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Stats Data And Models 4th Edition Richard D. De Veaux, Paul D. Velleman, David E. Bock - Solutions

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 residuals plot
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 newborn's length and weight don't fit this
The data set on roller coasters from Chapter 6, Exercise 23 lists the Duration of the ride in seconds in addition to the Drop height in feet. One coaster (the "Tower of Terror") is unusual for having large drop but a short ride. After setting it aside, a regression to predict Duration from Drop for
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.
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 slops most likely to be 0.1, 1, 10, or 100? Explain.
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 model is appropriate.b) A
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 that the Literacy Rate determines
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 home 2 SDs below
The regression of Duration of a roller coaster ride on the height of its initial Drop, described in Exercise 30, had R2 = 32.0%.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 standard deviation
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. The
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? Exercise 3 A least squares regression line was calculated to relate the length (cm) of newborn boys to their weight in
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 Illustrated
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 market?c) A real estate
Consider the roller coasters (with the outlier removed) described in Exercise 30 again. The regression analysis gives the model Duration = 85.83 + 0.397 Drop.a) Explain what the slope of the line says about how long a roller coaster ride may last and the height of the coaster.b) A new roller
Is the nicotine content of a cigarette related to the "tar"? A collection of data (in milligrams) on 29 cigarettes produced the scatterplot, residuals plot, and regression analysis shown:Dependent variable is Nicotine R-squared = 92.4% Variable Coefficient Constant
In the previous chapter, you looked at the relationship between the number of wins by American League baseball teams and the average attendance at their home games for the 2013 season. Here are the scatterplot, the residuals plot, and part of the regression analysis:Dependent variable is Home
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 deviations below average in Tar
Consider again the regression of Average Attendance on Wins for the baseball teams examined in Exercise 44.Dependent variable is Home AttendanceR-squared = 6.45%Variable CoefficientIntercept ………...
Take another look at the regression analysis of tar and nicotine content of the cigarettes in Exercise 43.Dependent variable is NicotineR-squared = 92.4%VariableCoefficientConstant €¦€¦€¦€¦0.154030Tar €¦€¦€¦€¦€¦€¦.0.065052a) Write the equation of the regression line.
Refer again to the regression analysis for average attendance and games won by American League baseball teams, seen in Exercise 44.Dependent variable is Home AttendanceR-squared = 6.45%VariableCoefficientIntercept €¦€¦€¦...16484.0Wins €¦€¦€¦......... 147.4a) Write the equation
In Chapter 6, Exercise 39, we learned that 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) vs. the Median Family Income (MFI) for the 50
Recall the data we saw in Chapter 6, exercise 3 for a bookstore. The 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
In Chapter 6, Exercise 40, we saw a plot of mortgages in the United States (in trillions of 2013 dollars) vs. the interest rate at various times over the past 25 years. The correlation is r = -0.80. The mean mortgage amount is $3,926 T and the mean interest rate is 7.194%. The standard deviations
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 of Total Yearly
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 regression equation for
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 used to predict the
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 deviation of 123. In
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 context?d) A
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?In Exercise 54Colleges use SAT scores in the admissions process because they believe these scores provide some insight into how a high school
The National Interagency Fire Center (www.nifc.gov) reports statistics about wildfires. Here€™s an analysis of the number of wildfires between 1985 and 2012.Dependent variable is FiresR-squared = 0.032%s = 11690Variable CoefficientIntercept €¦€¦€¦€¦€¦€¦€¦.75609.0Years
We saw in Exercise 57 that the number of fires was nearly constant. But has the damage they cause remained constant as well? Here's a regression that examines the trend in Acres per Fire, (in hundreds of thousands of acres) together with some supporting plots:Dependent variable is
