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intro stats

Intro Stats 4th International Edition Richard D. De Veaux, Paul F. Velleman, David Bock - Solutions

57. Wildfires 2010 The National Interagency Fire Center(www.nifc.gov) reports statistics about wildfires. Here’s an analysis of the number of wildfires between 1985 and 2010.a) Is a linear model appropriate for these data?Explain.b) Interpret the slope in this context.c) Can we interpret the
56. Success, part 2 Based on the statistics for college freshmen given in Exercise 54, what SAT score would you predict for a freshmen who attained a first-semester GPA of 3.0?
55. SAT, take 2 Suppose we wanted to use SAT math scores to estimate verbal scores based on the information in Exercise 53.a) What is the correlation?b) Write the equation of the line of regression predicting verbal scores from math scores.c) In general, what would a positive residual mean in this
54. Success in college Colleges use SAT scores in the admissions process because they believe these scores provide some insight into how a high school student will perform at the college level. Suppose the entering freshmen at a certain college have mean combined SAT Scores of 1222, with a standard
53. SAT scores The SAT is a test often used as part of an application to college. SAT scores are between 200 and 800, but have no units. Tests are given in both Math and Verbal areas. SAT-Math problems require the ability to read and understand the questions, but can a person’s verbal score be
52. Online clothes II For the online clothing retailer discussed in the previous problem, the scatterplot of Total Yearly Purchases by Income looks like this:The correlation between Total Yearly Purchases and Income is 0.722. Summary statistics for the two variables are:a) What is the linear
51. Online clothes An online clothing retailer keeps track of its customers’ purchases. For those customers who signed up for the company’s credit card, the company also has information on the customer’s Age and Income.A random sample of 500 of these customers shows the following scatterplot
50. Interest rates and mortgages The correlation of a plot of mortgages in the United States (in thousands of dollars)versus the interest rate at various times over the past 26 years is r = -0.86. The mean mortgage amount is$121.8 thousand and the mean interest rate is 7.74%. The standard
49. Income and housing The Office of Federal Housing Enterprise Oversight (OFHEO) collects data on various aspects of housing costs around the United States. Here’s a scatterplot (by state) of the Housing Cost Index (HCI)versus the Median Family Income (MFI) for the 50 states.The correlation is r
48. Last inning 2010 Refer again to the regression analysis for average attendance and games won by American League baseball teams, seen in Exercise 44.a) Write the equation of the regression line.b) Estimate the Average Attendance for a team with 50 Wins.c) Interpret the meaning of the slope of
47. Last cigarette Take another look at the regression analysis of tar and nicotine content of the cigarettes in Exercise 43.a) Write the equation of the regression line.b) Estimate the Nicotine content of cigarettes with 4 milligrams of Tar.c) Interpret the meaning of the slope of the regression
46. Second inning 2010 Consider again the regression of Average Attendance on Wins for the baseball teams examined in Exercise 44.a) What is the correlation between Wins and Average Attendance?b) What would you predict about the Average Attendance for a team that is 2 standard deviations above
45. Another cigarette Consider again the regression of Nicotine content on Tar (both in milligrams) for the cigarettes examined in Exercise 43.a) What is the correlation between Tar and Nicotine?b) What would you predict about the average Nicotine content of cigarettes that are 2 standard
44. Attendance 2010 The relationship between the number of wins by American League baseball teams and the average attendance at their home games for the 2010 season are given in the following scatterplot, residuals plot, and part of the regression analysis:a) Do you think a linear model is
41. More real estate Consider the Albuquerque home sales from Exercise 29 again. The regression analysis gives the model Price = 47.82 + 0.061 Size.a) Explain what the slope of the line says about housing prices and house size.b) What price would you predict for a 3000-square-foot house in this
40. SI jinx Players in any sport who are having great seasons, turning in performances that are much better than anyone might have anticipated, often are pictured on the cover of Sports Illustrated. Frequently, their performances then falter somewhat, leading some athletes to believe in a “Sports
39. ESP People who claim to “have ESP” participate in a screening test in which they have to guess which of several images someone is thinking of. You and a friend both took the test. You scored 2 standard deviations above the mean, and your friend scored 1 standard deviation below the mean.
