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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).

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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.

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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.

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Concept Map. Data Plotting a scatter diagram DirectionDirection, form & strength of relationshipform strength of relationship Drawing the line of best fit Data

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

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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.

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Caution: Scatter diagram cannot show causality. It only shows how these data are related to each other. Map

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

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

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

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A Challenge: Describe the relationship between height of tide and time. Sine or Cosine.

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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 DABCDABC Map

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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.

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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.

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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).

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

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