Carmax.com lists numerous Toyota Corollas for sale within a 250 mile radius of Redlands, CA. Listed at the top of the next column are the ages of the cars and the advertised prices. a) Make a scatterplot for these data. b) Describe the association between Age and Price of a used Corolla. c) Do you
Recall the data on disk drives we saw in chapter 6 exercise 4. Suppose 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
In the exercises of the last chapter, you examined results of a survey conducted in the United States and 10 countries of Western Europe to determine the percentage of teenagers who had used marijuana and other drugs. Below is the scatterplot. Summary statistics showed that the mean percent that
Use the advertised prices for Toyota Corollas given in Exercise 59 to create a linear model for the relationship between a car's Age and its Price.a) Find the equation of the regression line.b) Explain the meaning of the slope of the line.c) Explain the meaning of the y-intercept of the line.d) If
Burger King introduced a meat-free burger in 2002. The nutrition label is shown here:a) Use the regression model created in this chapter, Fat = 6.8 + 0.97 Protein, to predict the fat content of this burger from its protein content.b) What is its residual? How would you explain the residual?c) Write
In the last chapter, you examined the association between the amounts of Fat and Calories in fast-food hamburgers. Here are the data:a) Create a scatterplot of Calories vs. Fat.b) Interpret the value of R2 in this context.c) Write the equation of the line of regression.d) Use the residuals plot to
Chicken sandwiches are often advertised as a healthier alternative to beef because many are lower in fat. Tests on 11 brands of fast-food chicken sandwiches produced the following summary statistics and scatterplot from a graphing calculator:a) Do you think a linear model is appropriate in this
In Exercise 63, you created a model that can estimate the number of Calories in a burger when the Fat content is known.a) Explain why you cannot use that model to estimate the fat content of a burger with 600 calories.b) Using an appropriate model, estimate the fat content of a burger with 600
Numbeo.com lists the cost of living (COL) for many cities around the world. These rankings scale New York City as 100, and express the cost of living in other cities as a percentage of the New York cost. For example, the table below shows 25 of the most expensive cities in the world, and indicates
We saw in this chapter that in Tompkins County, New York, older bridges were in worse condition than newer ones. Tompkins is a rural area. Is this relationship true in New York City as well? Here are data on the Condition (as measured by the state Department of Transportation Condition Index) and
The table shows the number of live births per 1000 population in the United States, starting in 1965.a) Make a scatterplot and describe the general trend in Birthrates. (Enter Year as years since 1900: 65, 70, 75, etc.)b) Find the equation of the regression line.c) Check to see if the line is an
The earth's climate is getting warmer. The most common theory attributes the increase to an increase in atmospheric levels of carbon dioxide (CO2), a greenhouse gas. Here is a scatterplot showing the mean annual CO2 concentration in the atmosphere, measured in parts per million (ppm) at the top of
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?
In Exercise 69, we saw the relationship between CO2 measured at Mauna Loa and average global temperatures from 1970 to 2013. Here is a plot of average global temperatures plotted against the yearly average of the Dow Jones Industrial Average for the same time periodA regression produces the
It is difficult to determine a person's body fat percentage accurately without immersing him or her in water. Researchers hoping to find ways to make a good estimate immersed 20 male subjects, then measured their waists and recorded their weights shown in the table at the top of the next column.a)
Would a model that uses the person's Waist size be able to predict the %Body Fat more accurately than one that uses Weight? Using the data in Exercise 71, create and analyze that model.
We discussed the women's 2012 Olympic heptathlon in Chapter 6. Here are the results from the high jump, 800-meter run, and long jump for the 26 women who successfully completed all three events in the 2004 Olympics (www.espn.com):Let's examine the association among these events.Perform a regression
We saw the data for the women's 2004 Olympic heptathlon in Exercise 73. Are the two jumping events associated? Perform a regression of the long-jump results on the high-jump results.a) What is the regression equation? What does the slope mean?b) What percentage of the variability in long jumps can
In an investigation of environmental causes of disease, data were collected on the annual mortality rate (deaths per 100,000) for males in 61 large towns in England and Wales. In addition, the water hardness was recorded as the calcium concentration (parts per million, ppm) in the drinking water.
