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Scatter Diagram Line of Best Fit.

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**1. **Scatter Diagram &Line of Best Fit. Prepared by
Lee Kok Ming
Li Po Chun United World College of Hong Kong
For the Statistical Section of Mathematics at
International Baccalaureate Diploma Level (equivalent to grade 11 and 12).

**2. **Objectives: At the end of this presentation you should be able to:
plot a scatter diagram,
find out the direction, form, and the qualitative strength of the relationship, and
to draw a line of best fit by inspection.

**3. **Introduction: Scatter Diagram is often used as the initial visualization aid for two sets of data.
Ideally, these data should be continuous.
The purpose: to find out whether or not these data are related.

**4. **Concept Map.

**5. **An example: Each dot on the diagram represents a pair of the data on the left.

**6. **No matter how you draw it, height and weight in this sample has a positive association (relationship or correlation).
That is, as height increases there is also a tendency for weight to increase.

**7. **Caution:

**8. **Questions: What is the relationship between x and y?
Negative association.
What is the form of this relationship?
Linear (negative association)

**9. **There are non-linear associations. How would you describe the association between
Radioactivity & time ?
Exponential decay.
Level of pollution & economic development?
Quadratic function.

**10. **Another Question: Describe the relationship between x and y.
Exponential growth.

**11. **A Challenge:

**12. **Qualitative Strength: Correlation coefficient (r) measures the strength of a linear association.
Please match the “qualitative” tags below to diagrams A, B, C & D above:
No association
Perfect positive association
Strong positive association
Weak positive association

**13. **Which is the Line of Best Fit?Revisiting our first example. The line of best fit should pass through most points in such a way that data points are distributed as evenly as possible above and below the line.

**14. **Line of Best Fit: The line of best fit always passes through the point that has both means as its coordinates (red point)
The line of best fit:
Gives us an algebraic function.
Gives us “power” to predict.

**15. **Summary: Scatter Diagram:
Visualization
Direction, form & strength of relationship
Line of Best Fit gives us an algebraic relationship
Line of Best Fit always passes through the point (mean of x, mean of y).

**16. **Links for Correlation & Regression. A good start to more correlation and regression with examples. Also uses Excel for calculation. Click here.
To try a hand-on calculation with Excel. Click here. (Please enable Macro to activate the spreadsheet.)
Return to Statistical Method website.