Unit 4-1

Unit 4-1 - Correlation Suppose we found the age and weight...

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Unformatted text preview: 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 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 closer the points in a The farther away from a scatterplot are to a straight straight line – the weaker the line - the stronger the relationship relationship. Identify as having a positive association, positive a negative association, or no association. negative no 1. Heights of mothers & heights of their adult + daughters 2. Age of a car in years and its current value3. Weight of a person and calories consumed + 4. Height of a person and the person’s birth NO month 5. Number of hours spent in safety training and the number of accidents that occur Correlation Coefficient (r)• A quantitative assessment of the strength quantitative & direction of the linear relationship between bivariate, quantitative data • Pearson’s sample correlation is used most • parameter - ρ ( rho) • statistic - r xi − x yi − y 1 r= ∑ s s n − 1 x y Speed Limit (mph) Avg. # of accidents (weekly) 55 50 45 40 30 20 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 are [-1,1] No Correlation Strong correlation Moderate Correlation Weak correlation -1 -.8 -.5 0 .5 .8 1 •value of r does not depend on the unit unit of measurement for either variable x (in mm) 12 15 y 47 21 10 32 14 26 9 19 8 24 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 x y 12 4 15 7 21 10 32 14 26 9 19 8 24 12 Switch x & y & find r. The correlations are the same. •value of r is non-resistant non-resistant x y 12 4 15 7 21 10 32 14 26 9 19 8 Find r. Outliers affect the correlation coefficient 24 22 •value of r is a measure of the extent to which x & y are linearly related linearly A value of r close to zero does not rule out any strong relationship between x and y. r = 0, but has a definite relationship! Minister data: r = .9999 (Data on Elmo) So does an increase in ministers cause an increase in consumption of cause rum? Correlation does not imply causation Correlation does not imply causation Correlation does not Correlation imply causation imply ...
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Unit 4-1 - Correlation Suppose we found the age and weight...

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