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Probability and Statistics – Mrs. LeahyUnit 3 Homework Packet: Correlation and RegressionProblems should be completed on your own paper. Questions are due the class period after they are assigned.Scatter Diagrams and Linear Correlation1. When drawing a scatter diagram, along which axis is the a) explanatory variable placed? b) response variable placed?2. Textbook Pg 164 #23. Textbook pg 164 #54. Textbook pg 164 #65. Textbook pg 165 #116. Textbook pg 165/166 #127. Over the past few years, there has been a strong positive correlation between the annual consumption of diet soda drinks and the number of traffic accidents.a) Do you think increasing consumption of diet soda drinks causes traffic accidents?b) What lurking variables might be causing the increase in one or both of the variables? Explain.8. Over the past decade, there has been a strong positive correlation between teacher salaries and prescriptiondrug costs.a) Do you think paying teachers more causes prescription drugs to cost more?b) What lurking variables might be causing the increase in one or both of the variables? Explain.9. Over the past 50 years, there has been a strong negative correlation between average annual incomes andrecord times to run 1 mile. In other words, average annual incomes have been rising while the record time to run 1 mile has been decreasing.a) Do you think increasing incomes cause decreasing times to run the mile?b) What lurking variables might be causing the increase in one variable and the decrease in the other variable? Explain.10. Over the past 30 years in the United States, there has been a strong negative correlation between the number of infant deaths at birth and the number of people over the age of 65. In other words, the number of infant deaths at birth has been decreasing and the number of people over the age of 65 has been increasing.a) Do you think that people living longer is causing a decrease in infant mortalities at birth?b) What lurking variables might be causing the increase in one variable and the decrease in the other variable? Explain.11. Pg 168 #34 (Use graph paper for the scatterplot part)Questions 12-14 refer to the following:35477454445How much should a healthy Shetland pony weigh? Let x be the age of the pony (in months) and let y be the average weight of the pony (in kilograms). The following information is based on data from the Merck Veterinary Manual (a reference used in most veterinary colleges).12. Make a scatter diagram and draw the line you think best fits the data. (Use graph paper)13. Would you say the correlation is low, moderate, or strong? Is it positive or negative?14. Given the following values, compute “r”x=63 , x2=1089, y=650 , y2=95,350, and xy=99303463925407670Questions 15-17 refer to the following: The following data are based on information from Domestic Affairs. Let x be the average number of employees in a group health insurance plan, and let y be the average administrative cost as a percentage of claims.15. Find x, x2, y, y2, and xy16. Use your answers from #15 to compute “r”. 17. As x increases, does the value of r imply that y should tend to increase or decrease? Explain.Linear Regression and the Coefficient of Determination18. For the least squares line, y=5-2x, what is the value of the slope? 19. For the least square line, y=5+3x, what is the value of the y-intercept?Questions 20 - 25 refer to the following: An economist is studying the job market in Denver area neighborhoods. Let x represent the total number of jobs in a given neighborhood, and let y represent the number of entry level jobs in the same neighborhood. A sample of six Denver neighborhoods gave the following information (units in hundreds of jobs).3843655977909148998409Given that 3844092-508020. Draw a scatter diagram displaying the data. (Use graph paper!)21. Compute the correlation coefficient, r22. Find x, y, a and b. Then, find the equation of the least squares line y=a+bx23. Graph your least squares line on your scatter diagram. (for #20) 24. Find the value of the coefficient of determination r2. What percentage of the variation in y can be explained by the corresponding variation in x and the least squares line? What percentage is unexplained?25. For a neighborhood with x = 40 jobs, how many are predicted to be entry level jobs?Questions 26 –34 refer to the following. Data for this problem are based on information from STATS Basketball Scoreboard. It is thought that basketball teams that make too many fouls in a game tend to lose the game even if they otherwise play well. Let x be the number of fouls more than (i.e., over and above) the opposing team. Let y be the percentage of times the team with the larger number of fouls wins the game.293370104140SHOW YOUR WORK: DO NOT USE A GRAPHING CALCULATOR.24574510223526. 27. Calculate the correlation coefficient “r”2101851079528.29. Compute the value of a and b. 30. What is the equation of the least squares line?31. Make a scatterplot (use graph paper!). Graph the least squares line on your scatter plot.32. Find the coefficient of determination “r2”. 33. What % of variation in y can be explained? What % of variation in y cannot be explained?34. If a team had x = 4 fouls over and above the opposing team, what does the least-squares equation predict for y?---------------------Questions 35 – 43 Refer to the following: Let x be the age of a licensed driver in years. Let y be the percentage of all fatal accidents (for a given age) due to failure to yield the fight of way. For example, the first data pair states that 5% of all fatal accidents involving 37-year-olds are due to failure to yield the right of way. The Wall Street Journal reported the following data:21018555245SHOW YOUR WORK: DO NOT USE A GRAPHING CALCULATOR.27940012573035. 36. Calculate the correlation coefficient “r”2101851079537. 38. Compute the value of a and b. 39. Write the equation of the least squares line.40. Make a scatterplot (use graph paper!). Graph the least squares line on your scatter plot.41. Find the coefficient of determination “r2”. 42. What % of variation in y can be explained? What % of variation in y cannot be explained?43. Predict the percentage of all fatal accidents due to failing to yield the right of way for 70-year-olds.Questions 44 – 48 Refer to the following: It is thought that prehistoric Indians did not take their best tools, pottery, and household items when they visited higher elevations for their summer camps. It is hypothesized that archaeological sites tend to lose their cultural identity and specific cultural affiliation as the elevation of the site increases. Let x be the elevation (in thousands of feet) of an archaeological site in the southwesten United States. Let y be the percentage of unidentified artifacts (no specific cultural affiliation) at a given elevation. The follow data were obtained for a collection of archaeological sites in New Mexico:44. Find the least squares line for the data.45. Find the correlation coefficient “r”46. Find the coefficient of determination “r2”. 47. What % of variation in y can be explained? What % of variation in y cannot be explained?48. Predict the percentage of unidentified objects at an elevation of x = 6.5 (thousand feet).49. When we use the least squares line to predict y values for x values beyond the range of x values found in the data, are we extrapolating or interpolating? Are there any concerns about such predictions?50. Ok, so there actually isn’t a question #50, but it just feels wrong to have 49 questions. Instead, read this comic:1996440381000 ................
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