Presentation on theme: "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."— Presentation transcript:
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
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?
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 How do I determine strength?
Moderate Correlation Strong correlation Properties of r (correlation coefficient) legitimate values of r is [-1,1] No Correlation Weak correlation
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.
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
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
non-resistantvalue of r is non-resistant x 12152132261924 y4710149822 Find r. Outliers affect the correlation coefficient
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!