Regression equation for Fit Regression Model and Linear Regression

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

In This Topic

Regression equation
Regression equation in coded units
Regression equation in uncoded units

Regression equation

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 for the linear model takes the following form: Y= b₀ + b₁x₁. In the regression equation, Y is the response variable, b₀ is the constant or intercept, b₁ is the estimated coefficient for the linear term (also known as the slope of the line), and x₁ is the value of the term.

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

y = b₀ + b₁X₁ + b₂X₂ + ... + b_kX_k

In the regression equation, the letters represent the following:

y is the response variable
b₀ is the constant
b₁, b₂, ..., b_k are the coefficients
X₁, X₂, ..., X_k are the values of the term

If the model contains both continuous and categorical variables, the regression equation table can display an equation for each combination of levels for the categorical variables. To use these equations for prediction, you must choose the correct equation, based on the values of the categorical variables, and then enter the values of the continuous variables.

Regression equation in coded units

When the output indicates that the regression equation is in coded units, both of the following are true:

Because you chose an option to standardize the continuous variables, Minitab used coded units to fit the model.
Minitab cannot transform the coded coefficients into uncoded coefficients for the regression equation because the model is nonhierarchical. To obtain a regression equation in uncoded units, either specify a hierarchical model or use uncoded units.

If the regression equation table does not specify coded or uncoded units, it is in uncoded units.

Interpretation

For a regression equation in coded units, interpret the coefficients using the coded values instead of the natural units. For more information, go to All statistics for Coefficients table and click "Coded coefficients".

Regression equation in uncoded units

When the output indicates that the regression equation is in uncoded units, both of the following are true:

Because you chose an option to standardize the continuous variables, Minitab used coded units to fit the model.
Minitab was able to transform the coded coefficients into uncoded coefficients for the regression equation table.

If the regression equation table does not specify coded or uncoded units, it is in uncoded units.

Interpretation

For a regression equation that is in uncoded units, interpret the coefficients using the natural units of each variable. For more information, see "Regression equation".

You can view the coded coefficients in the Coefficients table.