Multiple Linear Regression - Estimated Regression Equation
[t] = + 827.286 + 0.693429`bouwvergunningen(t-1)`[t] + 0.0547028`bouwvergunningen(t-2)`[t] -0.21035`bouwvergunningen(t-3)`[t] + 394.269M1[t] + 561.79M2[t] + 143.17M3[t] + 630.011M4[t] + 295.46M5[t] + 147.689M6[t] + 561.323M7[t] + 115.461M8[t] + 176.606M9[t] + 286.727M10[t] + 272.342M11[t] -2.11833t + e[t]


Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STAT
H0: parameter = 0		2-tail p-value1-tail p-value
(Intercept)+827.3 242.2+3.4160e+00 0.0009436 0.0004718
`bouwvergunningen(t-1)`+0.6934 0.1013+6.8480e+00 7.938e-10 3.969e-10
`bouwvergunningen(t-2)`+0.0547 0.1241+4.4090e-01 0.6603 0.3301
`bouwvergunningen(t-3)`-0.2104 0.101-2.0830e+00 0.04004 0.02002
M1+394.3 143.6+2.7450e+00 0.007266 0.003633
M2+561.8 147.5+3.8090e+00 0.0002505 0.0001253
M3+143.2 149.1+9.6010e-01 0.3395 0.1698
M4+630 149.2+4.2240e+00 5.601e-05 2.801e-05
M5+295.5 153.5+1.9250e+00 0.05734 0.02867
M6+147.7 152.3+9.6960e-01 0.3348 0.1674
M7+561.3 151.5+3.7050e+00 0.0003581 0.000179
M8+115.5 150.4+7.6760e-01 0.4447 0.2223
M9+176.6 149.5+1.1810e+00 0.2406 0.1203
M10+286.7 148.8+1.9260e+00 0.05712 0.02856
M11+272.3 145.3+1.8740e+00 0.06402 0.03201
t-2.118 1.045-2.0260e+00 0.04559 0.0228


Multiple Linear Regression - Regression Statistics
Multiple R 0.7946
R-squared 0.6314
Adjusted R-squared 0.5719
F-TEST (value) 10.62
F-TEST (DF numerator)15
F-TEST (DF denominator)93
p-value 2.331e-14
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation 307.6
Sum Squared Residuals 8.8e+06


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 2842 2524 318.3
2 3440 2928 511.8
3 2678 2990-311.6
4 2981 2896 84.81
5 2260 2602-342.2
6 2844 2129 714.8
7 2546 2842-296.5
8 2456 2371 84.55
9 2295 2229 66.07
10 2379 2283 95.95
11 2471 2335 136.1
12 2057 2163-105.7
13 2280 2255 24.85
14 2351 2533-182.2
15 2276 2261 15.03
16 2548 2651-102.7
17 2311 2484-172.6
18 2201 2200 1.014
19 2725 2465 260
20 2408 2424-16.26
21 2139 2315-176.3
22 1898 2109-211.2
23 2539 1978 561.5
24 2070 2191-121
25 2063 2344-280.6
26 2565 2344 221.3
27 2443 2369 73.67
28 2196 2798-602.4
29 2799 2178 620.8
30 2076 2459-382.6
31 2628 2454 174.3
32 2292 2222 69.91
33 2155 2230-75.4
34 2476 2109 367.1
35 2138 2378-240.2
36 1854 1916-61.72
37 2081 2025 56.08
38 1795 2403-608.3
39 1756 1856-100.4
40 2237 2251-13.68
41 1960 2306-345.6
42 1829 1998-169.1
43 2524 2202 321.5
44 2077 2288-210.5
45 2366 2102 263.8
46 2185 2240-54.92
47 2098 2208-109.7
48 1836 1802 33.74
49 1863 2046-183
50 2044 2234-190.1
51 2136 1996 140.5
52 2931 2548 382.8
53 3263 2730 533.2
54 3328 2834 493.7
55 3570 3142 428.2
56 2313 2795-482.3
57 1623 1982-359.3
58 1316 1492-176.2
59 1507 1489 17.56
60 1419 1476-56.77
61 1660 1882-221.9
62 1790 2169-379.5
63 1733 1871-137.6
64 2086 2272-186.2
65 1814 2150-335.8
66 2241 1843 398.4
67 1943 2461-518.1
68 1773 1887-114
69 2143 1722 420.9
70 2087 2140-53.03
71 1805 2141-335.7
72 1913 1590 323.2
73 2296 2053 242.8
74 2500 2549-49.4
75 2210 2268-58.35
76 2526 2483 43.42
77 2249 2306-57.25
78 2024 2043-18.57
79 2091 2216-125.4
80 2045 1861 184.1
81 1882 1939-57.01
82 1831 1917-86.37
83 1964 1866 97.74
84 1763 1716 47.48
85 1688 1986-298.3
86 2149 2061 88.28
87 1823 1998-174.8
88 2094 2297-203.5
89 2145 2034 111.1
90 1791 2003-211.8
91 1996 2115-118.6
92 2097 1779 318.3
93 1796 1993-197.5
94 1963 1855 107.9
95 2042 1917 125.3
96 1746 1770-23.5
97 2210 1926 284.4
98 2968 2380 588.1
99 3126 2572 553.5
100 3708 3111 597.4
101 3015 3027-11.71
102 1569 2395-825.9
103 1518 1643-125.4
104 1393 1227 166.3
105 1615 1500 114.6
106 1777 1766 10.75
107 1648 1901-252.5
108 1463 1499-35.77
109 1779 1722 57.5


Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
19 0.4376 0.8753 0.5624
20 0.7029 0.5942 0.2971
21 0.5786 0.8428 0.4214
22 0.4489 0.8978 0.5511
23 0.5086 0.9827 0.4914
24 0.466 0.9321 0.534
25 0.3918 0.7837 0.6082
26 0.3259 0.6518 0.6741
27 0.3354 0.6707 0.6646
28 0.3256 0.6511 0.6744
29 0.6446 0.7109 0.3554
30 0.59 0.82 0.41
31 0.5309 0.9382 0.4691
32 0.4666 0.9331 0.5334
33 0.3949 0.7898 0.6051
34 0.4774 0.9548 0.5226
35 0.4288 0.8575 0.5712
36 0.3768 0.7537 0.6232
37 0.3116 0.6233 0.6884
38 0.489 0.9779 0.511
39 0.4684 0.9367 0.5316
40 0.4298 0.8596 0.5702
41 0.3845 0.769 0.6155
42 0.326 0.6519 0.674
43 0.3335 0.6671 0.6665
44 0.3018 0.6036 0.6982
45 0.3628 0.7257 0.6372
46 0.3219 0.6439 0.6781
47 0.2705 0.5409 0.7295
48 0.2187 0.4374 0.7813
49 0.1782 0.3565 0.8218
50 0.1458 0.2916 0.8542
51 0.128 0.2561 0.872
52 0.2633 0.5267 0.7367
53 0.5523 0.8953 0.4477
54 0.6595 0.6811 0.3405
55 0.7675 0.4649 0.2325
56 0.8539 0.2922 0.1461
57 0.8544 0.2912 0.1456
58 0.8304 0.3393 0.1696
59 0.7893 0.4215 0.2107
60 0.7423 0.5153 0.2577
61 0.697 0.606 0.303
62 0.7249 0.5502 0.2751
63 0.6711 0.6578 0.3289
64 0.6515 0.697 0.3485
65 0.6395 0.7209 0.3605
66 0.812 0.3761 0.188
67 0.8919 0.2161 0.1081
68 0.8575 0.285 0.1425
69 0.9092 0.1817 0.09084
70 0.8891 0.2217 0.1109
71 0.8674 0.2653 0.1326
72 0.9008 0.1983 0.09917
73 0.8802 0.2396 0.1198
74 0.8775 0.245 0.1225
75 0.8326 0.3349 0.1674
76 0.7817 0.4366 0.2183
77 0.7168 0.5663 0.2832
78 0.7954 0.4092 0.2046
79 0.7532 0.4936 0.2468
80 0.6959 0.6083 0.3041
81 0.612 0.776 0.388
82 0.5217 0.9566 0.4783
83 0.4931 0.9863 0.5069
84 0.3998 0.7996 0.6002
85 0.3934 0.7868 0.6066
86 0.3082 0.6164 0.6918
87 0.4222 0.8444 0.5778
88 0.817 0.3659 0.183
89 0.9389 0.1222 0.06112
90 0.8777 0.2445 0.1223


Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level0 0OK
5% type I error level00OK
10% type I error level00OK


Ramsey RESET F-Test for powers (2 and 3) of fitted values
> reset_test_fitted
	RESET test
data:  mylm
RESET = 3.5773, df1 = 2, df2 = 91, p-value = 0.03195
Ramsey RESET F-Test for powers (2 and 3) of regressors
> reset_test_regressors
	RESET test
data:  mylm
RESET = 0.72655, df1 = 30, df2 = 63, p-value = 0.8302
Ramsey RESET F-Test for powers (2 and 3) of principal components
> reset_test_principal_components
	RESET test
data:  mylm
RESET = 6.2591, df1 = 2, df2 = 91, p-value = 0.002839


Variance Inflation Factors (Multicollinearity)
> vif
`bouwvergunningen(t-1)` `bouwvergunningen(t-2)` `bouwvergunningen(t-3)` 
               2.576087                3.815185                2.509704 
                     M1                      M2                      M3 
               1.980365                1.898567                1.940463 
                     M4                      M5                      M6 
               1.941558                2.056594                2.024735 
                     M7                      M8                      M9 
               2.002387                1.974384                1.951396 
                    M10                     M11                       t 
               1.933338                1.842257                1.246279