Presentation on theme: "Linear regression 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
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.
Moderate Correlation Strong correlation Properties of r (correlation coefficient) legitimate values of r is [-1,1] No Correlation Weak correlation
unitvalue of r does not depend on the unit of measurement for either variable x (in mm) 12152132261924 y 4710149812 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 x 12152132261924 y4710149812 Switch x & y & find r. The correlations are the same.
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 A value of r close to zero does not rule out any strong relationship between x and y. definite r = 0, but has a definite relationship!
Minister data: (Data on Elmo) r =.9999 cause So does an increase in ministers cause an increase in consumption of rum?