Statistics How To

Linear Relationship: Definition, Examples

Regression Analysis > Linear Relationship

What is a Linear Relationship?

A linear relationship means that you can represent the relationship between two sets of variables with a line (the word “linear” literally means “a line”). In other words, a linear line on a graph is where you can see a straight line with no curves.

This data shows a linear relationship.

This data, for force stretching a rubber band, shows a linear relationship.




This set of data shows a set of curves (it isn't linear).

This set of data shows a set of curves (it isn’t linear).



Linear Equations

If a set of data is linearly related, you can show that relationship using a linear equation. A linear equation has the form:
y = mx + b
Where:
“m” is the slope of the line,
“x” is any point (an input or x-value) on the line,
and “b” is where the line crosses the y-axis.

linear relationship

The “b” in the slope formula is the y-intercept and the “m” is the slope.


Y = mx + b is sometimes called the Slope Formula.

Positive and Negative Linear Relationships

lin rel

  • If a straight line on a graph travels upwards from left to right, it has a positive linear relationship. It shows a steady rate of increase.
  • If a straight line on a graph travels downwards from left to right, it has a negative linear relationship. It shows a steady rate of decrease.

Determining Linear Relationships from Data

If you have a set of data and you want to find out if the data has a perfectly linear relationship, you could make a scatter plot and draw a line through the dots. If all of the dots are on the line, you have a perfect relationship.

Variables on a scatter plot showing a linear relationship.

Variables on a scatter plot showing a linear relationship.




If you have a very large data set, you may not want to make a scatter plot of your data, as large numbers of dots can clutter up your graph. In this case, you may want to consider figuring out the correlation coefficient, which is a mathematical measure of how linearly related your variables are.

Next: Pearson’s Correlation Coefficient.

If you prefer an online interactive environment to learn R and statistics, this free R Tutorial by Datacamp is a great way to get started. If you’re are somewhat comfortable with R and are interested in going deeper into Statistics, try this Statistics with R track.

Linear Relationship: Definition, Examples was last modified: September 11th, 2017 by Andale

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