### Example 58.3 Reading Regression Results from a DATA= EST Data Set

This example creates an EST-type data set that contains regression coefficients and their corresponding covariance matrices computed from imputed data sets. These estimates are then combined to generate valid statistical inferences about the regression model.

The following statements use the REG procedure to generate regression coefficients:

```proc reg data=outmi outest=outreg covout noprint;
model Oxygen= RunTime RunPulse;
by _Imputation_;
run;
```

The following statements display (in Output 58.3.1) output regression coefficients and their covariance matrices from PROC REG for the first two imputed data sets:

```proc print data=outreg(obs=8);
var _Imputation_ _Type_ _Name_
Intercept RunTime RunPulse;
title 'REG Model Coefficients and Covariance Matrices'
' (First Two Imputations)';
run;
```

Output 58.3.1: EST-Type Data Set

 REG Model Coefficients and Covariance Matrices (First Two Imputations)

Obs _Imputation_ _TYPE_ _NAME_ Intercept RunTime RunPulse
1 1 PARMS   86.544 -2.82231 -0.05873
2 1 COV Intercept 100.145 -0.53519 -0.55077
3 1 COV RunTime -0.535 0.10774 -0.00345
4 1 COV RunPulse -0.551 -0.00345 0.00343
5 2 PARMS   83.021 -3.00023 -0.02491
6 2 COV Intercept 79.032 -0.66765 -0.41918
7 2 COV RunTime -0.668 0.11456 -0.00313
8 2 COV RunPulse -0.419 -0.00313 0.00264

The following statements combine the results for the imputed data sets. The EDF= option is specified to request that the adjusted degrees of freedom be used in the analysis. For a regression model with three independent variables (including the Intercept) and 31 observations, the complete-data error degrees of freedom is 28.

```proc mianalyze data=outreg edf=28;
modeleffects Intercept RunTime RunPulse;
run;
```

Output 58.3.2: Variance Information

The MIANALYZE Procedure

Variance Information
Parameter Variance DF Relative
Increase
in Variance
Fraction
Missing
Information
Relative
Efficiency
Between Within Total
Intercept 45.529229 76.543614 131.178689 9.1917 0.713777 0.461277 0.915537
RunTime 0.019390 0.106220 0.129487 18.311 0.219051 0.192620 0.962905
RunPulse 0.001007 0.002537 0.003746 12.137 0.476384 0.355376 0.933641

The Variance Information table in Output 58.3.2 displays the between-imputation, within-imputation, and total variances for combining complete-data inferences.

The Parameter Estimates table in Output 58.3.3 displays the estimated mean and standard error of the regression coefficients. The inferences are based on the t distribution. The table also displays a 95% mean confidence interval and a t test with the associated p-value for the hypothesis that the regression coefficient is equal to zero. Since the p-value for `RunPulse` is 0.1597, this variable can be removed from the regression model.

Output 58.3.3: Parameter Estimates

Parameter Estimates
Parameter Estimate Std Error 95% Confidence Limits DF Minimum Maximum Theta0 t for H0:
Parameter=Theta0
Pr > |t|
Intercept 90.837440 11.453327 65.01034 116.6645 9.1917 83.020730 100.839807 0 7.93 <.0001
RunTime -3.032870 0.359844 -3.78795 -2.2778 18.311 -3.204426 -2.822311 0 -8.43 <.0001
RunPulse -0.068578 0.061204 -0.20176 0.0646 12.137 -0.112840 -0.024910 0 -1.12 0.2842