Scatter Plot Maker
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A scatter plot shows each pair of values as a point, so you can see whether y tends to rise or fall as x grows. The line of best fit summarizes the trend, and the correlation r (from −1 to 1) says how tightly the points follow a straight line.
Red line: least-squares line of best fit.
| Data | |
| Points n | 8 |
| Mean of x | 4.5 |
| Mean of y | 67.5 |
| Trend line (least squares) | |
| Equation | y = 4.71429x + 46.2857 |
| Slope | 4.7142857 |
| y-intercept | 46.285714 |
| Correlation r | 0.99756 |
| r² (share of variation explained) | 99.51% |
| Relationship | strong positive linear relationship |
Show steps
- Means: x̄ = 4.5, ȳ = 67.5.
- Slope: \(m = \frac{\sum (x – \bar{x})(y – \bar{y})}{\sum (x – \bar{x})^{2}}\) = 198 ÷ 42 = 4.7142857.
- Intercept: b = ȳ − m x̄ = 67.5 − (4.7142857)(4.5) = 46.285714.
- Correlation: \(r = \frac{\sum (x – \bar{x})(y – \bar{y})}{\sqrt{\sum (x – \bar{x})^{2}\sum (y – \bar{y})^{2}}}\) = 0.99756, so r² = 0.995126.
How to use the scatter plot maker
- Enter one x, y pair per line, or paste two columns from a spreadsheet.
- Optionally label the axes.
- Press Make plot to see the graph, the line of best fit, r and r².
Reading a scatter plot
- Positive association: points rise from left to right (r > 0).
- Negative association: points fall (r < 0).
- No association: no clear pattern (r near 0).
- Outliers: points far from the overall pattern.
As a rough guide, |r| ≥ 0.8 is strong, 0.5 to 0.8 moderate, and below 0.3 weak.
The line of best fit
The least-squares line ŷ = mx + b makes the sum of squared vertical distances from the points to the line as small as possible: \(m = \frac{\sum (x – \bar{x})(y – \bar{y})}{\sum (x – \bar{x})^{2}}\) and \(b = \bar{y} – m\bar{x}\). r² tells what share of the variation in y the line explains.
Correlation is not causation
Two variables can move together because a third factor drives both, or by coincidence. A scatter plot shows association; deciding cause needs a designed experiment or more evidence.
Scatter plot practice quiz: 10 questions
Test yourself with 10 multiple-choice questions. Choose an answer and press Submit to see if you are right and why. Your score appears at the end.
Quiz complete
Frequently asked questions
How do I make a scatter plot?
Put the explanatory variable on the x-axis and the response on the y-axis, then plot one point per pair. This tool does it from pasted data.
What is the line of best fit?
The straight line that minimizes the sum of squared vertical distances from the points. It is also called the least-squares regression line.
What is a good correlation coefficient?
It depends on the field, but |r| above 0.8 usually counts as strong and below 0.3 as weak.
Can I paste data from Excel or Google Sheets?
Yes. Copy two columns and paste; tabs, commas or spaces between the values all work.
What if my data is curved?
A straight line may fit poorly even if there is a strong curved pattern, and r can be near 0. Look at the plot, not just r.
Sources
- OpenStax Introductory Statistics 2e: Linear Regression and Correlation
- NIST/SEMATECH e-Handbook: Scatter Plot
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