Wildlife researchers monitor many wildlife populations by taking aerial photographs. Can they estimate the weights of alligators accurately from the air? Here is a regression analysis of the Weight of alligators (in pounds) and their Length (in inches) based on data collected about captured
Consider the four points (10, 10), (20, 50), (40, 20), and (50, 80). The least squares line is = 7.0 + 1.1x. Explain what "least squares" means, using these data as a specific example.
Consider the four points (200, 1950), (400, 1650), (600, 1800), and (800, 1600). The least squares line is = 1975 – 0.45x. Explain what "least squares" means, using these data as a specific example.
Here are the residuals for a regression of Sales on Number of Sales People Working for the bookstore of exercise 5: Number of Sales People Working Residual 2 ………………………. 0.07 3 ………………………. 0.16 7 ………………………. -1.49 9
The researcher in Exercise 9 is content with the second regression. But he has found a number of shells that have large residuals and is considering removing all them. Is this good practice?
Is there evidence that the age at which women get married has changed over the past 100 years? The scatterplot shows the trend in age at first marriage for American women (www.census.gov).a) Is there a clear pattern? Describe the trend.b) Is the association strong?c) Is the correlation high?
The Centers for Disease Control and Prevention track cigarette smoking in the United States. How has the percentage of people who smoke changed since the danger became clear during the last half of the 20th century? The scatterplot shows percentages of smokers among men 18-24 years of age, as
The United Nations Development Programme (UNDP) uses the Human Development Index (HDI) in an attempt to summarize in one number the progress in health, education, and economics of a country. In 2012, the HDI was as high as 0.955 for Norway and as low as 0.304 for Niger. The gross domestic product
In justifying his choice of a model, a student wrote, "I know this is the correct model because R2 = 99.4%." a) Is this reasoning correct? Explain. b) Does this model allow the student to make accurate predictions? Explain.
A concert production company examined its records. The manager made the following scatterplot. The company places concerts in two venues, a smaller, more intimate theater (plotted with blue circles) and a larger auditorium-style venue (red x's).a) Describe the relationship between Talent Cost and
A student who has created a linear model is disappointed to find that her R2 value is a very low 13%. a) Does this mean that a linear model is not appropriate? Explain. b) Does this model allow the student to make accurate predictions? Explain.
Here's a scatterplot of the production budgets (in millions of dollars) vs. the running time (in minutes) for major release movies in 2005. Dramas are plotted as red x's and all other genres are plotted as blue dots. (The re-make of King Kong is plotted as a black €œ-€. At the
In Exercise 16, we examined the percentage of men aged 18-24 who smoked from 1965 to 2011 according to the Centers for Disease Control and Prevention. How about women? Here's a scatterplot showing the corresponding percentages for both men and women:a) In what ways are the trends in smoking
The scatterplot below shows the number of passengers at Oakland (CA) airport month by month since 1997. (www.oaklandairport.com)a) Describe the patterns in passengers at Oakland airport that you see in this time plot. b) Until 2009, analysts got fairly good predictions using a linear model. Why
In a previous chapter, we saw data on the errors (in nautical miles) made by the National Hurricane Center in predicting the path of hurricanes. The scatterplot at the top of the next page shows the trend in the 24-hour tracking errors since 1970 (www.nhc.noaa.gov).Dependent variable is
Each of these four scatterplots shows a duster of points and one "stray" point. For each, answer these questions:1) In what way is the point unusual? Does it have high leverage, a large residual, or both?2) Do you think that point is an influential point?3) If that point were removed, would the
Each of the following scatterplots shows a cluster of points and one "stray" point. For each, answer these questions:1) In what way is the point unusual? Does it have high leverage, a large residual, or both?2) Do you think that point is an influential point?3) If that point were removed, would the
The scatterplot shows five blue data points at the left. Not surprisingly, the correlation for these points is r = 0. Suppose one additional data point is added at one of the five positions suggested below in green. Match each point (a-e) with the correct new correlation from the list given.1)
The original five points in Exercise 27 produce a regression line with slope 0. Match each of the green points (a-e) with the slope of the line after that one point is added:1) -0.452) -0.303) 0.004) 0.055) 0.85In Exercise 27
Suppose a researcher studying health issues measures blood pressure and the percentage of body fat for several adult males and finds a strong positive association. Describe three different possible cause-and-effect relationships that might be present.
