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? Age 24 30 41 28 50 46 49 35 20 39 Wt 256 124 320 185 158 129 103 196 110 130

Create a scatterplot of the data below. 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? Ht 74 65 77 72 68 60 62 73 61 64 Wt 256 124 320 185 158 129 103 196 110 130

The farther away from a straight line – the weaker the relationship 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

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 -

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

Calculate r. Interpret r in context. Speed Limit (mph) 55 50 45 40 30 20 Avg. # of accidents (weekly) 28 25 21 17 11 6 Calculate r. Interpret r in context. There is a strong, positive, linear relationship between speed limit and average number of accidents per week.

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

The correlations are the same. 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.

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

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

r = 0, but has a definite relationship! 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!

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

Correlation does not imply causation