# Linear Relationship and Non-Linear Relationship in Statistics

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#### Linear Relationship

A linear relationship is a statistical term that describes the relationship between two variables, where one variable (the independent variable) is used to predict the other variable (the dependent variable). This relationship is represented by a straight line, and the slope of the line indicates the strength and direction of the relationship.

A positive slope means that as the independent variable increases, the dependent variable also increases. A negative slope means that as the independent variable increases, the dependent variable decreases. A slope of zero means that there is no relationship between the two variables.

Linear relationships are commonly used in statistical analysis and can be represented using a linear regression model. This model uses a line of best fit to predict the value of the dependent variable based on the value of the independent variable. Linear relationships are also known as linear association or linear correlation.

It’s important to note that linear relationship is just one of the many types of relationships that can exist between two variables, and it’s not always the case that the real-world phenomena can be described by a linear relationship.

#### Non-Linear Relationship

A non-linear relationship is a statistical term used to describe a relationship between two variables that cannot be represented by a straight line. This means that a change in one variable does not result in a predictable change in the other variable, and the relationship between the two variables is not linear.

Non-linear relationships can take many different forms, such as a curve, a polynomial, or a more complex function. These relationships can be represented using non-linear regression models, which use complex mathematical equations to estimate the relationship between the variables.

There are many different types of non-linear relationships, such as:

• Exponential relationship: one variable is a constant raised to the power of the other variable.
• Logarithmic relationship: one variable is the logarithm of the other variable.
• Power relationship: one variable is raised to a power of the other variable.
• Polynomial relationship: one variable is a polynomial function of the other variable.
• Sinusoidal relationship: one variable is a sine or cosine function of the other variable.

It’s important to note that non-linear relationships are more complex and harder to model than linear relationships. It’s not always obvious what type of non-linear relationship exists between variables and it may require more data and exploratory analysis to identify the underlying relationship.

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Author and Assistant Professor in Finance, Ardent fan of Arsenal FC. Always believe "The only good is knowledge and the only evil is ignorance - Socrates"
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