38. Another ride The regression of Duration of a roller coaster ride on the height of its initial Drop, described in Exercise 30, had R2 = 15.2%.a) What is the correlation between Drop and Duration?b) What would you predict about the Duration of the ride on a coaster whose initial Drop was 1
37. Real estate redux The regression of Price on Size of homes in Albuquerque had R2 = 71.4%, as described in Exercise 29.a) What is the correlation between Size and Price?b) What would you predict about the Price of a home 1 SD above average in Size?c) What would you predict about the Price of a
36. More misinterpretations A Sociology student investigated the association between a country’s Literacy Rate and Life Expectancy, and then drew the conclusions listed below. Explain why each statement is incorrect. (Assume that all the calculations were done properly.)a) The R2 of 64% means
35. Misinterpretations A Biology student who created a regression model to use a bird’s Height when perched for predicting its Wingspan made these two statements.Assuming the calculations were done correctly, explain what is wrong with each interpretation.a) My R2 of 93% shows that this linear
34. Coasters again Exercise 30 examined the association between the Duration of a roller coaster ride and the height of its initial Drop, reporting that R2 = 15.2%. Write a sentence (in context, of course) summarizing what the R2 says about this regression.
33. Real estate again The regression of Price on Size of homes in Albuquerque had R2 = 71.4%, as described in Exercise 29. Write a sentence (in context, of course)summarizing what the R2 says about this regression.
32. What slope again? If you create a regression model for estimating the Height of a pine tree (in feet) based on the Circumference of its trunk (in inches), is the slope most likely to be 0.1, 1, 10, or 100? Explain.
31. What slope? If you create a regression model for predicting the Weight of a car (in pounds) from its Length(in feet), is the slope most likely to be 3, 30, 300, or 3000? Explain.
30. This question has been intentionally omitted from this text.
29. Real estate A random sample of records of home sales from Feb. 15 to Apr. 30, 1993, from the files maintained by the Albuquerque Board of Realtors gives the Price and Size (in square feet) of 117 homes. A regression to predict Price (in thousands of dollars) from Size has an R2 of 71.4%. The
28. Residuals Tell what each of the residual plots below indicates about the appropriateness of the linear model that was fit to the data. + b) + c)
27. Residuals Tell what each of the residual plots below indicates about the appropriateness of the linear model that was fit to the data. b)
26. More regression equations Fill in the missing information in the following table. X a) 30 54 y Sy 18 6 -0.2 b) 100 18 60 10 0.9 c) 0.8 50 15 = -10 + 15x d) 18 4 = -0.6 30- 2x
25. Regression equations Fill in the missing information in the following table. X ST y Sy = b + bx a) 10 2 20 3 0.5 b) 2 0.06 7.2 1.2 -0.4 12 6 -0.8 =200-4x d) 2.5 1.2 100 = -100 + 50x
24. Last tank! For Exercise 16’s regression model predicting fuel economy (in mpg) from the car’s horsepower, se = 2.435. Explain in this context what that means.
23. Last bowl! For Exercise 15’s regression model predicting potassium content (in milligrams) from the amount of fiber (in grams) in breakfast cereals, se = 30.77. Explain in this context what that means.
22. Another car The correlation between a car’s horsepower and its fuel economy (in mpg) is r = -0.909. What fraction of the variability in fuel economy is accounted for by the horsepower?
21. Cereal again The correlation between a cereal’s fiber and potassium contents is r = 0.903. What fraction of the variability in potassium is accounted for by the amount of fiber that servings contain?
20. More horsepower In Exercise 16, the regression model mpg = 43.45 - 0.070 HP relates cars’ horsepower to their fuel economy (in mpg). Explain what the slope means.
19. Another bowl In Exercise 15, the regression model Potassium = 38 + 27 Fiber relates fiber (in grams) and potassium content (in milligrams) in servings of breakfast cereals. Explain what the slope means.
18. Horsepower again Exercise 16 describes a regression model that uses a car’s horsepower to estimate its fuel economy. In this context, what does it mean to say that a certain car has a positive residual?
17. More cereal Exercise 15 describes a regression model that estimates a cereal’s potassium content from the amount of fiber it contains. In this context, what does it mean to say that a cereal has a negative residual?
16. Horsepower The relationship between the fuel economy(mpg) and horsepower for 15 models of cars produces the regression model mpg = 43.45 - 0.070 HP. If the car you are thinking of buying has a 200-horsepower engine, what does this model suggest your gas mileage would be?
