# Regression equation for Analyze Response Surface Design

Find definitions and interpretations for every statistic in the Regression Equation table.

## Regression equation in coded units

The output indicates that the regression equation is in coded units when the model is nonhierarchical. For more information on hierarchy, go to What are hierarchical models?.

### Interpretation

Use the regression equation to describe the relationship between the response and the terms in the model. The regression equation is an algebraic representation of the response surface.

The first-order regression equation with more than one term takes the following form:

If the response surface contains curvature, then a polynomial model of higher degree is used. The second-order model is:

In the regression equation, the letters represent the following:
• y is the response variable
• b0 is the constant
• b1, b2, ..., bk are the coefficients
• X1, X2, ..., Xk are the values of the terms
• ε is the error term

For a regression equation in coded units, the low level of a factor is −1 and the high level of a factor is +1. Because the equation is averaged over blocks, no coefficients for any blocks are in the equation.

## Regression equation in uncoded units

The output indicates the the regression equation is in uncoded units when the model is hierarchical. For more information on hierarchy, go to What are hierarchical models?.

### Interpretation

Use the regression equation to describe the relationship between the response and the terms in the model. The regression equation is an algebraic representation of the regression model. The regression equation with more than one term takes the following form:

y = b0 + b1X1 + b2X2 + ... + bkXk

In the regression equation, the letters represent the following:
• y is the response variable
• b0 is the constant
• b1, b2, ..., bk are the coefficients
• X1, X2, ..., Xk are the values of the terms

For a regression equation that is in uncoded units, interpret the coefficients using the natural units of each variable. You can examine the coded coefficients in the Coefficients table. Because the equation is averaged over blocks, no coefficients for any blocks are in the equation.

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