Obtaining Confidence Intervals for Effect SIzes in Multiple Regression:  SAS Proc GLM

    I generally prefer Proc Reg for doing multiple regression, but it does give confidence intervals for effect sizes.  I have provided my students with SAS and SPSS code that will obtain such confidence intervals, but another option is to use PROC GLM, as shown below.

Data CI;

infile 'C:\Users\Vati\Documents\_XYZZY\_Stats\SimData\MultRegr\Productivity-01.dat';

INPUT PRODUCT MORALE FAIRNESS JOBSKILL PAY TIMEOUT;

Proc GLM; Model Product = Morale -- Timeout / SS3 EFFECTSIZE alpha =.1;

run; quit;


 
The GLM Procedure

 

Number of Observations Read 77
Number of Observations Used 77

 
 
Dependent Variable: PRODUCT

 

Source DF Sum of Squares Mean Square F Value Pr > F
Model 5 1724.594680 344.918936 31.11 <.0001
Error 71 787.119606 11.086192    
Corrected Total 76 2511.714286      

 
R-Square Coeff Var Root MSE PRODUCT Mean
0.686621 3.930380 3.329593 84.71429


    What GLM is calling Eta-Squared here is R-Squared.

Proportion of Variation Accounted for
Eta-Square 0.69
Omega-Square 0.66
90% Confidence Limits (0.56,0.74)

 
Source DF Type III SS Mean Square F Value Pr > F Total Variation Accounted For Partial Variation Accounted For
Semipartial Eta-Square Semipartial Omega-Square Conservative
90% Confidence Limits
Partial Eta-Square Partial Omega-Square 90% Confidence Limits
MORALE 1 362.1360039 362.1360039 32.67 <.0001 0.1442 0.1392 0.0417 0.2640 0.3151 0.2914 0.1631 0.4235
FAIRNESS 1 1.5011896 1.5011896 0.14 0.7140 0.0006 -0.0038 0.0000 0.0308 0.0019 -0.0114 0.0000 0.0453
JOBSKILL 1 349.4080293 349.4080293 31.52 <.0001 0.1391 0.1341 0.0387 0.2584 0.3074 0.2838 0.1564 0.4165
PAY 1 3.2535983 3.2535983 0.29 0.5897 0.0013 -0.0031 0.0000 0.0408 0.0041 -0.0093 0.0000 0.0568
TIMEOUT 1 16.2419977 16.2419977 1.47 0.2301 0.0065 0.0020 0.0000 0.0660 0.0202 0.0060 0.0000 0.0960

    Here we have confidence intervals for the squared semipartial correlation coefficients.

 

Parameter Estimate Standard Error t Value Pr > |t|
Intercept 36.63575215 5.13429951 7.14 <.0001
MORALE 0.72849970 0.12746317 5.72 <.0001
FAIRNESS -0.04529749 0.12309701 -0.37 0.7140
JOBSKILL 0.61436519 0.10943377 5.61 <.0001
PAY -0.07779428 0.14360081 -0.54 0.5897
TIMEOUT 0.00860670 0.00711063 1.21 0.2301
 

    Here is the confidence interval for R2 produced by my SAS Code.

Obs eta_squared eta2_lower eta2_upper
1 0.68660 0.55863 0.73672

    Here is the confidence interval for R2 produced by my SAS Code.

 

Doing it with R

Karl L. Wuensch, February, 2019