15. Cereals For many people, breakfast cereal is an important source of fiber in their diets. Cereals also contain potassium, a mineral shown to be associated with maintaining a healthy blood pressure. An analysis of the amount of fiber (in grams) and the potassium content (in milligrams) in
14. Disk drives last time Here is a scatterplot of the residuals from the regression of the hard drive prices on their sizes from Exercise 6.a) Are any assumptions or conditions violated? If so, which ones?b) What would you recommend about this regression? Residuals 10 0 -10 -20 100 200 Predicted
13. Residual plots Here are residual plots (residuals plotted against predicted values) for three linear regression models. Indicate which condition appears to be violated(linearity, outlier or equal spread) in each case.a)b)c) Residual 15 10 5+ 0 -5+ -10 + -10 0 10 20 30 40 50 60 70 Fitted Value
12. Disk drives encore For the hard drive data of Exercise 6, find and interpret the value of R2.
11. Bookstore sales last time For the regression model for the bookstore of Exercise 5, what is the value of R2 and what does it mean?
10. Disk drives once more Here are the residuals for a regression of Price on Capacity for the hard drives of Exercise 6 a) Which residual contributes the most to the sum that is minimized by the Least Squares criterion?b) Two of the residuals are negative. What does that mean about those drives?
9. Bookstore sales once more Here are the residuals for a regression of Sales on Number of Sales People Working for the bookstore Exercise 5:a) What are the units of the residuals?b) Which residual contributes the most to the sum that was minimized according to the Least Squares Criterion to find
8. Sophomore slump again? An online investment blogger advises investing in mutual funds that have performed badly the past year because “regression to the mean tells us that they will do well next year.” Is he correct?
7. Sophomore slump? A CEO complains that the winners of his “rookie junior executive of the year” award often turn out to have less impressive performance the following year. He wonders whether the award actually encourages them to slack off. Can you offer a better explanation?
you expected to pay?h) Does the model overestimate or underestimate the price?
Capacity.f) What would you predict for the price of a 3.0 TB drive?g) You have found a 3.0 TB drive for $300. Is this a good buy? How much would you save compared to what
6. Disk drives Some data on hard drives look like this: we want to predict Price from Capacity.a) Find the slope estimate, b1.b) What does it mean, in this context?c) Find the intercept, b0.d) What does it mean, in this context? Is it meaningful?e) Write down the equation that predicts Price from
5. Bookstore sales A manager wants to predict Sales from Number of Sales People Working.a) Find the slope estimate, b1.b) What does it mean, in this context?c) Find the intercept, b0.d) What does it mean, in this context? Is it meaningful?e) Write down the equation that predicts Sales from Number
4. Residual interpretations The newborn grandson of one of the authors was 48 cm long and weighed 3 kg. According to the regression model of Exercise 3, what was his residual? What does that say about him?
3. Least squares interpretations A least squares regression line was calculated to relate the length (cm)of newborn boys to their weight in kg. The line is weight = -5.94 + 0.1875 length. Explain in words what this model means. Should new parents (who tend to worry) be concerned if their
2. True or false II If false, explain briefly.a) Some of the residuals from a least squares linear model will be positive and some will be negative.b) Least Squares means that some of the squares of the residuals are minimized.c) We write yn to denote the predicted values and y to denote the
1. True or false If false, explain briefly.a) We choose the linear model that passes through the most data points on the scatterplot.b) The residuals are the observed y-values minus the y-values predicted by the linear model.c) Least squares means that the square of the largest residual is as small
52. Flights 2010 Here are the number of domestic flights flown in each year from 2000 to 2010 (www.TranStats.bts.gov/Data_Elements.aspx?Data=2). Year Flights 2000 7,905,617 2001 7,626,312 2002 8,089,140 2003 9,458,818 2004 9,968,047 2005 10,038,373 2006 9,712,750 2007 9,839,578 2008 9,376,251 2009
51. Planets (more or less) On August 24, 2006, the International Astronomical Union voted that Pluto is not a planet. Some members of the public have been reluctant to accept that decision. Let’s look at some of the data. Is there any pattern to the locations of the planets? The table shows the
50. Vehicle weights The Minnesota Department of Transportation hoped that they could measure the weights of big trucks without actually stopping the vehicles by using a newly developed “weight-in-motion” scale. To see if the new device was accurate, they conducted a calibration test. They
49. Thrills III For the roller coaster data in Exercise 47:a) Explain why in looking for a variable that explains rank, you will be hoping for a negative correlation.b) Do any of the provided variables provide a strong predictor for roller coaster rank?c) What other (unaccounted) for variables
48. Thrills II For the roller coaster data in Exercise 47:a) Examine the relationship between Initial Drop and Speed.b) Examine the relationship between Initial Drop and Height.c) What conclusions can you safely draw about the initial drop of a roller coaster? Is Initial Drop strongly correlated
