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AP Statistics Section 3.1B Correlation

AP Statistics Section 3.1B Correlation. A scatterplot displays the direction , form and the strength of the relationship between two quantitative variables. Linear relations are particularly important because a straight line is a simple pattern that is quite common.

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AP Statistics Section 3.1B Correlation

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  1. AP Statistics Section 3.1BCorrelation

  2. A scatterplot displays the direction, form and the strengthof the relationship between two quantitative variables. Linear relations are particularly important because a straight line is a simple pattern that is quite common.

  3. We say a linear relation is strong if and weak if the points lie close to a straight line they are widely scattered about the line.

  4. Relying on our eyes to try to judge the strength of a linear relationship is very subjective. We will be determining a numerical summary called the __________. correlation

  5. The correlation ( r) measures the direction and the strength of the linear relationship between two quantitative variables.

  6. The formula for correlation of variables x and y for n individuals is:

  7. TI 83/84: Put data into 2 lists, say STAT CALC 8:LinReg(a+bx) ENTER Note: If r does not appear,2nd0 (Catalog) Scroll down to “Diagnostic On” Press ENTER twice

  8. Find r for the data on sparrowhawk colonies from section 3.1 A

  9. Important facts to remember when interpreting correlation:1. Correlation makes no distinction between __________ and ________ variables. explanatory response

  10. 2. r does not change when wechange the unit of measurement of x or y or both.

  11. 3. Positive r indicates a ________ association between the variables and negative r indicates a ________ association. positive negative

  12. 4. The correlation r is always between ___ and ___. Values of r near 0 indicate a very _____ relationship. weak

  13. Example 1: Match the scatterplots below with their corresponding correlation r

  14. 6 4 2 1 3 5

  15. Cautions to keep in mind:

  16. 1. Correlation requires both variables be quantitative.

  17. 2. Correlation does not describe curvedrelationships between variables, no matter how strong.

  18. 3. Like the mean and standard deviation, the correlation is NOT resistant to outliers.

  19. What effect does adding an outlier have on r and why?

  20. 4. Correlation is not a complete summary of two-variable data. Ideally , give the mean and standard deviations of both x and y along with the correlation.

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