Multiple Linear Regression - Estimated Regression Equation
Cropland_Footprint[t] = -0.106538 -5.18308e-05`Population_(millions)`[t] + 0.947745HDI[t] + 4.04396e-06GDP_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)-0.1065 0.1247-8.5450e-01 0.3941 0.197
`Population_(millions)`-5.183e-05 0.0001519-3.4130e-01 0.7333 0.3667
HDI+0.9477 0.1989+4.7660e+00 4.239e-06 2.12e-06
GDP_per_Capita+4.044e-06 1.581e-06+2.5590e+00 0.01145 0.005726


Multiple Linear Regression - Regression Statistics
Multiple R 0.5914
R-squared 0.3497
Adjusted R-squared 0.3374
F-TEST (value) 28.32
F-TEST (DF numerator)3
F-TEST (DF denominator)158
p-value 1.044e-14
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation 0.2904
Sum Squared Residuals 13.32


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 0.3 0.3304-0.03036
2 0.78 0.6035 0.1765
3 0.6 0.6053-0.005283
4 0.33 0.4041-0.07408
5 0.78 0.7327 0.04728
6 0.74 0.599 0.141
7 2.68 1.043 1.637
8 0.82 0.9344-0.1144
9 0.66 0.6325 0.02748
10 0.97 0.7243 0.2457
11 0.52 0.7688-0.2488
12 0.29 0.4196-0.1296
13 0.56 0.7057-0.1457
14 1.32 0.6766 0.6433
15 1.15 0.9307 0.2193
16 0.49 0.3509 0.1391
17 0.5 0.4623 0.03772
18 0.37 0.5181-0.1481
19 0.63 0.6042 0.02584
20 0.3 0.5786-0.2786
21 0.62 0.6475-0.02751
22 0.31 0.8895-0.5795
23 0.6 0.6631-0.06312
24 0.47 0.2649 0.2051
25 0.21 0.2637-0.05369
26 0.54 0.3714 0.1686
27 1.46 0.965 0.495
28 0.3 0.2459 0.05411
29 0.36 0.2671 0.09287
30 0.61 0.7379-0.1279
31 0.55 0.5253 0.02465
32 0.35 0.6029-0.2529
33 0.33 0.3708-0.04078
34 0.22 0.4413-0.2213
35 0.15 0.2895-0.1395
36 0.4 0.6498-0.2498
37 0.74 0.7291 0.01088
38 0.48 0.6436-0.1636
39 0.77 0.8262-0.05619
40 0.62 0.8051-0.1851
41 1.18 1.013 0.1665
42 0.64 0.6045 0.0355
43 0.35 0.5904-0.2404
44 0.3 0.6055-0.3055
45 0.68 0.5551 0.1249
46 0.44 0.5336-0.0936
47 0.27 0.5404-0.2704
48 0.1 0.2645-0.1645
49 0.31 0.2978 0.01223
50 0.55 0.5928-0.04278
51 1.23 0.9174 0.3126
52 0.53 0.5768-0.04685
53 0.46 0.3124 0.1476
54 0.39 0.6191-0.2291
55 1.1 0.941 0.159
56 0.56 0.4389 0.1211
57 1.07 0.813 0.257
58 0.37 0.4934-0.1234
59 0.39 0.2833 0.1067
60 0.35 0.2942 0.05582
61 0.7 0.5037 0.1963
62 0.27 0.3509-0.08088
63 0.28 0.4804-0.2004
64 0.42 0.7266-0.3066
65 0.34 0.4041-0.06413
