Hierarchical Multiple Regression

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Hierarchical Multiple Regression
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Original Data Set
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Correlation Super Matrix
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Correlated Predictors
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Order of Entry

• Based on
• Logic or Theory

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Order of Entry
First Entry X1
Second Entry X2
Third Entry X3
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Orthogonalize Three PredictorsbySuccessive
Partialing Method
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Remove the Effect of X1 from X2
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Predict X2

• Primary Predictor X1
• Criterion X2

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Bivariate Regression Analysis
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Predicted and Error Components
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X2

• Predicted Component
• The Effect of X1

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Remove X2
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X2

• Residual Component To Be Retained

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Replace X2 by X2
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Correlation X1 and X2
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Remove the Effect of X1 and X2 from X3
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Predict X3

• Orthogonalized Predictors X1 and X2
• Criterion X3

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Multiple Regression Analysis
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Predicted and Error Components
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Components

• X3 Predicted Component To Be Removed
• X3 Residual Component To Be Retained

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Replace X3 by X3
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Three Orthogonalized Predictors
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New Data Set
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Correlation Supper Matrix
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Semi-Partial Correlations
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Semi-Partial Correlation .577

• between X2 and Y, after removing the effect of X1
  from X2

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Semi-Partial Correlation .502

• between X3 and Y, after removing X1 and X2 from
  X3

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Coefficients of Determination
.25 .33 .25 .83
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Percentage Accounted for
First Predictor .25
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Percentage Accounted for
First Predictor .25
Second Predictor .33
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Percentage Accounted for
First Predictor .25
Second Predictor .33
Third Predictor .25
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Multiple Regression Analysis