Scatter Plots and Trend Lines
Scatter Plots and Trend Lines
When you want to see if two different sets of data are related, a scatter plot is the perfect tool. By graphing paired data as coordinate points , you can quickly spot patterns, trends, and relationships between variables.
Types of Associations
When looking at a scatter plot, the pattern the points make is called an association (or correlation).
- Positive Association: As the -values increase, the -values also increase. The points trend upward from left to right. (Example: The more hours you study, the higher your test score).
- Negative Association: As the -values increase, the -values decrease. The points trend downward from left to right. (Example: The older a car gets, the lower its resale value).
- No Association: The points are scattered randomly with no clear pattern. (Example: Shoe size and favorite color).
Associations can also be described as strong (points are tightly clustered together in a line) or weak (points are loosely spread out but still show a general direction).
Trend Lines (Line of Best Fit)
If a scatter plot shows a linear (straight-line) association, you can draw a trend line—also known as a line of best fit. This is a straight line drawn through the center of the data points that best represents the overall trend.
How to draw a good trend line:
- Follow the general direction of the data points.
- Try to have roughly an equal number of points above and below the line.
- The line doesn't have to touch every point (in fact, it usually won't touch many at all!).
Making Predictions
Once you have a trend line, you can use it to estimate or predict values. You can either read the value directly off the graph or find the equation of the line, , to calculate it.
Example: Suppose you draw a trend line for a set of data, and its equation is . If you want to predict the -value when , simply plug into the equation:
Based on the trend line, when , the predicted value for is .