Results: expseries.sas

Experimental data with autocorrelated errors

The GLM Procedure

The GLM Procedure

Data

Class Levels

Class Level Information
Class Levels Values
group 3 1 2 3

Number of Observations

Number of Observations Read 150
Number of Observations Used 150

Experimental data with autocorrelated errors

The GLM Procedure

 

Dependent Variable: y

Analysis of Variance

y

Overall ANOVA

Source DF Sum of Squares Mean Square F Value Pr > F
Model 2 6.5766093 3.2883047 4.18 0.0171
Error 147 115.5570740 0.7861025    
Corrected Total 149 122.1336833      

Fit Statistics

R-Square Coeff Var Root MSE y Mean
0.053848 9.098870 0.886624 9.744333

Type I Model ANOVA

Source DF Type I SS Mean Square F Value Pr > F
group 2 6.57660933 3.28830467 4.18 0.0171

Type III Model ANOVA

Source DF Type III SS Mean Square F Value Pr > F
group 2 6.57660933 3.28830467 4.18 0.0171

Box Plot

Fit Plot for y by group

Experimental data with autocorrelated errors

The GLM Procedure

Means

group

y

Distribution of y by group

Distribution of y by group

Means

Level of
group		 N y
Mean Std Dev
1 50 9.45360000 1.06639151
2 50 9.93840000 0.74053307
3 50 9.84100000 0.82019970

Experimental data with autocorrelated errors

Durbin-Watson test and diagnostics

The AUTOREG Procedure

The Autoreg Procedure

Model 1

Dependent Variable

Dependent Variable y

Experimental data with autocorrelated errors

Durbin-Watson test and diagnostics

The AUTOREG Procedure

Ordinary Least Squares Estimates

Fit Summary

Ordinary Least Squares Estimates
SSE 115.557074 DFE 147
MSE 0.78610 Root MSE 0.88662
SBC 401.582855 AIC 392.550949
MAE 0.71491467 AICC 392.715333
MAPE 7.4719097 HQC 396.220325
Durbin-Watson 0.4637 Total R-Square 0.0538

Durbin-Watson Statistics

Durbin-Watson Statistics
Order DW Pr < DW Pr > DW
1 0.4637 <.0001 1.0000

NOTE: Pr<DW is the p-value for testing positive autocorrelation, and Pr>DW is the p-value for testing negative autocorrelation.

Parameter Estimates

Parameter Estimates
Variable DF Estimate Standard
Error		 t Value Approx
Pr > |t|
Intercept 1 9.8410 0.1254 78.48 <.0001
g1 1 -0.3874 0.1773 -2.18 0.0305
g2 1 0.0974 0.1773 0.55 0.5837

Experimental data with autocorrelated errors

Durbin-Watson test and diagnostics

The AUTOREG Procedure

Fit Diagnostics Plots

Fit Diagnostics for y

Fit Diagnostics for y

Experimental data with autocorrelated errors

Test higher lags

The AUTOREG Procedure

The Autoreg Procedure

Model 1

Dependent Variable

Dependent Variable y

Experimental data with autocorrelated errors

Test higher lags

The AUTOREG Procedure

Ordinary Least Squares Estimates

Fit Summary

Ordinary Least Squares Estimates
SSE 115.557074 DFE 147
MSE 0.78610 Root MSE 0.88662
SBC 401.582855 AIC 392.550949
MAE 0.71491467 AICC 392.715333
MAPE 7.4719097 HQC 396.220325
Durbin-Watson 0.4637 Total R-Square 0.0538

Parameter Estimates

Parameter Estimates
Variable DF Estimate Standard
Error		 t Value Approx
Pr > |t|
Intercept 1 9.8410 0.1254 78.48 <.0001
g1 1 -0.3874 0.1773 -2.18 0.0305
g2 1 0.0974 0.1773 0.55 0.5837

Autoregressive Error Analysis

Autocorrelations

Estimates of Autocorrelations
Lag Covariance Correlation -1 9 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 1 
0 0.7704 1.000000 |                    |********************|
1 0.5716 0.741920 |                    |***************     |
2 0.3959 0.513919 |                    |**********          |
3 0.2585 0.335529 |                    |*******             |
4 0.2046 0.265530 |                    |*****               |
5 0.1284 0.166614 |                    |***                 |
6 0.0612 0.079444 |                    |**                  |

Estimates of Autocorrelations

Estimates of Autocorrelations

Preliminary MSE

Preliminary MSE 0.3341

Estimates of Autoregressive Parameters

Estimates of Autoregressive Parameters
Lag Coefficient Standard
Error		 t Value
1 -0.812171 0.084151 -9.65
2 0.052453 0.108216 0.48
3 0.139210 0.106924 1.30
4 -0.204846 0.106924 -1.92
5 0.082987 0.108216 0.77
6 0.038942 0.084151 0.46

Final Model Estimation

Convergence Status

Algorithm converged.

