1. Chapter 5 Summarizing Bivariate Data Correlation

2. Variables: Response variable (y) measures an outcome (dependent) Explanatory variable (x) helps explain or influence changes in a response variable (independent)

3. 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

4. Does there seem to be a relationship between age and weight of these adults?

5. 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?

6. Does there seem to be a relationship between height and weight of these adults?

7. When describing relationships between two variables, you should address: Direction (positive, negative, or neither) Strength of the relationship (how much scattering?) Form ( linear or some other pattern) Unusual features (outliers or influential points) And ALWAYS in context of the problem!

8. 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 -

9. 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

10. Correlation measures the direction and the strength of a linear relationship between 2 quantitative variables.

11. Height (in) Weight (lb) 74256 65124 77320 72185 68158 60129 62103 73196 61110 64130 = Find the mean and standard deviation of the heights and weights of the 10 students:

12. Height (in) Weight (lb) 74256 1.061.211.28 65124 -.43-.67.29 77320 1.552.123.29 72185.73.20.14 68158.07-.19-.01 60129 -1.25-.60.75 62103 -.92-.97.90 73196.89.35.32 61110 -1.09-.87.95 64130 -.59.35 = 8.24/9=.9157 Find the mean and standard deviation of the heights and weights of the 10 students:

13. 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

14. 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. r =.9964

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

16. Some Correlation Pictures

22. x (in mm) 12152132261924 y 4710149812 Find r. Interpret r in context..9181 There is a strong, positive, linear relationship between speed limit and the number of weekly accidents.

23. transformations value of r is not changed by any transformations x (in mm) 12152132261924 y 4710149812 Find r. Change to cm & find r. The correlations are the same..9181 Do the following transformations & calculate r 1) 5(x + 14) 2) (y + 30) ÷ 4 STILL =.9181

24. 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

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

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

27. 1)Correlation makes no distinction between explanatory and response variable. It is unitless. 2) Correlation does not change when we change the units of measurement of x, y, or both. 3) Correlation requires both variables to be quantitative. 4) Correlation does not describe curved relationship between variables, no matter how strong. Only the linear relationship between variables. 5) Like the mean and standard deviation, the correlation is not resistant: r is strongly affected by a few outlying observations.

28. Correlation does not imply causation