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2.5 Correlation and Best-Fitting Lines

Learn to use scatter plots to identify data correlation and approximate best-fitting lines. Understand positive, negative, and no correlations. Practice sketching lines and deriving equations.

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2.5 Correlation and Best-Fitting Lines

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  1. 2.5 Correlation and Best-Fitting Lines

  2. In this lesson you will: • Use a scatter plot to identify the correlation shown by a set of data. • Approximate the best-fitting line for a set of data.

  3. Scatter Plot A scatter plot is a graph used to help determine whether there is a relationship between paired data. Sometimes scatter plots follow patterns that are approximately linear.

  4. Scatter Plot In the scatter plot shown, y tends to increase as x increases. Positive Correlation We say the paired data has a positive correlation.

  5. Scatter Plot In the scatter plot shown, y tends to decrease as x increases. Negative Correlation We say the paired data has a negative correlation.

  6. Scatter Plot No Linear Pattern?? No Correlation We say the paired data has a Relatively no correlation.

  7. Approximating Best-Fitting Lines for a Scatter Plot Sketch a line that appears to the pattern of the line. (9,6) There should be as many points above the line are there are below the line. (-1,-4) Pick two points on the line, and estimate the coordinates of each. These two points do not have to be original data points. Use the point-slope formula to find the equation of the line. y = x-3 This equation models the data

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