836 CHAPTER 12 Statistics a) Determine the correlation coefficient for the time and the percent of chlorine remaining. 0.977 − b) Determine whether a correlation exists at 0.01. α= Yes c) Determine the equation of the line of best fit for the time and the amount of chlorine remaining. y x 12.93 99.59 = − + d) Use the equation in part (c) to estimate the average amount of chlorine remaining after 4.5 hr. 41.4% Challenge Problems/Group Activities 45. Interchanging Variables a) Assume that a set of bivariate data yields a specific correlation coefficient. If the x- and y-values are interchanged and the correlation coefficient is recalculated, will the correlation coefficient change? Correlation will not change. b) Make up a table of five pieces of bivariate data and determine r using the data. Then switch the values of the x’s and y’s and recompute the correlation coefficient. Has the value of r changed? Answers will vary. 46. Height vs. Length a) Do you believe that a correlation exists between a person’s height and the length of a person’s arm? Answers will vary. b) Select 10 people from your class and measure (in inches) their height and the length of one of their arms. Answers will vary. c) Plot the 10 ordered pairs on a scatter diagram. Answers will vary. d) Calculate the correlation coefficient, r. Answers will vary. e) Determine the equation of the line of best fit. Answers will vary. f) Estimate the length of the arm of a person who is 58 in. tall. Answers will vary. 47. Calculating a Correlation Coefficient a) Select a category of bivariate data that you think has a strong positive correlation. Designate the independent variable and the dependent variable. Explain why you believe that Stockbyte/Getty Images the bivariate data have a strong positive correlation. Answers will vary. b) Collect at least 10 pieces of bivariate data that can be used to determine the correlation coefficient. Explain how you chose these data. Answers will vary. c) Plot a scatter diagram. Answers will vary. d) Calculate the correlation coefficient. Answers will vary. e) Does there appear to be a strong positive correlation? Explain your answer. Answers will vary. f) Calculate the equation of the line of best fit. Answers will vary. g) Explain how the equation in part (f) may be used. Answers will vary. 48. Consumer Price Index The following table shows the consumer price index (CPI) for the years 2017–2022. DS Year 2017 2018 2019 2020 2021 2022 CPI 245.1 251.1 255.7 258.8 271.0 292.7 a) Determine the linear correlation coefficient, r, between the year and the CPI. 0.936 b) If 2017 is subtracted from each year, the table obtained becomes: Year 0 1 2 3 4 5 CPI 245.1 251.1 255.7 258.8 271.0 292.7 If r is calculated from these values, how will it compare with the r determined in part (a)? Explain. Should be the same c) Calculate r from the values in part (b) and compare the results with the value of r determined in part (a). Are they the same? If not, explain why. 0.936; the values are the same. 49. a) There are equivalent formulas that can be used to determine the correlation coefficient and the equation of the line of best fit. A formula used in some statistics books to determine the correlation coefficient is r SS xy SS x SS y ( ) ( ) ( ) = where = Σ − Σ = Σ − Σ = Σ − Σ Σ SS x x x n SS y y y n SS xy xy x y n ( ) ( ) ( ) ( ) ( ) ( )( ) 2 2 2 2
RkJQdWJsaXNoZXIy NjM5ODQ=