# Regression equation table for Analyze Definitive Screening Design

## 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.

## 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 regression line. 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 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. The units for covariates are always the units in the data, even when the factors are coded. Because the equation is averaged over blocks, no coefficients for any blocks are in the equation.

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