AP Statistics Monday, 26 October 2015 OBJECTIVE TSW investigate the role of correlation in statistics. EVERYONE needs a graphing calculator. DUE NOW –Gummi Bear Project (assessment grade) at the beginning of the period. READ –Chapter 6: pp TODAY’S ASSIGNMENT (due on Tuesday, 10/27/15) –Chapter 6: pp (3-5 all, all)

Chapter 6 Scatterplots, Association, and 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 Wt NO

Now 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? Ht Wt Is it positive or negative? Weak or strong? YES POSITIVE????????

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

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 -

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

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

Moderate Correlation Strong correlation Properties of r (correlation coefficient) Legitimate values of r exist in the interval [-1,1]. No Correlation Weak correlation

unit The value of r does not depend on the unit of measurement for either variable. x (in mm) y Find r. Change to cm & find r. The correlations are the same

x y Find r. Switch x & y and find r. The value of r does not depend on which of the two variables is labeled x and which is labeled y. The correlations are the same.

non-resistant The value of r is non-resistant. x y Find r. Outliers affect the correlation coefficient

r linearly r is a measure of the extent to which x & y are linearly related. A value of r close to zero does not rule out any strong relationship between x and y. definite r = 0, but there is a definite relationship!

Correlation does not imply causation

Correlation Coefficient on the Calculator >> CATALOG >> DiagnosticsOn >> Enter When you ask for a linear regression equation, the correlation coefficient r is also displayed.

Assignment Chapter 6: pp (3-5 all, all) –Due tomorrow, Tuesday, 27 October 2015.