Experimental data with autocorrelated errors

Test higher lags

The AUTOREG Procedure

Fit Summary

Maximum Likelihood Estimates
SSE 46.6587847 DFE 141
MSE 0.33091 Root MSE 0.57525
SBC 296.681658 AIC 269.58594
MAE 0.43803943 AICC 270.871655
MAPE 4.53261649 HQC 280.594069
Log Likelihood -125.79297 Transformed Regression R-Square 0.0045
Durbin-Watson 1.9149 Total R-Square 0.6180
    Observations 150

Parameter Estimates

Parameter Estimates
Variable DF Estimate Standard
Error		 t Value Approx
Pr > |t|
Intercept 1 9.8483 0.2905 33.90 <.0001
g1 1 -0.2739 0.4043 -0.68 0.4992
g2 1 -0.009457 0.3656 -0.03 0.9794
AR1 1 -0.8348 0.0844 -9.89 <.0001
AR2 1 0.0226 0.1110 0.20 0.8389
AR3 1 0.1620 0.1127 1.44 0.1528
AR4 1 -0.2204 0.1123 -1.96 0.0517
AR5 1 0.0991 0.1139 0.87 0.3860
AR6 1 0.0243 0.0869 0.28 0.7801

Parameter Estimates with AR Parameters Assumed Given

Autoregressive parameters assumed given
Variable DF Estimate Standard
Error		 t Value Approx
Pr > |t|
Intercept 1 9.8483 0.2896 34.01 <.0001
g1 1 -0.2739 0.4035 -0.68 0.4984
g2 1 -0.009457 0.3633 -0.03 0.9793

Experimental data with autocorrelated errors

Test higher lags

The AUTOREG Procedure

The Autoreg Procedure

Model 1

Dependent Variable

Dependent Variable y

Experimental data with autocorrelated errors

Test higher lags

The AUTOREG Procedure

Ordinary Least Squares Estimates

Fit Summary

Ordinary Least Squares Estimates
SSE 115.557074 DFE 147
MSE 0.78610 Root MSE 0.88662
SBC 401.582855 AIC 392.550949
MAE 0.71491467 AICC 392.715333
MAPE 7.4719097 HQC 396.220325
Durbin-Watson 0.4637 Total R-Square 0.0538

Parameter Estimates

Parameter Estimates
Variable DF Estimate Standard
Error		 t Value Approx
Pr > |t|
Intercept 1 9.8410 0.1254 78.48 <.0001
g1 1 -0.3874 0.1773 -2.18 0.0305
g2 1 0.0974 0.1773 0.55 0.5837

Test GROUP

Test GROUP
Source DF Mean
Square		 F Value Pr > F
Numerator 2 3.288305 4.18 0.0171
Denominator 147 0.786103    

Autoregressive Error Analysis

Estimates of Autocorrelations

Estimates of Autocorrelations

Preliminary MSE

Preliminary MSE 0.3463

Estimates of Autoregressive Parameters

Estimates of Autoregressive Parameters
Lag Coefficient Standard
Error		 t Value
1 -0.741920 0.055490 -13.37

Final Model Estimation

Convergence Status

Algorithm converged.

Experimental data with autocorrelated errors

Test higher lags

The AUTOREG Procedure

Fit Summary

Maximum Likelihood Estimates
SSE 48.2614905 DFE 146
MSE 0.33056 Root MSE 0.57494
SBC 276.561592 AIC 264.519051
MAE 0.44132885 AICC 264.794913
MAPE 4.58378853 HQC 269.411552
Log Likelihood -128.25953 Transformed Regression R-Square 0.0023
Durbin-Watson 1.8478 Total R-Square 0.6048
    Observations 150

Parameter Estimates

Parameter Estimates
Variable DF Estimate Standard
Error		 t Value Approx
Pr > |t|
Intercept 1 9.8353 0.3211 30.63 <.0001
g1 1 -0.2100 0.4430 -0.47 0.6363
g2 1 0.0000922 0.3899 0.00 0.9998
AR1 1 -0.7800 0.0520 -15.01 <.0001

Test GROUP

Test GROUP
Source DF Mean
Square		 F Value Pr > F
Numerator 2 0.054820 0.17 0.8473
Denominator 146 0.330558    

Parameter Estimates with AR Parameters Assumed Given

Autoregressive parameters assumed given
Variable DF Estimate Standard
Error		 t Value Approx
Pr > |t|
Intercept 1 9.8353 0.3209 30.65 <.0001
g1 1 -0.2100 0.4429 -0.47 0.6361
g2 1 0.0000922 0.3899 0.00 0.9998

Experimental data with autocorrelated errors

Test higher lags

The AUTOREG Procedure

Fit Diagnostics Plots

Fit Diagnostics for y

Fit Diagnostics for y