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intro stats
Questions and Answers of
Intro Stats
Climate change 2016 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. The mean
Birthrates 2015 The table shows the number of live births per 1000 population in the United States, starting in 1965. (National Center for Health Statistics, www.cdc.govchs/)a) Make a scatterplot and
Bridges We saw in this chapter that in a certain town, older bridges were in worse condition than newer ones. The given town is a rural area. Is this relationship true in cities as well?Here are data
Cost of living 2016 A website records the cost of living (COL)for 100 cities around the world. It reports the typical cost of a number of staples. Here are a scatterplot and regression relating the
A second helping of burgers 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
Chicken 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
Burgers revisited In Chapter 6, 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
Veggie burger 2014 Burger King introduced a meat-free burger in 2002. The nutrition label for the 2014 BK Veggie burger (no mayo) is shown here: (Data in Burger King items)a) Use the regression model
More used cars 2014 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
Drug abuse revisited Chapter 6, Exercise 42 examines results of a survey conducted in the United States and 10 countries of Western Europe to determine the percentage of teenagers who had used
Used cars 2014 A website lists numerous used cars for sale within a 250-mile radius of a town. The table lists the ages of the cars and the advertised prices.a) Make a scatterplot for these data.b)
Wildfires 2015—sizes 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
Wildfires 2015 The number of wildfires in a country has been declining. A scatterplot and analysis of the amount of land(in millions of acres) lost to wildfires is shown below.a) Is a linear model
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
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
Interest rates and mortgages 2015 again 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
Income and housing revisited 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
Attendance 2016, last inning Refer again to the regression analysis for home average attendance and games won by baseball teams, seen in Exercise 44.a) Write the equation of the regression line.b)
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
Attendance 2016, revisited Consider again the regression of Home Average Attendance on Runs for the baseball teams examined in Exercise 44.a) What is the correlation between Runs and Home Average
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
Attendance 2016, revisited In Chapter 6, Exercise 45 looked at the relationship between the number of runs scored by American League baseball teams and the average attendance at their home games for
Cigarettes 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
Last ride Consider the roller coasters (with the outlier removed)described in Exercise 30 again. The regression analysis gives the model Duration = 87.22 + 0.389 Drop.a) Explain what the slope of the
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
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.
ESP People who claim to have “extrasensory perception (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
Another ride The regression of Duration of a roller coaster ride on the height of its initial Drop, described in Exercise 30, had R2 = 29.4%.a) What is the correlation between Drop and Duration?b)
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
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
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
Coasters 2015 again Exercise 30 examined the association between the Duration of a roller coaster ride and the height of its initial Drop, reporting that R2 = 29.4,. Write a sentence(in context, of
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
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,
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.
Coasters 2015, revisited The dataset on roller coasters lists the Duration of the ride in seconds in addition to the Drop height in feet for some of the coasters. One coaster (the “Tower of
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
Last tank! For Exercise 16’s regression model predicting fuel economy (in mpg) from the car’s engine size, se = 3.522.Explain in this context what that means.
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
Another car The correlation between a car’s engine size and its fuel economy (in mpg) is r = -0.774. What fraction of the variability in fuel economy is accounted for by the engine size?
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
More engine size In Exercise 16, the regression model CombinedMPG = 33.46 - 3.23 Displacement relates cars’engine size to their fuel economy (Combined mpg). Explain what the slope means.
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
Engine size again Exercise 16 describes a regression model that uses a car’s engine displacement to estimate its fuel economy.In this context, what does it mean to say that a certain car has a
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
Engine size In Chapter 6, Exercise 41 we examined the relationship between the fuel economy (CombinedMPG) and Displacement (in liters) for 1211 models of cars. (Data in Fuel economy 2016) Further
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.
Disk drives 2016, residuals again 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
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
Disk drives encore For the hard drive data of Exercise 6, find and interpret the value of R2.
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?
Disk drives 2016, residuals Here are the residuals for a regression of Price on Capacity for the hard drives of Exercise 6(based on the hand-computed coefficients).a) Which residual contributes the
Bookstore sales once more Here are the residuals for a regression of Sales on Number of Sales People Working for the bookstore of Exercise 5:a) What are the units of the residuals?b) Which residual
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
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
Disk drives 2016 again 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
Bookstore sales revisited 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)
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
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 = -5.36 + 0.1675 length.Explain in
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
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
Planets (more or less) Is there any pattern to the locations of the planets in a distant solar system? The table shows the average distance of each of the planets from the star.a) Make a scatterplot,
Vehicle weights The department of transportation hoped that they could measure the weights of big trucks without actually stopping the vehicles by using a newly developed “weight-inmotion”scale.
Thrills III For the roller coaster data in Exercise 49: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
Thrills II For the roller coaster data in Exercise 49:a) Examine the relationship between Initial Drop and Speed.b) Examine the relationship between Initial Drop and Height.c) What conclusions can
Thrills 2013 In a poll, a roller-coaster ride called Bizarro dropped to 4th after earning the top steel coaster rank for six straight years. Data on the top 11 steel coasters from this poll are at
Housing price sampled In a dataset of 1057 New York homes offered for sale, a histogram of the ages looks like this:We drew 1000 samples of 105 homes from this dataset and found the IQR and the range
Coasters 2015 sampled Return to the data on roller coasters seen in Exercise 23. Here is the distribution of the lengths of the rides of 241 coasters.We drew samples of 60 coasters from the full set
Second inning 2016 Perhaps fans are just more interested in teams that win. The displays below are based on American League teams for the 2016 season. (Data in Attendance 2016)a) Do winning teams
Attendance 2016 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
Burgers again 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:a)
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.a)
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
Fuel economy 2016 Here are engine size (displacement, in liters) and gas mileage (estimated combined city and highway) for a random sample of 10 model cars (taken from Fuel economy 2016 and
Interest rates and mortgages 2015 Since 1980, average mortgage interest rates have fluctuated from a low of nearly 3%to a high of over 14%. Is there a relationship between the amount of money people
Income and housing Here is a scatterplot of the Housing Cost Index vs. the Median Family Income for 10 regions in a country. The correlation is 0.66.a) Describe the relationship between the Housing
Sample survey A polling organization is checking its database to see if the data sources it used sampled the same ZIP codes.The variable Datasource = 1 if the data source is MetroMedia, 2 if the data
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)
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
Correlation conclusions I The correlation between Age and Income as measured on 120 people is r = 0.65. Explain whether or not each of these possible conclusions is justified:a) When Age increases,
Smartphones and life expectancy A survey of the world’s nations in 2014 shows a strong positive correlation between percentage of the country using smartphones and life expectancy in years at
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
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
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
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
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
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
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
Traffic headaches A study of traffic delays in 68 cities found the following relationship between Total Delay (in total hours lost) and Mean Highway Speed:Is it appropriate to summarize the strength
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
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
Coasters 2015 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
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
Politics A candidate for office claims that “there is a correlation between television watching and crime.” Criticize this statement on statistical grounds.
Matching II Here are several scatterplots. The calculated correlations are -0.977, -0.021, 0.736, and 0.951. Which is which? (a) (c) + (b)
Matching Here are several scatterplots. The calculated correlations are 0.006, -0.977, -0.487, and 0.777. Which is which? (a) + (b) + + (c) (d) +
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
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
Kentucky Derby 2017 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
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
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