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Slope and Correlation: Understanding the Relationship

Learn how the slope and correlation of a least squares regression line (LSRL) are related, and how to find the correlation of given scores. Also, explore the difference between correlation and causation and the role of lurking variables in interpreting relationships.

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Slope and Correlation: Understanding the Relationship

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  1. Section 3.3 Day 3

  2. Slope and Correlation Slope of an LSRL, b1, and the correlation, r, are related by the equation

  3. Slope and Correlation Slope of an LSRL, b1, and the correlation, r, are related by the equation where sx is the standard deviation of the x-values and sy is the standard deviation of the y-values.

  4. Slope and Correlation Slope of an LSRL, b1, and the correlation, r, are related by the equation where sx is the standard deviation of the x’s and sy is the standard deviation of the y’s. This means if you standardize the data so sx = 1 and sy = 1, then the slope equals the correlation.

  5. Page 156, P15(a) Find the correlation of these scores.

  6. Page 156, P15(a) a) Find the correlation of these scores. Use

  7. Page 156, P15(a)

  8. Page 156, P15(b)

  9. Page 156, P15(b) Exam 2 score = a + b(Exam 1 score)

  10. Page 156, P15(b) Exam 2 score = a + b(Exam 1 score) Exam 2 score = a + 0.368(Exam 1 score)

  11. Page 156, P15(b) Exam 2 score = a + b(Exam 1 score) Exam 2 score = a + 0.368(Exam 1 score) We know point of averages lies on regression line so ( ? , ? ) is on the line.

  12. Page 156, P15(b) Exam 2 score = a + b(Exam 1 score) Exam 2 score = a + 0.368(Exam 1 score) We know point of averages lies on regression line so ( 72.99, 75.80 ) is on the line.

  13. Page 156, P15(b) Exam 2 score = a + b(Exam 1 score) Exam 2 score = 48.94 + 0.368(Exam 1 score)

  14. Page 156, P15(b) Exam 2 score = a + b(Exam 1 score) Exam 2 score = 48.94 + 0.368(Exam 1 score) If 80 on Exam 1: predict score on Exam 2

  15. Page 156, P15(b) Exam 2 score = a + b(Exam 1 score) Exam 2 score = 48.94 + 0.368(Exam 1 score) If 80 on Exam 1: predict 78.38 on Exam 2

  16. Correlation vs Causation If you take a random sample of U.S. cities and measure the number of fast-food franchises in each city and the number of cases of stomach cancer per year in the city, you will find a high correlation. Can you conclude that an increase in fast-food availability caused an increase in cases of stomach cancer?

  17. Correlation vs Causation No, you can not conclude that an increase in fast-food availability caused an increase in cases of stomach cancer. Correlation does not imply causation!

  18. Correlation vs Causation Correlation does not imply causation! The value of r tells you nothing about why the explanatory variable and response variable are related. A lurking variable may cause the strong relationship.

  19. Correlation vs Causation What is the lurking variable in this situation?

  20. Correlation vs Causation The lurking variable is the size of the city’s population. As the size of the city’s population increases, the number of fast-food franchises and the number of stomach cancer cases per year would increase.

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