###### Curvilinear Relationships Definition

A curvilinear relationship could be a sort of any relationship, for instance, it may be square, cubic, etc. other than a linear relationship between two variables or among a set of variables.

###### Overview of Curvilinear Relationships

A convex or U-shaped graph will form if one of the variables decreases and another variable increases but only up to a certain point, since after that both the variables increase.

And a concave graph or inverted U-shape graph will form if both the variables increases up to a certain point but after that one variable increases and another variable decreases. Other curvilinear graphs are cubic, then polynomial, etc.

###### When is a curvilinear relationship used?

Sometimes, upon analyzing data regarding correlation and linear regression, it may be observed that the relationship between an independent and a dependent variable (Let X, be the former and Y be the latter), follows a curved line. This is in contrast to the straight line that would ordinarily have been observed.

In cases like these, the line of linear regression would not be able to properly describe and predict the relationship between these variables. It would also mean that the *P* value cannot accurately test the null hypothesis, and the variables would appear to be un-associated. So, in such a case, options that may be considered, are-

- Data transformation
- Finding a curvilinear relationship.

Before trying curvilinear regression, we should try data transformation. Data transformation is a method where we take logarithmic or exponent of the variable and then find a linear relationship. It is bit easier and take less time compare to the curvilinear regression. But in curvilinear relationships we take the square, cubic or pth power of the independent variables p=2,3,4, 5,… and then find a relationship between pth power of independent variables and dependent variables.

###### Curvilinear regression hypothesis and assumptions

Hypothesis:

The null hypothesis states Ho: There is no association between the dependent variable and independent variable. It means that the independent variable, X cannot predict the dependent Y variable. Adjusted-R2 is used to measure the association between the two variables.