47. Thrills Since 1994, the Best Roller Coaster Poll (www.ushsho.com/bestrollercoasterpoll.htm) has been ranking the world’s best roller coasters. In 2011, Bizarro earned the top steel coaster rank for the sixth straight year. Here are data on the top 10 steel coasters from this poll:What do
46. Second inning 2010 Perhaps fans are just more interested in teams that win. The displays below are based on American League teams for the 2010 season. (espn.go.com) Are the teams that win necessarily those which score the most runs?a) Do winning teams generally enjoy greater attendance at their
45. Attendance 2010 American League baseball games are played under the designated hitter rule, meaning that pitchers, often weak hitters, do not come to bat. Baseball owners believe that the designated hitter rule means more runs scored, which in turn means higher attendance. Is there evidence
44. Burgers II In the previous exercise you analyzed the association between the amounts of fat and sodium in fast food hamburgers. What about fat and calories?Here are data for the same burgers:Analyze the association between fat content and calories using correlation and scatterplots. Fat (g)
43. Burgers Fast food is often considered unhealthy because much of it is high in both fat and sodium. But are the two related? Here are the fat and sodium contents of several brands of burgers.Analyze the association between fat content and sodium using correlation and scatterplots. Fat (g) 19 31
42. Drug abuse A survey was conducted in the United States and 10 countries of Western Europe to determine the percentage of teenagers who had used marijuana and other drugs. The results are summarized in the following table.a) Create a scatterplot.b) What is the correlation between the percent of
41. Fuel economy 2010 Here are advertised horsepower ratings and expected gas mileage for several 2010 vehicles. (www.kbb.com)a) Make a scatterplot for these data.b) Describe the direction, form, and strength of the plot.c) Find the correlation between horsepower and miles per gallon.d) Write a few
40. Interest rates and mortgages Since 1985, average mortgage interest rates have fluctuated from a low of under 6% to a high of over 14%. Is there a relationship between the amount of money people borrow and the interest rate that’s offered? Here is a scatterplot of Mortgage Loan Amount in the
39. Income and housing The Office of Federal Housing Enterprise Oversight (www.fhfa.gov) collects data on various aspects of housing costs around the United States. Here is a scatterplot of the Housing Cost Index versus the Median Family Income for each of the 50 states. The correlation is 0.65.a)
38. Sample survey A polling organization is checking its database to see if the two data sources it used sampled the same ZIP codes. The variable Datasource = 1 if the data source is MetroMedia, 2 if the data source is DataQwest, and 3 if it’s RollingPoll. The organization finds that the
37. Baldness and heart disease Medical researchers followed 1435 middle-aged men for a period of 5 years, measuring the amount of Baldness present (none = 1, little = 2, some = 3, much = 4, extreme = 5) and presence of Heart Disease (No = 0, Yes = 1). They found a correlation of 0.089 between the
36. Correlation conclusions II The correlation between Fuel Efficiency (as measured by miles per gallon) and Price of 150 cars at a large dealership is r = -0.34.Explain whether or not each of these possible conclusions is justified:a) The more you pay, the lower the fuel efficiency of your car
35. Correlation conclusions I The correlation between Age and Income as measured on 100 people is r = 0.75.Explain whether or not each of these possible conclusions is justified:a) When Age increases, Income increases as well.b) The form of the relationship between Age and Income is straight.c)
34. Smart phones and life expectancy A survey of the world’s nations in 2010 shows a strong positive correlation between percentage of the country using smart phones and life expectancy in years at birth.a) Does this mean that smart phones are good for your health?b) What might explain the strong
33. Height and reading A researcher studies children in elementary school and finds a strong positive linear association between height and reading scores.a) Does this mean that taller children are generally better readers?b) What might explain the strong correlation?
32. More correlation errors Students in the Economics class discussed in Exercise 31 also wrote these conclusions.Explain the mistakes they made.a) “There was a very strong correlation of 1.22 between Life Expectancy and GDP.”b) “The correlation between Literacy Rate and GDP was 0.83. This
31. Correlation errors Your Economics instructor assigns your class to investigate factors associated with the gross domestic product (GDP) of nations. Each student examines a different factor (such as Life Expectancy, Literacy Rate, etc.) for a few countries and reports to the class.Apparently,
30. More predictions Hurricane Katrina’s hurricane force winds extended 120 miles from its center. Katrina was a big storm, and that affects how we think about the prediction errors. Suppose we add 120 miles to each error to get an idea of how far from the predicted track we might still find
29. Prediction units The errors in predicting hurricane tracks (examined in this chapter) were given in nautical miles. A statutory mile is 0.86898 nautical mile. Most people living on the Gulf Coast of the United States would prefer to know the prediction errors in statutory miles rather than
28. Association V A researcher investigating the association between two variables collected some data and was surprised when he calculated the correlation. He had expected to find a fairly strong association, yet the correlation was near 0. Discouraged, he didn’t bother making a scatterplot.
