESET = 1.3197, df1 = 2, df2 = 166, p-value = 0.27


Variance Inflation Factors (Multicollinearity)
> vif
 Grazing_Land   Forest_Land Fishing_Water      Cropland 
     1.110049      2.600970      2.618816      1.119633