Results: expseries.sas

Experimental data with autocorrelated errors

The GLM Procedure

The GLM Procedure

Data

Class Levels

Class Level Information
Class Levels Values
dose 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 5.6270893 2.8135447 2.73 0.0685
Error 147 151.5002980 1.0306143    
Corrected Total 149 157.1273873      

Fit Statistics

R-Square Coeff Var Root MSE y Mean
0.035812 9.752894 1.015192 10.40913

Type I Model ANOVA

Source DF Type I SS Mean Square F Value Pr > F
dose 2 5.62708933 2.81354467 2.73 0.0685

Type III Model ANOVA

Source DF Type III SS Mean Square F Value Pr > F
dose 2 5.62708933 2.81354467 2.73 0.0685

Experimental data with autocorrelated errors

The GLM Procedure

Means

dose

Means

Level of
dose		 N y
Mean Std Dev
1 50 10.1912000 0.95983978
2 50 10.3744000 0.97722464
3 50 10.6618000 1.10253454

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 151.500298 DFE 147
MSE 1.03061 Root MSE 1.01519
SBC 442.206311 AIC 433.174405
MAE 0.795608 AICC 433.338788
MAPE 7.73618678 HQC 436.843781
Durbin-Watson 0.7280 Total R-Square 0.0358

Durbin-Watson Statistics

Durbin-Watson Statistics
Order DW Pr < DW Pr > DW
1 0.7280 <.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 10.6618 0.1436 74.26 <.0001
d1 1 -0.4706 0.2030 -2.32 0.0218
d2 1 -0.2874 0.2030 -1.42 0.1590

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 151.500298 DFE 147
MSE 1.03061 Root MSE 1.01519
SBC 442.206311 AIC 433.174405
MAE 0.795608 AICC 433.338788
MAPE 7.73618678 HQC 436.843781
Durbin-Watson 0.7280 Total R-Square 0.0358

Parameter Estimates

Parameter Estimates
Variable DF Estimate Standard
Error		 t Value Approx
Pr > |t|
Intercept 1 10.6618 0.1436 74.26 <.0001
d1 1 -0.4706 0.2030 -2.32 0.0218
d2 1 -0.2874 0.2030 -1.42 0.1590

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 1.0100 1.000000 |                    |********************|
1 0.6348 0.628535 |                    |*************       |
2 0.1682 0.166527 |                    |***                 |
3 -0.1744 -0.172711 |                 ***|                    |
4 -0.1087 -0.107662 |                  **|                    |
5 -0.0490 -0.048469 |                   *|                    |
6 -0.0677 -0.067046 |                   *|                    |

Estimates of Autocorrelations

Estimates of Autocorrelations

Preliminary MSE

Preliminary MSE 0.4132

Estimates of Autoregressive Parameters

Estimates of Autoregressive Parameters
Lag Coefficient Standard
Error		 t Value
1 -0.915110 0.083499 -10.96
2 0.205198 0.112917 1.82
3 0.528676 0.105034 5.03
4 -0.533234 0.105034 -5.08
5 0.150678 0.112917 1.33
6 0.130183 0.083499 1.56

Final Model Estimation

Convergence Status

Algorithm converged.

Experimental data with autocorrelated errors

Test higher lags

The AUTOREG Procedure

Fit Summary

Maximum Likelihood Estimates
SSE 58.6231579 DFE 141
MSE 0.41577 Root MSE 0.64480
SBC 331.919757 AIC 304.82404
MAE 0.49562873 AICC 306.109754
MAPE 4.77802201 HQC 315.832169
Log Likelihood -143.41202 Transformed Regression R-Square 0.2146
Durbin-Watson 1.9605 Total R-Square 0.6269
    Observations 150

Parameter Estimates

Parameter Estimates
Variable DF Estimate Standard
Error		 t Value Approx
Pr > |t|
Intercept 1 10.6830 0.1014 105.31 <.0001
d1 1 -0.4833 0.0805 -6.00 <.0001
d2 1 -0.2676 0.0820 -3.26 0.0014
AR1 1 -0.9349 0.0840 -11.13 <.0001
AR2 1 0.2070 0.1151 1.80 0.0741
AR3 1 0.5734 0.1060 5.41 <.0001
AR4 1 -0.5702 0.1076 -5.30 <.0001
AR5 1 0.1639 0.1186 1.38 0.1693
AR6 1 0.1466 0.0868 1.69 0.0937

