Scatter Plots and Trend Lines
Construct and interpret scatter plots and use trend lines to make predictions.
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Scatter Plots and Trend Lines
What Is a Scatter Plot?
A scatter plot shows the relationship between two sets of numerical data. Each point represents one data pair.
Correlation
| Pattern | Type | Example |
|---|---|---|
| Points go up | Positive correlation | Height and weight |
| Points go down | Negative correlation | TV time and grades |
| No pattern | No correlation | Shoe size and IQ |
Strength of Correlation
- Strong: Points are close together, nearly forming a line
- Weak: Points are spread out
- None: No pattern at all
Trend Lines (Lines of Best Fit)
A trend line is a straight line that best represents the data in a scatter plot.
Properties:
- Passes through or near most points
- Has roughly equal numbers of points above and below
- Follows the general direction of the data
Making Predictions
Use the trend line equation to predict values:
If the trend line is and :
Interpolation vs. Extrapolation
- Interpolation: Predicting within the data range (reliable)
- Extrapolation: Predicting outside the data range (less reliable)
Clusters, Gaps, and Outliers
- Cluster: A group of points close together
- Gap: A space with no data points
- Outlier: A point far from the general pattern
Two-Way Tables
For categorical data, use two-way tables to find relationships:
| Likes Math | Doesn't Like Math | Total | |
|---|---|---|---|
| Grade 7 | 30 | 20 | 50 |
| Grade 8 | 35 | 15 | 50 |
| Total | 65 | 35 | 100 |
Caution: Correlation does NOT mean causation! Just because two variables are related doesn't mean one causes the other.
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