574 CHAPTER 10 Correlation and Regression FROM DATA TO DECISION Critical Thinking: Do we report body measurements that are different from the actual measurements? Use Data Set 4 “Measured and Reported’ in Appendix B to address the following. 1. Correlation with Weights a. For males, is there a significant linear correlation between measured weights and reported weights? b. For females, is there a significant linear correlation between measured weights and reported weights? 2. Correlation with Heights a. For males, is there a significant linear correlation between measured heights and reported heights? b. For females, is there a significant linear correlation between measured heights and reported heights? 3. Conclusions a. Does it appear that data are distorted when reported values are used in place of actual measurements? b. Does there appear to be a difference between males and females in how they report weights? c. Does there appear to be a difference between males and females in how they report heights? Cooperative Group Activities 1.In-class activity For each student in the class, measure shoe print length and height. Test for a linear correlation and identify the equation of the regression line. Measure the shoe print length of the professor and use it to estimate his or her height. How close is the estimated height to the actual height? 2.Out-of-class activity Each student should estimate the number of footsteps that he or she would walk between the door of the classroom and the door used to exit the building. After recording all of the estimates, each student should then count the number of footsteps while walking from the classroom door to the door most students use to exit the building. After all of the estimates and actual counts have been compiled, explore correlation and regression using the tools presented in this chapter. 3. In-class activity Divide into groups of 8 to 12 people. For each group member, measure the person’s height and also measure his or her navel height, which is the height from the floor to the navel. Is there a correlation between height and navel height? If so, find the regression equation with height expressed in terms of navel height. According to one theory, the average person’s ratio of height to navel height is the golden ratio: 11 + 252>2 ≈ 1.6. Does this theory appear to be reasonably accurate? 4.In-class activity Divide into groups of 8 to 12 people. For each group member, use a string and ruler to measure head circumference and forearm length. Is there a relationship between these two variables? If so, what is it? 5.In-class activity Leonardo DaVinci did extensive research on human bodies and he formed many different conclusions including this one: “Length of arm span is equal to height.” Arm span is the distance between the ends of the fingers when the arms are extended like the wings on an airplane. Divide into groups of two and use the ANSUR II data to investigate that claim. Is there a correlation between height and arm span? If so, find the regression equation with height expressed in terms of arm span. Can arm span be used as a reasonably good predictor of height? 6. In-class activity Divide into groups of 8 to 12 people. For each group member, measure height and arm span. For the arm span, the subject should stand with arms extended, like the wings on an airplane. Using the paired sample data, is there a correlation between height and arm span? If so, find the regression equation with height expressed in terms of arm span. Can arm span be used as a reasonably good predictor of height?
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