Learn how to read and interpret scatterplots, identify relationships between variables, and understand the basics of correlation and line of best fit.
Scatterplots are graphs that show the relationship between two quantitative variables. Each point represents an individual data point with coordinates (x, y).
| Correlation Type | Description | Example |
|---|---|---|
| Positive | As x increases, y tends to increase | Study time vs. test scores |
| Negative | As x increases, y tends to decrease | Speed vs. fuel efficiency |
| No correlation | No apparent relationship between variables | Shoe size vs. intelligence |
| Non-linear | Relationship exists but isn't a straight line | Age vs. height (in children) |
A line of best fit (or trend line) is a straight line that best represents the data on a scatterplot. It can be used to make predictions.
The scatterplot below shows the relationship between the number of hours students studied for a test and their test scores (out of 100 points). A line of best fit has been drawn.
Based on the line of best fit, what would be the predicted test score for a student who studied for 6.5 hours?
The line of best fit equation is given in the graph placeholder (y = 5x + 45). To find the predicted score for 6.5 hours, substitute x = 6.5 into this equation and solve for y.
Step 1: Identify the equation of the line of best fit: y = 5x + 45
Step 2: Substitute x = 6.5 into the equation: y = 5(6.5) + 45
Step 3: Calculate: y = 32.5 + 45 = 77.5
The predicted test score is 77.5, which corresponds to answer choice B.