A researcher studying violent behavior in elementary school children asks the children's parents how much time each child spends playing computer games and has their teachers rate each child on the level of aggressiveness they display while playing with other children. Suppose that the researcher
To measure progress in reading ability, students at an elementary school take a reading comprehension test every year. Scores are measured in "grade-level" units; that is, a score of 4.2 means that a student is reading at slightly above the expected level for a fourth grader. The school principal
A college admissions officer, defending the college's use of SAT scores in the admissions process, produced the following graph. It shows the mean GPAs for last year's freshmen, grouped by SAT scores. How strong is the evidence that SAT Score is a good predictor of GPA? What concerns you about the
After keeping track of his heating expenses for several winters, a homeowner believes he can estimate the monthly cost from the average daily Fahrenheit temperature by using the model Cost = 133 - 2.13 Temp. Here is the residuals plot for his data:a) Interpret the slope of the line in this
How does the speed at which you drive affect your fuel economy? To find out, researchers drove a compact car for 200 miles at speeds ranging from 35 to 75 miles per hour. From their data, they created the model Fuel Efficiency = 32 €“ 0.1 Speed and created this residual plot:a) Interpret the
Here's a plot showing the federal rate on 3-month Treasury bills from 1950 to 1980, and a regression model fit to the relationship between the Rate (in %) and Years Since 1950.a) What is the correlation between Rate and Year?b) Interpret the slope and intercept.c) What does this model predict for
The graph shows the ages of both men and women at first marriage (www.census.gov).Clearly, the patterns for men and women are similar. But are the two lines getting closer together?Here's a timeplot showing the difference in average age (men's age €” women's age) at first marriage, the
In Exercise 35, you investigated the federal rate on 3-month Treasury bills between 1950 and 1980. The scatterplot below shows that the trend changed dramatically after 1980, so we computed a new regression model for the years 1981 to 2013.Here's the model for the data from 1981 to 2013:Dependent
Has the trend of decreasing difference in age at first marriage seen in Exercise 36 gotten stronger recently? The scatterplot and residual plot for the data from 1980 through 2011, along with a regression for just those years, are below.Dependent variable is Men €“ WomenR-squared = 49.4%s =
For humans, pregnancy lasts about 280 days. In other species of animals, the length of time from conception to birth varies. Is there any evidence that the gestation period is related to the animal's life span? The first scatterplot shows Gestation Period (in days) vs. Life Expectancy (in years)
The concert production company of Exercise 2 made a second scatterplot, this time relating Total Revenue to Ticket Sales.a) Describe the relationship between Ticket Sales and Total Revenue.b) How are the results for the two venues similar?c) How are they different?