Parameter Estimates with AR Parameters Assumed Given

Autoregressive parameters assumed given
Variable DF Estimate Standard
Error		 t Value Approx
Pr > |t|
Intercept 1 10.6830 0.1011 105.72 <.0001
d1 1 -0.4833 0.0781 -6.19 <.0001
d2 1 -0.2676 0.0812 -3.29 0.0012

Experimental data with autocorrelated errors

Test for dose differences with AR(4) model

The AUTOREG Procedure

The Autoreg Procedure

Model 1

Dependent Variable

Dependent Variable y

Experimental data with autocorrelated errors

Test for dose differences with AR(4) model

The AUTOREG Procedure

Ordinary Least Squares Estimates

Fit Summary

Ordinary Least Squares Estimates
SSE 151.500298 DFE 147
MSE 1.03061 Root MSE 1.01519
SBC 442.206311 AIC 433.174405
MAE 0.795608 AICC 433.338788
MAPE 7.73618678 HQC 436.843781
Durbin-Watson 0.7280 Total R-Square 0.0358

Parameter Estimates

Parameter Estimates
Variable DF Estimate Standard
Error		 t Value Approx
Pr > |t|
Intercept 1 10.6618 0.1436 74.26 <.0001
d1 1 -0.4706 0.2030 -2.32 0.0218
d2 1 -0.2874 0.2030 -1.42 0.1590

Test DOSE

Test DOSE
Source DF Mean
Square		 F Value Pr > F
Numerator 2 2.813545 2.73 0.0685
Denominator 147 1.030614    

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 1.0100 1.000000 |                    |********************|
1 0.6348 0.628535 |                    |*************       |
2 0.1682 0.166527 |                    |***                 |
3 -0.1744 -0.172711 |                 ***|                    |
4 -0.1087 -0.107662 |                  **|                    |

Estimates of Autocorrelations

Estimates of Autocorrelations

Preliminary MSE

Preliminary MSE 0.4545

Estimates of Autoregressive Parameters

Estimates of Autoregressive Parameters
Lag Coefficient Standard
Error		 t Value
1 -0.859232 0.078829 -10.90
2 0.163261 0.100626 1.62
3 0.422970 0.100626 4.20
4 -0.333775 0.078829 -4.23

Final Model Estimation

Convergence Status

Algorithm converged.

Experimental data with autocorrelated errors

Test for dose differences with AR(4) model

The AUTOREG Procedure

Fit Summary

Maximum Likelihood Estimates
SSE 65.873839 DFE 143
MSE 0.46066 Root MSE 0.67872
SBC 338.768935 AIC 317.694488
MAE 0.53474079 AICC 318.48322
MAPE 5.1572987 HQC 326.256366
Log Likelihood -151.84724 Transformed Regression R-Square 0.1722
Durbin-Watson 1.8002 Total R-Square 0.5808
    Observations 150

Parameter Estimates

Parameter Estimates
Variable DF Estimate Standard
Error		 t Value Approx
Pr > |t|
Intercept 1 10.6626 0.1549 68.84 <.0001
d1 1 -0.4983 0.0922 -5.40 <.0001
d2 1 -0.2929 0.0949 -3.09 0.0024
AR1 1 -0.8707 0.0784 -11.10 <.0001
AR2 1 0.1529 0.1002 1.53 0.1292
AR3 1 0.4514 0.1009 4.47 <.0001
AR4 1 -0.3564 0.0797 -4.47 <.0001

Test DOSE

Test DOSE
Source DF Mean
Square		 F Value Pr > F
Numerator 2 6.804487 14.77 <.0001
Denominator 143 0.460656    

Parameter Estimates with AR Parameters Assumed Given

Autoregressive parameters assumed given
Variable DF Estimate Standard
Error		 t Value Approx
Pr > |t|
Intercept 1 10.6626 0.1545 69.04 <.0001
d1 1 -0.4983 0.0919 -5.42 <.0001
d2 1 -0.2929 0.0944 -3.10 0.0023