Multiple Linear Regression - Estimated Regression Equation
Births[t] = + 9330.59 + 107.621M1[t] -635.532M2[t] -287.828M3[t] + 8.74534M4[t] -879.764M5[t] + 75.7257M6[t] -309.617M7[t] -141.294M8[t] -196.97M9[t] + 367.186M10[t] + 234.51M11[t] + 11.0098t + e[t]


Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STAT
H0: parameter = 0		2-tail p-value1-tail p-value
(Intercept)+9331 136.4+6.8390e+01 4.209e-60 2.104e-60
M1+107.6 163+6.6030e-01 0.5115 0.2558
M2-635.5 162.9-3.9010e+00 0.0002384 0.0001192
M3-287.8 162.9-1.7670e+00 0.0821 0.04105
M4+8.745 169.4+5.1620e-02 0.959 0.4795
M5-879.8 169.3-5.1970e+00 2.404e-06 1.202e-06
M6+75.73 169.2+4.4750e-01 0.656 0.328
M7-309.6 169.1-1.8310e+00 0.07195 0.03597
M8-141.3 169.1-8.3580e-01 0.4065 0.2032
M9-197 169-1.1650e+00 0.2483 0.1241
M10+367.2 169+2.1730e+00 0.0336 0.0168
M11+234.5 168.9+1.3880e+00 0.1701 0.08504
t+11.01 1.569+7.0170e+00 2.013e-09 1.006e-09


Multiple Linear Regression - Regression Statistics
Multiple R 0.8465
R-squared 0.7165
Adjusted R-squared 0.6617
F-TEST (value) 13.06
F-TEST (DF numerator)12
F-TEST (DF denominator)62
p-value 8.078e-13
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation 292.6
Sum Squared Residuals 5.309e+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 9449 250.8
2 9081 8717 363.9
3 9084 9076 8.211
4 9743 9383 359.6
5 8587 8506 81.13
6 9731 9472 258.6
7 9563 9098 465
8 9998 9277 720.6
9 9437 9233 204.3
10 1.004e+04 9808 230.1
11 9918 9686 231.8
12 9252 9463-210.7
13 9737 9581 155.7
14 9035 8849 185.8
15 9133 9208-74.91
16 9487 9515-28.49
17 8700 8638 62.01
18 9627 9604 22.51
19 8947 9230-283.2
20 9283 9409-126.5
21 8829 9365-535.8
22 9947 9940 7.01
23 9628 9818-190.3
24 9318 9595-276.8
25 9605 9713-108.5
26 8640 8981-341.3
27 9214 9340-126
28 9567 9648-80.61
29 8547 8770-223.1
30 9185 9737-551.6
31 9470 9362 107.7
32 9123 9542-418.6
33 9278 9497-218.9
34 1.017e+04 1.007e+04 97.89
35 9434 9950-516.4
36 9655 9727-71.94
37 9429 9846-416.6
38 8739 9113-374.4
39 9552 9472 79.86
40 9687 9780-92.73
41 9019 8902 116.8
42 9672 9869-196.7
43 9206 9494-288.4
44 9069 9674-604.7
45 9788 9629 158.9
46 1.031e+04 1.02e+04 107.8
47 1.01e+04 1.008e+04 22.44
48 9863 9859 3.941
49 9656 9978-321.7
50 9295 9246 49.45
51 9946 9604 341.7
52 9701 9912-210.8
53 9049 9034 14.66
54 1.019e+04 1e+04 189.2
55 9706 9627 79.49
56 9765 9806-40.84
57 9893 9761 131.8
58 9994 1.034e+04-342.3
59 1.043e+04 1.021e+04 218.3
60 1.007e+04 9991 81.82
61 1.011e+04 1.011e+04 2.193
62 9266 9378-111.7
63 9820 9736 83.62
64 1.01e+04 1.004e+04 53.04
65 9115 9166-51.46
66 1.041e+04 1.013e+04 278
67 9678 9759-80.63
68 1.041e+04 9938 470
69 1.015e+04 9893 259.7
70 1.037e+04 1.047e+04-100.5
71 1.058e+04 1.035e+04 234.2
72 1.06e+04 1.012e+04 473.7
73 1.068e+04 1.024e+04 438.1
74 9738 9510 228.2
75 9556 9868-312.5


Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
16 0.08579 0.1716 0.9142
17 0.0525 0.105 0.9475
18 0.0231 0.04621 0.9769
19 0.2315 0.463 0.7685
20 0.4558 0.9116 0.5442
21 0.5046 0.9908 0.4954
22 0.4377 0.8754 0.5623
23 0.3404 0.6807 0.6596
24 0.3109 0.6217 0.6891
25 0.2672 0.5345 0.7328
26 0.2069 0.4137 0.7932
27 0.2399 0.4798 0.7601
28 0.2056 0.4113 0.7944
29 0.1533 0.3065 0.8467
30 0.173 0.346 0.827
31 0.268 0.536 0.732
32 0.2614 0.5228 0.7386
33 0.2685 0.5369 0.7315
34 0.343 0.686 0.657
35 0.3588 0.7175 0.6412
36 0.4319 0.8638 0.5681
37 0.3804 0.7607 0.6196
38 0.3291 0.6582 0.6709
39 0.4505 0.901 0.5495
40 0.4032 0.8064 0.5968
41 0.4851 0.9702 0.5149
42 0.4543 0.9086 0.5457
43 0.3808 0.7615 0.6192
44 0.6061 0.7877 0.3939
45 0.675 0.65 0.325
46 0.7523 0.4954 0.2477
47 0.7288 0.5424 0.2712
48 0.7041 0.5917 0.2959
49 0.7471 0.5057 0.2529
50 0.6994 0.6012 0.3006
51 0.9162 0.1676 0.08378
52 0.8727 0.2546 0.1273
53 0.8376 0.3248 0.1624
54 0.7913 0.4174 0.2087
55 0.7895 0.421 0.2105
56 0.7759 0.4481 0.2241
57 0.6731 0.6539 0.3269
58 0.5395 0.9211 0.4605
59 0.4161 0.8322 0.5839


Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level0 0OK
5% type I error level10.0227273OK
10% type I error level10.0227273OK


Ramsey RESET F-Test for powers (2 and 3) of fitted values
> reset_test_fitted
	RESET test
data:  mylm
RESET = 1.3552, df1 = 2, df2 = 60, p-value = 0.2657
Ramsey RESET F-Test for powers (2 and 3) of regressors
> reset_test_regressors
	RESET test
data:  mylm
RESET = 0.91359, df1 = 24, df2 = 38, p-value = 0.5849
Ramsey RESET F-Test for powers (2 and 3) of principal components
> reset_test_principal_components
	RESET test
data:  mylm
RESET = 17.31, df1 = 2, df2 = 60, p-value = 1.161e-06


Variance Inflation Factors (Multicollinearity)
> vif
      M1       M2       M3       M4       M5       M6       M7       M8 
1.969007 1.967364 1.966087 1.850159 1.847778 1.845714 1.843968 1.842540 
      M9      M10      M11        t 
1.841429 1.840635 1.840159 1.010755