The POWER Procedure 
MULTREG Statement 
The MULTREG statement performs power and sample size analyses for Type III tests of sets of predictors in multiple linear regression, assuming either fixed or normally distributed predictors.
Table 68.4 summarizes categories of options available in the MULTREG statement.
Task 
Options 

Define analysis 

Specify analysis information 

Specify effects 

Specify sample size 

Specify power 

Control sample size rounding 

Control ordering in output 
Table 68.5 summarizes the valid result parameters in the MULTREG statement.
Analyses 
Solve For 
Syntax 

TEST=TYPE3 
Power 

Sample size 
specifies the level of significance of the statistical test. The default is 0.05, corresponding to the usual 0.05 100% = 5% level of significance. See the section Specifying Value Lists in Analysis Statements for information about specifying the numberlist.
specifies the assumed distribution of the tested predictors. MODEL=FIXED indicates a fixed predictor distribution. MODEL=RANDOM (the default) indicates a joint multivariate normal distribution for the response and tested predictors. You can use the aliases CONDITIONAL for FIXED and UNCONDITIONAL for RANDOM. See the section Specifying Value Lists in Analysis Statements for information about specifying the keywordlist.
fixed predictors
random (multivariate normal) predictors
enables fractional input and output for sample sizes. See the section Sample Size Adjustment Options for information about the ramifications of the presence (and absence) of the NFRACTIONAL option.
specifies the number of predictors in the full model, not counting the intercept. See the section Specifying Value Lists in Analysis Statements for information about specifying the numberlist.
specifies a nointercept model (for both full and reduced models). By default, the intercept is included in the model. If you want to test the intercept, you can specify the NOINT option and simply consider the intercept to be one of the predictors being tested. See the section Specifying Value Lists in Analysis Statements for information about specifying the numberlist.
specifies the number of predictors in the reduced model, not counting the intercept. This is the same as the difference between values of the NFULLPREDICTORS= and NTESTPREDICTORS= options. Note that supplying a value of 0 is the same as specifying an test of a Pearson correlation. This option cannot be used at the same time as the NTESTPREDICTORS= option. See the section Specifying Value Lists in Analysis Statements for information about specifying the numberlist.
specifies the number of predictors being tested. This is the same as the difference between values of the NFULLPREDICTORS= and NREDUCEDPREDICTORS= options. Note that supplying identical values for the NTESTPREDICTORS= and NFULLPREDICTORS= options is the same as specifying an test of a Pearson correlation. This option cannot be used at the same time as the NREDUCEDPREDICTORS= option. See the section Specifying Value Lists in Analysis Statements for information about specifying the numberlist.
specifies the sample size or requests a solution for the sample size with a missing value (NTOTAL=.). The minimum acceptable value for the sample size depends on the MODEL=, NOINT, NFULLPREDICTORS=, NTESTPREDICTORS=, and NREDUCEDPREDICTORS= options. It ranges from to , where is the value of the NFULLPREDICTORS option. See Table 68.30 for further information about minimum NTOTAL values, and see the section Specifying Value Lists in Analysis Statements for information about specifying the numberlist.
controls how the input and default analysis parameters are ordered in the output. OUTPUTORDER=INTERNAL (the default) arranges the parameters in the output according to the following order of their corresponding options:
The OUTPUTORDER=SYNTAX option arranges the parameters in the output in the same order in which their corresponding options are specified in the MULTREG statement. The OUTPUTORDER=REVERSE option arranges the parameters in the output in the reverse of the order in which their corresponding options are specified in the MULTREG statement.
specifies the partial correlation between the tested predictors and the response, adjusting for any other predictors in the model. See the section Specifying Value Lists in Analysis Statements for information about specifying the numberlist.
specifies the desired power of the test or requests a solution for the power with a missing value (POWER=.). The power is expressed as a probability, a number between 0 and 1, rather than as a percentage. See the section Specifying Value Lists in Analysis Statements for information about specifying the numberlist.
specifies the difference in between the full and reduced models. This is equivalent to the proportion of variation explained by the predictors you are testing. It is also equivalent to the squared semipartial correlation of the tested predictors with the response. See the section Specifying Value Lists in Analysis Statements for information about specifying the numberlist.
specifies the of the full model, where is the proportion of variation explained by the model. See the section Specifying Value Lists in Analysis Statements for information about specifying the numberlist.
specifies the of the reduced model, where is the proportion of variation explained by the model. If the reduced model is an empty or interceptonly model (in other words, if NREDUCEDPREDICTORS=0 or NTESTPREDICTORS=NFULLPREDICTORS), then RSQUAREREDUCED=0 is assumed. See the section Specifying Value Lists in Analysis Statements for information about specifying the numberlist.
specifies a Type III test of a set of predictors adjusting for any other predictors in the model. This is the default test option.
To specify the number of predictors, use any two of these three options:
the number of predictors in the full model (NFULLPREDICTORS=)
the number of predictors in the reduced model (NREDUCEDPREDICTORS=)
the number of predictors being tested (NTESTPREDICTORS=)
To specify the effect, choose one of the following parameterizations:
partial correlation (by using the PARTIALCORR= option)
for the full and reduced models (by using any two of RSQUAREDIFF=, RSQUAREFULL=, and RSQUAREREDUCED=)
This section summarizes the syntax for the common analyses supported in the MULTREG statement.
You can express effects in terms of partial correlation, as in the following statements. Default values of the TEST=, MODEL=, and ALPHA= options specify a Type III test with a significance level of 0.05, assuming normally distributed predictors.
proc power; multreg model = random nfullpredictors = 7 ntestpredictors = 3 partialcorr = 0.35 ntotal = 100 power = .; run;
You can also express effects in terms of :
proc power; multreg model = fixed nfullpredictors = 7 ntestpredictors = 3 rsquarefull = 0.9 rsquarediff = 0.1 ntotal = . power = 0.9; run;
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