Linear

Definition

In statistics, 'linear' refers to relationships or functions that can be graphically represented as a straight line. Linear equations and models are used to describe the relationship between two variables.

5 Must Know Facts For Your Next Test

1. A linear relationship between two variables can be represented by the equation $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept.
2. The correlation coefficient $r$ measures the strength and direction of a linear relationship between two variables.
3. In a scatter plot, a strong linear relationship will show data points closely clustered around a straight line.
4. A positive correlation coefficient indicates a positive linear relationship, while a negative coefficient indicates a negative linear relationship.
5. The value of $r$ ranges from -1 to 1; an $r$ of 0 indicates no linear relationship.

Review Questions

• What does the slope ($m$) represent in a linear equation?
• How would you interpret an $r$ value of -0.85?
• What type of graph is typically used to visualize a linear relationship?

Related terms

Correlation Coefficient:

A measure that determines the strength and direction of the linear relationship between two variables.

Scatter Plot: A graphical representation that uses dots to represent values obtained for two different variables, often used to identify correlations.

Slope:

The rate at which one variable changes with respect to another in a linear equation; represented by $m$ in $y = mx + b$.