### Linear, nonlinear, and monotonic relationships - Minitab

So far we have visualized relationships between two quantitative variables using . seen two very strong non-linear (sometimes called curvilinear) relationships. Apr 25, Some pairs of variables are related positively. These are called nonlinear. A relationship between two variables may be strong or weak. Apr 19, This can mean the relationship between the two variables is doesn't fit the definition of a linear relationship is called a nonlinear relationship.

Some of these can be described mathematically. Often, a scatter plot of two variables can help to illustrate the type of relationship between them.

There are also statistical tools for testing various relationships. Negative Versus Positive Relationships Some pairs of variables are related positively. This means that as one variable goes up, the other tends to go up as well.

### Bivariate relationship linearity, strength and direction (video) | Khan Academy

For example, height and weight are positively related because taller people tend to be heavier. Other pairs are negatively related, which means that as one goes down the other tends to go up. For example, gas mileage and the weight of a car are negatively related, because heavier cars tend to get lower mileage. Linear and Nonlinear Relationships Two variables may be related linearly. This means that a straight line can represent their relationship. For example, the amount of paint needed to paint a wall is linearly related to the area of the wall.

Other relationships cannot be represented by a straight line. These are called nonlinear.

For example, the relationship between height and weight in humans is nonlinear, because doubling height usually more than doubles weight. The points in Plot 2 follow the line closely, suggesting that the relationship between the variables is strong. Weak linear relationship Plot 4: Nonlinear relationship The data points in Plot 3 appear to be randomly distributed.

They do not fall close to the line indicating a very weak relationship if one exists. If a relationship between two variables is not linear, the rate of increase or decrease can change as one variable changes, causing a "curved pattern" in the data. This curved trend might be better modeled by a nonlinear function, such as a quadratic or cubic function, or be transformed to make it linear. Plot 4 shows a strong relationship between two variables.

This relationship illustrates why it is important to plot the data in order to explore any relationships that might exist.

## Bivariate relationship linearity, strength and direction

Monotonic relationship In a monotonic relationship, the variables tend to move in the same relative direction, but not necessarily at a constant rate. In a linear relationship, the variables move in the same direction at a constant rate. Plot 5 shows both variables increasing concurrently, but not at the same rate. This relationship is monotonic, but not linear.

The Pearson correlation coefficient for these data is 0.