Regression on Categories
Linear Relationships
Select (Designs, Regression Models)
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and click on the Regression on Categories - Linear Relationships command. Select (Analysis I, Regression on Categories)
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check the predictor Categorical Variable and the criterion Variable, and click the Accept command. Select Descriptive Statistics
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check the Standardize Variance option and Select the Standardizing Variable Y. Click the Accept command.
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Select (Functions, Polynomial Approximations), to display polynomial of the first degree
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Select (Analysis I, Coefficients of Correlation)
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check variables X and Y, and click on the Accept command
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Select (Analysis I, Correlation Ratio)
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check variables X and Y and click on the Accept command.
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Notice that, for linear relationships, the Coefficient of Determination (.900) and the Eta Square (.900) are identical.
Curvilinear Relationships
Select (Designs, Regression Models)
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and click on the Regression on Categories - Curvilinear Relationships command. Select (Analysis I, Regression on Categories)
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check the predictor Categorical Variable and the criterion Variable, and click the Accept command. Select Descriptive Statistics
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check the Standardize Variance option and Select the Standardizing Variable Y. Click the Accept command.
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Select (Functions, Polynomial Approximations), to display polynomial of the second degree
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Select (Analysis I, Coefficients of Correlation)
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check variables X and Y, and click on the Accept command
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Select (Analysis I, Correlation Ratio)
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check variables X and Y and click on the Accept command.
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Notice that, for non-linear relationships, the Coefficient of Determination (.000) and the Eta Square (.750) are not identical and that the Coefficient of Correlation, in the case of non-linear relationships, underestimates the strength of a relationship..