Definition

1. Noun:
   • A statistical relationship between variables where the regression equation is nonlinear: "Curvilinear regression" describes a type of statistical analysis used to model a relationship between a dependent variable and one or more independent variables that is not a straight line. The regression equation involves polynomial terms (like quadratic, cubic) or other nonlinear functions.

Usage Examples

• Noun:
  • The data showed a clear curve, so the analyst used curvilinear regression to model the relationship.
  • A simple linear model was insufficient; curvilinear regression provided a much better fit to the experimental results.

Advanced Usage

• "to fit a curvilinear regression": to apply a curvilinear regression model to a dataset.
  • The researcher decided to fit a curvilinear regression to account for the diminishing returns effect.

Variants and Related Words

• Curvilinear relationship (n): The nonlinear association between variables that curvilinear regression aims to model.

  • The scatter plot revealed a curvilinear relationship between temperature and reaction rate.

• Polynomial regression (n): A specific and common type of curvilinear regression where the relationship is modeled with polynomial terms.

  • Quadratic regression, a form of polynomial regression, is a simple case of curvilinear regression.

• Nonlinear regression (n): A broader category of regression analysis that includes curvilinear regression as a subset.

  • Curvilinear regression is one approach within the field of nonlinear regression.

Synonyms

• Nonlinear regression: A general term for regression analysis that models data with a nonlinear equation.

Related Terms and Concepts

• Linear regression (n): The contrasting statistical method that models the relationship between variables with a straight line.

  • When the data plot is not a straight line, curvilinear regression is preferred over linear regression.

• Coefficient of determination (R-squared) (n): A statistical measure used in both linear and curvilinear regression to indicate how well data fits the model.

  • The R-squared value improved significantly when we switched from a linear to a curvilinear regression model.

Noun

1. the relation between variables when the regression equation is nonlinear (quadratic or higher order)