# Power Analysis of Univariate Linear Regression Test

This feature requires IBM® SPSS® Statistics Base Edition.

Power analysis plays a pivotal role in a study plan, design, and conduction. The calculation of power is usually before any sample data have been collected, except possibly from a small pilot study. The precise estimation of the power may tell investigators how likely it is that a statistically significant difference will be detected based on a finite sample size under a true alternative hypothesis. If the power is too low, there is little chance of detecting a significant difference, and non-significant results are likely even if real differences truly exist.

Univariate linear regression is a basic and standard statistical approach in which researchers use the values of several variables to explain or predict values of a scale outcome.

The Power Analysis of Univariate Linear Regression test estimates the power of the type III F-test in univariate multiple linear regression models. With the effect size represented by multiple (partial) correlations, approaches for both fixed and random predictors are provided. For fixed predictors, the power estimation is based on the non-central F-distribution. For random predictors, it is assumed that the target variable and the predictors jointly follow a multivariate normal distribution. In which case, power estimation is based on the distribution of the sample multiple correlation coefficient.

Analyze > Power Analysis > Regression > Univariate Linear

2. Select a test assumption Estimate setting (Sample size or Power).
3. When Sample size is selected, enter either a Single power value for sample size estimation value (the value must be a single value between 0 and 1), or select Grid power values and then click Grid to view projected sample sizes for a range of specific Power values.

4. When Estimate power is selected, enter an appropriate Sample size for power estimation value. The value must be a single integer greater than or equal to the total number of model predictors +2 (when Include the intercept term in the model is enabled). Otherwise the value must be a single integer greater than or equal to the total number of model predictors +1.
5. Specify the value of the multiple partial correlation coefficient in the Population multiple partial correlation field. The value must be a single value between -1 and 1.
Note: When a Power value is specified, the Population multiple partial correlation value cannot be 0.

The following settings are enabled when Population multiple partial correlation is selected:

Total number of predictors in the model
Specify the number of either the total predictors, or the predictors in the full model (not including the intercept, if applicable). The value must be a single integer greater than or equal to 1.
Number of test predictors
Specify the number of either the test predictors, or the predictors in the nested model (not including the intercept, if applicable). The value must be greater than or equal to 1, but no larger than the Total number of predictors in the model value.
6. Specify R-squared values for multiple correlation coefficients for both Full model and Nested model. The values must be a single values between 0 and 1.
Note: When a Power value is specified, the Full model value must be greater than the Nested model value.

The following settings are enabled when R-squared values for is selected:

Total number of predictors - Full model
Specify the number of total predictors for the full model (not including the intercept, if applicable). The value must be a single integer greater than or equal to 1.
Total number of predictors - Nested model
Specify the number of total predictors for the nested model (not including the intercept, if applicable). The value must be greater than or equal to 1, but less than the Total number of predictors - Full model value.
7. Optionally, specify the significance level of the Type I error rate for the test in the Significance level field. The value must be a single double value between 0 and 1. The default value is 0.05.
8. You can optionally select the Include the intercept term in the model setting. The setting is enabled by default. When not selected, the intercept term is excluded from the power analysis.
9. You can optionally select whether model predictors are Fixed or Random. Fixed is the default setting.
10. You can optionally click Plot to specify Power Analysis of Univariate Linear Regression: Plot settings (chart output, two-dimensional plot settings, and three-dimensional plot settings).
Note: Plot is available only when Power is selected as the test assumption.

This procedure pastes POWER UNIVARIATE LINEAR command syntax.