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Chapter 5

Chapter 5. Correlation. Suppose we found the age and weight of a sample of 10 adults. Create a scatterplot of the data below. Is there any relationship between the age and weight of these adults?. Suppose we found the height and weight of a sample of 10 adults.

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Chapter 5

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  1. Chapter 5 Correlation

  2. Suppose we found the age and weight of a sample of 10 adults. Create a scatterplot of the data below. Is there any relationship between the age and weight of these adults?

  3. Suppose we found the height and weight of a sample of 10 adults. Create a scatterplot of the data below. Is there any relationship between the height and weight of these adults? Is it positive or negative? Weak or strong?

  4. The closer the points in a scatterplot are to a straight line - the stronger the relationship. The farther away from a straight line – the weaker the relationship

  5. Identify as having a positive association, a negative association, or no association. + • Heights of mothers & heights of their adult daughters - • Age of a car in years and its current value + • Weight of a person and calories consumed • Height of a person and the person’s birth month NO • Number of hours spent in safety training and the number of accidents that occur -

  6. Correlation Coefficient (r)- • A quantitative assessment of the strength & direction of the linear relationship between bivariate, quantitative data • Pearson’s sample correlation is used most • parameter - r (rho) • statistic - r

  7. Calculate r. Interpret r in context. There is a strong, positive, linear relationship between speed limit and average number of accidents per week.

  8. Strong correlation No Correlation Moderate Correlation Weak correlation Properties of r(correlation coefficient) • legitimate values of r is [-1,1]

  9. value of r does not depend on the unit of measurement for either variable x (in mm) 12 15 21 32 26 19 24 y 4 7 10 14 9 8 12 Find r. Change to cm & find r. The correlations are the same.

  10. value of r does not depend on which of the two variables is labeled x x 12 15 21 32 26 19 24 y 4 7 10 14 9 8 12 Switch x & y & find r. The correlations are the same.

  11. value of r is non-resistant x 12 15 21 32 26 19 24 y 4 7 10 14 9 8 22 Find r. Outliers affect the correlation coefficient

  12. value of r is a measure of the extent to which x & y are linearly related Find the correlation for these points: x -3 -1 1 3 5 7 9 Y 40 20 8 4 8 20 40 Sketch the scatterplot r = 0, but has a definite relationship!

  13. Minister data: (Data on Elmo) r = .9999 So does an increase in ministers cause an increase in consumption of rum?

  14. Correlation does not imply causation Correlation does not imply causation Correlation does not imply causation

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