66 0.44 0.5401-0.1001
67 0.69 0.6402 0.04984
68 0.43 0.5314-0.1014
69 1.08 0.9694 0.1106
70 0.89 0.8729 0.01708
71 0.91 0.8702 0.03982
72 0.41 0.5968-0.1868
73 0.53 0.9172-0.3872
74 0.54 0.6226-0.08257
75 0.58 0.6775-0.09747
76 0.25 0.4073-0.1573
77 0.71 0.8321-0.1221
78 0.55 0.8396-0.2896
79 0.59 0.5137 0.07627
80 0.57 0.4289 0.1411
81 2.28 0.7166 1.563
82 0.67 0.6505 0.01952
83 0.22 0.3537-0.1337
84 0.23 0.2929-0.0629
85 0.79 0.6182 0.1718
86 1.89 0.7381 1.152
87 1.1 1.201-0.1006
88 0.62 0.6156 0.004389
89 0.27 0.3775-0.1075
90 0.43 0.3022 0.1278
91 0.67 0.6632 0.006829
92 0.52 0.2843 0.2357
93 0.39 0.3733 0.0167
94 0.52 0.6588-0.1388
95 0.55 0.6389-0.08895
96 0.43 0.5457-0.1157
97 0.29 0.5813-0.2913
98 0.64 0.681-0.04095
99 0.6 0.4921 0.1079
100 0.31 0.2829 0.02709
101 0.8 0.3976 0.4024
102 0.33 0.5047-0.1747
103 0.43 0.4067 0.02335
104 0.76 0.9812-0.2212
105 0.63 0.9073-0.2773
106 0.34 0.4968-0.1568
107 0.67 0.2165 0.4535
108 0.53 0.3691 0.1609
109 0.57 0.7335-0.1635
110 0.27 0.3914-0.1214
111 0.36 0.657-0.297
112 0.3 0.3745-0.07453
113 1.11 0.5425 0.5675
114 0.5 0.6068-0.1067
115 0.36 0.5236-0.1636
116 0.84 0.7433 0.09673
117 1.03 0.7734 0.2566
118 0.57 1.101-0.531
119 0.72 0.6783 0.04169
120 0.77 0.6886 0.08137
121 0.43 0.3503 0.07967
122 0.51 0.6472-0.1372
123 0.38 0.6166-0.2366
124 0.97 0.5733 0.3967
125 0.36 0.4203-0.06031
126 0.74 0.774-0.03404
127 0.34 0.3331 0.006922
128 0.49 0.6392-0.1492
129 0.47 0.2743 0.1957
130 0.67 0.9705-0.3005
131 0.31 0.7625-0.4525
132 0.64 0.8286-0.1886
133 0.47 0.374 0.09603
134 0.44 0.549-0.109
135 0.78 0.845-0.06502
136 0.31 0.6148-0.3048
137 0.43 0.5995-0.1695
138 0.35 0.4145-0.06454
139 1.47 0.9861 0.4839
140 0.75 1.132-0.3824
141 0.46 0.484-0.02403
142 0.44 0.3774 0.06257
143 0.67 0.5945 0.07546
144 0.25 0.4829-0.2329
145 0.34 0.3409-0.000907
146 1.19 0.5933 0.5967
147 0.46 0.6972-0.2372
148 0.76 0.5927 0.1673
149 0.87 0.6521 0.2179
150 0.73 0.5591 0.1709
151 0.34 0.3489-0.008927
152 0.62 0.6069 0.01305
153 0.82 0.9089-0.08889
154 0.8 0.8447-0.04468
155 1.13 0.9405 0.1895
156 0.19 0.6996-0.5096
157 0.62 0.5333 0.08672
158 0.45 0.6572-0.2072
159 0.5 0.5205-0.02046
160 0.34 0.3714-0.03136
161 0.19 0.4495-0.2595
162 0.2 0.3606-0.1606


Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
7 0.07408 0.1482 0.9259
8 0.9978 0.004436 0.002218
9 0.9948 0.01047 0.005233
10 0.9895 0.02092 0.01046
11 0.9931 0.01377 0.006886
12 0.9906 0.0188 0.009399
13 0.9867 0.02669 0.01335
14 0.9976 0.004797 0.002398
15 0.9975 0.004958 0.002479
16 0.9964 0.007208 0.003604
17 0.9938 0.01231 0.006156
18 0.9907 0.01869 0.009343
19 0.9851 0.02976 0.01488
20 0.9846 0.03085 0.01543
21 0.9773 0.04538 0.02269
22 0.9991 0.001854 0.0009269
23 0.9985 0.003056 0.001528
24 0.998 0.003935 0.001968
25 0.9969 0.006269 0.003135
26 0.9957 0.008658 0.004329
27 0.9956 0.008761 0.004381
28 0.9933 0.01331 0.006656
29 0.9903 0.01947 0.009737
30 0.987 0.02594 0.01297
31 0.9814 0.03717 0.01858
32 0.979 0.04203 0.02101
33 0.971 0.05807 0.02903
34 0.9657 0.06863 0.03431
35 0.9568 0.08641 0.04321
36 0.9514 0.09721 0.04861
37 0.9361 0.1277 0.06386
38 0.9206 0.1588 0.07941
39 0.9077 0.1845 0.09226
40 0.8962 0.2075 0.1038
41 0.8888 0.2224 0.1112
42 0.8639 0.2722 0.1361
43 0.8488 0.3025 0.1512
44 0.8416 0.3167 0.1584
45 0.8223 0.3554 0.1777
46 0.7891 0.4219 0.2109
47 0.811 0.378 0.189
48 0.7858 0.4284 0.2142
49 0.7482 0.5037 0.2518
50 0.708 0.5839 0.292
51 0.6927 0.6147 0.3073
52 0.6492 0.7016 0.3508
53 0.6185 0.7631 0.3815
54 0.5902 0.8196 0.4098
55 0.5565 0.887 0.4435
56 0.5228 0.9544 0.4772
57 0.5069 0.9862 0.4931
58 0.4648 0.9297 0.5352
59 0.4244 0.8487 0.5756
60 0.3799 0.7597 0.6201
61 0.3645 0.729 0.6355
62 0.3239 0.6478 0.6761
63 0.2984 0.5969 0.7016
64 0.3003 0.6006 0.6997
65 0.2632 0.5264 0.7368
66 0.2305 0.4611 0.7695
67 0.2002 0.4003 0.7998
68 0.1718 0.3437 0.8282
69 0.1563 0.3126 0.8437
70 0.1324 0.2648 0.8676
71 0.1126 0.2252 0.8874
72 0.09767 0.1953 0.9023
73 0.1489 0.2978 0.8511
74 0.125 0.2499 0.875
75 0.1042 0.2085 0.8958
76 0.0902 0.1804 0.9098
77 0.07582 0.1516 0.9242
78 0.08771 0.1754 0.9123
79 0.07393 0.1479 0.9261
80 0.06376 0.1275 0.9362
81 0.973 0.05407 0.02703
82 0.9652 0.06967 0.03484
83 0.958 0.08408 0.04204
84 0.9477 0.1047 0.05234
85 0.941 0.118 0.05901
86 0.9999 0.000223 0.0001115
87 0.9999 0.0002238 0.0001119
88 0.9998 0.0003472 0.0001736
89 0.9998 0.0004839 0.0002419
90 0.9997 0.000699 0.0003495
91 0.9995 0.001053 0.0005263
92 0.9994 0.001242 0.0006209
93 0.9991 0.001869 0.0009344
94 0.9987 0.002625 0.001312
95 0.9982 0.003573 0.001787
96 0.9975 0.004974 0.002487
97 0.9975 0.004978 0.002489
98 0.9964 0.007158 0.003579
99 0.9951 0.009737 0.004869
100 0.9932 0.01365 0.006827
101 0.995 0.009965 0.004982
102 0.9937 0.01252 0.006259
103 0.9912 0.01759 0.008793
104 0.9892 0.02155 0.01078
105 0.9876 0.02483 0.01241
106 0.9845 0.03098 0.01549
107 0.9909 0.01827 0.009137
108 0.9877 0.02453 0.01226
109 0.9841 0.03189 0.01595
110 0.9824 0.03519 0.01759
111 0.9824 0.03514 0.01757
112 0.9764 0.04714 0.02357
113 0.9936 0.01286 0.00643
114 0.9912 0.01766 0.008832
115 0.9903 0.01942 0.009708
116 0.9871 0.02583 0.01291
117 0.9897 0.02064 0.01032
118 0.9925 0.01494 0.007472
119 0.9897 0.02059 0.01029
120 0.9853 0.02949 0.01474
121 0.9796 0.04086 0.02043
122 0.9722 0.05552 0.02776
123 0.9669 0.06627 0.03314
124 0.9831 0.03376 0.01688
125 0.976 0.04795 0.02398
126 0.9668 0.06633 0.03316
127 0.9541 0.09184 0.04592
128 0.9391 0.1217 0.06087
129 0.9288 0.1424 0.0712
130 0.9177 0.1646 0.08231
131 0.9399 0.1202 0.06008
132 0.9243 0.1514 0.07572
133 0.907 0.1859 0.09297
134 0.881 0.2379 0.119
135 0.8458 0.3084 0.1542
136 0.8582 0.2837 0.1418
137 0.8307 0.3387 0.1693
138 0.7825 0.4349 0.2175
139 0.9472 0.1056 0.05282
140 0.9291 0.1418 0.07091
141 0.8985 0.2029 0.1015
142 0.8623 0.2753 0.1377
143 0.8126 0.3748 0.1874
144 0.778 0.4439 0.222
145 0.7157 0.5687 0.2843
146 0.9532 0.09351 0.04676
147 0.9328 0.1345 0.06723
148 0.9301 0.1398 0.06989
149 0.934 0.1319 0.06595
150 0.9612 0.07763 0.03882
151 0.9271 0.1457 0.07286
152 0.9051 0.1898 0.09489
153 0.8304 0.3392 0.1696
154 0.9084 0.1832 0.09162
155 0.8747 0.2505 0.1253


Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level25 0.1678NOK
5% type I error level630.422819NOK
10% type I error level760.510067NOK


Ramsey RESET F-Test for powers (2 and 3) of fitted values
> reset_test_fitted
	RESET test
data:  mylm
RESET = 5.9551, df1 = 2, df2 = 156, p-value = 0.003219
Ramsey RESET F-Test for powers (2 and 3) of regressors
> reset_test_regressors
	RESET test
data:  mylm
RESET = 2.2789, df1 = 6, df2 = 152, p-value = 0.03904
Ramsey RESET F-Test for powers (2 and 3) of principal components
> reset_test_principal_components
	RESET test
data:  mylm
RESET = 2.4239, df1 = 2, df2 = 156, p-value = 0.0919


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