# Regression equation table for Analyze Factorial Design

Find definitions and interpretation guidance for every statistic in the Regression equation table.

## Regression equation in uncoded units

The output indicates that 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. For a categorical variable, the natural units of the variable are −1 for the low level and +1 for the high level, just as if the variable was coded. You can examine the coded coefficients in the Coefficients table. For the center point term, the variable is 1 if all of the continuous factors are at their midpoints, and is 0 otherwise. 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. For the center point term, the variable is 1 if all of the continuous factors are at their midpoints, and is 0 otherwise. Because the equation is averaged over blocks, no coefficients for any blocks are in the equation.

By using this site you agree to the use of cookies for analytics and personalized content.  Read our policy