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Chapter 5 Correlation

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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? Age 24304128504649352039 Wt256124320185158129103196110130

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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? Ht74657772686062736164 Wt256124320185158129103196110130 Is it positive or negative? Weak or strong?

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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

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positive negativeno Identify as having a positive association, a negative association, or no association. 1.Heights of mothers & heights of their adult daughters + 2. Age of a car in years and its current value 3.Weight of a person and calories consumed 4.Height of a person and the person’s birth month 5.Number of hours spent in safety training and the number of accidents that occur - + NO -

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Correlation Coefficient (r)- quantitativeA quantitative assessment of the strength & direction of the linear relationship between bivariate, quantitative data Pearson’s sample correlation is used most parameter - rho) statistic – r How do I determine strength?

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

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Calculate r. Interpret r in context. Speed Limit (mph) 555045403020 Avg. # of accidents (weekly) 28252117116 There is a strong, positive, linear relationship between speed limit and average number of accidents per week.

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linear transformationsvalue of r is not changed by any linear transformations x (in mm) 12152132261924 y 4710149812 Find r. Change to cm & find r. The correlations are the same. Do the following transformations & calculate r 1) 5(x + 14) 2) (y + 30) ÷ 4

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value of r does not depend on which of the two variables is labeled x Switch x & y & find r. The correlations are the same. Type: LinReg L2, L1

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non-resistantvalue of r is non-resistant x 12152132261924 y4710149822 Find r. Outliers affect the correlation coefficient

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linearlyvalue 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 Y40 20 8 4 8 20 40 What does this correlation mean? Sketch the scatterplot definite r = 0, but has a definite relationship!

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Correlation does not imply causation

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