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.
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
“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.
Y = mx + b is sometimes called the Slope Formula.
Positive and Negative Linear Relationships
- 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.
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.