Multiple Linear Regression - Estimated Regression Equation
Births[t] = + 9793 + 52.5714M1[t] -679.571M2[t] -320.857M3[t] -79.3333M4[t] -956.833M5[t] + 9.66667M6[t] -364.667M7[t] -185.333M8[t] -230M9[t] + 345.167M10[t] + 223.5M11[t] + e[t]


Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STAT
H0: parameter = 0		2-tail p-value1-tail p-value
(Intercept)+9793 158.7+6.1700e+01 4.709e-58 2.354e-58
M1+52.57 216.3+2.4300e-01 0.8088 0.4044
M2-679.6 216.3-3.1420e+00 0.00256 0.00128
M3-320.9 216.3-1.4830e+00 0.143 0.07149
M4-79.33 224.5-3.5340e-01 0.725 0.3625
M5-956.8 224.5-4.2620e+00 6.893e-05 3.447e-05
M6+9.667 224.5+4.3060e-02 0.9658 0.4829
M7-364.7 224.5-1.6240e+00 0.1093 0.05463
M8-185.3 224.5-8.2560e-01 0.4121 0.2061
M9-230 224.5-1.0250e+00 0.3095 0.1547
M10+345.2 224.5+1.5380e+00 0.1291 0.06457
M11+223.5 224.5+9.9560e-01 0.3232 0.1616


Multiple Linear Regression - Regression Statistics
Multiple R 0.701
R-squared 0.4914
Adjusted R-squared 0.4026
F-TEST (value) 5.535
F-TEST (DF numerator)11
F-TEST (DF denominator)63
p-value 4.088e-06
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation 388.8
Sum Squared Residuals 9.524e+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 9700 9846-145.6
2 9081 9113-32.43
3 9084 9472-388.1
4 9743 9714 29.33
5 8587 8836-249.2
6 9731 9803-71.67
7 9563 9428 134.7
8 9998 9608 390.3
9 9437 9563-126
10 1.004e+04 1.014e+04-100.2
11 9918 1.002e+04-98.5
12 9252 9793-541
13 9737 9846-108.6
14 9035 9113-78.43
15 9133 9472-339.1
16 9487 9714-226.7
17 8700 8836-136.2
18 9627 9803-175.7
19 8947 9428-481.3
20 9283 9608-324.7
21 8829 9563-734
22 9947 1.014e+04-191.2
23 9628 1.002e+04-388.5
24 9318 9793-475
25 9605 9846-240.6
26 8640 9113-473.4
27 9214 9472-258.1
28 9567 9714-146.7
29 8547 8836-289.2
30 9185 9803-617.7
31 9470 9428 41.67
32 9123 9608-484.7
33 9278 9563-285
34 1.017e+04 1.014e+04 31.83
35 9434 1.002e+04-582.5
36 9655 9793-138
37 9429 9846-416.6
38 8739 9113-374.4
39 9552 9472 79.86
40 9687 9714-26.67
41 9019 8836 182.8
42 9672 9803-130.7
43 9206 9428-222.3
44 9069 9608-538.7
45 9788 9563 225
46 1.031e+04 1.014e+04 173.8
47 1.01e+04 1.002e+04 88.5
48 9863 9793 70
49 9656 9846-189.6
50 9295 9113 181.6
51 9946 9472 473.9
52 9701 9714-12.67
53 9049 8836 212.8
54 1.019e+04 9803 387.3
55 9706 9428 277.7
56 9765 9608 157.3
57 9893 9563 330
58 9994 1.014e+04-144.2
59 1.043e+04 1.002e+04 416.5
60 1.007e+04 9793 280
61 1.011e+04 9846 266.4
62 9266 9113 152.6
63 9820 9472 347.9
64 1.01e+04 9714 383.3
65 9115 8836 278.8
66 1.041e+04 9803 608.3
67 9678 9428 249.7
68 1.041e+04 9608 800.3
69 1.015e+04 9563 590
70 1.037e+04 1.014e+04 229.8
71 1.058e+04 1.002e+04 564.5
72 1.06e+04 9793 804
73 1.068e+04 9846 834.4
74 9738 9113 624.6
75 9556 9472 83.86


Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
15 0.0005841 0.001168 0.9994
16 0.004892 0.009784 0.9951
17 0.001376 0.002752 0.9986
18 0.0003672 0.0007344 0.9996
19 0.01312 0.02623 0.9869
20 0.05195 0.1039 0.9481
21 0.09374 0.1875 0.9063
22 0.05652 0.113 0.9435
23 0.0431 0.08619 0.9569
24 0.03064 0.06127 0.9694
25 0.01864 0.03727 0.9814
26 0.02389 0.04779 0.9761
27 0.01603 0.03207 0.984
28 0.009066 0.01813 0.9909
29 0.005914 0.01183 0.9941
30 0.01516 0.03032 0.9848
31 0.01001 0.02001 0.99
32 0.01871 0.03742 0.9813
33 0.01745 0.0349 0.9825
34 0.01121 0.02241 0.9888
35 0.02351 0.04701 0.9765
36 0.02827 0.05654 0.9717
37 0.03958 0.07916 0.9604
38 0.05218 0.1044 0.9478
39 0.05495 0.1099 0.9451
40 0.03878 0.07756 0.9612
41 0.03723 0.07447 0.9628
42 0.04388 0.08776 0.9561
43 0.04179 0.08357 0.9582
44 0.1869 0.3738 0.8131
45 0.2391 0.4782 0.7609
46 0.199 0.398 0.801
47 0.2324 0.4648 0.7676
48 0.293 0.586 0.707
49 0.4917 0.9834 0.5083
50 0.4745 0.949 0.5255
51 0.5379 0.9243 0.4621
52 0.5189 0.9622 0.4811
53 0.4436 0.8872 0.5564
54 0.439 0.8781 0.561
55 0.3615 0.7231 0.6385
56 0.4897 0.9794 0.5103
57 0.4483 0.8967 0.5517
58 0.4048 0.8096 0.5952
59 0.3256 0.6513 0.6744
60 0.3726 0.7452 0.6274


Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level4 0.08696NOK
5% type I error level160.347826NOK
10% type I error level240.521739NOK


Ramsey RESET F-Test for powers (2 and 3) of fitted values
> reset_test_fitted
	RESET test
data:  mylm
RESET = 0, df1 = 2, df2 = 61, p-value = 1
Ramsey RESET F-Test for powers (2 and 3) of regressors
> reset_test_regressors
	RESET test
data:  mylm
RESET = 0, df1 = 22, df2 = 41, p-value = 1
Ramsey RESET F-Test for powers (2 and 3) of principal components
> reset_test_principal_components
	RESET test
data:  mylm
RESET = 0, df1 = 2, df2 = 61, p-value = 1


Variance Inflation Factors (Multicollinearity)
> vif
      M1       M2       M3       M4       M5       M6       M7       M8 
1.964444 1.964444 1.964444 1.840000 1.840000 1.840000 1.840000 1.840000 
      M9      M10      M11 
1.840000 1.840000 1.840000