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Correlation

Correlation. In this lesson you will cover:. How to measure and interpret correlation About the effects of scaling data on correlation.

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Correlation

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  1. Correlation

  2. In this lesson you will cover: • How to measure and interpret correlation • About the effects of scaling data on correlation

  3. When two sets of random variables (bivariate data) are displayed on a scatter graph, we are used to describing the correlation - but how do you measure how good it is?

  4. Two sets of random variables (bivariate data) we can describe correlation but how do you measure it? x - = - y - = + - × + = - x - = + y - = + + × + = + x - = - y - = - - × - = + x - = + y - = - + × - = -

  5. Covariance – how do you interpret it? • When the covariance is positive it suggests positive correlation • When covariance is negative it suggests negative correlation • When the covariance is close to zero it suggests no correlation.

  6. Covariance – can you see any potential problems with this method alone? • When the covariance is positive it suggest positive correlation • When covariance is negative it suggest negative correlation • When the covariance is close to zero it suggests no correlation. • You guessed it: • (you don’t know the range)

  7. Pearson Moment Correlation Coefficient • Is to standardise the covariance so that it can interpreted easily. It converts the covariance to a number between -1 to 1, where: • -1 is a perfect negative correlation • 1 is a perfect positive correlation • 0 is no correlation Karl Pearson 1857 - 1936

  8. Pearson Moment Correlation Coefficient can be simplified to: This is the covariance r = This is the standard deviation of y This is the standard deviation of x

  9. Pearson Moment Correlation Coefficient To calculate r, we need to work out Sxy, Sxx and Syy efficiently. The following formulae can be used: Sxy = Sxx = = Sxy = = Karl Pearson 1857 - 1936

  10. Task 1 • For the following data set, calculate Sxx, Syy and Sxy. Then calculate the Product Moment Correlation Coefficient (the PMCC) for the data and comment on what you find.

  11. Task 2 • A university department wishes to attract students to their subject by suggesting that it leads to a rising income even though the starting salary might be low. They do a random sample of 8 of their past students with the following results: • Calculate the PMCC for these data. • Does this figure bear out the department’s claim?

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