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; |
Number of Observations Read | 77 |
---|---|
Number of Observations Used | 77 |
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 |
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.
Karl L. Wuensch, February, 2019