People swam across Lake Ontario 52 times between 1974 and 2013 (www.soloswims.com). We might be interested in whether they are getting any I faster or slower. Here are the regression of the crossing Times (minutes) against the Year since 1974 of the crossing and the residuals plot:Dependent
We removed humans from the scatterplot in Exercise 39 because our species was an outlier in life expectancy. The resulting scatterplot (below) shows two points that now may be of concern. The point in the upper right corner of this scatterplot is for elephants, and the other point at the far right
In Exercise 40, we saw that Vicki Keith's round-trip swim of Lake Ontario was an obvious outlier among the one-way times. Here is the new regression after this unusual point is removed: Dependent variable is Time R-Squared = 4.5% s = 322.7 Variable Coefficient Intercept
Suppose you wanted to predict the trend in marriage age for American women into the early part of this century.a) How could you use the data graphed in Exercise 15 to get a good prediction? Marriage ages in selected years starting in 1900 are listed below. Use all or part of these data to create an
In Chapter 7, (Data in Tompkins County Bridges 2014) we found a relationship between the age of a bridge in Tompkins County, New York, and its condition as found by inspection. But we considered only bridges built or replaced since 1886. Tompkins County is the home of the oldest covered bridge in
Data for 26 Western Hemisphere countries can be used to examine the association between life expectancy and the birth rate (number of births per 1000 population).a) Create a scatterplot relating Life Expectancy to Birth Rate and describe the association. Are the regression assumptions satisfied? b)
We met the Tour de France data set in Chapter 1 (in Just Checking). One hundred years ago, the fastest rider finished the course at an average speed of about 25.3 kph (around 15.8 mph). By the 21st century, riders were averaging over 40 kph (nearly 25 mph). a) Make a scatterplot of Avg Speed
The Consumer Price Index (CPI) tracks the prices of consumer goods in the United States, as shown in the following table. The CPI is reported monthly, but we can look at selected values. The table shows the January CPI at five-year intervals. It indicates, for example, that the average item costing
Look once more at the data from the Tour de France. In Exercise 46, we looked at the whole history of the race, but now let's consider just the post-World War II era. a) Find the regression of Avg Speed by Year only for years from 1947 to the present. Are the conditions for regression met? b)
A regression of Total Revenue on Ticket Sales by the concert production company of Exercises 2 and 4 finds the model Revenue = -14,228 + 36.87 TicketSales. a) Management is considering adding a stadium-style venue that would seat 10,000. What does this model predict that revenue would be if the new
Suppose you have fit a linear model to some data and now take a look at the residuals. For each of the following possible residuals plots, tell whether you would try a re-expression and, if so, why.
For each of the models listed below, predict y when x = 2.a) ŷ = 1.2 + 0.8 logxb) log ŷ = 1.2 + 0.8xc) ln ŷ = 1.2 + 0.8 lnxd) ŷ2 = 1.2 + 0.8xe) 1 / √ŷ = 1.2 + 0.8x
As the example in the chapter indicates, one of the important factors determining a car's Fuel Efficiency is its Weight. Let's examine this relationship again, for 11 cars.a) Describe the association between these variables shown in the scatterplot.b) Here is the regression analysis for the linear
In a Chance magazine article (Summer 2005), Danielle Vasilescu and Howard Wainer used data from the United Nations Center for Human Settlements to investigate aspects of living conditions for several countries. Among the variables they looked at were the country's per capita gross domestic product
Let's try the re-expressed variable Fuel Consumption (gal/100 mi) to examine the fuel efficiency of the 11 cars in Exercise 11. Here are the revised regression analysis and residuals plot:Dependent variable is: Fuel ConsumptionR-squared = 89.2%Variable
In Exercise 12 we looked at United Nations data about a country's GDP and the average number of people per room (Crowdedness) in housing there. For a re-expression, a student tried the reciprocal €”10000/GDP, representing the number of people per $10,000 of gross domestic product. Here are the
The scatterplot shows the gross domestic product (GDP) of the United States in billions of (2013) dollars plotted against years since 1950.A linear model fit to the relationship looks like this: Dependent variable is: GDP R-squared = 98.3% s = 553.2 Variable Coefficient Intercept
Scientist Robert Boyle examined the relationship between the volume in which a gas is contained and the pressure in its container. He used a cylindrical container with a moveable top that could be raised or lowered to change the volume. He measured the Height in inches by counting equally spaced
The following table shows stopping distances in feet for a car tested 3 times at each of 5 speeds. We hope to create a model that predicts Stopping Distance from the Speed of the car.a) Explain why a linear model is not appropriate. b) Re-express the data to straighten the scatterplot. c) Create an

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