27. Cold nights Is there an association between time of year and the nighttime temperature in North Dakota? A researcher assigned the numbers 1–365 to the days January 1–December 31 and recorded the temperature at 2:00 a.m. for each. What might you expect the correlation between DayNumber and
26. Traffic headaches A study of traffic delays in 68 U.S.cities found the following relationship between Total Delays (in total hours lost) and Mean Highway Speed:Is it appropriate to summarize the strength of association with a correlation? Explain. Total Delay (hr) 600,000 450,000- 300,000
25. Streams and hard water In a study of streams in the Adirondack Mountains, the following relationship was found between the water’s pH and its hardness (measured in grains):Is it appropriate to summarize the strength of association with a correlation? Explain. 8.0+ 7.6 7.2. 6.8 6.4 + + 125
24. Antidepressants A study compared the effectiveness of several antidepressants by examining the experiments in which they had passed the FDA requirements. Each of those experiments compared the active drug with a placebo, an inert pill given to some of the subjects. In each experiment some
23. Roller coasters Most roller coasters get their speed by dropping down a steep initial incline, so it makes sense that the height of that drop might be related to the speed of the coaster. Here’s a scatterplot of top Speed and largest Drop for 75 roller coasters around the world.a) Does the
22. Car thefts The National Insurance Crime Bureau reports that Honda Accords, Honda Civics, and Toyota Camrys are the cars most frequently reported stolen, while Ford Tauruses, Pontiac Vibes, and Buick LeSabres are stolen least often. Is it reasonable to say that there’s a correlation between
21. Politics A candidate for office claims that “there is a correlation between television watching and crime.”Criticize this statement on statistical grounds.
20. Matching II Here are several scatterplots. The calculated correlations are -0.977, -0.021, 0.736, and 0.951.Which is which? (c) (b) (p) H
19. Matching Here are several scatterplots. The calculated correlations are -0.923, -0.487, 0.006, and 0.777. Which is which? (a) + (a) H + + +
18. Coffee sales Owners of a new coffee shop tracked sales for the first 20 days and displayed the data in a scatterplot(by day).a) Make a histogram of the daily sales since the shop has been in business.b) State one fact that is obvious from the scatterplot, but not from the histogram.c) State one
17. Firing pottery A ceramics factory can fire eight large batches of pottery a day. Sometimes a few of the pieces break in the process. In order to understand the problem better, the factory records the number of broken pieces in each batch for 3 days and then creates the scatterplot shown.a) Make
16. Kentucky Derby 2011 The fastest horse in Kentucky Derby history was Secretariat in 1973. The scatterplot shows speed (in miles per hour) of the winning horses each year.What do you see? In most sporting events, performances have improved and continue to improve, so surely we anticipate a
c) a linear association?d) a moderately strong association?e) a very strong association?15. Performance IQ scores vs. brain size A study examined brain size (measured as pixels counted in a digitized magnetic resonance image [MRI] of a cross section of the brain) and IQ (4 Performance scales of the
14. Scatterplots II Which of these scatterplots showa) little or no association?b) a negative association?
13. Scatterplots Which of these scatterplots showa) little or no association?b) a negative association?c) a linear association?d) a moderately strong association?e) a very strong association? (1) + H + H (4) +
12. Association IV Suppose you were to collect data for each pair of variables. You want to make a scatterplot.Which variable would you use as the explanatory variable and which as the response variable? Why? What would you expect to see in the scatterplot? Discuss the likely direction, form, and
11. Association III Suppose you were to collect data for each pair of variables. You want to make a scatterplot.Which variable would you use as the explanatory variable and which as the response variable? Why? What would you expect to see in the scatterplot? Discuss the likely direction, form, and
10. Dexterity scores Scores on a test of dexterity are recorded by timing a subject who is inverting pegs by picking them up with one hand, manipulating them to turn them over, and then placing them back in a frame. A typical 4-year-old needs about 2.5 seconds to invert a peg, but a 9-year-old

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